I Introduction
With the popularizing of user devices, we have never stopped our efforts on the challenging network optimization problems to improve the energy or spectrumefficiency (EE/SE) of wireless networks, with the aim of accommodating the users’ demanding data rate and diverse quality of service (QoS) requirements, e.g., [tradeoff] and [eebig18]. Currently, the performance optimization of wireless networks either focuses on the user side or the network controller, e.g., the base station (BS) and network operator. For wireless network operators, the everincreasing traffic demand can be fulfilled by deploying energyefficient small cells in a dense network or using multiple antennas at the BS to increase spectrum efficiency [antenna6g]. Thus, the BS’s transmit beamforming or power allocation can be optimized to adapt against the channel variations. At the user side, multiple users can join collaboration, e.g., via devicetodevice (D2D) [d2dsurvey] and relay communications [multihop]. These features can potentially provide the benefits of improved link quality and coverage, increased EE/SE performance, reduced interference and power consumption [densenetwork]. A joint optimization can be made possible when the information exchange and coordination between end users and the network controller are available. This can be more preferred as it generally yields a higher performance gain if it is solvable with affordable cost. Hence, numerous research works in the literature have proposed joint system optimizations to improve the EE/SE performance of wireless networks by a combination of different techniques, e.g., [opt_wsn18] and [opt_pls]. These may include the optimization for wireless power transfer, cooperative relaying, beamforming, and resource allocation, etc.
However, in the current paradigm of wireless network optimization, the radio environment itself remains an uncontrollable factor and thus it is not accounted for in the problem formulations. Due to randomness in the radio environment, the signal propagation typically experiences reflections, diffractions, and scattering before reaching the receiver with multiple randomly attenuated and delayed copies of the original signals in different paths. Such a channel fading effect becomes a major limiting factor for the maximization of EE/SE performance of wireless networks. Recently, a novel concept of intelligent reflecting surface (IRS) has been introduced in the wireless communications research community [18scm_ian3, joint_overview, 19survey_renzo]. The IRS is a manmade twodimensional (2D) surface of electromagnetic (EM) material, namely metasurface, that is composed of a large array of passive scattering elements with specially designed physical structure.^{1}^{1}1In the literature, we have observed different names referring to the same concept of using reconfigurable metasurface to assist wireless communications, e.g., softwaredefined hypersurface, large intelligent surface/antenna (LISA), reconfigurable intelligent surface, and holographic MIMO surface (HMIMOS). For consistence, we use the terms of intelligent reflecting surface (IRS) throughout this paper. Each scattering element can be controlled in a softwaredefined manner to change the EM properties (e.g., the phase shift) of the reflection of the incident RF signals upon the scattering elements. By a joint phase control of all scattering elements, the reflecting phase and angles of the incident RF signals can be arbitrarily tuned to create a desirable multipath effect. In particular, the reflected RF signals can be added coherently to improve the received signal power or destructively to mitigate interference. A typical system model of IRSassisted wireless communications is illustrated in Fig. 1(a). By deploying the IRS in the environment, e.g., the walls of buildings, the IRS can turn the radio environment for wireless communications into a smart space that is more flexible to support diverse mobile user requirements, e.g., enhanced data rate, extended coverage, minimized power consumption, and more secure transmissions [irs_survey, huang2019holographic, optimization_zhaojun, liang_survey]. Therefore, by integrating the smart radio environment into the network optimization, IRSassisted wireless networks are envisioned to revolutionize the current network optimization paradigm and expected to play an active role in beyond 5G networks [antenna6g, 19learning_renzo].
The specific benefits of IRSassisted wireless communications can be summarized as follows:

Easy deployment and sustainable operations: The IRS is made of lowcost passive scattering elements embedded in the metasurface. It can be in any shape, thus providing high flexibility for its deployment and replacement. It can be easily attached to and removed from facades of buildings, indoor walls, and ceilings, etc. Without the use of active components for powerconsuming signal processing algorithms, the IRS can be batteryless and wirelessly powered by RFbased energy harvesting.

Flexible reconfiguration via passive beamforming: The IRS can bring additional phase shifts to the reflected signals. By jointly optimizing the phase shifts of all scattering elements, namely passive beamforming, the signal reflections can be coherently focused at the intended receiver and nulled at other directions. The number of reflecting elements can be extremely large, e.g., from tens to hundreds [irs_survey], depending on the traverse size of the IRS. This implies a great potential for performance improvement of wireless networks. The IRS’s phase control, combined with the transceivers’ operational parameters, e.g., transmit beamforming, power allocation, and resource allocation, can be jointly optimized to explore the performance gain of IRSassisted wireless networks.

Enhanced Capacity and EE/SE performance: By using the IRS, the wireless channel can be programmed to support a higher link capacity with reduced power consumption for pointtopoint communications. Interference suppression also becomes effective by using the IRS, which implies a better signal quality for the celledge users. For multiuser (MU) wireless networks, the scattering elements can be partitioned and allocated to assist data transmissions of different users. As such, the IRSassisted wireless network can provide better QoS provisioning and potentially improve the sumrate performance or maxmin fairness among different users.

Exploration of Emerging Wireless Applications: The development of the IRS is expected to pave the way for new promising research directions. For example, the IRS has recently been introduced to be a novel approach for preventing wireless eavesdropping attacks by simultaneously controlling the transmission at the transmitter and the reflections at the IRS. Many other emerging research areas also benefit from the use of the IRS such as wireless power transfer, unmanned aerial vehicle (UAV) communications, and mobile edge computing (MEC), which will be reviewed in this survey.
Although the IRS’s operation resembles that of a multiantenna relay, it is fundamentally different from the existing relay communications. By using passive scattering elements, the IRS can realize fully controllable beam steering without dedicated energy supply and sophisticated active circuitry for channel estimation, information decoding, and amplifying and forwarding. Compared to the conventional amplifyandforward (AF) relay that actively generates new RF signals, the IRS does not use an active transmitter but only reflects the ambient RF signals as a passive array, which incurs no additional power consumption. It also differs from the conventional backscatter communications, where the backscatter transmitter communicates with its receiver by modulating and reflecting the ambient RF signals
[liang_survey]. The backscattered information is piggybacked in the ambient RF signals. The difference among three communication schemes is illustrated in Fig. 1. Such a different feature of IRSassisted wireless networks thus motivates the necessity of presenting a comprehensive literature review, which aims at providing fundamental knowledge about the IRS’s physical properties and implementations, its applications and analysis in different network scenarios, and the optimizations of IRSassisted wireless networks.There are a few review papers in the literature, either focusing on the physical design and implementations of the reconfigurable metasurface, e.g., [12surface_review, metasurface16, 17surface_review], or its conceptual applications in wireless communications and networking, e.g., [19survey_renzo, irs_survey, huang2019holographic]. In particular, the review papers [12surface_review, metasurface16, 17surface_review] mainly focus on the theoretical basis, physics characterization, and classification of metasurfaces as well as their applications at different operational frequencies. Motivated by the IRS’s appealing EM properties, the authors in [19survey_renzo] discuss the feasibility and methodologies of using the IRS to realize the concept of smart radio environments, and also analyze potential solutions to some fundamental challenges towards its massive deployment and applications in future wireless networks. Following on, the review paper in [irs_survey] provides a more technical overview with a special focus on the analysis of signal models and the physical layer channel enhancement in IRSassisted wireless communications. The authors in [huang2019holographic] introduce the concept of holographic multipleinput multipleoutput (MIMO) surface (HMIMOS) comprising subwavelength metallic or dielectric scattering particles, which shares a similar idea with the use of the IRS in wireless communications. An overview of HMIMOS communications is provided by introducing the hardware architectures, classifications, and main characteristics. Several short survey papers also appear in the literature, e.g., [joint_overview, liang_survey, zhao2019survey], mainly discussing the recent applications of the IRS in typical wireless scenarios. Comparing to these works, our survey offers a comprehensive review on both the theoretical basis of the IRS and its most recent applications in wireless networks. Specifically, our major contributions are summarized as follows:

A systematic organization of the literature under extensive review is provided (as shown in Fig. 2
) for readers with different backgrounds and interests to comprehend the IRS technology more effectively. We start from the physical characterization of the IRS and its EM properties, covering both design methodologies and experimental prototypes. Then we focus on IRSassisted wireless networks by classifying different papers according to their design objectives and control variables.

We provide an extensive review on the stochastic analysis of performance limit and asymptotic behavior of IRSassisted wireless networks, which are not covered by the existing review papers. The pervasive deployment of the IRS will change the random nature of the channel environment, which calls for different analytical tools and performance metrics to characterize the performance limits. Corroborated by the stochastic analysis, the potential increase in performance gain then motivates the further optimization of IRSassisted wireless networks.

Some common shortcomings of the current literature are analyzed and technical insights are highlighted for future exploration. For example, several current optimization frameworks for IRSassisted wireless networks mainly rely on a simple alternating optimization method, which implies that a higher performance gain can be achieved with a more sophisticated algorithm design. Besides, a majority of the papers in the literature focus on joint active and passive beamforming optimization. In fact, the passive beamforming can be also jointly optimized with the other control strategies, e.g., information encoding, transmission scheduling, access control, and fullduplex communications. We also notice that the energy consumption of the IRS is usually omitted in the literature, which may lead to overoptimistic conclusions.
Abbreviation  Description 
IRS  Intelligent Reflecting Surface 
UAV  Unmanned Aerial Vehicle 
RF  Radio Frequency 
EE/SE  Energy or SpectrumEfficiency 
QoS  Quality of Service 
BS/AP  Base Station/Access Point 
D2D  DevicetoDevice 
3D/2D  3Dimensional/2Dimensional 
EM  Electromagnetic 
MU  Multiuser 
AF/DF  Amplifyandforward/Decodeandforward 
FPGA/IC  FieldProgrammable Gate Array/Integrated Circuit 
NoC  NetworkonChip 
MAC  Medium Access Control 
mmWave  Millimeter Wave 
FSS  FrequencySelective Surface 
MSE  MeanSquared Error 
ANN  Artificial Neural Network 
MIMO  MultipleInput and MultipleOutput 
MISO  MultipleInput and SingleOutput 
OFDM  Orthogonal Frequency Division Multiplexing 
OFDMA  Orthogonal Frequency Division Multiple Access 
NOMA  NonOrthogonal Multiple Access 
LOS  LineofSight 
SM/SMM  Spatial Modulation/Spatial Microwave Modulator 
CSI  Channel State Information 
BER/SER  Bit Error Rate/Symbol Error Rate 
SNR/SINR  SignaltoNoise Ratio/SignaltoInterference plus Noise Ratio 
CRLB  CramerRao Lower Bound 
AI  Artificial Intelligence 
SDR/SDP  Semidefinite Relaxation/Semidefinite Programming 
DL/DNN  Deep Learning/Deep Neural Network 
MM  Majorization Minimization 
BCD  Block Coordinate Descent 
DC  DifferenceofConvex 
SOCP  SecondOrder Cone Programming 
ADMM  Alternating Direction Method of Multipliers 
ZF  ZeroForcing 
SVD  Singular Value Decomposition 
LT/LR  Legitimate Transmitter/Legitimate Receiver 
SWIPT  Simultaneous Wireless Information and Power Transfer 
KKT  KarushKuhnTucker 
SCA  Successive Convex Approximation 
RL  Reinforcement Learning 
MEC  Mobile Edge Computing 
GHz/THz  Gigahertz/Terahertz 
HetNets  Heterogeneous Networks 
The rest of this paper is organized as follows. Section II presents the basic theory and implementation of the IRS. Section III reviews the applications of the IRS in wireless communication networks, in particular, the concept and construction of a smart radio environment. After this, this paper focuses on IRSassisted wireless networks. Section IV discusses the performance metrics and provide a stochastic analysis of IRSassisted wireless networks, considering the random deployment of scattering elements in the radio environment. Section V presents the performance optimization of IRSassisted wireless networks, typically by a joint optimization of the IRS’s passive beamforming and the transceivers’ transmit control. Section VI discusses more emerging applications of the IRS in wireless communications. Finally, we discuss some important challenges and future research directions in Section VII, and then conclude the paper in Section VIII. The main topics covered in this paper are shown in Fig. 2. A list of abbreviations used in this survey is given in Table I.
Ii Theory and Design of Intelligent Reflecting Surfaces
The metasurface is a kind of twodimensional (i.e., with nearzero thickness) manmade material that exhibits special EM properties depending on its structural parameters. As illustrated in Fig. 3, the metasurface is composed of a large array of passive scattering elements, e.g., metallic or dielectric particles, that can transform the impinging EM waves in different ways [dielectric]. The subwavelength structural arrangement of the scattering elements determines how the incident waves are transformed, i.e., the direction and strength of the reflected and diffracted waves. In general, when EM waves propagate to a boundary between two different media, the strength and directions of the reflected and diffracted waves typically follow the Fresnel equations and Snell’s law respectively [metasurface16]. The situation becomes different when the same wave impinges upon a metasurface. The periodical arrangement of the scattering elements can cause a shift of the resonance frequency and thus a change of boundary conditions. As a result, the reflected and diffracted waves will carry additional phase changes.
Once the metasurface is fabricated with a specific physical structure, it will have fixed EM properties and therefore can be used for a specific purpose, e.g., a perfect absorber operating at a certain frequency. The analysis of EM properties can be based on the generalpurpose fullwave EM simulator or approximate computational techniques [approx_design18]. More efficient analytical approaches rely on sophisticated boundary conditions to describe the metasurface discontinuity and its EM responses [18surface_analysis, 18surface_nature]. However, it becomes very inflexible as a new metasurface has to be redesigned and fabricated to serve another purpose or operate at a different frequency. In particular, based on the application requirements, the structural parameters of the scattering elements constituting the metasurface have to be recalculated by a synthesis approach [15surface_tensor, 18surface_prop3], which is in general computational demanding.
The IRS is built from a reconfigurable metasurface, which can fully control the phase shifts incurred by individual scattering elements. This can be achieved by imposing external stimuli on the scattering elements and thus alter their physical parameters, leading to the change of EM properties of the metasurface without refabrication [tuning18]. The first design issue for the IRS lies in a control mechanism to connect and communicate with a large array of scattering elements, and thus agilely and jointly control their EM behaviors on demand. The other main issue is the realization of reconfigurability to achieve full phase control of the reflected or diffracted waves. In the sequel, we first discuss the IRS’s structural design and intercell communications mechanism to connect and control all scattering elements. After that, we discuss and compare different phase tuning mechanisms to achieve a variety of tunable functions and their applications. We also provide a review on prototypes and experiments in the literature to verify the feasibility of using the IRS in practice.
Iia The IRS’s Structure and Control Mechanism
IiA1 IRS Controller and Tunable Chips
In general, the IRS’s reconfiguration of its EM behaviors is achieved by a joint phase control of individual scattering elements. This implies an integration of tunable chips within the structure of the metasurface, where each tunable chip interacts locally with a scattering element and communicates to a central controller, e.g., [16surface_focusing, tuning18]. Hence, it allows a softwaredefined implementation of the control mechanism [nano15]. For example, the IRS controller can be implemented in a fieldprogrammable gate array (FPGA) and the tunable chips are typical PIN diodes [16surface_focusing]. As illustrated in Fig. 3, the embedded IRS controller can communicate and receive reconfiguration request from external devices, and then optimize and distribute its phase control decisions to all tunable chips. Upon receiving the control information, each tunable chip can change its state and allow the corresponding scattering element to reconfigure its behavior. The IRS can be also equipped with embedded sensors with the capability of sensing the environment [19survey_renzo]. Such sensing information can be used by the IRS controller to automatically update its configuration to maintain consistent EM behaviors under dynamic environmental conditions.
The tunable chips can be a PIN diode with ON and OFF states. This allows the change of input impedance to match or mismatch with the free space impedance [tuning18]. The authors in [14surface_design] design and demonstrate through experiments a binary state tunable chip based on the hybridized resonator controlled by a PIN diode as the unit cell of the metasurface, operating with the resonance frequency around 2.466 GHz. The tunable chips can also be varactor diodes, which can be adjusted in a continuous way given different voltage bias, e.g., [varacitor13, kim16]. The integrated circuits (ICs) with continuously tunable load impedance are designed in [19surface_review1] to control the phase shifts of scattering elements. Both tunable resistance and capacitance in the ICs can be controlled by imposing upon a gate voltage. Hence, wave manipulation can be realized by optimizing the biasing voltages. As an example, the authors in [tuning18] demonstrate the perfect absorption at 5 GHz for different polarizations and incidence angles.
The authors in [nano15] and [17surface_survey] propose to integrate a network of tiny controllers within the metasurface and wirelessly connect it to an external device. Each controller is capable of interpreting external instructions and tuning its varactor to achieve a desired impedance configuration. The change of connectivity at different locations of the controller network can realize the reconfiguration of the IRS’s physical structure, resulting in multiple tunable functionalities. In contrast, the authors in [18surface_survey2] design the IRS by connecting the scattering elements to a smaller group of controller chips. Each controller chip serves four metallic scattering elements. The controller chips can adjust the EM behaviors of the metasurface by attributing additional local resistance and reactance on demand. The designed metasurfaces can be used for perfect absorption and anomalous reflection operating in the microwave regime. Similar to [18surface_survey2], the metasurface designed in [18surface_verification] is composed of reconfigurable metamaterial strips arranged in a grid. A set of four strips is controlled by an intratile controller (i.e., tunable chip). All intratile controllers are interconnected to constitute the intratile network, which can receive external configuration instructions from gateway controllers.
IiA2 Intercell Communications
The IRS’s reconfigurability depends on the intercell communications among the tunable chips jointly controlling the scattering elements of the metasurface to exhibit desirable tunable functions. Communications among the underlying chip controllers can be either wired or wireless [18surface_survey2]. Wired communication can be preferable as it can be integrated with the controllers within the same chip. Wireless intercell communication becomes a compelling alternative in either largescale or dense metasurfaces. The design of intercommunications protocols has to comply with stringent energy, latency, and robustness requirements [18surface_routing].
The authors in [18surface_survey2] propose two approaches for wireless intercell communications. The first approach exploits the metasurface structure, while the second approach employs a dedicated communication channel beneath the metasurface structure. In the first approach, the communication channel is the space between the scattering elements and the substrate, which acts as a waveguide for signal propagation. The second approach is achieved by adding an extra metallic plate below the chip. The dedicated communication channel provides an obstaclefree waveguide for information communication between tunable chips. To ensure reliable communications among controllers embedded in the metasurface structure, the authors in [18surface_routing] adopt the traditional NetworkonChip (NoC) methodologies and develop two fault adaptive routing algorithms, which can bypass the faulty links by using a properly designed faulttolerant routing metric. The first algorithm is to alternate between XY and YX routing schemes, conventionally used for NoC and verified in [18surface_verification]
. Cycles can be avoided by using turn prevention. The other algorithm aims at maximizing the success delivery probabilities, which can achieve high reliability by detecting two disjoint paths between any two nodes in the network. When a fault occurs in a path, the information packet will be rerouted to the alternative path.
The authors in [18surface_circuit] develop embedded ICs within the metasurface structure, which uses minirouters to move control information among an arbitrarilylarge size of scattering elements. All ICs are connected to a shared gateway, which can receive configuration instructions from external wireless devices. Each IC can configure the load impedance at different locations of the metasurface. The authors design a handshaking mechanism to coordinate the information exchange among different metasurface cells. Such a design can achieve salient benefits, including delay insensitivity, low EM emissions, and low power consumption. Medium access control (MAC) strategies are investigated in [18mac_chip] to share the wireless medium efficiently among metasurface cells. The analysis of physical constraints, performance objectives, and traffic characteristics of onchip communications shreds some insights on the MAC protocol designs for a large number of metasurface cells.
IiA3 Phase Tuning Mechanism
The IRS’s reconfigurability depends on manipulating the phase of individual scattering elements. When the external or ambient stimulus changes, the physical parameters of the scattering elements and substrate will be tuned accordingly. Typical stimulus includes electric, magnetic, light, and thermal stimulus, which can tune the main body of a metasurface and thus provide a global control over its EM properties, e.g., absorption level, resonance frequency, and polarization of waves. Individual phase control of each scattering element is also possible, by applying the stimuli locally to each scattering element. This method is expected to achieve more sophisticated wave manipulations, such as beam steering, focusing, imaging, and holography [tuning18].
The most straightforward way to achieve local tuning is by changing the physical dimension of the scattering element, resulting in the change of resonant frequency and hence the phase shift, as illustrated in Fig. 4. The authors in [15surface_tera] implement the full controllable phase shifts by combining two different scattering elements. The overall wave reflections can be minimized by optimizing the array pattern. More prevailing tuning approaches are based on the electrically controlled binaryphase tuning or continuous reactance tuning mechanism, e.g., by using diodes or varactors, respectively, e.g., [varacitor13, kim16, 19surface_review1]. The authors in [17surface_liquid] use the electronically controllable liquid crystal for realtime wave manipulation. Each metasurface cell is loaded with a thin layer of the liquid crystal. By controlling the voltage bias on each cell, the effective dielectric constant will change and therefore lead to desirable phase shifts at various locations of the metasurface. Fullwave simulation results verify that effective beam steering can be achieved in real time. The authors in [18surface_prop2]
experimentally verify that the use of an acoustic cell architecture can provide enough degrees of freedom to control a refractive metasurface. In particular, a normal incident wave can be redirected over
with the efficiency up to 90%.IiB Typical Tunable Functions
Empowered by various tuning mechanisms, the IRS can support a wide range of tunable functions, such as perfect absorption, anomalous reflection, beam shaping, and steering [17surface_review, 18surface_prop1, 16surface_focusing], as illustrated in Fig. 5. Moreover, it is capable of sensing and communicating with the external devices [irs_survey, joint_overview], which allow it to be integrated with the modern wireless communication systems and utilized in a variety of wireless applications. For example, its applications in the millimeter wave (mmWave) (30100 GHz) and submmWave (greater than 100 GHz) are discussed in [surfacerelay]. The spectral efficiency becomes significant when the IRS’s size is large compared to the wavelength of the impinging waves.
IiB1 Perfect Absorption
The phase shifts of a metasurface can be designed to ensure minimal reflected and/or refracted power of the impinging waves. Such a metasurface can be used to design an ultrathin invisibility skin cloak, typically used for visible light [18surface_nature, cloaking18]. In particular, absorbing metasurface can be used as carpet cloaking of a scatterer on a flat ground plane [cloaking15]. This is achieved by ensuring the same reflection angle as the incident angle everywhere on the metasurface. The authors in [15surface_tera] propose a singlelayer terahertz (THz) metasurface to produce ultralow reflections across a broadfrequency spectrum and wide incidence angles. The authors in [kim16] show that perfect absorption can be achieved at an operating frequency in the range of 46 GHz by applying a change in the reverse biasing voltage of the varactor. In [17surface_review], the authors introduce the design of broadband absorbers of light by using unit cells featuring with multiple adjacent resonances. A tunable metasurface absorber is presented in [18surface_optical] by using an opticallyprogrammable capacitor as the tunable chip of each cell. The designed metasurface can operate at 5.5 GHz and achieve a tuning bandwidth of 150 MHz. The authors in [19surface_review1] realize a reconfigurable metasurface that exhibits perfect absorption at 5 GHz with different incidence angles, by changing the capacitance of each cell.
IiB2 Anomalous Reflection
It is one of the most widely investigated wave manipulation functions, which have potential applications in diverse fields of wireless communications [18coding_nature]. Abnormal reflection can be observed when light beams impinge upon optical metasurfaces [light11, 13surface_control, optic_meta17]. The authors in [light11] realize anomalous reflection of light beams in optically thin arrays of metallic antennas on silicon. The authors in [13surface_control] study the optical properties of different metasurfaces and present a metasurface design that can reflect two orthogonal polarization states in a broad wavelength range. The authors in [optic_meta17] design optical metasurfaces to facilitate tuning of the reflection phase and polarization. The experiment demonstrates the feasibility of tuning the reflection phase over by controlling the resonant properties of the antennas. An acoustic metasurface is constructed in [13surface_acoustic], which can tailor the reflected waves with discrete phase shifts covering the full span. The authors in [17surface_control] show that perfect phase control can be realized by completely eliminating the metasurface’s parasitic reflections into unwanted directions. The resulting power efficiency of reflection can be over 90% at 8 GHz. A lossless metasurface is proposed in [18surface_bmcontrol], where the incident wave can be perfectly received and converted into a surface wave along the surface, before it is radiated into space without power loss from a different location from the receiving point.
IiB3 Wave Manipulation
Besides abnormal reflection to a single direction, wave manipulation/modulation can create multiple reflections in different directions simultaneously based on perfect phase control of the metasurface. That is, the power of the reflected waves can be temporalspatially distributed to create an exotic radiation pattern of the metasurface, as shown in Fig. 5, which can be exploited to carry information by spatial modulation [indexmod16]. Using PIN diode as binary state control of each scattering element, the authors in [16surface_focusing]
propose the genetic algorithm and inverse fast Fourier transform technique to optimize the binary coding matrix and thus create different wave manipulations of a large metasurface, including anomalous reflection, diffusion, beam steering and beamforming. The realtime switch among these radiation patterns can be achieved by an FPGAbased controller. A similar genetic algorithm is also employed in
[17surface_modulating] for arbitrary wave modulations to create desirable radiation patterns according to application requirements. The effectiveness of the genetic algorithm is experimentally verified at an operating frequency of 10 GHz, showing that the accuracy of wave modulation increases with the size of scattering elements. Different from the aforementioned spatial wave modulations, the authors in [18coding_nature]verify the possibility of simultaneous wave manipulations in both space and frequency domains. The perfect control of the reflection angles and power distribution can be achieved by using a spacetime modulated digital coding metasurface.
IiB4 Analog Computing
As a further step forward from wave manipulations, it becomes also possible for the IRS to perform more complicated mathematical operations (such as spatial differentiation, integration, convolution, and even neural network training) as the impinging wave propagates through the scattering elements. This is referred to as wavebased analog computing, achieving a higher energy efficiency compared to conventional digital signal processing paradigms. The authors in [14science] introduce the concept of metamaterial analog computing that uses optical metasurfaces to perform mathematical operations in the spatial Fourier domain. This offers the possibility of miniaturized, potentially integrable, wavebased computing systems. Analog computing of acoustic metasurfaces is also demonstrated in [acoustic_math18] by using thin planar metamaterials to perform mathematical operation in spatial domain. This is promising for various applications including high throughput image processing, ultrafast equation solving, and realtime signal processing. The authors in [18analog_comput] experimentally demonstrate that the offtheshelf wireless infrastructure in combination with a tunable binaryphase metasurface can perform analog computation with WiFi signals.
Some other exotic tunable functions also appear in the literature. The authors in [sensing11] use the metasurface directly as advanced sensing devices for diagnostic applications, e.g., cancer detection, biological tissue characterization and chemical analysis, based on the interactions of EM waves with the metasurface. The authors in [storage13] show the possibility of storage and retrieval of EM waves by introducing varactor diodes to manipulate the metasurface’s structure. The authors in [storage17] demonstrate that the slowdown, storage and retrieval of multimode EM waves can be achieved through the active manipulation of a control field. This work shows the possibility for multimode memory of EM waves and its practical applications in information processing.
Reference  Controller  Size or Dimension  Phase Control  Frequency range  Realized Tunable Functions 
[16surface_focusing]  FPGA  array  Binary PIN diodes  912 GHz  Wave manipulation including anomalous reflection, diffusion, shaped scattering 
[18surface_prop2]  –  7 cells  –  3.0 GHz  Redirecting a normal incident wave to , , and , with efficiency over 90% 
[18coding_nature]  FPGA  array  Binary PIN Diodes  810 GHz  Simultaneous wave manipulations in both space and frequency domains 
[13surface_acoustic]  –  8 cells  Traverse length  Acoustic  Discrete phase shifts covering the full span with steps of 
[17surface_modulating]  –  array  Cell layout  8.711.3 GHz  Generating different radiation patterns. Even distribution of reflection phases from to . 
[irsptype17]  DC voltage source  array  PIN switches and varactor diodes  11.513.5 GHz  Dynamical beam deflection, splitting, and polarization. 180 reflection phase difference 
[thz_metamaterial19]  –  cm  Geometric parameters  0.60.9 THz  Broadband reflector with a bandwidth of 0.15 THz and efficiency up to 95% 
[xbandant12]  –  244 cells  Byinary PIN diode  10.1010.70 GHz  Beam switching between and 
[ra12]  –  array  Varactor diodes  5 GHz  Beam scanning over a window 
[absorber10]  Bias network  cm  Binary PIN Diodes  2.754.0 GHz  Switching between total reflection and absorption 
IiC Experiments and Prototypes
Prototypes of reconfigurable metasurfaces have been developed to verify the feasibility of different tunable functions. Table II summarizes recent experiments and prototypes developed in the literature for the verification. The authors in [16surface_focusing] implement a metasurface containing 1600 individually controllable cells to demonstrate the feasibility of dynamic wave manipulations. Each cell of the metasurface is integrated with one PIN diode that can switch between two states. By optimizing a binary coding matrix, the metasurface can be controlled to realized anomalous reflection, diffusion, and shaped scattering. The authors in [18surface_prop2] propose and experimentally verify the use of an acoustic cell architecture to provide enough degrees of freedom for full phase control. Three refractive metasurfaces are designed to redirect a normally incident plane wave by , , and , respectively, with the efficiency up to 90%. The authors in [16surface_expment] design a grapheneintegrated metasurface to induce a tunable phase change to the incident wave, which can be controlled at an ultrafast speed. The designed prototype is shown to change the reflection phase up to 55 degrees. The authors [thz_metamaterial19] develop a largescale THz alldielectric metamaterials with the outer dimension 900 cm 900 cm by using the templateassisted fabrication method. Using such metamaterials, the authors implement a broadband reflector with a bandwidth of 0.15 THz and demonstrate its reflection up to 95%, which implies a wide variety of applications in lowloss and highefficiency THz devices.
VISORSURF is an interdisciplinary program funded by Horizon 2020 FETOPEN [18surface_verification, h2020]. Its objective is to develop a hardware platform for reconfigurable metasurfaces, namely Hypersurface, featured with programmable EM behavior by controlling a network of switches. Conceptual applications of IRS are proposed to realize the vision of a smart radio environment, leveraging its sensing capability and reconfigurability to adapt itself according to the dynamics of the radio environment, e.g., [18scm_ian3, joint_overview, irs_survey, 19survey_renzo]. For example, a prototype of the reconfigurable metasurface is implemented in [irsptype17] to achieve multifunctional control of EM waves, e.g., beam splitting, deflection, and abnormal reflection at microwave frequencies. This is achieved by controlling the PIN switches and varactor diodes associated with each scattering element. The realtime switch between different EM functionalities is controlled by a computercontrolled voltage source. Realizing wave manipulations in both space and frequency domains, the authors in [18coding_nature] design a spacetime modulated digital coding metasurface to control the propagation direction and power distribution simultaneously in the frequency range of 810 GHz. The experimental results demonstrate a good performance of the proposed approach by implementing an FPGA controlled metasurface prototype for beam steering, beam shaping, and scatteringsignature control.
Note that the development of reconfigurable metasurfaces shares a similar idea with the classical concept of reconfigurable reflectarrays, in which the resulting radiation pattern is altered as desired by changing the current distribution [irs_survey]. Comparing to reconfigurable reflectarrays, IRS is featured with the additional requirement of having realtime control and reconfigurability [antenna6g]. A reconfigurable reflectarray antenna is implemented in [xbandant12], consisting of a group of 244 radiating elements phase controlled by PIN diodes. The antenna is designed to operate in the band from 10.10 GHz to 10.70 GHz, capable of switching the beam between and . Different from the PIN diodes in [xbandant12], the authors in [ra12] implement a transmitarray controlled by varactor diodes to verify its beamforming capability. Experiments demonstrate its capability of beam scanning over a degree window at the operating frequency of 5 GHz. To reduce the size of transmitarray, the authors in [compact17] design and verify a compact reconfigurable antenna for wireless communications. By controlling the states of two PIN diodes, the proposed antenna is capable of generating four different radiation patterns at the operating frequency of 2.45 GHz, which can be employed for information transmission by spatial modulation [indexmod16].
In the following, we focus on the applications of the IRS in wireless communications. We first introduce the recent works discussing the novel concept of a smart/programmable wireless environment, which is envisioned to change the wireless networking paradigm by using the IRS in wireless communications. As such, we review the system modeling, performance analysis, and optimizations of IRSassisted wireless networks.
Iii Applications of IrsAssisted Wireless Networks
Conventionally, the physical radio environment of wireless networks is typical uncontrollable. Due to randomness in the radio environment, the transmission of RF signals may experience reflection, diffraction, and scattering before reaching the intended receiver with multiple copies of the original signals with random amplitudes, phases, and delays. This effect, known as multipath fading, is the main factor that causes distortion to the received signal and thus deteriorates the communication performance. Due to the lowpower consumption, low cost for implementation, and the flexibility in deployment and reconfiguration, the IRS is envisioned to play a pivotal role in improving the transmission performance of future wireless communication networks, e.g., mmWave 5G communications and future THz 6G communications, which face with a critical issue of dead spots due to the blockage of lineofsight (LOS) signal propations. The use of the IRS can reshape the propagation of radio waves in a fully softwarecontrolled way and thus tune the highly probabilistic wireless channels into a deterministic space for reliable communications. As such, the radio environment becomes a usable resource that can actively improve the performance of information transmissions.
Iiia Smart Radio Environment
The authors in [joint_overview] review the IRS techniques and their applications in wireless networks, including the physical properties, hardware implementations as well as novel signal models. It is shown that the IRSassisted wireless networks can more flexibly manage the wireless resources by the IRS’s tuning of amplitude and phase shifts, along with the conventional transmit control strategies. The concept of a smart radio environment is proposed by the authors in [19survey_renzo] by covering the physical objects with IRSs that can turn the radio environment into a smart space and thus play an active role to assist information sensing, analog computing, and wireless communications. As such, the IRS’s reconfigurability becomes an indispensable component for the era of artificial intelligence (AI) enabled wireless network design [19learning_renzo].
The concept of active wall is introduced in [12smart_wall2] by using an active frequencyselective surface (FSS) to manipulate the wireless environment. The FSS provides a narrowband frequency filtering of incoming signals [Chang2008Equivalent], which can be used to build up a cognitive engine and make the walls intelligent. The idea is to switch the PIN diodes on the metasurface between ON/OFF states by an external bias. When the PIN diodes are off, the metasurface becomes almost transparent, allowing the incident signals passing through. When the PIN diodes are on, most of the incoming signals are reflected. The proposed design can be realized by embedding PIN diodes on the metal connection parts of the IRS’s scattering elements. Through systemlevel simulations of a cognitive indoor scenario, the authors show that the system performance can be improved by up to 80 by dynamically changing the propagation environment via the active wall. Reference [12smart_wall1] extends the intelligent wall paradigm by employing an artificial neural network (ANN) to explore an optimal setting for a cognitive engine. Specifically, ANN is used to estimate the relative spatial distribution of the users. The learning process of the ANN terminates once the meansquared error (MSE) of the measured network performance is below a target value. Afterward, the cognitive engine begins to make decisions to control the intelligent wall based on the learned knowledge. The simulation demonstrates that the network performance increases with the duration of the learning process.
The concept of programmable wireless channels or environment is proposed in [18scm_ian1] and [18scm_ian2] by using hypersurfaces, i.e., softwarecontrolled metamaterials, to cover the superficies of physical objects in the radio environment. The mechanism is to control the distribution of the current over the hypersurface by changing the states of electronically controlled switches embedded throughout the hypersurface. This allows it to shape the incident RF signals with a desirable response in a softwarecontrolled manner. Embedding hypersurfaces in the environmental objects creates a reconfigurable indoor wireless environment. Consequently, the scattering objects in the environment can be viewed as a kind of wireless resource and tailored to meet the demands of wireless devices. Similarly, the outdoor environment can be programmed by embedding hypersurfaces into building facades. By alleviating signal path loss, multipath fading, and cochannel interference, the programmable wireless environment is capable of improving transmission performance in various aspects, e.g., signal quality, communication range, and EE/SE performance. Reference [19pls_ian1] generalizes the control methods for the hypersurface based system in [18scm_ian1] by proposing different approaches to mitigate interference, multipath distortion, and degrade eavesdropping channels for multiple users. The proposed approaches are shown to achieve maximized signal power and minimized delay spread at randomly located users.
By using the IRS, the wireless channel can be reconfigured in a softwaredefined manner to meet various QoS requirements simultaneously. The authors in [18scm_ian1] and [18scm_ian2] consider a specific MU scenario as shown in Fig. 6. Client 1 would like to have optimal signal quality, while client 2 demands wireless power transfer. Besides, the unauthorized client can either cause interference to the legitimate client or attempt unapproved access. In the natural environment, it is very difficult to satisfy these objectives efficiently. However, with the use of multiple IRSs, each IRS can receive command signals from a centralized controller and then customize its EM properties. As a result, the IRS can help client 1 to receive maximal downlink signal power and avoid interference from wireless power transfer and unauthorized access. Besides, the IRS can maximize wireless power transfer to client 2 through beam steering. The unauthorized access can be also prevented by absorbing the transmissions from the unauthorized client.
By using IRScoated wall inside a random environment, the authors in [19ch_diversity] demonstrate the capability of shaping the propagation characteristics to achieve enhanced wireless channel diversity and thus improve the link capacity limit. The authors implement a metasurface composed of binaryphase units, which can be electronically switched between and at the standard WiFi operating frequency. An experiment is conducted to show that perfect orthogonality of wireless channels can be achieved by using the IRScoated cavity wall with an appropriate phase configuration. Besides channel enhancement to a receiver, interference suppression also becomes more flexibly by using the IRS with a largescale array of scattering elements. The authors in [sarkar2019]
demonstrate that the deployment of the IRS near the BS can be used to control massive MIMO channel characteristics by selectively enhancing or suppressing certain channel eigenvalues. The authors in
[17smartspace_longfei] propose to integrate passive reflections and active transmissions in the programmable radio environment, by deploying hybrid activepassive elements embedded in the walls of a building, as shown in Fig. 7. By tuning elements to finelyspaced phases, the signals can be steered to interfere or cancel at the receiver. The experimental study demonstrates that the hybrid system can 1) mitigate the destructive effect of multiple paths for legacy wireless communications; 2) eliminate poorly conditioned similar channels in a largescale MIMO system; and 3) simultaneously attenuate interference power and increase signal strength at different receivers.More implementations and evaluations are conducted to verify the capability of the IRSenabled smart radio environment. Reference [18smart_mmwave] designs and implements a 60 GHz reconfigurable reflectarrays to assist IEEE 802.11adbased mmWave communications, creating additional reflection links when there exists no LOS links. The idea is to use controllable switches to change the incoming RF signals. The authors in [18smart_mmwave] propose an array control algorithm for beam searching that can guarantee an optimized signal quality at the target receiver. The authors also develop an optimal array deployment scheme to maximize the connectivity in an indoor mobile mmWave network. Both simulations and testbed experiments are conducted to validate the proposed design. The implementation with a binaryphase control is shown to cause a significant signaltonoise ratio (SNR) loss in practice. This problem can be addressed by using highaccuracy phase control of the beamform direction at the cost of high hardware requirements. Based on the EM properties of the IRS, the authors in [tang2019wireless] build and experimentally verify analytical freespace path loss channel models for IRSassisted wireless communications in different scenarios. It is revealed that the freespace path loss depends on the distances from the IRS to the transceivers, the antennas’ radiation patterns, and the IRS’s EM properties, including the size and topology, and the near or farfield EM properties. The authors in [19modeling_ian] implement and evaluate several physical layer buildingblock technologies for a programmable wireless environment. Focusing on the internetworking capabilities of different IRScoated objects, a central server is used to connect different IRSs, sense their operation states and customize the tunable functions. The authors devise and implement a networklayer scheme to reconfigure the radio environment. Extensive hardware evaluation reveals the benefits of programmable environments over nature environments.
IiiB Spatial Modulation via Reconfigurable Antennas
The smart radio environment relies on the use of the IRS as signal reflectors to create the desirable multipath effect. Here we show that the IRS itself can also be used as the source signal transmitter. As stated in the previous section, the IRS’s most widely studied tunable function is the capability of creating abnormal reflections, in both time and spatial dimensions [18coding_nature]. By controlling the phase shifts of the IRS’s scattering elements, the reflected waves can create different radiation patterns, which can be used to carry information if these radiation patterns can be sensed and differentiated at the receiver. This is the main design principle of spatial modulation. The IRS’s superior reconfigurability and flexibility potentially make it much easier for the applications of spatial modulation in future wireless networks, e.g., [indexmod16] and [indexmod17].
Spatial modulation or spatial multiplexing (SM) is a promising lowcomplex modulation technique for multipleantenna transmitters. Each antenna adopts different transmit power and phase to create a difference in the depth of modulation. Compared to the conventional MIMO techniques, SM techniques have the potential to enhance the transmission rate with reduced hardware complexity and energy consumption. Reference [17ee_renzo1] introduces the concept of spatial modulation for reconfigurable antennas. The authors highlight that the key advantage of developing spatial modulation for reconfigurable antennas is lowcomplexity, and no channel state information (CSI) is required at the receiver. Reference [19spatial_renzo] introduces a solution of single carrier spatial modulation for uplink and downlink communications. In the uplink, the user can transmit with spatial modulation by using a compact reconfigurable antenna to achieve high bitrate with high energy efficiency. At the base station, the spacetime digital processing can be employed to detect the uplink transmission. In the downlink, the spacetime beamforming can be utilized to transmit preequalized signals so that spatial modulation can be achieved by a compact multiport antenna. The realworld experiment shows that the proposed solutions are more energyefficient and less complicated than traditional modulation schemes.
Reference [14shaping_wave] presents a spatial microwave modulator (SMM) made of electronically tunable metasurfaces. The SMM is designed to passively shape the existing microwave fields through binaryphase tunable metasurfaces with noncoherent energy feedback. The experimental results show that in an indoor environment the SMM can either improve the pointtopoint transmission by an order of magnitude or fully cancel the transmission. Moreover, the energy consumption of SMM is typically comparable to or lower than the amount of RF energy it can recycle. Reference [irs_im19] brings the concept of IRSassisted wireless communications to the realm of index modulation, which can be realized at either the transceiver or the IRS. As illustrated in Fig. 8, the active beams are shown in red. The authors design space shift keying and spatial modulation methods for the IRS. The proposed methods can be realized by either smartly reflecting the incident signal to enhance the endtoend transmission or utilizing the index modulation of multiple receive antennas to render improved spectrum efficiency. The authors in [irs_im19] also propose a greedy detector and a maximum likelihood detector and derive their corresponding bit error rate (BER). Numerical results demonstrate that IRSassisted SM methods provide a large capacity with ultralow BER. Thus, it can serve as an enabling technique for futuregeneration MIMO systems.
Summary: The abovereviewed applications of the IRS in wireless communications are summarized and compared in Table III. Most of the existing applications either utilize the IRS to recycle the environment resources or create different radiation patterns for spatial modulation. The applied network scenarios are rather broad, ranging from lowpower sensors to highpower mmWave systems. The existing applications mainly target for indoor scenarios where the locations of the transmitters and receivers are static or deterministic. In this context, it is relatively easy for the IRS to discover the locations of wireless devices and conduct performance optimization. On the other hand, in outdoor scenarios, the timevarying location of wireless devices due to mobility makes device discovery more challenging. This inevitably imposes high requirements on the IRS’s signal detection capability. Although references [18scm_ian1] and [19pls_ian1] suggest the use of the conceptual softwarecontrolled hypersurface in outdoor scenarios, the authors do not provide solutions to differentiate the signals from statics and mobile devices. Thus, realtime EM wave manipulation for mobile devices remains an open issue. Another limitation of the existing applications in recent literature is that most of them are only evaluated by simulations. Their empirical performances in practical systems remain unknown. Therefore, it is imperative to develop proofofconcept prototypes and conduct realworld experiments.
Reference  Scheme  Design  Application scenario  Control  Validation 
[12smart_wall2]  Intelligent walls  Switching the FSS between ON and OFF to transform its EM properties which accordingly shape the propagation environment and improve system performance  Indoor  Passive  Simulation 
[12smart_wall1]  ANNbased intelligent walls  Using ANN to explore the optimal setting for the cognitive engine to control the intelligent walls  Indoor  Passive  Simulation 
[17smartspace_longfei]  Programmable radio environment for smart spaces  Embedding lowcost devices in the walls to passively reflect or transmit active RF signals  Indoor  Active, passive  Experiment 
[18smart_mmwave]  Smart reflectarray  Using reconfigurable 60 GHz reflectarrays to increase the nonLOS connectivity for mmWave communications  Indoor  Passive  Simulation, experiment 
[14shaping_wave]  Spatial microwave modulator  Using electronically configurable metasurfaces as spatial microwave modulators  Indoor  Passive  Experiment 
[18scm_ian1]  Softwarecontrolled hypersurface  Building programmable wireless environments based on the hypersurface tile architecture  Indoor, outdoor  Active, passive  Simulation 
[19pls_ian1]  Softwarecontrolled hypersurface  Hypersurface designed for interference cancellation, eavesdropping, and distortion mitigation  Indoor, outdoor  Active, passive  Simulation 
Iv Performance Analysis of IrsAssisted Wireless Networks
The vision of the smart radio environment can be realized by coating IRS to the facades of physical objects in the radio environment, such as the walls and ceilings. This implies that the IRS’s scattering elements are distributed in nature relating to the spatial distribution of the environmental objects. Therefore, the modeling and performance analysis of IRSassisted wireless networks necessitate analytical models that take into account 1) the spatial locations of IRSs, ii) the IRS’s EM properties, and iii) the wave manipulations adopted by the coexisting IRSs in the environment. In this part, we review analytical studies that contribute to the understanding of the performance limit of different IRSassisted network scenarios, including performance bounds and asymptotic behaviors that are hard to obtain from simulation studies. Such a theoretical performance analysis can provide design insights on the deployment and configuration of IRSassisted wireless systems without the need for extensive simulations. A fundamental difference between IRSassisted and nonIRSassisted wireless networks is that the IRS can make the radio environment controllable in favor of information transmissions by abnormal reflections. Therefore, a majority of the literature analyzes the transmission performance of wireless networks using the IRS as signal reflectors. In another aspect, the use of the IRS as signal receivers also attracts recent research attention, e.g., [17capacity_sha] and [19rate_walid]. In the sequel, we review the existing literature according to the IRS’s roles in wireless communications.
Iva Using IRS as the Signal Reflector
The performance metrics of interest mainly include the probabilistic metrics to characterize the uncertainty in wireless transmissions of individual transceivers, as well as the ergodic metrics to characterize the averaged network performance, considering the randomness in network topology, the distribution of reflectors, channel conditions, and interference variations, etc. Typical performance metrics proposed for IRSassisted wireless systems include the following aspects.

Reflection probability: The probability that an IRS can reflect the signals from a transmitter to the receiver.

Coverage or outage probability: The probability that the received SNR is above or below a target threshold.

Bit error probability: The probability that the decoded information bit differs from the transmitted one.

Ergodic capacity: The expectation of channel capacity measured by Shannon’s formula.

Transport capacity: The aggregated data rate that can be reliably communicated in the entire system.
IvA1 Probabilistic Performance
The reflection probability is studied in [19ref_prob_renzo] considering a largescale IRS randomly distributed by a Boolean model of line segments [14blockage]. The authors derive the exact probability that a random IRS can reflect for a given transceiver according to the generalized laws of reflection. The analytical result reveals that the reflection probability of a randomly located reflector is independent of its length. However, this work assumes that all the IRSs have a fixed length, which cannot capture the realworld network environment. Besides, the authors only analyze the reflection probability, without an evaluation on the improvement of transmission performance by using the largescale IRS. The authors in [18smart_mmwave] propose the use of the IRS to improve the LOS probability for indoor mmWave communications. Compared to the existing relaybased approaches that create LOS links for mmWave communications, the reflectionbased approach exempts from selfinterference of a fullduplex relay and compromised throughput of a halfduplex relay.
Considering the downlink transmission from an mmWavebased access point (AP) to a user with only the reflection links (i.e., no direct link due to obstacles), the authors in [18smart_mmwave] derive the outage probability in terms of an integral expression. Based on the derived expression, the authors further minimize the outage probability by optimizing the IRS’s deployment position. The authors in [outage_multi_irs] study the outage probability of IRSassisted systems under Rician fading where the IRS’s phase shifts only adapt to the LOS components. The outage performance is firstly analyzed and optimized in the slow fading scenario for the nonLOS components. It can be shown that the optimal outage probability decreases with the size of the IRS when the LOS components are stronger than the nonLOS ones. Then, the authors characterize the asymptotically optimal outage probability in the high SNR regime, and show that it decreases with the powers of the LOS components. The authors in [stoch_relay] investigate the downlink performance of an IRSassisted MIMO system to randomly distributed users based on the stochastic geometry analysis. The outage probability and average capacity can be derived in closed forms. Furthermore, the authors in [stoch_relay] study the diversity orders of the outage probability and high SNR slopes of the ergodic rate. Numerical results indicate that the fading channel distribution has a trivial impact on the diversity order.
The coverage probability is studied for an IRSassisted wireless network in [17coverage]. Different from [18smart_mmwave] which studies pointtopoint mmWave communications, the authors in [17coverage]
consider a generalized mmWave downlink cellular network coexisting with random obstacles and reflectors. A stochastic geometry method is proposed to analyze the downlink coverage probability under the assumption that the locations of base stations follow a homogeneous Poisson point process. Besides, the blockages and reflectors are deployed in straight line segments with uniformly distributed orientation and length. The study indicates that only the deployment of reflectors with high density can cause a noticeable improvement in the mmWave coverage. However, the deployment with low density may not benefit mmWave coverage as the reflected signals go through longer distances than the direct links. A limitation of this work is that only the reflections from the nearest reflector is considered. In fact, reflections from other nearby reflectors could also be strong and should not be ignored.
In contrast to above efforts that focus on an analytical study, reference [18errorpb_renzo1] presents a joint analytical and empirical study for the bit error probability of spatial modulation based on reconfigurable antennas. Different from conventional spatial modulation which encodes the information bits on the indices of an array of antennas, spatial modulation with reconfigurable antennas manages to encode information bits on the radiation patterns of a reconfigurable antenna. To evaluate the impact of the radiation patterns on the error performance, the authors in [18errorpb_renzo1] introduce an analytical framework to characterize the bit error probability. With the aid of the analytical results, the best radiation pattern among the available ones can be identified to minimize the average error performance.
IvA2 Ergodic Capacity and Data Rate
The authors in [optimality] analyze the asymptotic achievable rate in an IRSassisted downlink system. A passive beamformer is designed to achieve the optimal asymptotic performance by tuning the EM properties of signal waves. To maximize the data rate, a modulation scheme is designed for the IRS that is interferingfree for existing devices. The authors also derive the expected asymptotic symbol error rate (SER) of the considered system. Based on the proposed modulation scheme, the authors further devise a protocol for joint user scheduling and power control. Simulation results confirm that the protocol design agrees with the upper bounds with a large number of scattering elements, thereby verifying that the achievable rate in a practical IRSassisted system satisfies the asymptotic optimality. Considering an IRSassisted mmWave MIMO system, the authors in [he2019adaptive] characterize the achievable data rate from the BS and to a mobile user, by designing the IRS’s optimal phase shifts based on limited feedback from the mobile user. Besides improvement on data rate, simulation results show that the positioning error bound and orientation error bound both can be reduced by using the IRS with perfect CSI. Different from [optimality] and [he2019adaptive], which optimize a fixed passive beamforming strategy to maximize the data rate, the authors in [karasik2019maxsnr] derive an informationtheoretic limit for the IRSassisted link capacity, by joint information encoding and the IRS’s phase tuning. That is, the IRS’s phase control not only depends on the channel conditions, but also relates to the information bits. Numerical results demonstrate that the joint encoding and tuning scheme achieves more than 30% increase in SNR, comparing to that of the tuningonly scheme.
The authors in [irsdf] aim at making a fair performance comparison between IRSassisted wireless communications and the conventional decodeandforward (DF) relaying communications. Both of these techniques are promising for capacity improvement. In comparison, the achievable rates for both cases are derived and then maximized by analytically optimizing the transmit power and the size of the IRS. The main observation is that a very largesize IRS is needed to yield better performance than the DF relaying in terms of transmit power minimization and EE/SE performance maximization. In [18ee_chau1], a similar comparison with an AF relay reveals that high energy efficiency can be achieved by using an IRS. The authors in [snrraterelay] optimize the endtoend SNR and achievable rate of halfduplex, fullduplex, AF, and DF relayassisted communications, respectively, and compare them to that of the IRSassisted wireless systems. The aforementioned works focus on the use of ideal IRS with infinite phase resolution. The authors in [phaseshifts] characterize the performance degradation when a practical IRS is implemented with limited phase shifts. Considering IRSassisted uplink communications from an end user to the BS, the authors in [phaseshifts] derive an approximation of the achievable data rate and then obtain the required number of phase shifts given a data rate degradation constraint.
Different from the above capacity characterization of a single communication link, the authors in [16sharing_capacity] propose the IRSassisted spectrum sharing scheme for multiple transmitters. As shown in Fig. 9, the idea is to use the IRS for steering the signal beams from different transmitters to enhance the useful signals and cancel the interference towards their respective receivers. This paradigm allows multiple transmitters to simultaneously operate on the same spectrum band without causing interference to each other. Considering an indoor wireless scenario using the spectrum sharing scheme, the authors derive both upper bound and achievable bound of the transport capacity under practical deployment constants. A realworld testbed is also developed to study the effect of the system parameters and validate the practicality of the proposed spectrum sharing concept. The experimental results demonstrate that the use of the IRS realizes a significant improvement on spectrum efficiency for the legacy transceivers. However, the testbed only implements two transceivers. The practical performance of a large number of indoor communication pairs sharing the same spectrum band is still unknown.
Reference  Performance Metrics  System Model  Characterization  Evaluation 
[19ref_prob_renzo]  Reflection probability  Pointtopoint communications in the presence of random metasurfaces  Exact performance  Analysis simulation 
[18smart_mmwave]  Outage probability  Pointtopoint mmWave communications with only reflection links  Exact performance  Analysis, simulation 
[17coverage]  Coverage probability  Downlink mmWave communications in the presence of LOS blockages and reflectors  Approximation  Analysis, simulation 
[18errorpb_renzo1]  Bit error probability  Pointtopoint MIMO communications  Exact performance  Analysis, simulations, experiment 
[16sharing_capacity]  Transport capacity  Spectrum sharing among multiple transceivers through a reconfigurable metasurface  Upper bound  Analysis, simulation, experiment 
[17capacity_sha]  Normalized capacity  Multiple devices in 3D space transmit to a vertical metasurface with LOS interference  Approximation, asymptotic performance  Analysis, simulation 
[19rate_walid]  Ergodic capacity  Multiple devices in 3D space transmit to a vertical metasurface with LOS and nonLOS interferences  Approximation, asymptotic performance  Analysis, simulation 
[18capacity_degrade_sha]  Ergodic capacity  A singleantenna devices in 3D space transmit to a vertical 2D metasurface with hardware impairments  Upper bound  Analysis, simulation 
[18positioning_sha]  Positioning coverage  Terminal positioning for a singleantenna device located in front of an IRS  CramerRao lower bound  Analysis, simulation 
IvB Using IRS as the Signal Receiver
Instead of using the IRS as a signal reflector for performance enhancement of wireless communications, the authors in [17capacity_sha] and [19rate_walid] examine the performance of using the IRS as the signal receiver. In particular, the authors consider an uplink scenario where multiple singleantenna devices distributed in a threedimensional (3D) space transmit to a vertical plane metasurface (e.g., hung on the wall), as shown in Fig. 10. Under the assumptions that the IRS has a very large size and all the interferers have LOS paths to the IRS, the normalized capacity per unit of the IRS with perfect channel estimations is characterized into an integral expression. The analytical expression demonstrates an asymptotic behavior that, given a constant transmit power, the normalized capacity approaches half of the transmit power divided by the spatial power spectral density of noise. Moreover, based on sampling theory, the authors find that the hexagonal lattice is optimal to minimize the area of the metasurface under the constraint that each transmit antenna achieves a target spatial degree of freedom.
Compared with [17capacity_sha], reference [19rate_walid]
considers a more practical scenario where the IRS has a finite area and the interfering channels could either be LOS or nonLOS, modeled by a probabilistic model to account for the spatial correlation among the interferers. By assuming imperfect channel estimations, the authors derive the asymptotic capacity, which reveals a channel hardening effect, i.e., the impacts of channel estimation errors and the nonLOS path are negligible when the number of scattering elements becomes large. The simulation results also demonstrate that, compared to conventional massive MIMO, a largescale IRS can achieve a better reliability in terms of expectation and variance of capacity.
The focus of [18capacity_degrade_sha] is to investigate the performance of IRS with hardware impairments which induce a higher effective noise level. The authors derive a closedform expression to characterize the capacity of the uplink transmission from a singleantenna device to an IRS with hardware impairments. The study reveals that increasing the area of an impaired IRS may decrease the capacity. Based on this finding, the authors propose to split a largescale IRS into an array of smaller IRS units in order to mitigate the negative effects of hardware impairments. Both analytical and numerical evaluations demonstrate that the proposed approach can effectively suppress the negative impact of hardware impairments.
Different from the previous works focusing on capacity performance, reference [18positioning_sha] explores the potential of using an IRS with a large number of scattering elements for terminal positioning. The authors study the Fisherinformation and CramerRao lower bounds (CRLBs) for positioning a singleantenna terminal at different locations with respect to an IRS. The analysis shows that the CRLB decreases in the third order of the IRS’s size. The authors also demonstrate that deploying IRSs in a distributed manner is an effective way to improve the coverage for terminal positioning.
Table IV summarizes and compares the existing literature reviewed in Section IV. The majority of these research works studies the performance of a standalone IRS system, i.e., either pointtopoint communications or multiple communication pairs. References [19ref_prob_renzo] and [17coverage] analyze the performance of deploying the IRS reflectors in largescale systems, however, under unrealistic assumptions such as the fixedlength model for random environmental reflectors [19ref_prob_renzo] and LOS links for all the reflectors [17coverage]. Hence, there is a need for more realistic models to analyze the performance of using the IRS in practical largescale communications systems. Moreover, the abovementioned literature hardly takes the user mobility into account, neither for indoor nor outdoor scenarios. User mobility introduces not only handoffs among different IRS units but also a spatial correlation in user distribution that may cause nonnegligible impacts on the system performance. Hence, it becomes a critical research direction in the future to incorporate different mobility models into the performance analysis of IRSassisted wireless systems. Additionally, the performance metrics currently under investigation are also limited in the literature. The theoretical performance of IRSassisted wireless systems can be more thoroughly understood from the potential aspects as follows:

Pairwise error probability which measures the probability that the decoded signal is a certain symbol given the transmitted signal.

Average area spectral efficiency which is the sum of the capacity of all the communication channels normalized over spectral bandwidth and spatial area.

Energy efficiency which measures the capacity normalized over the energy consumption of IRS systems.

Handoff rate which is the frequency of occurrences that a user handoffs to another IRS.
Summary: The stochastic performance analysis for IRSassisted wireless systems mainly investigates the potential of the informationtheoretic performance gain. For a specific network design problem, the maximization of performance gain requires a joint optimization of the active transceivers and the IRS’s passive scattering elements. The joint phase control of scattering elements can be regarded as passive beamforming, which is closely coupled with the control variables of the active transceivers. This not only makes the performance analysis of IRSassisted wireless systems more complicated, due to randomness and ubiquity of the scattering elements in the radio environment, but also results in new optimization problems that require novel solutions to account for the interactions between active and passive devices.
V Joint Active and Passive Beamforming
By smartly adjusting the phase shifts of all scattering elements, as illustrated in Fig. 1, the reflected signals can be combined coherently at the intended receiver to improve the received strength or destructively at the nonintended receiver to mitigate interference. This can be verified by the experimental demonstration and channel measurements in [tang2019wireless], which pave the way for further theoretical studies and system optimization. In the sequel, we review the main optimization formulations and solutions proposed for IRSassisted wireless systems. The typical design objectives include SNR or rate maximization, transmit power minimization, EE/SE performance maximization, and physical layer security issues.
Va SNR or Capacity Maximization
VA1 IRSassisted PointtoPoint Communications
Considering a simple pointtopoint scenario, the authors in [18pbf_rui1] focus on an IRSassisted multipleinput singleoutput (MISO) wireless communication, where one IRS is deployed to assist the communication from a multiantenna AP to a singleantenna user. The IRS is composed of passive scattering elements physically arranged in an array and installed on a surrounding wall. By optimizing the phase shift of each reflecting element according to the channel conditions, the IRS can enhance the information transfer from the AP to the user. A joint beamforming problem is formulated to maximize the received signal power at the user, by jointly optimizing the AP’s transmit beamforming and the phase shift of each scattering element, which is fully controllable over the entire phase region . Though the joint optimization problem is nonconvex and difficult to solve optimally, semidefinite relaxation (SDR) is firstly proposed to obtain an approximate solution as a performance upper bound. Then, a distributed algorithm based on alternating optimization is employed to update the active and passive beamforming strategies iteratively. Given the fixed passive beamforming, the AP’s optimal beamforming can be easily obtained by the maximumratio transmission strategy. Given the AP’s beamforming, the IRS’s optimal beamformer can be simply aligned with the direct channel to enhance signal reception at the receiver. The simulation results show that the SNR can be significantly improved comparing to nonIRSassisted MISO system, e.g., the SNR is improved by around 10 dB if assisted by an IRS with 100 scattering elements. Another important finding in [18pbf_rui1] is that the SNR at the receiver increases with the number of scattering elements in the order of . The authors in [scaling_law] further study the power scaling law and compare it with the massive MIMO system. Analytical results show that a large number of reflecting elements are required to obtain the SNR comparable to massive MIMO systems.
A similar MISO system is studied in [mmwavejoint], using the IRS to assist mmWave communications from a BS to a singleantenna receiver. Through joint active and passive beamforming optimization, the IRS can provide enhanced paths of reflection for mmWave signals, and thus maximize the signal power at the receiver and then extend the network coverage. Although the joint beamforming design is generally nonconvex, both of the phase shifts and transmit beamforming can be derived optimally in closed forms for the singleIRS case. This is achieved by exploiting the characteristics of mmWave channels, i.e., assuming a rankone channel matrix between the BS and the IRS. A nearoptimal analytical solution is also derived for the multiIRS case. The analysis and simulation results reveal that the received signal power increases quadratically with the number of reflecting elements for both the single IRS and multiIRS cases, which verifies the power scaling law revealed in [18pbf_rui1].
Different from the MISO systems in [18pbf_rui1] and [mmwavejoint], the authors in [capacity_rui] focus on pointtopoint MIMO systems and characterize the fundamental capacity limit of IRSassisted data transmissions from a multiantenna transmitter to a multiantenna receiver, by jointly optimizing the IRS’s reflection coefficients and the MIMO transmit covariance matrix. Firstly, considering narrowband transmissions in frequencyflat fading channels, the alternating optimization is employed to iteratively optimize the transmit covariance matrix and the IRS’s reflection coefficients one by one. The capacity maximization for broadband transmissions is also considered in frequencyselective fading channels, where transmit covariance matrices can be optimized for different OFDM subcarriers. Based on convex relaxation, the alternating optimization algorithm is modified to find a highquality suboptimal solution. Numerical results show that the proposed algorithm achieves substantial capacity improvement compared to traditional MIMO systems without using IRS, e.g., the capacity can be improved over 45% in the high SNR regime when using an IRS with 80 scattering elements. The authors in [capacitymmwave]
study the channel capacity optimization of IRSassisted indoor mmWave communications. In the first scheme, only the IRS is adapted to enhance the capacity and an approximate expression is derived to connect the channel capacity gains and the system parameters. In the second scheme, a joint optimization of active and passive beamforming is proposed and solved by a heuristic phase control algorithm with low complexity. Simulation results verify that the second scheme can achieve more than 10% performance improvement compared to that of the IRSonly scheme.
We note that all the research works in [18pbf_rui1, mmwavejoint, capacity_rui] rely on the ideally designed IRS with infinite phase resolution, i.e., the phase shift of each scattering element can be fully controllable over the entire region . However, this is difficult for practical implementation and also complicated for designing exact phase control algorithms. The authors in [19mmwave_joint] extend the design problem in [mmwavejoint] to a more practical case with lowresolution IRS that has finite phase shifts for tuning its scattering elements. The theoretical analysis reveals that the lowresolution IRS can still achieve the same power scaling law as that in [18pbf_rui1], i.e., the received signal power increases quadratically with the number of reflecting elements. Ideally, the reflection amplitude is constant and assumed to be independent of the phase shift. Based on experimental results, the authors in [shiftmodel] notice the nonideality in controlling the IRS’s phase shifts, and thus propose a practical phase shift model that captures the nonlinear dependence between phase and amplitude. Employing this new model in an IRSassisted MISO system, a joint beamforming design problem is formulated to maximize the achievable rate in MISO downlink transmissions, which can be solved by the alternating optimization approach similar to that in [18pbf_rui1].
Besides, the aforementioned joint beamforming problems all assume full channel information for the IRS controller to make perfect phase control. This implies that the overhead of information exchange can be prohibitively high, especially for selfsustainable IRS via wireless energy harvesting. Considering the channel estimation errors and training overhead, the authors in [you2019intelligent] formulate an optimization problem to maximize the achievable data rate by designing the IRS’s discrete phase tuning strategy. Instead of a greedy search algorithm, a lowcomplexity successive refinement algorithm is devised to achieve a highquality suboptimal solution with proper algorithm initialization. To reduce the overhead in channel training and estimation, the authors in [irs_ofdm] propose a novel element grouping method to exploit the channel spatial correlation in an IRSassisted OFDM system under frequencyselective channel conditions. By estimating the combined channel of each group, the training overhead can be substantially reduced. After that, the alternating optimization method is used to maximize the achievable rate by jointly optimizing the BS’s power allocation and the IRS’s passive beamforming in an iterative manner. A highquality suboptimal solution can be achieved with a customized method for algorithm initialization. Simulation results show a significant performance improvement on the link rate, compared to the cases without using IRS. The authors also show that there exists an optimal size for element grouping to maximize the achievable rate, due to the tradeoff between the training overhead and the flexibility of passive beamforming.
The joint active and passive beamforming optimization is typically formulated by a nonconvex problem and mostly solved with local optimum by the alternating optimization method. However, as the size of scattering elements becomes large, e.g., up to hundreds [irs_survey], the optimization problem usually has high computational complexity and thus becomes difficult for practical implementation in a dynamic radio environment. Different from optimization methods, the authors in [19phase_chau] propose a deep learning (DL) method for efficient online reconfiguration of the IRS to enhance the performance of wireless communications in a complex indoor environment. It is based on the fact that the IRS’s optimal phase configuration depends on the receiver’s location to maximize the received signal strength. To save time for online optimization, the deep neural network (DNN) is employed to construct a direct mapping between the receiver’s location and the optimal phase configuration. The offline training of the DNN is based on a fingerprinting database that records the optimal phase configuration at each receiver’s position. However, the optimal phase configuration in offline training is still achieved by exhaustive search or the alternating optimization method. The authors in [19dl_irs] present a DL approach for estimating and detecting symbols transmitted from IRS. A DNN is firstly trained offline using simulated channel and phase instances, and then deployed to estimate channels and phase angles from the received symbols. Without the need for any pilot signaling, this method can reduce the overhead in online channel estimation and achieve better BER performance comparing to the traditional detectors.
VA2 Multiuser or Multicell Coordinated Communications
The aforementioned SNR or capacity maximization problems can be easily extended to the MU scenario. The authors in [18maxrate_chau] present an efficient design for sumrate maximization in IRSassisted downlink MISO communications, subject to the AP’s power budget constraint. With the minimum data rate requirement at each user, the sumrate maximization problem is firstly simplified by using the zeroforcing (ZF) transmission scheme and then following an iterative procedure to optimize the transmit power and the phase shift matrix. This is achieved by combining the alternating maximization with the majorizationminimization method. In the ideal case with infinite phase resolution, the authors in [18maxrate_chau] show that the system throughput can be increased by at least 40%, without additional energy consumption. Considering an IRSaided mmWave MU system, the authors in [mu_coverage] formulate a similar joint beamforming problem to maximize the weighted sumrate, which is solved by the alternating optimization method with closedform expressions. The IRSassisted MU MISO OFDM system is investigated in [mumisoofdm], where the authors aim at maximizing the average sumrate over all subcarriers by jointly designing the transmit beamformer and the IRS’s reflection coefficients. The sumrate maximization is transformed into the MSE minimization problem and then solved efficiently. Simulation results illustrate that the proposed algorithm can offer significant average sumrate enhancement. The MSE minimization is also studied in [msemmwave], where IRS is used to assist mmWave MU MISO downlink communications. The joint optimization of the BS’s precoding and the IRS’s phase shifts is similarly solved by the alternating optimization method with guaranteed convergence. Numerical results verify a significant improvement on spectrum efficiency over a few baseline methods.
Using a practical lowresolution IRS, the authors in [symbol_precoding]
design a symbollevel precoding scheme for MU MISO/MIMO downlink transmissions to minimize the worstcase symbolerrorrate (SER). This problem is shown to be NPhard. To proceed, the lowresolution phase shifts are firstly relaxed as continuous design variables, and then optimized by the Riemannian conjugate gradient algorithm. Next, the lowresolution symbollevel precoding vector is obtained by direct quantization. The quantitative projection is also employed in
[mu_coverage] to convert continuous phase variables to discrete phase shifts. As a special case, the 1bit symbollevel precoding vector is optimized by the branchandbound method to reduce the quantization error. Similarly, the authors in [di2019hybrid] employ the lowresolution IRS to enhance the sumrate from a multiantenna BS to multiple users. Based on a joint beamforming design, a good sumrate performance gain can be achieved by using the IRS with a reasonable size and a small number of discrete phase shifts. Considering weighted sumrate maximization in a similar MU MISO system, the authors in [guo2019weighted] propose three iterative methods to optimize the discrete phase levels of the IRS’s scattering elements, in addition to the BS’s beamforming optimization based on the fractional programming method. Numerical results show that the IRS with 2bit phase resolution achieves sufficient capacity gain with only a small performance degradation. A nonideal IRS with discrete phase shift is also studied in [mu2019exploiting] focusing on MU MIMO NOMA downlink system. Based on the alternating optimization method, a novel algorithm is developed for the joint beamforming design by utilizing the sequential rankone constraint relaxation approach. Then, a quantizationbased scheme is proposed to determine the optimal discrete phase shifts. Numerical results verify that sumrate performance achieved with the 3bit phase resolution is almost the same as that of an ideal IRS. We observe that the aforementioned sumrate maximization problems all require the knowledge of CSI of all users. This makes the channel estimation involving the IRS more complicated than before.Besides sumrate maximization, the user fairness is also a critical performance metric for MU networks. The authors in [multiaccessnoma] aim at maximizing the minimum signaltointerference plus noise ratio (SINR) of all users, which can be treated as a fairness measure, in an IRSassisted nonorthogonal multiple access (NOMA) system by jointly optimizing the BS’s power allocation and the IRS’s passive beamforming. The authors in [gaofeijoint] study the problem of joint active and passive beamforming for IRSassisted MU massive MIMO downlink communications, aiming to maximize the users’ minimum SINR. An interesting automatic interference cancelation property is revealed as the number of passive elements approaches infinity. This implies that the IRS can create interferencefree beamforming to serve individual users. This property further allows the reformulation of the maxmin problem into an IRSuser association problem, which can be solved by exhaustive search and greedy search schemes. Theoretical analysis shows that the resulting SINR performance scales quadratically with the number of scattering elements. Besides, the BS’s energy consumption can be also significantly reduced by increasing the number of scattering elements.
Similarly, the authors in [17maxrate_sha] also formulate a maxmin problem to maximize the minimum userrate in the wireless system assisted by a set of distributed IRS units. Each IRS unit has a separate signal process unit and is connected to a central process unit that coordinates the behaviors of all the IRS units. With such a distributed IRS system, a user assignment scheme between each user and the IRS is proposed to improve the minimum userrate. The optimal user assignment scheme can be effectively found by solving classical linear assignment problems defined on a bipartite graph. Numerical results show that the proposed user assignment scheme is close to optimum both under LOS and scattering environments. The authors in [19irsmimo_slim] focus on user fairness in a singlecell MU downlink system, assisted by the IRS in LOS of the BS. To maximize the minimum SINR among all users, a new passive beamforming design is proposed based on the largescale statistic channel information. A deterministic approximation of the SNR is firstly proposed under the optimal precoding scheme, and then an efficient algorithm is proposed to optimize the phase control strategy based on the projected gradient ascent method. Numerical results reveal that the proposed system can achieve massive MIMO like gains with a much fewer number of active antennas at the BS [18positioning_sha].
The authors in [ofdma] consider the integration of IRS to an orthogonal frequency division multiple access (OFDMA) based MU downlink communications. A joint optimization of the IRS’s reflection coefficients and OFDMA timefrequency resource block as well as power allocations is proposed to maximize the users’ minimum rate. A novel dynamic passive beamforming scheme is designed that allows the IRS’s reflection coefficients to dynamically change over different time slots within each channel coherence block. Then, only a subset of the users will be selected and simultaneously served in each time slot, thus achieving a higher passive beamforming gain. Numerical results show that the proposed dynamic passive beamforming outperforms the fixed passive beamforming scheme that employs a common set of reflection coefficients in each channel coherence block. The performance improvement becomes larger as the size of scattering elements increases. Note that the aforementioned research works all assume perfect or static channel information. In fact, the channel estimation in a dynamic network environment with massive reflecting elements is inevitably contaminated by error estimate and thus leading to channel uncertainty, which has not been studied in the current literature.
Reference  Optimization  System Model  Resolution  Design Variables  Main Results 
[18pbf_rui1]  Max. signal power  MISO downlink  Continuous  Transmit and active beamforming  The IRS with size achieves a total beamforming gain of 
[mmwavejoint]  Max. signal power  MISO mmWave downlink  Continuous  Transmit and active beamforming  The received signal power increases quadratically with 
[capacity_rui]  Max. capacity  MIMO downlink  Continuous  Transmit covariance matrix, passive beamforming  Substantially increased capacity compared to MIMO channels without using the IRS 
[capacitymmwave]  Max. capacity  Indoor MIMO mmWave comm.  Continuous  Transmit and active beamforming  The joint scheme achieves significant performance gain compared to the IRSonly scheme 
[19mmwave_joint]  Max. signal power  MISO mmWave downlink  Discrete  Transmit beamforming, discrete phase control  Lowresolution IRS still achieves a received signal power that increases quadratically with 
[you2019intelligent]  Max. data rate  SISO uplink  Discrete  Discrete phase control  Significant rate improvement is achieved by a lowcomplexity successive refinement algorithm 
[irs_ofdm]  Max. data rate  SISO OFDM downlink  Continuous  Transmit power allocation, passive beamforming  An optimal grouping size exists to maximize the achievable rate 
[19phase_chau]  Max. signal power  MU MISO downlink  Continuous  Passive beamforming  The DNNbased phase configuration significantly improves the data rate at target user location 
[18maxrate_chau]  Max. sumrate  MISO MU downlink  Continuous  Transmit power allocation, passive beamforming  Throughput increased by at least 40%, without requiring additional energy consumption 
[mu_coverage]  Max. weighted sumrate  MU MIMO mmWave downlink  Continuous  Precoding matrix, passive beamforming  Distributed IRSs can effectively support MU mmWave transmissions 
[mumisoofdm]  Max. average sumrate  MU MIMO OFDM downlink  Continuous  Precoding matrix, passive beamforming  Significant average sumrate enhancement 
[msemmwave]  Min. MSE  MU MISO mmWave downlink  Continuous  Precoding matrix, passive beamforming  Improved EE/SE performance 
[symbol_precoding]  Min. worstcase SER  MU MIMO downlink  Discrete, binary  Precoding matrix, discrete phase control  Enhanced SER performance can be achieved 
[guo2019weighted]  Max. weighted sumrate  MU MISO downlink  Discrete  Transmit beamforming, discrete phase control  The IRS with 2bit resolution achieves sufficient capacity gain 
[di2019hybrid]  Max. sumrate  MU MISO downlink  Discrete  Transmit and passive beamforming  A good performance gain achieved by using the IRS with a few discrete phase shifts 
[mu2019exploiting]  Max. sumrate  MU MISO NOMA downlink  Discrete  Transmit beamforming, discrete phase control  The sumrate performance with the 3bit phase resolution is close to that of an ideal IRS 
[multiaccessnoma]  Max. minimum SNR  MU SISO NOMA downlink  Continuous  Power allocation, passive beamforming  The IRS with 1bit phase resolution improves the maxmin rate by 20% compared to that of traditional NOMA 
[gaofeijoint]  Max. minimum SINR  MU MIMO downlink  Continuous  Transmit and passive beamforming  Automatic interference cancelation is revealed as approaches infinity. The SINR performance scales quadratically with 
[17maxrate_sha]  Max. minimum rate  MU transmissions to the IRS  Continuous  UserIRS assignment, passive beamforming  The user assignment scheme performs close to the optimum under both LOS and scattering environments 
[19irsmimo_slim]  Max. minimum SNR  MU MIMO downlink  Continuous  Passive beamforming, resource block and power allocation  The dynamic passive beamforming outperforms the fixed passive beamforming. The performance improvement becomes larger as increases 
[ofdma]  Max. minimum SNR  OFDMA MU downlink  Continuous  Passive beamforming  The IRSassisted system achieves massive MIMO like gains with a much fewer number of active antennas at the AP 
[programchannel]  Min. interference  MU MIMO downlink  Continuous  Passive beamforming  A single set of optimal weights can form multiple interferencefree beams to achieve the multistream MIMO transmission 
[multigroup]  Max. sumrate  Multicell MU multicast downlink  Continuous  Precoding matrix, passive beamforming  Improved EE/SE performance over conventional massive MIMO systems 
[multicellrelaying]  Max. weighted sumrate  Multicell MU MIMO downlink  Continuous  Precoding matrix, passive beamforming  Significant performance gain is achieved over the conventional counterpart without the IRS 
The goals of the sumrate maximization and user fairness considerations are intrinsically fighting against the resource competition or interference among different users. The use of the IRS can make the wireless propagation channels more flexible to control and thus easier for interference suppression. Considering a typical MU MIMO system, the authors in [programchannel] show the feasibility of constructing multiple interferencefree beams by using the IRS with a large number of passive elements. Based on the characterization of MUMIMO channel, the authors propose the novel beamformer to minimize the interference power while providing desirable beam response at each user. Analysis of the beam pattern shows that a single set of optimal weights can form multiple interferencefree beams for multistream MIMO transmissions. The interference among multiple users in a more sophisticated multicell multicast downlink system is investigated in [multigroup]. The BS has transmit antennas and serves multicasting groups. Each user can only belong to one group. The information destined for different groups are independent and different, which implies the existence of intergroup interference. The authors in [multigroup] aim at maximizing the sumrate of all groups by a joint optimization of the BS’s precoding matrix and the IRS’s passive beamforming. A concave lower bound of the objective function is firstly derived, and then the alternating optimization method is used to update two sets of variables iteratively. To reduce the computational complexity, the authors in [multigroup] further adopt the majorization minimization (MM) method and obtain a closedform solution for each set of variables at every iteration. The simulation results demonstrate that the sumrate can be improved by more than 100% when assisted by the IRS with only 8 scattering elements, comparing to a massive MIMO system with 256 antennas at the BS. To mitigate intercell interference, the authors in [multicellrelaying] deploy the IRS at the cell boundary of a multicell system to assist the downlink MIMO transmissions to celledge users. The maximization of weighted sumrate is solved with a similar alternating optimization to that in [multigroup]. The BS’s active precoding and the IRS’s passive beamforming are iteratively optimized by using the block coordinate descent (BCD) algorithm.
Summary: In this part, we have reviewed the potentials of using the IRS to improve transmission performance, in terms of SNR or data rate at the target receiver for both pointtopoint communications and multigroup/multicell MU cases. A summary of existing works on SNR or capacity maximization is listed in Table V. In particular, we have discussed the applications of the IRS under different communication models, e.g., MISO, MIMO, OFDM, NOMA, mmWave, multicell systems, and LOS or nonLOS channel conditions. Different system models are illustrated and compared in Fig. 11. The system optimizations of IRSassisted wireless communications in different scenarios are typically formulated into a joint optimization problem of the IRS’s passive beamforming and the BS’s transmit beamforming or power allocation strategy. Along this main line of research, some special cases are also discussed, including the phase shift optimization for the nonideal IRS with finite phase resolution, or with incomplete or uncertain channel information. We have noticed that the main solution methods to the nonconvex joint optimization problems are based on a simple alternating optimization method, which can guarantee the convergence to suboptimal solutions. However, comparing the optimum, the performance loss by using the alternating optimization is not known exactly and seldom characterized in literature. By developing more sophisticated algorithms in the future work, we envision that the IRSassisted wireless networks can achieve a higher performance gain than that in the current literature.
Besides SNR and rate maximization at the receiver, the IRSassisted wireless networks can also help minimize the transmit power of the BS or maximize the overall EE/SE performance, due to more preferable channel conditions programmed by the IRS. By passive beamforming, the IRS can configure wireless channels in favor of information transmission between transceivers. This results in a more energyefficient communication paradigm, e.g., the BS can maintain the same transmission performance with a reduced power consumption compared to the cases without using the IRS. As such, IRSassisted communications can be envisioned as a green technology for future wireless networks. Nonetheless, system and network optimizations are required to achieve maximum EE/SE performance in IRSassisted wireless networks, which are our focus in the following part.
[18ee_chau1]  Max. energy efficiency  MISO downlink  Continuous  Power allocation, passive beamforming  IRSassisted system provides up to 300% increase in energy efficiency than AF relay communications 
[18pbf_rui2]  Min. transmit power  MISO downlink  Continuous  Transmit and passive beamforming  Transmit power can be scaled down in the order of without compromising the SNR at the receiver 
[han2019intelligent]  Min. transmit power  MISO downlink broadcasting  Continuous  Transmit and passive beamforming  A lower bound is derived for the BS’s minimum transmit power 
[19minfu_noma]  Min. transmit power  MISO NOMA downlink  Continuous  Transmit and passive beamforming  Verified effectiveness and superiority of using IRS to reduce the total transmit power 
[bf_multicluster]  Min. transmit power  MISO NOMA downlink  Continuous  Transmit and passive beamforming  The IRSassisted ZF scheme outperforms the SDPbased algorithm when is large 
[sumpath_gain]  Max. spectrum efficiency  MIMO downlink  Continuous  Transmit and passive beamforming  Significant performance improvement over the nonIRSassisted schemes 
[19pbf_rui2]  Minimize transmit power  MISO downlink  Discrete  Transmit beamforming, discrete phase control  A discrete IRS can achieve the same power gain as that with infinite phase resolution 
[19ee_chau2]  Max. energy efficiency  MU MISO downlink  Discrete, binary  Transmit beamforming, discrete phase control  1bit resolution IRS significantly improves energy efficiency compared to relayassisted communications 
[miso_robert]  Max. spectrum efficiency  MISO downlink  Continuous  Transmit and passive beamforming  It achieves higher EE/SE performance by using the IRS than increasing the size of AP’s antenna array 
[zhou2019robust]  Min. transmit power  MU MISO downlink  Continuous  Transmit and passive beamforming  Robust beamforming design guarantees the satisfaction of all users’ data rate requirements 
VB Power Minimization or EE/SE Maximization
Focusing on an IRSassisted MISO downlink scenario as that in [18pbf_rui1], the authors in [18pbf_rui2] aim at minimizing the AP’s transmit power under individual users’ SINR constraints, by jointly optimizing the AP’s transmit beamforming and the IRS’s passive beamforming strategies. Following a similar SDR procedure and the alternating optimization method as that in [18pbf_rui1], the AP’s transmit beamforming can be efficiently optimized in a secondorder cone program, and the optimization of the IRS’s passive beamforming is degenerated to a conventional relay beamforming optimization problem. By an asymptotic performance analysis with infinite number of scattering elements, it is shown that the AP’s transmit power can be scaled down in the order of without compromising the SNR at the receiver, where denotes the number of passive elements. Numerical results verify that the AP’s transmit power can be reduced by more than 55% for the wireless user far away from the AP (e.g., 50 meters). The authors in [han2019intelligent] focus on an IRSassisted MISO broadcasting system under SINR constraints at mobile users and derive a lower bound of the BS’s minimum transmit power, which is much lower than those cases without using the IRS. Moreover, the BS’s transmit power can approach the lower bound with an increase of the number of the IRS’s scattering elements. Transmit power minimization is also considered in an IRSassisted NOMA downlink system [19minfu_noma]. The joint optimization the active and passive beamforming strategies is found to be a highly intractable biquadratic program, which is firstly relaxed via the SDR approach and then solved by the differenceofconvex (DC) algorithm. To further reduce its complexity, the authors in [19minfu_noma_jrl] propose a novel user ordering scheme which is critical for transmit power minimization in the NOMA system. Simulation results demonstrate that the proposed alternating DC algorithm can reduce the AP’s transmit power by more than 8 dB when using an IRS with 50 scattering elements.
The authors in [bf_multicluster] study a multicluster MISO downlink communication scenario, in which a multiantenna BS transmits superimposed signals to multiple receivers simultaneously. The users are grouped into different clusters and NOMA protocol is employed in each cluster to improve spectrum efficiency for information transmission. The design objective is to minimize the total transmit power by jointly optimizing the BS’s transmit beamforming and the IRS’s passive beamforming strategies. This problem is previously solved by an SDPbased alternating optimization method, e.g., [18pbf_rui1, 19minfu_noma, 19minfu_noma_jrl], which has prohibitively high computational complexity and deteriorating performance. Here, the authors in [bf_multicluster] propose an effective secondorder cone programming (SOCP) based alternating direction method of multipliers (ADMM) to obtain a locally optimal solution. A ZFbased suboptimal algorithm is further proposed to reduce the computational complexity. The simulation results demonstrate significant performance gain over the conventional SDPbased algorithm.
Instead of minimizing transmit power, the authors in [18ee_chau1] aim at maximizing the energy efficiency by jointly optimizing the IRS’s passive beamforming and the AP’s power allocation over different users, subject to the AP’s maximum power and the users’ minimum QoS constraints. The total power consumption includes the transmit power, the constant circuit power, as well as the IRS’s power consumption, which relates to the size and implementation of reflecting elements. The IRS’s finer phase resolution and larger size of scattering elements both imply a higher power consumption. Based on the alternating optimization, a gradient descent method is firstly used for optimizing the IRS’s phase control, and then the transmit power allocation is optimized by a fractional programming method. The simulation results in a realistic environment show that the IRSassisted wireless system can provide up to 300% higher energy efficiency than that of the multiantenna AF relay communications. The authors in [sumpath_gain] propose a joint beamforming design for spectrum efficiency maximization in an IRSassisted MIMO downlink system, which is a mixed integer problem and can be approximately solved by the alternating optimization method. The ADMM algorithm is leveraged to find the phase shifts of individual scattering elements. Then, the active beamforming can be obtained by classic singular value decomposition (SVD) and waterfilling solutions. The spectrum efficiency maximization is also studied in [miso_robert] focusing on a pointtopoint MISO downlink system. The joint optimization of the AP’s transmit beamforming and the IRS’s phase shifts is solved by two efficient algorithms exploiting fixed point iteration and manifold optimization techniques, respectively, which not only achieve a higher spectrum efficiency but also require a reduced computational complexity. Simulation results reveal that it can achieve higher EE/SE performance by using the IRS than increasing the size of AP’s antenna array.
Prior works mostly assume infinite phase resolution for the IRS, which however is practically difficult to realize due to the hardware limitation. Considering a more practical case, the authors in [19pbf_rui2] aim at minimizing the AP’s transmit power in downlink MISO communications, assisted by an IRS with finite phase resolution, similar to [19mmwave_joint, symbol_precoding, mu_coverage]. The joint optimization of active beamforming and the IRS’s discrete phase tuning strategies is usually very difficult to solve due to the combinatorial nature. To proceed, the discrete phase constraints can be firstly relaxed into continuous phase values, and then the popular alternating optimization used in [18ee_chau1, bf_multicluster, sumpath_gain] can be applied. After that, the feasible discrete phase shifts can be obtained by quantization projection. While this approach generally reduces the computation time, it is suboptimal for the original discrete optimization problem and may subject to performance loss due to quantization errors. Analytical results show that a practical IRS with discrete phase shifts can still achieve the same power scaling law as that with continuous phase shifts, the finding similar to [18pbf_rui1]. More interestingly, the performance loss is shown to be irrelevant to while only dependent on , where denotes the resolution of phase shifts. Numerical results reveal that the discrete phase shifts with or are sufficient to achieve the closetooptimal performance. A special case with the 1bit phase resolution is studied in [19ee_chau2]. The optimization of phase shift matrix and power allocation for each user follows a similar alternating optimization method. The IRS’s perfect phase control for both infinite and finite phase resolutions depends on the knowledge of exact CSI, which however is practically challenging to obtain due to the lack of signal processing capability at the IRS and the large size of passive scattering elements. In [zhou2019robust], the imperfect CSI is considered in a robust beamforming problem to minimize the transmit power for an IRSassisted MU MISO system, subject to the minimum rate constraints of all users. The robust beamforming design can be solved by a squence of SDP subproblems transformed by Schur’s complement and the penalized convexconcave procedure [ccp].
Summary: In this part, we have reviewed the use of the IRS in wireless networks to minimize the transmit power or maximize the EE/SE performance. The literature reveals an important power scaling law showing that, through optimal passive beamforming, the BS’s power consumption can be scaled down in the order of without compromising the SNR at the receiver. The similar power scaling rule still holds for a practical implementation of the IRS with finite or discrete phase tuning resolution. The power saving becomes more significant for wireless users far away from the transmitter.
Though significant performance improvement can be verified by numerical results and simulations, we observe that the research focus of almost all papers in literature is limited to the joint optimization of active and passive beamforming under different network scenarios. In fact, the overall performance gain can be better explored in the future work if the size of the IRS’s scattering elements, the orientation of the IRS tiles, their partitions and grouping strategies, etc., are all taking into account, in combination with the transceivers’ access control, user association, information encoding, transmit scheduling, QoS provisioning, etc. Besides, we notice that the maximization of EE/SE performance relies on the characterization of total power consumption in IRSassisted wireless networks. The IRS’s power consumption is modeled to be linearly correlated with the size and tuning resolution of individual reflecting elements. However, almost all the reviewed papers consider the selfsustainable IRS with sufficient energy supply, which may lead to overoptimistic conclusions on the EE/SE performance. The joint system optimization can be more complicated with the introduction of IRS’s energy budget constraint, which is worthy further investigation in future research.
VC IRSassisted Physical Layer Security
The IRS’s wave manipulation has the flexibility of simultaneously creating enhanced beam to an intended receiver and the suppressed beams to unintended receivers. This can be used to enhance physical layer security in wireless communications. The authors in [Yu2019Enabling] introduce the idea of using IRS as an effective solution to defend eavesdroppers. In particular, the authors consider a scenario in which an eavesdropper is placed in the communication range between a legitimate transmitter (LT) and a legitimate receiver (LR). The LT is equipped with multiple antennas, while both the LR and eavesdropper have a single antenna. The IRS is placed near the LR to prevent the eavesdropper from eavesdropping, by controlling the reflected signals to maximize the achievable secrecy rate at the LR, which is defined as the amount of information per time unit that can be securely sent over a communication channel [Oggier2011The]. To achieve this goal, the joint control problem of the LT’s transmit beamforming and the IRS’s phase shift matrix is approximately solved by the BCD and MM based algorithms, similar to that in [multigroup]. Simulation results show that the secrecy rate achieved by using the IRS can be significantly improved comparing to the cases without using the IRS. Instead of BCD algorithm in [Yu2019Enabling], the secrecy rate maximization problem in [feng2019physical] is solved by a computationallyefficient algorithm exploiting fractional programming and manifold optimization techniques. One interesting result is that a higher secrecy rate can be achieved with an IRS with a larger size. This idea is then extended in the recent research works, i.e., [secrecy_max] and [secure_irs], by considering multiple antennas at the eavesdropper and rankone/fullrank communication channels, respectively. However, all current approaches are based on approximate methods, and thus their performance can be improved in the future work.
Considering a similar IRSassisted secure wireless communication system to that in [Yu2019Enabling], the authors in [secure_rui] focus on a more challenging scenario in which the eavesdropping channel is better than the legitimate communication channel and they are also highly correlated in space. This makes the achievable secrecy rate of the system very limited. A joint optimization of the LT’s transmit beamforming and the IRS’s passive beamforming is proposed to improve the secrecy rate. The optimal solution requires that the IRS’s reflections and the LT’s beamforming signals are destructively added at the eavesdropper, thereby enhancing the achievable secrecy rate of the system. This idea is then extended to a more general scenario in which multiple eavesdroppers and LRs coexist in the system [19pls_liang]. By jointly optimizing the beamforming strategies of LT and IRS, the authors in [19pls_liang] formulate the minimumsecrecyrate maximization problems with both continuous and discrete reflecting coefficients for the IRS’s scattering elements. Due to the nonconvex problem structure, this problem can be approximately solved by the alternating optimization and pathfollowing algorithms in an iterative manner, similar to the previous works in [Yu2019Enabling] and [secure_rui]. Two suboptimal algorithms with closedform solutions are also proposed to reduce the computational complexity. The simulation results then verify the enhancement of secrecy rate, based on the known number of eavesdroppers and the CSI in advance. Nevertheless, this information is generally difficult to obtain in practice, and thus more practical solutions based on incomplete environmental information can be considered in future work. As such, the authors in [yu2019robust] consider a similar scenario with multiple multiantenna eavesdroppers and LRs. Focusing on a more practical case with unknown CSI, similar to [zhou2019robust], the authors in [yu2019robust] propose a robust optimization problem to maximize the sumrate constained by information leakage to the eavesdroppers. The design variables include the AP’s transmit beamforming and the covariance matrix of artificial noise, as well as the IRS’s phase shifts. An efficient algorithm is developed based on the combined use of alternating optimization, a penaltybased approach, successive convex approximation (SCA), and SDR approaches. Simulation results show that the use of the IRS can significantly improve the secrecy performance compared to conventional cases without using the IRS.
Besides the LT’s transmit beamforming, the authors in [guan_secrecy] also optimize the LT’s jamming signals to enhance the achievable secrecy rate, by actively injecting noiselike jamming signals to the channel. By incorporating jamming signals into transmit beamforming, along with the optimization of the IRS’s passive beamforming, the secrecy rate can be significantly improved comparing to the conventional methods without using the IRS and/or jamming beamforming. Unlike the popular joint transmit and passive beamforming in previous works, e.g., [Yu2019Enabling, secure_rui, 19pls_liang, guan_secrecy], the authors in [19pls_ian1] consider different approach to maximize the secrecy rate, by optimizing the number of IRS tiles (namely hypersurface tile) and their orientations to create desirable phase changes. To solve this problem, the LT is firstly controlled to transmit all its signals to the IRS. Then, the IRS optimizes its tiles to reflect all received signals to the direction of the LR. By this way, the received signal power at the eavesdropper becomes very small and thus insufficient for information decoding, even if the eavesdropper is located between the LT and LR. Though this is an effective solution to prevent eavesdropping, it requires the implementation of the hypersurface tile and thus its applications are limited in some particular scenarios such as smart offices and houses. All aforementioned works generally rely on the LT’s optimal control (e.g., artificial noise injection and transmit beamforming) in combination with the IRS’s passive beamforming to improve the secrecy performance. Different from them, the authors in [wang2019eefficient] introduce an interesting idea by using the thrid device, namely a friendly jammer, to cooperate with the LT and to fight against multiple eavesdroppers, as shown in Fig. 12. This problem is studied in an IRSassisted MISO downlink system, aiming to maximize the LT’s energy efficiency by a joint optimization of the LT’s transmit beamforming, the friend’s jamming beamforming, and the IRS’s passive beamforming. The solution method follows a similar approach as those in [yu2019robust, 19pls_liang, Yu2019Enabling], by leveraging the alternating optimization and SDR approaches.
The secrecy rate maximization merely aims at preventing legitimate transmissions from being deciphered or eavesdroppered by unlegitimated user. However, this may not be enough for some cases where exposure of transmission activities, location and movement of transmitters are sensitive information to the end users. This calls for covert communications that can provide stronger protection by hiding the presence of legitimate transmissions [covert18]. The authors in [lu2019intelligent] propose the use of the IRS to enhance communication covertness, by leveraging the IRS’s reconfigurability to reshape undesirable propagation conditions and thus avoid information leakage. Assuming perfect CSI condition, a joint optimization of the LT’s transmit power and the IRS’s passive beamforming is proposed to maximize the covert rate, i.e., the achievable rate satisfying the covertness requirement. The numerical results demonstrate a significant increase in covert rate compared to the conventional cases without using the IRS.
Summary: In this section, we have reviewed emerging applications of the IRS for physical layer security. In particular, IRS can be used as a very effective tool to prevent wireless eavesdropping attacks by simultaneously controlling the transmissions at the LT and the reflection at the IRS. As a result, the achievable secrecy rates obtained by the IRSassisted systems can be significantly improved compared with the conventional methods only relying on the LT’s transmission control. Many simulation results verify the improvement of secrecy performance of IRSassisted systems. This obviously paves the way for a flourish of new research problems relating to physical layer security issues in the future wireless networks. However, there are still some challenges which need to be addressed. For example, how to simultaneously control the LT’s transmissions and the IRS’s reflections in realtime systems, and how to obtain the eavesdropper’s channel information for accurate beamforming optimization are still major challenges for antieavesdropper systems.
Vi Emerging Applications of Irs in Wireless Networks
As demonstrated in previous sections, the use of the IRS is capable of bringing unprecedented performance enhancement for future wireless systems by reconfiguring the previously uncontrollable wireless channels in favor of network performance optimization. In particular, we have reviewed in previous sections the performance analysis and optimization of IRSassisted wireless networks with different design objectives, i.e., SNR/capacity maximization, transmit power minimization, EE/SE performance maximization, and physical layer security issues. However, the potentials of using the IRS in wireless systems are not limited to the above aspects. In fact, it is still developing and flourishing in various aspects far beyond the aforementioned topics. In this section, we review these emerging and diverse applications of the IRS in wireless networks. These issues include but not limited to IRSassisted wireless power transfer, IRSassisted UAV communication networks, and IRSassisted MEC techniques.
Via IRSassisted Wireless Power Transfer
As observed in [18pbf_rui1, mmwavejoint], the IRS’s passive beamforming can be designed to enhance the received signal strength at an information receiver (IR). This approach can also improve the efficiency of wireless power transfer to an energy receiver (ER). By leveraging massive lowcost passive scattering elements, the IRS can achieve a high passive beamforming gain, which is appealing for drastically enhancing the efficiency of wireless power transfer. The authors in [irs_swipt] consider an IRSaided simultaneous wireless information and power transfer (SWIPT) system, in which a multiantenna BS communicates with several multiantenna IRs, while guaranteeing the energy harvesting requirements of the ERs. The authors firstly formulate a weighted sumrate maximization problem by jointly optimizing the BS’s transmit precoding and the IRS’s phase shifts subject to a nonconvex unitmodulus constraint imposed by the phase shifts and the energy harvesting requirements imposed by the ERs. After that, the classic BCD algorithm together with the KarushKuhnTucker (KKT) technique are adopted to find the optimal operation parameters for the BS and the IRS. This approach allows us to quickly achieve the nearoptimal solution which is much better than those of baselines, i.e., with fixed phase or without using the IRS.
Considering a similar model, the authors in [wu2019joint] propose to use a set of distributed IRSs to assist SWIPT from a multiantenna AP to multiple IRs and ERs, respectively. Instead of sumrate maximization, the authors in [wu2019joint] focus on the minimization of the AP’s transmit power by jointly optimizing the AP’s transmit beamforming and the IRSs’ passive beamforming strategies, subject to the IRs’ SINR constraints and the ERs’ energy constraints. Based on proper transformations on the users’ SINR and energy constraints, the resulting problem is solved by a more efficient penaltybased method instead of the commonlyused alternating optimization method. A lowcomplexity algorithm is also proposed to speed up the optimization of the IRSs’ phase shifts. Simulation results demonstrate the significant performance gains achieved over benchmark schemes, e.g., the AP’s transmit power can be reduced by more than 50% with only 30 scattering elements in the demonstrated setup. Different from the weighted sumrate maximization problem in [irs_swipt], the authors in [powermaxswipt] aim at maximizing the weighted sum power received at the ERs in an IRSassisted SWIPT system. The weighted sum power is achieved by jointly optimizing the BS’s transmit beamforming and the IRS’s phase shifts, subject to individual IRs’ SNR constraints. A similar model is studied in [19miso_swipt], in which the authors consider using multiple energy beams to transfer energy to the ERs. Simulation results then show that the proposed IRSassisted SWIPT system achieves significant performance gains over the benchmarks without using the IRS.
ViB IRSassisted UAV Communications
The capacity maximization problems in [capacity_rui] and [irs_ofdm] can be extended to the emerging UAV networks. In [uav_bf_marco], the authors introduce an IRSassisted UAV communication network in which the IRS is used to enhance communication quality from UAV to the ground user. A joint optimization of the UAV trajectory and IRS’s passive beamforming strategy is formulated to maximize the average achievable rate. The passive beamforming and trajectory optimization are divided into two subproblems and solved by an alternating optimization method. Given the UAV trajectory, the IRS’s phase shift is firstly derived in a closed form to achieve phase alignment with the received signals from different paths. Then, with the fixed phase shifts, the locally optimal trajectory solution can be derived by using the SCA method. A similar scenario is studied in [uav_carry_irs] where the UAVcarried IRS is used to enhance the transmission performance of mmWave communication networks. The UAVcarried IRS is also capable of energy harvesting from the mmWave signals to sustain its operations. To deal with the dynamic radio environment, a reinforcement learning (RL) approach is proposed to find the optimal policy, i.e., the best location of UAV given the channel state, that maximizes the longterm average throughput of the downlink UAV transmissions. The simulation results then show that the proposed RLbased approach can significantly improve the network performance, i.e., up to 65%, comparing to conventional schemes without learning capability.
The authors in [ma2019enhancing] employ the wallmounted IRS to enhance the channel between cellular BS and UAVs, which previously suffers from poor signal strength as the BS’s signal beamforming is generally optimized to serve ground users. By controlling the IRS’s reflecting phase, the signal gain at the UAV is characterized based on the 3GPP groundtoair channel models as a function of various deploying parameters, including the UAV’s height, the IRS’s size, altitude, and distance to the BS. Thus, the maximum signal gain can be achieved by optimizing the IRS’s location, altitude, and distance to BS. Numerical results show that a significant signal gain can be achieved for UAVs even with a smallsize IRS, e.g., the signal gain quickly jumps to 20 dB when UAVs fly over 30 meters above the BS.
ViC IRSassisted Mobile Edge Computing
MEC allows data and computation offloading to resourcerich MEC servers. As such, the energy consumption and processing delay can be potentially reduced at the end users with insufficient computing capability. However, the benefit of MEC is not fully exploited, especially when the link for data and computation offloading is hampered. As the use of IRS can enhance both the EE/SE performance, it can be a promising technology to improve the MEC’s performance.
The authors in [latency_min] propose an IRSassisted MEC system in which singleantenna devices can offload a fraction of their computation workload to the MEC server. The offloading process is assisted by the IRS’s passive beamforming to enhance the channel conditions. The authors formulate a latency minimization problem for both the singledevice and multidevice scenarios, subject to the MEC resource constraint and the IRS’s phase shift constraints. The BCD algorithm used previously in [irs_swipt] is adopted to find the optimal MEC offloading strategy in this case. Extensive numerical results then verify the efficiency of using the IRS for the MEC system, especially in terms of latency. The authors in [hua2019reconfigurable] use the IRS in a green edge inference system, where the computation tasks at resourcelimited user devices can be offloaded to multiple resourcerich BSs. To minimize the network power consumption in both computation and uplink/downlink data transmissions, the authors in [hua2019reconfigurable] propose a joint optimization of the task allocation among different BSs, each BS’s transmit and receive beamforming vectors, the users’ transmit power, and the IRS’s passive beamforming strategies. Considering the combinatorial nature of the proposed problem, the authors firstly propose a reformulation by exploiting the group sparsity structure of the beamforming vectors, and then decouple the optimization variables by a blockstructured optimization approach. Instead of the widely used SDR approach, a novel differenceofconvexfunctions based threestage framework is introduced to solve the orginal problem with enhanced network performance. Numerical results reveal that the proposed approach can reduce the overall power consumption by around 20% compared to the conventional SDRbased approach.
Summary: The IRS is a cuttingedge technology possessing outstanding features expected to open new promising research directions, which have never been seen before in wireless communication networks. In this section, we have reviewed some emerging applications of the IRS in wireless networks including wireless power transfer, UAV communications, and MEC. It can be clearly seen that by using the IRS, energy, communications and computing efficiency of conventional wireless networks can be significantly enhanced. However, all results obtained so far are through simulations, and thus more proofofconcept prototypes are required to validate the IRS’s practical efficiency. Besides, there are more potential applications that can be enhanced by using the IRS, which can be studied further in the future work, such as vehicular and maritime communications, satellite and nextgeneration mobile networks.
Vii Challenges, Open Issues, and Future Research Directions
Different approaches reviewed in this survey evidently show that IRSassisted wireless networks can effectively enhance the signal reception at the receiver, extend the network coverage, increase the link capacity, minimize the transmit power, suppress the intercell interference, and enable better security and QoS provisioning to multiple users, etc, compared to nonIRSassisted counterparts. However, there still exists some challenges, open issues, and new research directions which are discussed as follows.
Viia Challenges and Open Issues
ViiA1 Energyefficient Channel Sensing and Estimation
The IRS is composed of a large array of passive scattering elements which are typically interconnected and controlled by a centralized controller, e.g., FPGA and embedded ICs [16surface_focusing, tuning18, 18surface_circuit]. The superiority of using the IRS relies on its reconfiguration of each scattering element’s phase shift, according to the channel conditions from the transmitter to its receiver. This requires the capability of channel sensing and signal processing algorithms, which become very challenging without dedicated signal processing capability at the passive scattering elements. Existing approaches for the IRS’s channel estimation generally assume that only one single scattering element is active, while all the other elements are inactive at a given time, e.g., [mumisoestimation]. Such an elementbyelement ON/OFFbased channel estimation scheme is practically costly for a largescale IRS with massive scattering elements. In particular, the IRS is not fully utilized as only a small portion of the scattering elements is active in each time. This degrades the channel estimation accuracy and produces a long estimation delay. A simple channel estimation scheme proposed in [lin2019channel] assumes that the IRS’s phase control can always maximize the modulus of the reflecting channel, which is very difficult to realize in practice with a large number of scattering elements. The authors in [ning2019channel] study a beamtraining based channel estimation scheme for an IRSassisted MIMO THz system, by exploiting the sparsity of THz channel and the characteristics of massive antenna array. The authors in [chen2019channel] formulate the channel estimation into a sparse channel matrix recovery problem with limited training overhead by exploiting the sparsity of the IRSassisted channels from BS to the receiver. It is obvious that more sophisticated signal processing algorithms (e.g., [chen2019channel, chestimate, wang2019channel, ofdm_estimation, xia2019intelligent]) can achieve better accuracy for channel estimation, however they generally demand higher power consumption for information exchange, signal processing, and computation, which may be not sustainable for passive IRS wirelessly powered by harvesting energy from RF signals. Thus, the cost of energy consumption for channel sensing and estimation becomes nonnegligible for the passive IRS especially when its size becomes large.
ViiA2 Practical Protocols for Information Exchange
Generally, the IRS’s channel sensing and estimation can be achieved by overhearing a training sequence sent by the active transceiver. In this process, information exchange between IRS and the active transceiver may be required to synchronize the operations. The information exchange also happens when a transmit scheduling protocol is employed to coordinate the data transmissions of multiple users. In this case, the IRS also needs to synchronize with different transmission frames and reconfigure its passive beamforming schemes according to the channel conditions of different users. If information exchange is inevitable, a practical protocol is thus required for the IRS to talk with the conventional transceivers. Information exchange can be made easy for conventional transceivers using a dedicated control channel. However, without sufficient energy supply, it becomes more challenging for the passive IRS to detect and decode the information from other active transceivers. Hence, the design of information exchange protocols firstly has to be of extremely low power consumption such that it is sustainable by wireless energy harvesting. Secondly, a practical information exchange protocol has to costeffective by minimizing the conflict with or the alteration of the existing systems. In particular, by using the IRS’s inherent sensing capability, it can be more energyefficient for the IRS to detect physical layer information, instead of MAC layer bit stream. Therefore, the information exchange can be made possible by modulating the packet length or transmit power, so that the passive IRS can sense the variations of signal power with lowpower consumption.
ViiA3 Reflection as a Resource for IRSassisted HetNets
In the future smart radio environment, the wireless networks can be assisted by a distributed IRS system with individually controlled IRS units due to the pervasive deployment of reconfigurable metasurfaces on different environmental objects. This implies a challenging situation for the realtime allocation and optimization of different IRSs to serve multiple data streams in dynamic and heterogeneous networks (HetNets). Conventionally, individual transceivers can independently adapt their operation parameters to the channel condition, which follows some stochastic model and can be predicated or estimated via a training process. However, with the IRS’s reconfigurability, the radio environment itself becomes controllable and nonstationary. Hence, it becomes more difficult for individual transceivers to understand the CSI via training. This implies a centralized coordination for the IRSassisted networks, at least for the distributed IRS units. Specifically, an efficient information exchange mechanism among different IRS units and a control protocol are required for the allocation and association of different IRS units to multiple users simultaneously.
ViiA4 Agile and Lightweight Phase Reconfiguration
The phase control of individual scattering element has to be coordinated with each other for effective beam steering. The large size of the IRS’s scattering elements can make the overall phase tuning more flexible even with limited phase shifts at individual scattering element. This requires an efficient algorithm design to jointly control the phase shifts of all scattering elements in a timely manner, according to the dynamics of the radio environment. More importantly, the IRS’s phase control is also strongly coupled with the optimal transmit control of the active transceivers. This makes it more challenging for the design of an agile and lightweight phase control algorithm with minimum energy consumption and communication overhead. In the existing literature, most of the phase control algorithms are based on the general alternating optimization method, that decouples the IRS’s phase control and the conventional transmit control (e.g., power allocation, transmit beamforming, and precoding matrix design) in separated subproblems. Though this simplification can provide a convergent solution to a suboptimum, the alternating optimization method for these design problems inevitably incurs large communication overhead and processing delay. It is also very challenging to characterize the performance loss of the convergent solution comparing to its optimum.
ViiB Future Research Directions
Based on extensive literature review and the analysis of common shortcomings of the current literature, we highlight a few potential research directions for future exploration.
ViiB1 Learning Approach for Passive Beamforming
Different from the alternating optimization commonly used in the literature, machine learning approaches can be more appealing for the IRS to realize agile and lightweight phase control based on locally observed information of the radio environment
[19learning_renzo, model_dnn19, 19dl_irs]. This can help minimize the overhead of information exchange between the IRS and active transceivers. The large number of scattering elements and their sensing capabilities further imply that rich information can be collected during channel sensing, providing the possibility for datadriven deep learning approaches [19survey_renzo, dlsurvey]. Furthermore, the potential analog computation can be also envisioned to realize ANNs via multilayer metasurfaces [14science], which potentially make the learning approach agile in computation and lightweight without the need for information exchange. For example, leveraging RL approaches, a decisionmaking agent can be employed at the IRS controller to adapt its phase configuration for each scattering element, solely based on the observed system state (e.g., the perceived CSI via its sensing capability) and the receivers’ feedback of its phase configuration. The system state can be estimated by the IRS via sensing or overhearing the ACK packets from the receiver to the transmitter. With specially designed ACK packets, e.g., the ACK packets with different time durations or transmit power, the channel sensing of IRS can be made easier without energy consumption on decoding the ACK packets. A similar idea has been used for information exchange in wireless backscatter communications [ambient_survey].ViiB2 IRSassisted D2D Communications
D2D communications technology is envisioned to connect billions of lowpower user devices constituting the future Internet of Things (IoT). Different from the typically downlink transmissions from multiantenna AP to receivers, D2D communications become more decentralized and diverse, which brings new research problems for IRSassisted D2D communications. In one aspect, The IRS can be dynamically reconfigured to enhance individual data link of D2D communications. This requires highly efficient channel sensing and estimation protocols, as well as agile phase reconfiguration algorithms. The insufficiency of energy supply for the IoT devices implies another difficult situation that demands minimized interactions between the IRS and the IoT devices. In another aspect, the distributed IRS units can be used to understand the system profile by learning from a large amount of IRSassisted transmissions in a spatialtemporal region [mobilebigdata]. The system profile may include the information about the potential bottleneck devices, the spatialtemporal traffic pattern, the energy distribution over the entire network, and the information for diagnosing potential network failures. Such information can be further used by the D2D networks to optimize the deployment and settings of the IRS units, the IoT devices’ transmit protocol strategy, the placement of relay nodes, and the power beacon stations.
ViiB3 IRSassisted mmWave and THz Communications
One of the promising applications of the IRS is in the extended coverage of 5G and beyond 5G communications. We expect that mmWave (e.g., 28GHz) 5G communication and future THz beyond 5G communication will face with a critical issue of deadspots which will not be covered well because of the severe blocking loss of such shortlength waveforms. In such situations, the IRS’s two salient EM properties of reflection and refraction can be exploited to resolve the critical issue of deadspots when IRSs are deployed in between the base stations and end users. For example, a user is located in the same side of the serving BS, in which case the incident EM wave on the IRS can be reflected toward the user, whereas if a user is in the opposite side, then the incident EM wave can be refracted through the IRS to reach the user with enhanced signal quality. It is envisioned that the 3D deployment of IRSs with 5G and beyond 5G wireless systems for eliminating such deadspots will be costeffective, and the current massive MIMO and mmWave technologies evolving will be integrated with the IRS technology for the extended coverage eventually.
ViiB4 Using IRS in Smart Wireless Sensing
The current research typically uses the IRS as an auxiliary way for enhancing transmission performance of the existing transceivers. In fact, each scattering element of the IRS can be individually phasetuned and thus showing different sensitivities to the incident signals from different directions. This implies that the IRS can be employed as an array of sensor devices that are configured to passively monitor the radio environment [19survey_renzo]. Given wired or wireless connections to a centralized IRS controller, all the sensing information from different scattering elements can be collected and analyzed jointly in an energyefficient way. From this view point, the use of the IRS as an array of smart sensors will have rich applications in wireless sensing, e.g., indoor positioning [18positioning_sha, he2019adaptive] and human pose understanding [rf_pose]. As such, IRSassisted wireless systems will not only enhance communications but also bring the possibility of humannetwork interactions, i.e., the communication performance and user satisfaction can be even better by using IRS to understand the human behavior or intention in wireless networks [bigdata_human_in_loop].
ViiB5 Tradeoff between Array Gain and LOS Path Loss
Using the IRS as passive relay provides the array gain thanks to no noise addition when reflecting elements are employed. In addition, if the reflecting element is of sufficiently large size (e.g., for the wavelength ), the IRS can act as the specular reflector like lens in which case the path loss follows the “sumdistance" path loss, unlike the active relay whose antenna size is on the order of , resulting in the severe “productdistance" path loss. Therefore, there exists a crucial tradeoff between achieving a larger array gain and guaranteeing the minimal LOS path loss because the number of reflecting elements varies per unit area depending on the size of the reflecting elements. Namely, to assure the LOS path loss, we have to sacrifice the array gain whereas the largest array gain can be achieved while compromising the LOS path loss. The latter is due to the minimum physical size of a reflecting element (like lens) that focuses the energy onto a focal point depending on the distance between the IRS and the receiver (i.e., focal point). Future research for characterizing the tradeoff, considering the 3D deployment of IRSs, will be of paramount importance, in that the smart radio environment can be fully utilized in terms of the density of IRSs and their sum gain, normalized by the implementation cost.
ViiB6 Environment AI for Smart Wireless
IRS can be used as one of the following three functions: 1) Passive Relay, 2) Passive Transmitter, 3) both of them, where the quality of primary signal is enhanced by passive beamforming via relay and at the same time, the secondary information generated from the IRS itself can be embedded in the primary signal (like ambient backscatter). For example, the IRS may be equipped with sensors monitoring environments, which generate such secondary information to be reported to the IoT gateway in the uplink. Therefore, the mode switching at IRS will need to be intelligently and remotely performed by the control center through the IoT gateway, e.g., edge node, considering the user objectives and device positions. Moreover, if a large number of IRS is deployed in a certain area to assist the primary transmission while transmitting their own secondary information (from IoT sensors), the global control of these IRSs will need to be handled by the control center by gathering the user objectives and device positions, so as to assure the optimal routing of air routes of IRSs in conjunction with the mode switching. However, due to the latency and privacy issues, the global control by the control center may not be feasible. Instead, the collaborative (federated) learning will play a crucial role to intelligently perform the required global control through the cooperation with the edge nodes, which perform the learning locally and upload their model parameters to the control center. This way we can resolve the latency and privacy issues.
Viii Conclusions
This paper has presented a comprehensive survey on the design and applications of the IRS to wireless communication networks. Firstly, we have presented an overview of the metasurface and its reconfigurability to realize the vision of IRS. Then, we have focused on its applications in wireless networks and reviewed different network scenarios that can benefit from its reconfigurability. Afterwards, we have provided detailed reviews on the performance analysis and optimization of IRSassisted wireless networks under different communication scenarios, including SNR/capacity maximization, transmit power minimization, EE/SE performance maximization, and secrecy rate maximization, etc. Due to its diversified applications, we have also reviewed the emerging use of the IRS to promote wireless power transfer, UAV communications, and MEC. Finally, we have outlined important challenges, open issues as well as future research directions.