I Introduction
The past decade has witnessed the rapid proliferation of wireless devices along with the exponential growth of data traffic, which significantly stimulates the research and development of 5G networks. Three key technologies are suggested to 5G networks for extensive capacity enhancement: Exploiting millimeter wave (mmWave) frequency, adopting massive multipleinput multipleoutput (MIMO) systems, and network densification by deploying picocells and femtocells. MmWave wireless communications, operating in the frequency bands of 30300 GHz, act as a bridge connecting these symbiotic technologies. To be more specific, the smaller wavelength of mmWave signals allows a large antenna array to be packed in a small physical dimension. This enables the deployment of massive MIMO systems for mobile devices, which is virtually impossible in the current cellular networks (e.g. large antenna arrays are typically employed at the basestations due to the huge size). In addition, the high operating frequency of mmWave communications is extremely suitable for picocells and femtocells for supporting high data rate with intended short coverage range. The narrow beampattern of mmWave MIMO systems is also very useful for mitigating the interference in the future ultradense networks. Therefore, mmWave MIMO communications have been considered as a promising candidate for 5G networks to fundamentally solve the spectrum congestion problem and support high data rates [1][3].
However, mmWave communications still need to overcome several technical difficulties before the realworld deployment. First of all, as a negative result of the tenfold increase of the carrier frequency, the propagation loss in mmWave bands is much higher than that of conventional frequency bands (e.g. 2.4 GHz) due to atmospheric absorption, rain attenuation, and low penetration. Therefore, mmWave communications require tight integration of massive MIMO techniques, especially the pre/postcoding mechanisms, which can provide sufficient beamforming gain to overcome the severe propagation loss of mmWave channels. Yet, another major difficulty of mmWave communications is the hardware constraints. Due to much higher carrier frequency and wider bandwidth in mmWave communications, the radio frequency (RF) components with highprecision analogtodigital converters (ADCs) and digitaltoanalog converters (DACs) lead to enormous economic cost and high power consumption. Therefore, it becomes difficult to dedicate an individual RF chain for each antenna and makes the conventional fulldigital beamforming infeasible in practical mmWave MIMO systems.
Recently, economical and energyefficient analog/digital hybrid beamforming provides a promising solution by allowing a small number of RF chains. The hybrid beamforming approaches generally adopt a largescale highresolution phase shifter (PS) network to implement highdimensional analog beamformer to compensate for the severe pathloss at mmWave bands, and a few RF chains to realize lowdimensional digital beamforming to provide the necessary flexibility to perform advanced multiplexing/multiuser techniques [4]. Since the power consumption and hardware complexity of the analog beamformer are proportional to the number and the resolution of PSs, the adoption of a largescale highresolution PS network in existing solutions frustrates the realworld deployment of hybrid beamforming architectures in mmWave small cell networks, where both base stations and mobile devices have strict limitations on the power consumption and hardware complexity. Recently proposed partiallyconnected architecture can reduce the number of PSs and improve the energy efficiency [5]. However, the cost of PSs is still unaffordable when a largescale antenna array is adopted (even trading off with some performance loss).
Targeting at realworld deployment, this article introduces a novel hardwareefficient hybrid precoding/combining architecture. Inspired by recent works [6][8], we utilize a limited number of simple phase oversamplers (POSs) and a switch (SW) network to realize the analog beamformer, which can achieve maximum hardware efficiency as well as maintain satisfactory spectral efficiency performance. The POS is implemented by a simple circuit and can simultaneously output several parallel signals with different phases. With the aid of a simple switch network, the analog precoder/combiner is realized by feeding the signals with appropriate phases to antenna arrays or RF chains. After presenting the details of this novel POSSWbased hybrid beamforming architecture, we analyze the design challenges and present potential solutions, especially the precoder/combiner design and the channel estimation mechanism. Then, the advantages of the proposed architecture for hybrid beamforming in mmWave MIMO systems will be illustrated by simulation studies. Finally, after highlighting the future research trends including potential performance improvements and technical extensions of the proposed scheme, some conclusion remarks are provided.
Ii Structure of HardwareEfficient Hybrid Beamformer
We consider a typical pointtopoint mmWave massive MIMO system as an example, where the transmitter employs antennas and RF chains to simultaneously transmit data streams to the receiver which is equipped with antennas and RF chains.
Iia Traditional PSbased Hybrid Beamforming Structure
In the traditional hybrid precoding/combining architecture, as shown in Fig. 1(a), the transmitted symbols are first processed by a baseband digital precoder , then upconverted to the RF domain via RF chains before being precoded with an analog precoder of dimension . While the baseband digital precoder enables both amplitude and phase modifications, the elements of the analog precoder , which are implemented by PSs, have a constant amplitude and resolution quantized phases in practice. Obviously, a larger provides a finer resolution of PSs (i.e. a finer resolution of beamformer) and potentially better performance, but also results in higher hardware complexity and power consumption. Similarly, the receiver employs an analog combiner under the same constraint as and a digital combiner to process the received signal. Let denote the channel matrix,
represent the transmitted signal vector,
represent transmit power, and represent the received complex Gaussian noise vector. Then, the received signal can be expressed as(1) 
This traditional PSbased hybrid beamforming structure requires a large number of PSs to implement analog beamforming. For example in the fullyconnected structure as shown in Fig. 1(a), each RF chain is connected to all antennas via a largescale PS network. Obviously, this largescale PS network will cause high power consumption and hardware implementation difficulty. Moreover, the impractical assumption of highresolution PSs in existing solutions frustrates the realworld deployment of hybrid beamforming architectures. The power consumption and cost of the PS at mmWave frequency band are proportional to its resolution. For example, a 4bit (i.e. ) resolution PS requires 45106 mW, while a 3bit (i.e. ) resolution PS needs only 15 mW [6]. Therefore, the hardware limitation, high power consumption and other problems in the traditional PSbased hybrid beamforming structures motivate us to seek for a hardwareefficient hybrid beamforming solution by reducing the number of PSs and the resolution of PSs while maintaining the performance of mmWave MIMO systems.
IiB HardwareEfficient PSSWbased Hybrid Beamforming Structure
To overcome the shortcomings of the traditional hybrid beamforming and achieve a better tradeoff between the hardware complexity and the system performance, we introduce a novel hardwareefficient structure in Fig. 1(b). Taking the transmitter as an example, instead of using a largescale PS network, each RF chain is connected to a phase oversampler (POS) which can simultaneously output parallel signals with different phases as . For example, if , the two output signals have binary phases of and ; if , the four output signals have quaternary phases of , , , and . Then, the analog beamformer can be easily implemented by feeding the signal with appropriated phase to each antenna via a simple switch (SW) network.
This POSSWbased hybrid beamforming architecture has low hardware complexity and power consumption. First of all, the transmitter only needs POSs, which have simpler hardware implementation than conventional digitallycontrolled PSs. For example, the twophases (binary) POS can be easily realized by an inverter [8] as shown in Fig. 2(a); the fourphases (quaternary) POS can be implemented using a sequence of phaseshifting stages [9] as shown in Fig. 2(b). For the narrowband systems, simple microstrip delaylines can be utilized to realize the phaseshifting stages. This scheme has significant advantage of low hardware complexity, but suffers from the phase nonlinearity problem (i.e. shifting different phases at different frequencies). Therefore, for the wideband scenarios, a bank of constant (nuntunable) LCbased wideband PSs should be employed to construct the phaseshifting stages to provide better performance in phase linearity [7]. In addition, variable gain amplifier (VGA) is usually adopted to provide different gain compensation for different phases, which are connected with different number of antennas and may have different circuit loads. Since only a limited number of POSs are employed, the overall hardware complexity is low and the power consumption is small. Moreover, a switch circuit typically has mW and the switch network has dramatically lower power consumption than the PS network. Therefore, instead of using a large number of PSs, this POSSWbased hybrid beamforming architecture can considerably reduce hardware complexity and power consumption.
Iii Design Challenges
In this section, we discuss two main challenges in realizing the POSSWbased hybrid beamforming and introduce potential solutions which can tackle these challenges.
Iiia LowComplexity Precoder and Combiner Designs
The objective of hybrid precoder and combiner design is to maximize the spectral efficiency of this POSSW architecture. The main difficulty comes from the lowresolution phase constraints of the analog beamformers. The optimal exhaustive search algorithm has exponential complexity in the number of antennas and is definitely impractical for realworld implementation. Thus, lowcomplexity designs of hybrid precoder and combiner for the POSSW architecture to achieve satisfactory performance is a critical issue.
Recently, several hybrid beamforming design algorithms for lowresolution PS schemes have been proposed, which essentially have similar objective function as the POSSW architecture. In [10], the authors proposed crossentropy minimization based analog beamformer design algorithms, where a large number of candidate beamformers are randomly generated and then iteratively refined to minimize the crossentropy. Nevertheless, the performance will experience serious degradation when the number of selected candidates or iterations is not sufficiently large. An alternative codebookfree hybrid beamforming designs with discrete phases PSs were investigated in [11]. The authors first derived the optimal analog precoder with infiniteresolution phases, then directly quantized the phase term of each element to a finite set. Although this approach reduces the complexity of the hybrid beamforming designs, it cannot always maintain satisfactory performance when the resolution of PSs is very low. More recently, a novel joint hybrid precoder and combiner design algorithm was introduced in [12], which has low complexity and nearoptimal performance. For the design of hybrid beamformer with binary POSs (), a small set of candidate codebooks are constructed based on rank1 approximation, from which the optimal analog beamformers can be selected with polynomial complexity in the number of antennas. For the case of , a lowcomplexity phase matching algorithm was proposed to iteratively optimize the lowresolution phase term of each element of analog beamformer. It has been verified that fast convergence within three iterations can be guaranteed.
IiiB Channel Estimation with POSSWbased Hybrid Beamforming
The hybrid precoder and combiner design requires full knowledge of channel state information (CSI), which is difficult to be obtained in mmWave MIMO systems since the channel is intertwined with analog beamformers and the baseband has no direct access to the entries of channel matrix. Thanks to the specific sparse characteristic of mmWave channels in the angle domain, compressed sensing based approaches are often leveraged to implement efficient channel estimation by exploring the channel sparsity in mmWave system. The seminal work [13] proposed an adaptive compressed sensing based channel estimation algorithm in conjunction with closedloop beam training mechanism which needs a feedback link between the transmitter and receiver. In this type of approaches, hierarchical multiresolution codebooks are designed to construct training beamformers with different beamwidths. In order to accurately generate beams with different beamwidths, the phase resolution of the analog components should be sufficiently high. However, those existing algorithms may be not applicable for the proposed POSSWbased architectures due to the low resolution of POSs. Therefore, hierarchical multiresolution codebook design for POSSW scheme with lowresolution phases needs to be studied to construct beams with adaptive beamwidths and sufficient gain within the coverage.
On the other hand, for the openloop systems which do not have a feedback link, the mmWave channel estimation problem was formulated as sparse signal reconstruction problem [6], which can be solved via a widely used orthogonal matching pursuit (OMP) solution. The training sequences of precoding/combining vectors can be designed using either pseudorandom sequences or deterministic measurement matrices. It has been verified that the deterministic matrices enjoy lower mutual coherence of the training sequences and offer an advantage for channel estimation. Therefore, fast design of deterministic training beamforming matrices with discrete entries (e.g. or ) should be studied for channel estimation of lowresolution POSSWbased architecture. In short, efficient channel estimation for lowresolution POSSWbased scheme is highly critical for mmWave MIMO communications, permeating through the future communication technologies.
Iv Performance Illustrations
In this section, we illustrate the performance of the POSSWbased hybrid beamforming architecture and compare with the traditional PSbased hybrid and fulldigital beamforming approaches. We adopt clustered mmWave channel model with scattering clusters, each of which contributes propagation paths [14]. The angles of arrival (AoA) and angles of departure (AoD) within a cluster are assumed to be Laplaciandistributed with angle spreads of
. The mean AoD of a cluster is assumed to be uniformly distributed over
, while the mean AoA of a cluster is uniformly distributed over an arbitrary sector. We first assume that the transmitter and receiver are both equipped with antenna ULAs and the numbers of RF chains and data streams are , respectively. Fig. 3 illustrates the spectral efficiency performance of the POSSWbased hybrid beamforming architecture as a function of signaltonoiseratio (SNR). Recently proposed algorithm in [12] is adopted for designing the precoders and combiners with phase resolutions , , and , respectively. For comparison purposes, we also include the spectral efficiency performance of fulldigital scheme with optimal SVDbased beamforming design and infiniteresolutionPSbased (IRPS) hybrid scheme (i.e. ) with phase extraction (PEAltMin) beamforming design algorithm [15]. We can observe that the POSSWbased hybrid beamforming with phase resolution can achieve satisfactory spectral efficiency performance close to the fulldigital beamforming scheme and the hybrid beamforming scheme with infiniteresolution PSs. Finer phase resolution (e.g. ) can improve the spectral efficiency performance but may suffer from higher hardware complexity and cost. For the case in which the hybrid beamforming architecture has lowest hardware complexity, there is notable performance loss due to the extreme low resolution of POSs.In Fig. 4, we turn to illustrate the energy efficiency of different beamforming architectures. The energy efficiency is defined as the ratio of spectral efficiency to the total power consumed at the transmitter side. The total power consists of the power for realizing beamformer and the power for transmitting signals. Note that for different architectures, the power for beamforming is consumed by different components. For the fulldigital scheme, the power consumption for beamforming comes from the baseband processor and RF chains. For the IRPSbased hybrid beamforming architecture, the beamforming power consists of the consumptions by the baseband processor, RF chains, and PSs. For the proposed POSSWbased hybrid beamforming architecture, the beamforming power is consumed by the baseband processor, RF chains, and SWs. We should emphasize that in the POSSW structure, a small number of POSs are implemented by simple inverters or microstrip delaylines as shown in Fig. 2 and have negligible power consumption. Therefore, the power consumption of POSSWbased architecture is the same as that of IRPSbased structure except for replacing the consumption of the PS network by the SW network. In the simulation, the power consumptions of the baseband processor and each RF chain are set as mW and mW [8], respectively. Moreover, the power consumption of each PS is mW and the power consumption of each SW is mW [8]. Finally, we also assume the transmit power is mW, which is a typical setting in existing literatures. Fig. 4 illustrates the energy efficiency performances versus the number of RF chains. It can be observed that the proposed POSSW architecture enjoys significant energy efficiency advantages compared with the conventional fulldigital and PSbased hybrid schemes.
Fig. 5 shows examples of beam patterns of the proposed scheme with different phase resolution, directions of departure (DoDs), and number of antennas. From this figure we find that the proposed scheme with and phase resolution can generate good beam patterns. For case, however, the beam pattern has small mainlobe and difficulty to steer at with small number of antennas () due to the extremely low phase resolution. This observation also verifies the results of the spectral efficiency performance evaluation in Fig. 3.
V Future Research Trends
Va Intelligent Connectivity Mechanisms for SW Networks
The POSSWbased hybrid precoding/combining structure can provide more degrees of freedom (DoF) in the analog domain by intelligently connecting the SW network. Fig. 1(b) introduces a representative fullyconnected structure in which the phasecontrolled signals of each POS are fed to all antennas to achieve full array gain. Certainly, it is of great interest to utilize the flexibility of the SW network to explore more efficient structural connections. Partiallyconnected structure as illustrated in Fig.
6(a) is another typical hybrid beamforming scheme, in which the signals of each POS are routed to a subset of antennas instead of all antennas. In conventional partiallyconnected structures, antenna array is equally divided into nonoverlapping subarrays. In order to achieve better spectral efficiency and energy efficiency performances, it would be more efficient to allow different subarray sizes as well as overlapped subarrays. This motivates us to seek for intelligent connection approaches that can dynamically select the antenna subarrays and connect the SW network based on the characteristics of mmWave MIMO channels.Moreover, with the flexibility of combining more than one phasedcontrolled signal of each POS as shown in Fig. 6(b), we are able to adjust the signals with more phases and magnitude levels and provide more DoF to potentially achieve better performance. Considering an example in Fig. 6(c) with a POS and two switches, the output signals may have eight different phases (e.g., , , , , , etc.) and three different magnitudes. While the POS can only offer signals with constant magnitude and 4 different phases, this solution can provide more DoF on adjusting both phases and magnitudes to obtain more accurate analog beam. This intelligent connectivity mechanism can be applied to both fullyconnected and partiallyconnected architectures to improve the spectral efficiency performance. However, the potential performance improvement is achieved at the expense of a more complicated switch network and more power consumption. Therefore, investigating the intelligent connection architecture and seeking efficient algorithms for channel estimation and beamforming design are important ongoing research challenges to balance the tradeoff between the spectral efficiency performance and hardware structural constraints.
VB Extension to Multiuser mmWave Systems
Based on the foundation of the pointtopoint hybrid precoding/combining architecture, the extension to multiuser mmWave systems is another important research topic. In the multiuser hybrid precoding/combining systems, each user should be assigned an analog beamformer to achieve maximum channel gain as well as mitigate interuser interference. The baseband digital processing will further suppress the interference between users. However, the POSSWbased hybrid beamforming structures may suffer from the difficulty of finely steering the analog beams, which will lead to stronger interuser interference. Therefore, it is of great interest to seek efficient beamforming designs to reduce the interference and improve the efficiency of a multiuser mmWave system. Moreover, efficient channel estimation mechanisms and algorithms for the multiuser mmWave systems are also desired.
VC Combining with LowPrecision ADCs and DACs
In mmWave systems, the sampling rate of the ADCs and DACs will dramatically scale up due to ordersofmagnitude wider bandwidth (e.g., GHz). Unfortunately, highspeed (e.g., GS/s) highprecision (e.g., 812 bits) ADCs/DACs are very powerhungry and costly. The hybrid beamforming architecture can significantly reduce the cost and power requirement by employing a limited number of RF components and ADCs. An alternative solution for mmWave systems is making use of lowprecision ADCs, especially onebit ADCs/DACs which have extremely low hardware complexity and power consumption (e.g., the power consumption of a onebit 3.6GS/s ADC is only ). While the lowprecision ADCs/DACs are advantageous in terms of power consumption and hardware complexity, they generally cause severe performance loss due to larger quantization error. For the transmission over signalantenna additive white Gaussian noise (AWGN) channel, there is 0.22dB spectral efficiency loss at low SNR (0dB) when 2bit ADCs are employed and 0.7dB loss at high SNR (20dB) with 3bit ADCs. Using larger antenna arrays in conventional MIMO systems can compensate for the spectral efficiency performance loss. Clearly, it is worths investigating the combination of lowprecision ADCs/DACs and lowresolution POSSWbase hybrid beamformer. The beamforming design and performance analysis of this integrated structure need to be studied, especially the closedform expression of performance which can help us to obtain insights of important design issues, such as how to determine the appropriate quantities and resolution of ADCs/DACs and POSs in order to achieve an appropriate tradeoff between hardware efficiency and system performance.
VD Beamforming Design for Wideband mmWave Systems
Most existing hybrid precoding/combining solutions are based on narrowband mmWave channels. However, we should emphasize that the mmWave systems are expected to operate in a wideband mode to enjoy the ordersofmagnitude wider bandwidth. The properties of wideband mmWave channels, such as frequency selectivity, path loss, delay spread, angel spread and the number of clusters, may be quite different from the narrowband mmWave channels. Therefore, the existing hybrid beamforming designs for the narrowband mmWave channels are not suitable for the wideband mmWave systems. Moreover, when the simple delaylines are utilized in the POS to generate signals with different phases, we should be aware of the nonlinearity problem in which signals with different frequencies will have different phase shift through a delayline. Even for LCbased PSs, the good phase linearity is also a critical performance parameter which should be concerned. Besides, when a largescale antenna array is employed, the wideband signal will be sensitive to the physical propagation delay across the large array aperture. This socalled “spatialwideband effect” is another important issue which is usually ignored in the past. Therefore, the research on the hybrid beamforming design, analysis on performance loss due to nonlinearity problem and spatialwideband effect, and precompensation strategy should be conducted in the future works for the expansion of POSSWbased hybrid beamforming structures in the wideband mmWave systems.
Vi Conclusions
Hybrid precoding and combining will be an important component of future mmWave MIMO communication systems. This article is dedicated to introducing a novel hardwareefficient hybrid beamforming structure which utilizes a limited number of simple POSs and a switch network to implement analog beamforming. We analyzed design challenges and presented potential solutions of precoder/combiner design and channel estimation for this hybrid beamforming architecture. Future research directions were also discussed. It is expected that this hardwareefficient hybrid beamforming structure will play an important role in future mmWave MIMO communication systems.
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