I-a Brief History of Wireless Standardization
Following the pioneering contributions of Maxwell and Hertz, Marconi demonstrated the feasibility of wireless communications across the Atlantic at the end of the 19th century. By 1928 this technology became sufficiently mature for the police, the gangsters as well as for the rich and famous to enjoy tetherless communications.
An early European development was the Swedish Mobile Telephone System introduced in 1957, which supported 125 users until 1967. In 1966 the Norwegian system was launched, which operated until 1990. Following these, the 1980s led to the roll-out of numerous national mobile phone systems, most of which relied on analogue frequency modulation and hence were unable to employ digital error correction codes. Consequently, their ability to exploit the radical advances in Digital Signal Processing remained limited. Hence the achievable speech quality was typically poor, especially when the Mobile Station (MS) roamed farther away from the Base Station (BS).
Hence during the 1980s the member states of the European Union launched a large-scale cooperative research programme, which led to the standardization of the second generation (2G) system known as the global system of mobile (GSM) communications. GSM was the first digital international mobile system, which rapidly spread across the globe. The success of GSM shows the sheer power and attraction of global standardization, motivating competitors to line up behind a common worldwide solution.
Shortly after the ratification of GSM, a number of other digital standards emerged, such as the pan-American digital advanced mobile phone system (D-AMPS) and the direct sequence code division multiple access (DS-CDMA) based Pan-American system known as IS-95. IS-95 also had an evolved counterpart, namely the Pan-American cdma2000 system, which had three parallel CDMA carriers, leading to the first standardized multi-carrier CDMA (MC-CDMA) system .
However, given the consumers’ thirst for higher bit rates, during the early 1990s the research community turned its attention to developing the third generation (3G) system, which was also based on various CDMA solutions. The detailed discussion and the performance characterization of 3G networks may be found in .
Despite the 40-year research history of OFDM , multi-carrier cellular solutions only emerged during the 2000s as the dominant modulation technique in the context of the 3G partnership project’s (3GPP) long-term evolution (LTE) initiative. Clearly, during the 2000s multi-carrier solutions have found their way into all the 802.11 wireless standards designed for wireless local area networks (WLANs), while using different-throughput modem and channel coding modes, depending on the near-instantaneous channel quality.
What is so beautiful about multi-carrier solutions is their impressive flexibility, since they have a host of different parameters which allow us to appropriately configure them and programme them, whatever the circumstances are - regardless of the propagation environment and regardless of the quality of service (QoS) requirements, as facilitated by the employment of adaptive modulation and coding (AMC).
Our hope is dear Colleague that would allow us now to briefly review the evolution of signal processing and communications techniques over the past three decades in an anecdotal style with reference to Fig. 1. At the time of writing we are gradually approaching the ‘5G Place’ on our road map of Fig. 1. We are indeed also approaching the bit-rate limits upper-bounded by the channel capacity of both the classic single-input/single-output systems as well as of the MIMO systems. Observe at the top left hand corner of Fig. 1, how the various MIMO solutions, such as bell lab’s layered space-time (BLAST) ‘Drive’, space-time coding (STC) ‘Street’, Beam-Forming ‘Close’ and linear dispersion coding (LDC) ‘Street’ merge into MIMO ‘Square’.
After decades of evolution, the classic orthogonal multiple access (OMA) schemes, such as time division multiple access (TDMA) ‘Street’, frequency division multiple access (FDMA), orthogonal variable spreading factor based code division multiple access (OVSF-CDMA), interleave division multiple access (IDMA) and orthogonal frequency division multiple access (OFDMA) ‘Street’ converged to OMA/non-orthogonal multiple access (NOMA) ‘Square’ of Fig. 1. They have also evolved further along spatial division multiple access (SDMA) and multi-functional antenna array ‘Street’ - these solutions have found their way into the 4G OFDMA systems. As seen at the bottom left corner of Fig. 1, the various advance channel coding schemes have competed for adoption in the 4G standard, which relies of a variety of coding arrangements, including automatic repeat request (ARQ).
At the time of writing the community turned towards the standardization of the 5G systems, with a special emphasis on the NOMA techniques detailed in this treatise, as indicated by the broad NOMA ‘Parkway’, which symbolizes 15 different NOMA proposals. The family of MFAAs also entails the recent spatial modulation (SM) and large-scale (LS) MIMO systems. Since the ‘road along millimeter wave (mmWave) Street’ is rather unexplored and the attenuation is high, the employment of BF is rather crucial, if we want to exploit these rich spectral reserves.
In the bottom right corner of Fig. 1 a number of novel technological advances converge at HetNet ‘Square’, where cognitive radio (CR) and software defined networks meet device-to-device (D2D) and Internet-of-Things (IoT) networks. A range of sophisticated ideas are also under intensive investigation to resolve the network-centric versus user-centric design options. There is a strong evidence that the latter is more promising, because it is also capable of simultaneous load-balancing. There are also strong proposals on decoupling the uplink and downlink tele-traffic, with the motivation that mobile-initiated uplink traffic can reach a small-cell BS at a lower transmit power than that of the BS’s downlink transmission. Optical wireless based on visible-light communications is also developing quite rapidly, with Giga-bit copper backhaul networks making promising progress. Whilst no doubt the classic RF systems will continue to evolve towards the next generation, an idea, whose time has come is Quantum communications, as demonstrated by the Science article “Satellite-based entanglement distribution over 1200 km” by Yin et al. .
As the LTE system is reaching maturity and the 4G systems have been commercially deployed, researchers have turned their attention to the 5G cellular network. The latest visual network index (VNI) reports pointed out that by 2020s, the data traffic of mobile devices will become an order of magnitude higher compared to that in 2014 . Apart from meeting the escalating data demands of mobile devices, other challenges of dealing with the deluge of data as well as with the high-rate connectivity required by bandwidth-thirsty applications such as virtual reality (VR), online health care and the IoT further aggravate the situation. Driven by this, the 5G networks are anticipated with high expectations in terms of making a substantial breakthrough beyond the previous four generations. The often-quoted albeit potentially unrealistic expectations include 1,000 times higher system capacity, 10 times higher system throughput and 10 times higher energy efficiency per service than those of the fourth generation (4G) networks . Several key directions such as ultra-densification, mmWave communications, massive MIMO arrangements, D2D and machine-to-machine (M2M) communication, full-duplex (FD) solutions, energy harvesting (EH), cloud-based radio access networks (C-RAN), wireless network virtualization (WNV), and software defined networks (SDN) have been identified by researchers [7, 8, 9]. Fig. 2 illustrates the whole 5G network structure, including most of the existing/promising techniques.
I-B State-of-the-art of Multiple Access Techniques
As mentioned before, sophisticated multiple access (MA) techniques have also been regarded as one of the most fundamental enablers, which have significantly evolved over the consecutive generations in wireless networks [10, 11]. Let us have a deeper looker at the development of MA techniques below. As illustrated in Fig. 1, the past three to four decades have witnessed historic developments in wireless communications and standardization in terms of MA techniques. Looking back to the development of the MA formats as we briefly discussed above, in the first generation (1G), FDMA was combined with an analog frequency modulation based technology, although digital control channel signaling was used. In the 2G GSM communications TDMA was used . Then CDMA, which was originally proposed by Qualcomm , became the dominant MA in the 3G networks. In an effort to overcome the inherent limitation of CDMA - namely that the chip rate has to be much higher than the information data rate - OFDMA was adopted for the 4G networks . Based on whether the same time or frequency resource can be occupied by more than one user, the existing MA techniques may be categorized into OMA and NOMA techniques . Amongst the above-mentioned MA techniques, FDMA, TDMA and OFDMA allow only a single user to be served within the same time/frequency resource block (RB), which belong to the OMA approach. By contrast, CDMA allows multiple users to be supported by the same RB with the aid of applying different unique, user-specific spreading sequences for distinguishing them.
Fuelled by the unprecedented proliferation of new Internet-enabled smart devices and innovative applications, the emerging sophisticated new services expedite the development of 5G networks requiring new MA techniques. NOMA techniques can be primarily classified into a pair of categories, namely,code-domain NOMA and power-domain NOMA 111Note that apart from the code-and power-domain, the spatial-domain can also be regarded as another domain for supporting multiple users within the same RB, which is achieved by exploiting the specific “spatial signature” constituted by the channel impulse responses (CIRs) of the users for distinguishing them [3, 10]. A representative MA technique is space division multiple access (SDMA) .
The most prominant representatives code-domain NOMA techniques include trellis coded multiple access (TCMA) , IDMA , low-density signature (LDS) sequence based CDMA . These solutions are complemented by the more recently proposed multi-user shared access (MUSA) technique , pattern division multiple access (PDMA) , and sparse code multiple access (SCMA).
The power-domain NOMA, which has been recently proposed to 3GPP LTE , exhibits a superior capacity region compared to OMA. The key idea of power-domain NOMA is to ensure that multiple users can be served within a given time/frequnecy RB, with the aid of superposition coding (SC) techniques at the transmitter and successive interference cancellation (SIC) at the receiver, which is fundamentally different from the classic OMA techniques of FDMA/TDMA/OFDMA as well as from the code-domain NOMA techniques. The motivation behind this approach lies in the fact that again, NOMA is capable of exploiting the available resources more efficiently by opportunistically capitalizing on the users’ specific channel conditions  and it is capable of serving multiple users at different QoS requirements in the same RB. It has also been pointed out that NOMA has the potential to be integrated with existing MA paradigms, since it exploits the new dimension of the power domain. The milestones of power-domain NOMA are summarized in the timeline of Table II.
I-C Motivation and Contributions
While the above literature review has laid the basic foundation for understanding the development of MA schemes in each generation of cellular networks, the power domain multiplexing based NOMA philosophy is far from being fully understood. There are some short magazine papers [16, 23, 43, 44] and surveys [45, 46] in the literature that introduce NOMA, but their focus is different from our work. More particularly, Dai et al. introduced some concepts of the existing NOMA techniques and identified some challenges and future research opportunities  both for power-domain and code-domain NOMA. A magazine paper on power-domain NOMA was presented by Ding et al. , with particular attention devoted to investigating the application of NOMA in LTE and 5G networks. Shin et al.  discussed the research challenges and opportunities in terms of NOMA in multi-cell networks, aiming for identifying techniques to manage the multi-cell interference in NOMA. As a further advance, Ali et al.  outlined a general framework for multi-cell downlink NOMA by adopting a coordinated multi-point (CoMP) transmission scheme by considering distributed power allocation (PA) strategy in each cell. Regarding surveys, in , Islam et al. have surveyed several recent research contributions on power-domain NOMA, while providing performance comparisons to OMA in different wireless communications scenarios. In , Tabassum et al. investigated the uplink and downlink of NOMA in single cell cellular networks, identifying the impact of distance of users on the performance attained.
Although the aforementioned research contributions present either general concepts or specific aspects of NOMA, some important NOMA models, the analytical foundations of NOMA, and some of its significant applications in wireless networks have not been covered. Besides, a clear illustration of the historic development of power-domain NOMA milestones is missing. Finally, the comparisons between power-domain NOMA and other practical forms of NOMA have not been discussed. Motivated by all the aforementioned inspirations, we developed this treatise. More explicitly, the goal of this survey is to comprehensively survey the state-of-the-art research contributions that address the major issues, challenges and opportunities of NOMA, with particular emphasis on both promising new techniques and novel application scenarios. Table III illustrates the comparison of this treatise with the existing magazine papers and surveys in the context of NOMA.
|et al.||et al.||et al.||et al.||et al.||et al.||et al.||et al.||work|
|Practical||EP of SIC|
Comparison of this work with available magazine papers and surveys. Here, “PD” refers to “Power-Domain”, “CD” refers to “Code-Domain”, “SD” refers to “Software-Defined”, “EP” refers to “Error Propagation”, and “CE” refers to “Channel Estimation”.
To highlight the significance of this contribution, we commence with a survey of NOMA starting with the basic principles, which provides the readers with the basic concepts of NOMA. We continue in the context of multiple antenna aided techniques combined with NOMA, followed by cooperative NOMA techniques. We then address another important issue of NOMA, namely its resource and PA problems. Finally, we elaborate on invoking other 5G candidate techniques in the context of NOMA networks. The contributions of this survey are at least five fold, which are summarized as follows:
We present a comprehensive survey on the recent advances and on the state-of-the-art in power-domain multiplexing aided NOMA techniques. The basic concepts of NOMA are introduced and key advantages are summarized. The research challenges, opportunities and potential solutions are also identified.
We investigate the application of multiple-antenna aided techniques to NOMA. The pair of most dominant solutions - namely cluster-based MIMO-NOMA and beamformer-based MIMO-NOMA - are reviewed and their benefits are examined. Furthermore, we highlight that specific massive-MIMO-NOMA solutions are capable of improving the performance of NOMA networks to a large extent. A range of important challenges are elaborated on in the context of multiple-antenna assisted NOMA and the associated future opportunities are also underlined.
By exploiting the specific characteristics of NOMA, we study the interplay between NOMA and cooperative communications. We demonstrate that cooperative NOMA constitutes a promising technique of improving the reliability of the users experiencing poor channel conditions.
We identify the potential issues associated both with power- and user-allocation, which constitute the fundamental problems to be solved for ensuring fairness in the NOMA networks. We point out the significance of designing efficient algorithms for dynamically allocating the resources to the users. Furthermore, we propose the novel concept of a software-defined NOMA (SD-NOMA) network architectures, where resource allocation - including the power - is performed on a generic hardware platform by taking into account the global view of the entire network.
We identify the major issues and challenges associated with the co-existence of NOMA and the other emerging 5G technologies. The potential solutions based on the current research contributions corresponding to these technologies are also surveyed. We have also discussed the implementation issues and recent standardization progress for NOMA. Finally, power-domain NOMA and other popular forms of NOMA are contrasted. We spotlight that the significance to provide a unified framework for NOMA.
The remainder of this paper is structured as follows. Section II presents the basic principles of NOMA, including a brief overview on multi-user detection and interference cancellation (IC), the key techniques adopted and its main advantages. Section III investigates the recent advances in multiple-antenna aided NOMA transmission and identifies the open research challenges. In Section IV, the associated research contributions are surveyed in terms of the interplay between NOMA and cooperative transmission. The resource allocation of NOMA - including user association and PA - are studied and summarized in Section V. Finally, Section VI investigates the co-existence of NOMA with other emerging 5G technologies. Section VII points out the implementation challenges as well as the standardization process of NOMA, while Section VIII discusses several other forms of NOMA techniques. Finally, Section IX concludes this treatise. Fig. 3 illustrates the organization of this paper.
Ii Basic Principles of NOMA
The fundamental concept of NOMA facilitates supporting multiple users in the power domain. In contrast to the conventional multiple access (MA) techniques, NOMA222The NOMA approach addressed in this survey implies the power-domain NOMA, unless stated otherwise. uses a new dimension to perform multiplexing within one of the classic time/frequecy domains. In other words, NOMA can be regarded as an “add-on” technique, which has the promising potential of facilitating harmonious integration with the existing legacy-solutions. In this section, we introduce the basic concept of NOMA by illustrating the associated key technologies and summarize its salient advantages. We also survey the pivotal research contributions both in downlink and uplink NOMA transmissions in single-antenna scenarios.
Ii-a Muti-User Detection and Interference Cancelation
Before diving into the deep description of the key techniques of NOMA, let us first give a brief overview for the multi-user detection (MUD) and IC.
Ii-A1 Muti-User Detection
The idea of simultaneously receiving the multiple users signals and detecting them is not new, its history goes back to the 1970s, please see Cover’s work on BCs  and Etten’s work on multi-user sequence estimator . Then Verdu discovered the optimal multi-user receiver of CDMA systems in the 1980s , which is based on the maximum-likelihood receiver detecting multiple users in parallel. We take CDMA as an example to illustrate MUD. Rather than allocating orthogonal RBs to different users as in FDMA and TDMA, CDMA codes superimposes the signals of multiple users with the aid of unique, user-specific signature referred to as spreading codes. If we use orthogonal -chip, we can only support users. But when using non-orthogonal -sequences in the spirit of NOMA, we can have many more users. Multiple access interference (MAI) limits the capacity and performance of CDMA systems. While the MAI caused by a single interfering user is generally small, the system becomes interference-limited as the number of interferers or their power increases [49, 50]. MUD exploiting the knowledge of both the spreading code and timing (and possibly amplitude and phase) information of multiple users has been regarded as an efficient strategy of improving the system capacity. Various MUD algorithms, such as the optimal maximum-likelihood sequence estimation [27, 51], turbo decoding, matched filter SIC , and parallel interference cancellation (PIC) have been designed to reduce the MAI at an affordable complexity cost. Table 1 of  illustrates the high-level comparison for different types of multi-user receivers.
Moreover, there are some recently developed joint detection techniques for downlink cellular systems, which are based on single-antenna interference cancellation (SAIC) receivers. More particularly, this technique relies on either maximum-likelihood detection or predetection processing, rather than on IC techniques. This development is attributed to the fact that joint detection has also been developed for asynchronous networks . As a further advance, the proposed SAIC technique has had successful field trial results in the GSM era in terms of suppressing the downlink inter-cell interference .
Ii-A2 Interference Cancellation
Commonly, the multi-user IC techniques can divided into two main categories, namely pre-interference cancelation (pre-IC) and post-interference cancellation (post-IC) . More specifically, pre-IC techniques are employed at the transmitter side by suppressing the interference by precoding approaches, such as the famous dirty paper coding (DPC)  upon exploiting the knowledge of the channel state information (CSI) at the transmitter. By contrast, the post-IC techniques are usually used at the receiver side for cancelling the interference. The post-IC approach can be further divided into two categories, which are parallel and successive . If we carry out accurate power control to ensure that all received signals are similar, PIC outperforms SIC. By contrast, SIC works better, when the received powers are different  because the strongest user’s signal can be detected first. The detected bit is the remodulate and its interference is deducted from the received signal. Repeating this action in a sequential order gives us the clean weakest signal. It is worth noting that in addition to the performance versus complexity trade-off, there are also a variety of other trade-offs between PIC and SIC.
There are also some recent IC techniques. Based on PIC, Sawahashi et al.  of NTT DoCoMo have developed a coherent three-stage interference canceller for DS-CDMA systems, which is capable of employing accurate pilot symbol-assisted channel estimation and IC. The corresponding performance was experimentally evaluated with the aid of a multipath fading simulator . Regarding the LTE Heterogeneous networks (HetNets), some companies such as Qualcomm and Fujitsu have also developed powerful IC techniques. More particularly, in the 3GPP meeting in 2008, Qualcomm proposed a new cell selection scheme, termed cell range extension , for allowing more small cell offloading to manage the strong macrocell interference at the handsets . Li et al.  of Fujitsu proposed a frequency domain cell-specific reference signal aided SIC scheme for 3GPP LTE-Advanced Rel-11 systems. While the aforementioned IC techniques mainly focus on the digital domain, there are also pioneering analog domain solutions. In full-duplex systems, self interference cancellation (IC) is the key issue . Duarte et al.  proposed an active analog cancellation aided full-duplex architecture to cancel the self-interference before the analog-to-digital converter (ADC). The suppression performance of  was also characterized with the aid of experimental results.
Ii-B Key Technologies of NOMA
Again, the basic principles of NOMA techniques rely on the employment of superposition coding (SC) at the transmitter and successive interference cancelation (SIC) techniques at the receiver. In fact, neither of these two techniques are new, their roots can be found in the existing literature [25, 62, 26, 63, 64, 65, 66, 35, 33, 28, 67, 68, 69, 70, 71].
Ii-B1 Superposition Coding
First proposed by Cover as early as in 1972 , the elegant idea of SC is regarded as one of the fundamental building blocks of coding schemes conceived for achieving the capacity of a scalar Gaussian BC . More particularly, it was theoretically demonstrated that SC is capable of approaching the capacities of both the Gaussian BC and of the general BC as defined by Bergmans’ paper published as early as 1973  and by Gallager . The fundamental concept of SC is that it is capable of encoding a message for a user associated with poor channel conditions at a lower rate and then superimpose the signal of a user having better channel conditions on it. Inspired by the solid foundations laid down from an information theory perspective, researchers became motivated to apply SC to diverse channels, such as interference channels , relay channels , MA channels  and wiretap channels . While the aforementioned contributions richly motivate the use of SC from a theoretical perspective, further research was required for evolving this technique from theory to practice [73, 35]. Specifically, Vanka et al.  designed an experimental platform using a software defined radio (SDR) system to investigate the performance of SC. The set of achievable rate-pairs under a specific packet-error constraint was determined.
Ii-B2 Successive Interference Cancelation
It has been widely exploited that the network capacity can be substantially improved with the aid of efficient interference management, hence SIC is regarded as a promising IC technique in wireless networks. By invoking the following procedure, it enables the user having the strongest signal to be detected first, who has hence the least interference-contaminated signal. Then, the strongest user re-encodes and remodulates its signal, which is then subtracted from the composite signal. The same procedure is followed by the second strongest signal, which has in fact become the strongest signal. When all but one of the signals was detected, the weakest user decodes its information without suffering from any interference at all.
Compared to the classic MUD techniques, we summarize the key advantages of SIC as follows:
In contrast to the MUD techniques of CDMA  or MIMO systems  where there are multiple observations at receivers [27, 76, 77], power-domain NOMA usually has a single observation at each receiver. In other words, rather than using join detection aided MUD considering all users simultaneously, SIC technique operate in an iterative manner, which imposes a lower hardware complexity at the receiver than the joint decoding approach .333Actually, if we consider the broad sense of power-domain NOMA, most of aforementioned MUD techniques can be potentially applied, depending on the receiving power of users. The number of multiplications and additions required was summarized in Hanzo et al .
It has been demonstrated that SIC is capable of approaching the boundaries of the capacity region of both the BCs and of MA channels .
As discussed before, SIC has a better performance than PIC when the received powers are different , which is more suitable for power-domain NOMA supporting the users via different power levels.
Hence, SIC has been widely studied and diverse versions have been employed in practical systems, such as CDMA  as well as SDMA  and the vertical-bell laboratories layered space-time (V-BLAST) . Furthermore, SIC has also been exploited in several practical scenarios, such as multi-user MIMO networks , multi-hop networks , random access systems , and in large-scale networks modeled by stochastic geometry , just to name a few. A particularly important fact concerning SIC is that it has been implemented in commercialized systems, such as IEEE 802.15.4. Another practical implementation is to use the SIC-aided spatial division multiplexing (SDM) detector in SDM-assisted orthogonal frequency division multiplexing (OFDM) systems for signal detection by distinguishing the users with the aid of their unique, user-specific impulse responses .
Ii-C Identifying OMA and NOMA
We commence with the mathematical definition of NOMA. The general definition of NOMA is a MA technique, which allows multiple users to simultaneously occupy the same time-and-frequency resource. Based on this definition, we may have power-domain NOMA, code-domain NOMA and spatial-domain NOMA, as mentioned in Section I. In this treatise, we focus on power-domain NOMA. The narrow sense definition of power-domain NOMA is to superimpose the signals in the same time-and-frequency resource at different power levels, and then to adopt SIC techniques at receivers for interference cancelation.444The broad sense definition of power-domain NOMA constitutes all MA techniques which apply SC technique at transmitters for power multiplexing. In this sense, some code-domain NOMA can also regarded as generalized power-domain NOMA techniques, which will be detailed in Section VII.
For illustrating the relationship between NOMA and OMA mathematically, below we provide a simple analytical characterization by examining the achievable performance with the aid of signal-noise ratio (SNR) expressions. Let us consider two-user downlink NOMA transmission. The channel coefficients of user and user are and . Let us denote the transmit SNR at the BS by and assume that we have without loss of generality.
OMA: According to Shannon’s capacity theorem, when power control is used, the throughput of OMA can be expressed for user and user as 
respectively, where and are the PA coefficients and satisfy , and is the resource allocation coefficient, having units of ‘Hz’ for frequency or ‘s’ for time. For the case that the power control is not considered at the BS, we set the . Then (1) and (2) can be rewritten as
NOMA: Regarding NOMA, the throughput of the user and user is given by 
In order to gain more insights into the spectral efficiency advantage of NOMA over OMA, we investigate the following special case as an example. At high SNRs, assuming that the time/frequency resources are equally allocated to each user, based on (3), (4), (5), and (6), the sum throughput of OMA and NOMA can be expressed as and , respectively. Then we can express the sum throughput gain of NOMA over OMA as follows:
When we have , the sum throughput of NOMA is higher than that of OMA, and this gain is imposed when the channel conditions of the two users become more different. Chen et al.  provided a rigorous mathematical proof to demonstrate that NOMA always outperforms the conventional OMA scheme.
Ii-D Main Advantages of NOMA
Whilst both SC and SIC continue to mature in terms of their theoretical and practical aspects, NOMA is also maturing. Hence it has been proposed for next-generation networks. By invoking the SC technique, the BS transmits the superposition coded signals of all users. Then the channel gains of the users are sorted in the increasing or decreasing order. In the traditional OMA schemes, strongest user benefits from the highest power, which is not always the case for NOMA. The NOMA transmission schemes exhibit the following main advantages.
High bandwidth efficiency: NOMA exhibits a high bandwidth efficiency and hence improves the system’s throughput, which is attributed to the fact that NOMA allows each RB (e.g., time/frequecy) to be exploited by multiple users .
Fairness: A key feature of NOMA is that it allocates more power to the weak users. By doing so, NOMA is capable of guaranteeing an attractive tradeoff between the fairness among users in terms of their throughput. There are sophisticated techniques of maintaining fairness for NOMA, such as the intelligent PA policies of [79, 24] and the cooperative NOMA scheme of , which will be detailed in this paper later.
Ultra-high Connectivity: The future 5G system is expected to support the connection of billions of smart devices in the IoT . The existence of NOMA offers a promising design alternative for efficiently solving this non-trivial task by exploiting its non-orthogonal characteristics. More specifically, in contrast to convectional OMA, which requires the same number of frequency/time RBs as the number of devices, NOMA is capable of serving them by using less RBs.
Compatibility: Again, from a theoretical perspective, NOMA can be invoked as an “add-on” technique for any existing OMA techniques, such as TDMA/FDMA/CDMA/OFDMA, due to the fact that it exploits a new dimension, namely the power-domain. Given the mature status of SC and SIC techniques both in theory and practice, NOMA may be amalgamated with the existing MA techniques.
Flexibility: Compared to other existing NOMA techniques, such as MUSA , PDMA , SCMA [82, 23, 16], NOMA is conceptually appealing and yields a low-complexity design. In fact, the fundamental principles of the aforementioned MA schemes and NOMA are very similar, relying on allocating multiple users to a single RB. Considering the comparison of NOMA and SCMA as an example, SCMA can be regarded as a variation of NOMA which integrates appropriate coding, modulation and subcarrier allocation.
Ii-E Investigating NOMA from an Information Theoretic Perspective
Having considered the potential benefits of NOMA, it is important to investigate its performance gain also from an information theoretic perspective. In fact, the concept of NOMA may also be interpreted as a special case of SC in the downlink broadcast channel (BC). More particularly, by using SC, the capacity region of a realistic imperfect discrete memoryless BC was established by Cover . As an extension of , Bergmans found the Gaussian BC capacity region of single-antenna scenarios . Inspired by [25, 83], several researchers began to explore the potential performance gain from an information theoretic perspective [84, 85, 86]. Xu et al.  developed a new evaluation criterion for quantifying the performance gain of NOMA over OMA. More specifically, considering a simple two-user single-antenna scenario in conjunction with the Gaussian BC, the comparison of TDMA and NOMA in terms of their capacity region was provided in . The analytical results showed that NOMA is capable of outperforming TDMA both in terms of the individual user-rates and the sum rate. In , Shieh and Huang focused their attentions on examining the capacity region of downlink NOMA by systematically designing practical schemes and investigated the gains of NOMA over OMA by designing practical encoders and decoders. Furthermore, by proposing to use NOMA for relaying broadcast channels (RBC) for the same of achieving a performance enhancement, So and Sung  examined the achievable capacity region of the RBC upon invoking both decode-and-forward (DF) relaying, as well as compress-and-forward (CF) relaying with/without dirty-paper coding (DPC). Regarding the family of MIMO-NOMA systems, in  the achievable capacity region of multiuser MIMO systems is investigated upon invoking iterative linear minimum mean square error (LMMSE) detection.
In contrast to the above research contributions considering NOMA in additive white Gaussian noise (AWGN) channels, Xing et al.  investigated the performance of a two-user case of downlink NOMA in fading channels to exploit the time-varying nature on multi-user channels. As shown in Fig. 4, NOMA achieves a superior performance over OMA for different distance settings, where the average sum-rate was maximized subject to a minimum average individual rate constraint.
Ii-F Downlink NOMA Transmission
Downlink NOMA transmission employs the SC technique at the BS for sending a combination of the signals and the SIC technique may be invoked by the users for interference cancelation, as shown in Fig. 5(b). Numerous valuable contributions have investigated the performance of NOMA in terms of downlink transmission [36, 89, 90, 37, 79]. In , a two-user NOMA downlink transmission relying on SIC receivers was proposed. Upon considering a range of further practical conditions in terms of the key link-adaptation functionalities of the LTE, the system-level performance was evaluated in [89, 90]. A more general NOMA transmission scheme was proposed in , which considered a BS communicating with
randomly deployed users. It was demonstrated that NOMA is capable of achieving superior performance compared to OMA in terms of both its outage probability and its ergodic rate. In, the fairness issues were addressed by adopting appropriate PA coefficients for the users in a general NOMA downlink transmission scenario.
Motivated by reducing the signalling overhead required for CSI estimation, some researchers embarked on investigating the performance of downlink NOMA transmissions using partial CSI at the transmitter [91, 92, 93]. More explicitly, Yang et al.  studied the outage probability of NOMA by assuming either imperfect CSI or second order statistics based CSI, respectively. In , by assuming the knowledge of statistical CSI, Shi et al. investigated the outage performance of NOMA by jointly considering both the decoding order selection and the PA of the users. In , by assuming that only the average CSI was obtained at the BS, Cui et al. studied both the optimal decoding order as well as the optimal PA of the users in downlink NOMA systems. Both the transmit power of the BS and rate-fairness of users were optimized. By considering only a single-bit feedback of the CSI from each user to the BS, the outage performance of a downlink transmission scenario was studied by Xu et al. . Based on the analytical results derived, the associated dynamic PA optimization problem was solved by minimizing the outage probability. In , Zhang et al. investigated an energy efficiency optimization problem in downlink NOMA systems in conjunction with different data rate requirements of the users. It was shown that NOMA is also capable of outperforming OMA in terms of its energy efficiency.
Apart from wireless communication systems, the potential use of NOMA in other communication scenarios has also attracted interests. A pair of representative communication scenarios are visible light communication (VLC) [96, 97, 98, 99] and quantum-aided communication . To elaborate, in , Marshoud et al. applied the NOMA technique in the context of VLC downlink networks. By doing so, the achievable throughput was enhanced. It is worth pointing out that although the potential performance enhancement is brought by invoking NOMA into VLC networks, the hardware implementation complexity is also increased at transmitters and receivers as SC and SIC techniques are adopted. In , Botsinis et al. considered quantum-assisted multi-user downlink transmissions in NOMA systems, where a pair of bio-inspired algorithms were proposed.
Ii-G Uplink NOMA Transmission
In uplink NOMA transmission, multiple users transmit their own uplink signals to the BS in the same RB, as shown in Fig. 5(c). The BS detects all the messages of the users with the aid of SIC. Note that there are several key differences between uplink NOMA and downlink NOMA, which are listed as follows:
Transmit Power: In contract to downlink NOMA, the transmit power of the users in uplink NOMA does not have to be different, it depends on the channel conditions of each user. If the users’ channel conditions are significantly different, their received SINR can be rather different at the BS, regardless of their transmit power.
SIC Operations: The SIC operations and interference experienced by the users in the uplink NOMA and downlink NOMA are also rather different. More specifically, as shown in Fig. 5(b) for downlink NOMA, the signal of User is decontaminated from the interference imposed by User , which is achieved by first detecting the stronger signal of User , remodulating it and then subtracting it from the composite signal. It means that SIC operation is carried out on strong user in downlink for canceling the weak user’s interference. By contrast, in uplink NOMA, SIC is carried out at the BS to detect strong User first by treating User as interference, as shown in Fig. 5(c). Then it remodulates the recovered signal and subtracts the interference imposed by User to detect User .
Performance Gain: The performance gain of NOMA over OMA is different for downlink and uplink. Fig. 1 of  illustrates the capacity region of NOMA and OMA both for downlink and uplink. The capacity region of NOMA is outside OMA, which means that the use of NOMA in downlink has superior performance in terms of throughput. While in uplink, NOMA mainly has the advantages in terms of fairness, especially compared to that that OMA with power control.
Recently, there have been less research contributions on uplink NOMA than on downlink NOMA [102, 103, 104, 105, 106, 107, 108]. The downlink and uplink NOMA throughput regions were quantified by Higuchi and Benjebbour  for both symmetric and asymmetric channels. They demonstrated that the performance benefits of NOMA over OMA become more significant, when the channel conditions of the users are more different. Al-Imari et al.  designed a novel NOMA scheme for the classic OFDMA uplink. The efficiency gains of the proposed scheme over the conventional OMA scheme were quantified both in terms of fairness and spectral efficiency. As an extension of , a novel iterative multiuser detection was designed in  for further enhancing the performance of the NOMA uplink. In an effort to reduce the implementation complexity, Chen et al.  conceived a user-pairing policy for the NOMA uplink. In , Zhang et al. proposed a novel power control strategy for the NOMA uplink and investigated both the outage probability and the delay-limited sum-rate. In , a wirelessly powered uplink NOMA transmission scheme was investigated by Diamantoulakis et al. by applying a harvest-then-transmit style EH protocol. A general MIMO-NOMA framework applying stochastic geometry both for downlink and uplink transmission was proposed by Ding et al. .
Ii-H Discussions and Outlook
Given the increasing number of research contributions on NOMA, its advantages are becoming increasingly clear, especially in terms of its bandwidth efficiency, energy efficiency and fairness. Stochastic geometry constitutes a powerful mathematical and statistical tool, which is capable of capturing the topological randomness of the networks and hence provides tractable analytical results for the average network behavior . This is particularly essential in large-scale networks supporting a large number of randomly distributed BSs and mobile users. At the time of writing the stochastic geometry based modelling of NOMA networks is still in its infancy [37, 110, 107, 111, 112, 113, 114]. The derivation of closed-form expressions for obtaining deep insights remains an open challenge. Hence further research efforts are required for analyzing the average performance of multi-user multi-cell NOMA networks [42, 115] in order to provide inspiration both for the long-term investigations in academia and practical guidelines for industry.
Another important issue to be addressed in the NOMA context is that of the ordering of users as required by SIC. Order statistics  can be a helpful tool to assist the associated performance analysis for the sake of obtaining insightful guidelines.
Most of the existing contributions are mainly focused on the theoretical performance analysis or optimization. Most of the implementation issues, such as the effect of imperfect CSI on both SISO-NOMA  and on MISO-NOMA [118, 119, 120], on limited channel feedback [121, 122], on efficient receiver designs , and its combination with advanced adaptive coding and modulation schemes, etc are still open areas. Correspondingly, further research is expected in the aforementioned areas to conceive a holistic architecture for NOMA.
Iii NOMA Combined with Multiple Antennas Techniques
Multiple antenna techniques are of significant importance, since they offer the extra dimension of the spatial domain, for further performance improvements. The application of multiple antenna techniques in NOMA has attached substantial interest both from academia [102, 124, 41, 40, 107, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134] and from industry [135, 102, 136, 36]. The distinct NOMA features such as channel ordering and PA inevitably require special attention in the context of multiple antennas. More specifically, in contrast to the SISO-NOMA scenarios whose channels are all scalars, the channels of MIMO-NOMA scenarios are represented in form of matrices, which makes the power-based ordering of users rather challenging. As a consequence, conceiving an appropriate beamforming/precoding design is essential for multi-antenna aided NOMA systems. NOMA relying on beamforming (BF) constitutes an efficient technique of improving the bandwidth efficiency by exploiting both the power domain and the angular domain. There are two popular MIMO-NOMA designs, namely the 1) Cluster-based (CB) MIMO-NOMA design; and the 2) Beamformer-based (BB) MIMO-NOMA design, which will be introduced in the following. Table IV summarizes some of the existing contributions on NOMA applying multiple antennas and illustrates their comparison.
|||MU-MISO||DL||Transmit power||Two stage BF|
|||MU-MISO||DL/UL||Throughput||Less constraint at the BS|
Ordered vector constraints
|||MU-MIMO||DL||Sum-rate gain||No need for perfect CSIT at the BS|
|||MU-MIMO||DL/UL||OP||Obtaining larger diversity gain|
|||SU-MIMO||DL||OP||Creating channel differences artificially|
|||SU-MIMO||DL||Ergodic capacity||Optimal/sub-optimal power allocation|
|||SU-MIMO||DL||Sum-rate||Low complexity decoding|
|||MU-MIMO||DL||OP||Limited feedback requirements|
|||MU-MIMO||DL||Max-min rate||Addressed max-min fairness issue|
|||MU-MISO||DL||Secrecy OP||Generating artificial noise|
Iii-a Cluster-Based MIMO-NOMA
One of the popular NOMA designs is associated with the cluster-based structure, partitioning users into several different clusters. Explicitly, as shown in Fig. 6, the NOMA users are partitioned into clusters and each cluster consists of users, where . Then we design appropriate beams for the corresponding clusters. Upon applying effective transmit precoding and detector designs, it becomes possible to guarantee that the beam associated with a particular cluster is orthogonal to the channels of users in other clusters. Hence the inter-cluster interference can be efficiently suppressed. When considering each cluster in isolation, there is a difference among the users’ channel conditions, hence we are faced again with the conventional NOMA scenarios. Thus, SIC can be readily invoked for mitigating the intra-cluster interference between users of the same cluster. Recently, many important research contributions investigated beamforming aided NOMA [40, 102, 41, 107, 127, 138].
Specifically, Choi  proposed two-stage multicast zero-forcing (ZF)-based beamforming for downlink inter-group/cluster interference mitigation, where the total transmitt power of each group/cluster was minimized during the second stage. Higuchi and Benjebbour  invoked receive beamforming at the NOMA users and a transmit beamformer at the BS. Higuchi and Kishiyama  then proposed a novel scheme, which combined open-loop random beamforming in conjunction with intra-beam SIC for downlink NOMA transmission. However, random beamforming fails to guarantee a constant QoS at the users’ side. To overcome this limitation, in , Ding et al. proposed a TPC and detection scheme combination for a cluster-based downlink MIMO-NOMA scenario relying on fixed PA. By adopting this design, their MIMO-NOMA system can be decomposed into several independent single-input single-output (SISO) NOMA arrangements. Furthermore, in order to establish a more general framework considering both downlink and uplink MIMO-NOMA scenarios, the so-called signal alignment (SA) technique was proposed in . Stochastic geometry based tools were invoked to model the impact of the NOMA users’ locations . In contract to the research contributions in [41, 107], which are inter-cluster interference free design, an inter-cluster interference allowance design for CB MIMO-NOMA was proposed in . More particularly, a user who experiences the highest channel condition was selected as a cluster-head and was capable of completely canceling all intra-cluster interference in . Note that the existing NOMA designs have routinely relied on assuming different channel conditions for the different users, which is however a somewhat restrictive assumption. In order to circumvent this restriction, Ding et al.  designed a new MIMO-NOMA scheme, which distinguishes the users according their QoS requirements with particular attention on IoT scenarios for the sake of supporting the SIC operation. Furthermore, they compared this new MIMO-NOMA design to two NOMA schemes, which order users according to the prevalent channel conditions. More particularly, the ZF-NOMA scheme of  and the SA-NOMA scheme  were used as benchmarks in . Fig. 7 illustrates the outage probability defined as the probability of erroneously detecting the message intended for User in the -th data stream, at User , where the QR decomposion is used to augmenting the differences between the users’ effective channel conditions according to the associated QoS requirements. As shown in Fig. 7, the QR-based MIMO-NOMA scheme is capable of outperforming both ZF-NOMA and SA-NOMA555Note that when , ZF-NOMA achieves the same performance as SA-NOMA . as well as MIMO-OMA666Fig. 7 is focused on the performance of User , since the QoS requirements have been guaranteed with the aid of appropriate PA ., since it exploits the heterogeneous QoS requirements of different users and applications. In , the fairness issues of the MIMO-NOMA scenario were addressed by applying appropriate user allocation algorithms among the clusters and dynamic PA algorithms within each cluster.
Iii-B Beamformer-Based MIMO-NOMA
Another technique of implementing MIMO-NOMA is to assign different beams to different users, as shown in Fig. 8. By doing so, the QoS can be satisfied by calculating the beamformer-weights in a predefined order, commencing with the most demanding QoS requirement. By adopting this approach, several contributions have been made in terms of MIMO-NOMA. Considering the illustration of Fig. 8 as an example, User to User occupy the same RB, similarly to user to user . Again, within the same RB we may employ SIC at each user, according to the particular ordering of the different users’ received signal power. In , Hanif et al. solved the downlink sum-rate maximization problems, which resulted in obtaining the corresponding optimal TPC vectors. Sun et al.  first investigated the power optimization problem constructed for maximizing the ergodic capacity and then showed that their proposed MIMO-NOMA schemes are capable of achieving significantly better performance than OMA. In an effort to reduce the decoding complexity imposed at the users, a layered transmission based MIMO-NOMA scheme was proposed by Choi , who also investigated the associated PA problem. It was demonstrated that upon invoking this layered transmission scheme, the achievable sum rate increases linearly with the number of antennas.
Massive MIMO may be considered as one of the key technologies  in 5G systems as a benefit of improving both the received SNR and the bandwidth efficiency. It was shown in  that massive MIMO is capable of substantially increasing both the capacity as well as the energy efficiency. These compelling benefits of massive MIMO sparked off the interest of researchers also in the context of NOMA. In , Ding and Poor conceived a two-stage TPC design for implementing massive-MIMO-NOMA. More particularly, a beamformer was adopted for serving to a cluster of angularly similar users and then they decomposed the MIMO-NOMA channels into a number of SISO-NOMA channels within the same cluster. A one-bit CSI feedback scheme was proposed for maintaining a low feedback overhead and a low implementation complexity.
Iii-D Discussions and Outlook
Although numerous research contributions have been made in the field of MIMO-NOMA scenarios, most of the existing treatises assumed that the perfect CSI is known at the transmitter. Under this assumption, the TPC matrix may be readily designed according to the ordered channels between the users and the BS based on their received power. However, in practical wireless communication systems, obtaining the channel state information at the transmitter (CSIT) is not a trivial problem, which requires the classic pilot based training process. This is particularly important for massive-MIMO-NOMA scenarios, where a large number of antennas is used at the BS, hence potentially imposing an excessive pilot-overhead and complexity. Additionally, when the Doppler-frequency is doubled, so is the pilot-overhead and the computational complexity. Although a low-complexity massive-MIMO-NOMA scheme relying on an one-bit feedback flag was proposed in , naturally, the performance was degraded compared to the case of perfect CSIT. Motivated by all the aforementioned problems, efficient CSIT estimation techniques are required for supporting massive-MIMO-NOMA systems. By exploiting the sparsity of the user’s channel matrix, compressive sensing (CS) can be invoked for reducing the pilot-overhead 
, as well as for reducing the feedback overhead transmitted from the downlink receivers to the BS. In the CS based CSI estimation conceived for massive-MIMO-NOMA, machine learning may be invoked both for identifying the measurement matrix design of CS and for the sparse domain selection process of channel estimation in massive-MIMO-NOMA. Explicitly, this is another valuable research topic.
The channel estimation problem can also be jointly considered with the data detection, where soft extrinsic-information is exchanged between the receiver blocks, such as the channel estimator, data detector and channel decoder. In this context it is worth emphasizing that once some of the soft estimates become sufficiently reliable, then they can be subjected to hand-decisions and then used as additional pilots in the context of decision directed channel estimation . Finally, non-coherent MIMO-NOMA dispensing with channel estimation has to be investigated. Additionally, when considering the practical implementation issues, the co-existence of NOMA and MIMO inevitably necessitates the redesign of receivers because of the distinct characteristics of SIC.
Iv Interplay between NOMA and Cooperative Communications
Due to the hostile characteristics of wireless channels, the attenuation of the signals may vary dramatically during their transmission. As a counter-measure, cooperative communication is a particularly attractive technique of offering cooperative diversity gains, hence extending the network’s coverage [143, 144]. In this section, we summarize the NOMA contributions on cooperative communications, mainly from the perspective of promising cooperative NOMA techniques and the application of NOMA in cooperative networks.
Iv-a Cooperative NOMA
The key idea behind cooperative NOMA is to rely on strong NOMA users acting as DF relays to assist weak NOMA users. Still considering the two-user downlink transmission of Fig. 5(b) as our example, cooperative NOMA requires two time slots for its transmission. The first slot is for the direct transmission phase, which is the same as the non-cooperative NOMA of Fig. 5(b) indicated by solid lines. During the second time slot, which is the cooperative phase, User will forward the decoded message to User by invoking the DF relaying protocol of Fig. 5(b) indicated by the dashed line. Proposed by Ding et al. , this novel concept intrigued researchers, since cooperative NOMA fully benefits from SIC and DF decoding. In , a general downlink NOMA transmission scenario was considered, where the BS supported users with the aid of cooperative NOMA protocols relying on slots. In an effort to seek a more efficient cooperative NOMA protocol, Liu et al.  proposed a new EH assisted cooperative NOMA scheme. A sophisticated stochastic geometry based model was invoked for evaluating the system’s performance and user pairing was adopted for reducing the implementation complexity. Compared to conventional NOMA, the key advantages of cooperative NOMA transmissions can be summarized as follows:
Low System Redundance: Again, upon applying SIC techniques in NOMA, the message of the weak user has already been decoded at the strong user, hence it is natural to consider the employment of the DF protocol for weak signal. Explicitly, the weak signal can be remodulated and retransmitted from a position closer to the destination.
Better fairness: A beneficial feature of cooperative NOMA is that the reliability of the weak user is significantly improved. As a consequence, the fairness of NOMA transmission can be improved , particularly in the scenarios when the weak user is at the edge of the cell illustrated by the BS.
Higher diversity gain: Cooperative NOMA is capable of achieving an improved diversity gain for the weak NOMA user, which is an effective technique of overcoming multi-path fading. It was analytically demonstrated  that the diversity gains of the weak users in cooperative NOMA are the same as those of the conventional cooperative networks, even for using EH relays .
Fig. 9 illustrates the superior performance of cooperative NOMA over non-cooperative NOMA as well as over OMA in terms of its outage probability. It is noted that cooperative NOMA achieves a higher diversity gain than non-cooperative NOMA and OMA, which demonstrates the effectiveness of cooperative NOMA, as aforementioned. Note that cooperative NOMA constitutes one of many techniques of improving the transmission reliability of NOMA networks, especially for the weak NOMA users who have poor channel conditions. There are also other techniques for enhancing the performance of NOMA networks, which will be detailed in the following subsection. It is also worth pointing out that the performance of cooperative NOMA is related to the error propagation issue for SIC, which will be introduced in Section VII.
Iv-B NOMA in Cooperative Transmission Based Networks
Cooperative communication and NOMA techniques mutually support each others, hence the joint action of both techniques further improves the cooperative network performance [145, 146, 147, 148, 149, 150, 151]. Relaying and CoMP transmission are capable of improving cooperative networks.
Iv-B1 Relay-aided NOMA Transmission
Relaying has recently attracted considerable attention as a benefit of its network coverage extension . In this context, Men and Ge investigated the outage performance of the single-antenna AF relay aided NOMA downlink . By contrast, in  multiple antennas were used. The potential gains of NOMA over OMA were quantified in both scenarios. As a further development, a DF based two-stage relay selection protocol was proposed in , which relied on maximizing the diversity gain and minimizing the outage probability. In , Duan et al. proposed a novel two-stage PA scheme for a dual-hop relay-aided NOMA system, where the destination jointly decoded the information received both from the source and from the relay by applying the classic MRC technique. In , Kim and Lee considered a coordinated direct and relay-aided transmission scheme, where the BS simultaneously transmitted both to a nearby user and to a relay by invoking NOMA techniques during the first phase, while reaching a distant user with the aid of the relay.
Iv-B2 Multi-Cell NOMA with Coordinated Multipoint Transmission
When considering multi-cell scenarios, the performance of the cell-edge users is of particular concern. This is particularly important for downlink NOMA, since the SIC operations are usually carried out for cell-center users rather than for cell-edge users. Hence the cell-edge users may not be well served. CoMP transmissions constitute an effective technique of improving the performance of cell-edge users. The key concept of CoMP in multi-cell NOMA is to enable multiple BSs to carry out coordinated beamforming or joint signal processing for the cell-edge users . There are several research contributions in the context of handling the inter-cell interference in NOMA networks [115, 147, 42, 148], as detailed below.
In , Han et al. extended a single cell NOMA to multi-cell network-NOMA. A new precoding approach was proposed for mitigating the inter-cell interference, which lead to an enhanced spectral efficiency and energy efficiency. In , Choi incorporated NOMA into CoMP for the sake of attaining a bandwidth efficiency improvement. A new coordinated superposition coding scheme relying on Alamouti’s space-time code was proposed. As a further advance, Shin et al.  investigated the performance of multi-cell MIMO-NOMA networks, applying coordinated beamforming for dealing with the inter-cell interference in order to enhance the cell-edge users’ throughput. Tian et al.  conceived an opportunistic NOMA scheme for CoMP systems and compared it to the conventional joint-transmission based NOMA. In , Vien et al. proposed a NOMA based PA policy for downlink cloud radio access network (C-RAN) scenarios, which can also be regarded as a coordinated transmission scenario, where the BSs jointly form a cloud. In , Martin et al. proposed a novel NOMA-aided C-RAN network, associated with using stochastic geometry. It revealed that the proposed framework is capable of substantially enhancing the performance of cell-edge users.
|Ref.||Model Topology||Direction||Techniques||Main Metrics||Characteristics|
|||Idealized topology||DL||DF||OP+ergodic rate||Maximum diversity gain achievable|
|||Stochastic geometry||DL||DF||OP||Wireless powered spatial randomly relays|
|||Idealized topology||DL||AF||OP+ergodic rate||Multiple-antenna aided relays|
|||Idealized topology||DL||DF||OP||Novel two-stage relay selection policy|
|||Idealized topology||DL||CoMP||SE + EE||Zero-forcing like distributed precoding|
|||Idealized topology||DL||CoMP||Sum-rate||Using Alamouti code at coordinated BSs|
|||Idealized topology||DL||CoMP||Sum-rate||MIMO-NOMA coordinated beamforming|
|||Idealized topology||DL||CoMP||OP+sum-rate||Joint transmission/Opportunistic NOMA in CoMP|
|||Idealized topology||DL||CoMP||OP+ergodic rate||Each stream achieves a diversity order of one|
|||Idealized topology||DL||CRAN||Throughput||All the BSs are controlled by a cloud|
|||Idealized topology||DL||DF||Sum-rate||Novel two-stage power allocation|
|||Idealized topology||DL||DF||OP||Invoking full-duplex technique at relays|
|||Stochastic geometry||DL||CRAN||OP||Cluster point process based model|
Iv-C Discussions and Outlook
Table V summarizes all the above-mentioned research contributions relying on the interplay between NOMA and cooperative communications. In Table V, “DL” and “OP” represent the downlink and outage probability, respectively. The terminology of “Idealized topology” in the table indicates that the users may not be randomly positioned and that the path loss is assumed to be constant. The aforementioned literature has investigated the potential performance enhancements of NOMA with the aid of cooperative techniques. Nonetheless, there are several open research opportunities. For example, although employing relays is capable of improving the reception reliability, whilst extending the coverage area, it requires an extra time slot for relaying. Developing full-duplex relays for NOMA networks constitutes a promising research direction for eliminating the requirement of an extra slot [156, 157, 155]. However, invoking full-duplex relays will require the elimination of both the self interference and of the inter-user interference.
Additionally, the existing research contributions on C-RAN NOMA are still in their infancy. It is worth pointing out that C-RAN techniques are capable of efficient interference management and large scale data control. This is particularly important for large-scale C-RAN NOMA networks, where sophisticated interference management (e.g. distributed beamforming design), dynamic user association and efficient PA can be jointly considered.
V Resource Management in NOMA Networks
One of the main challenges in NOMA networks is to strike an attractive compromise between the bandwidth efficiency and energy efficiency of the networks by intelligently controlling the PA of the superimposed signals , dynamically scheduling the users for the sub-channels or by forming spatially correlated clusters. Motivated by this, in this section, we provide a comprehensive review of the existing resource allocation contributions, mainly with a special emphasis on power control and user/resource allocation.
V-a Power Control for NOMA
Power control/allocation has been a pivotal research direction throughout each generation of networks, since inappropriately allocating power among users will inevitably increase the overall energy consumption whilst inflicting extra interference and hence degrading the overall performance of the networks. Again, in NOMA more power is required for users with poor channel conditions and less power for users with better channel conditions, which guarantees fairness among NOMA users.
Numerous valuable contributions have been published on the PA problem in NOMA, which may be divided into two main categories, optimal PA from the perspective of all users and cognitive PA from the perspective of the weak users, which will be detailed in the following two subsections.
V-A1 Optimal power allocation
The contributions on NOMA which investigate optimal PA can be also classified into two main categories: i) Single-channel/carrier PA; and ii) multiple-channel/carrier/cluster PA. In this subsection, we mainly focus our attention on single-channel/carrier PA, while multiple-channel/carrier/cluster power allocation will be introduced in Section V-B.
The aim of PA in single channel/carrier scenarios is to optimize the individual/sum rate whilst giving cognizance to the the fairness issues. Compared to OMA, optimal PA in NOMA imposes more constraints associated with channel-quality and power-based ordering in an effort to guarantee fairness by allocating reasonable data rates to weak users as well. The recent research contributions on the fairness issues of NOMA can be summarized as follows:
Ordered power allocation: An simple yet effective approach to guarantee the fairness of NOMA systems is to allocate more power to users with poor channel conditions. By doing so, weak users can still achieve adequate rates. It is worth pointing out that adding these transmit power based ordering constraints will impose additional complexity on the optimization problem formulated, especially for multi-antenna aided NOMA scenarios [40, 125].
Max-min rate-fairness: The max-min PA problem maximizes the rate of the weakest of all NOMA users [79, 138, 93]. In , the PA strategy was investigated under the scenarios of knowing either the instantaneous CSI or the average CSI. Note that by adopting the max-min rate as our objective function we can guarantee a certain grade of rate-fairness, but at the price of sacrificing the system’s sum-rate.
: Proportional fairness (PF) is capable of maximizing the geometric mean of user rates. In NOMA scenarios, a feasible proportional fairness policy is to schedule users based on the instantaneous user rates, whilst additionally guaranteeing a certain long-term-average target rate[158, 159].
utility function: The utility function constitutes a generalization of proportional fairness and max-min fairness. The definition of the utility function is as follows :
Note that for , Eq (8) reduces to that of proportional fairness, while for , it results in the max-min fairness optimization problem. Hence, the utility function is capable of treating the fairness issues of NOMA in a generic way.
Weighted sum rate: The key idea behind the weighted sum rate is to consider an additional positive weighing factor for each user’s achievable rate, which reflects the priority of each user in the context of resource allocation . By doing so, a certain grade of fairness can be achieved from the specific perspective of the media access control (MAC) layer.
Jain’s fairness index comparison: Jain’s fairness index , is widely used for striking a tradeoff between the sum-rate and fairness of a communication system. Motivated by this, many NOMA contributions characterized their PA in terms of Jain’s fairness index [103, 163, 108]. However, Jain’s fairness index is only a metric of evaluating a system’s fairness, which cannot prevent the weak users from having low rates. More intelligent algorithms are required for fair PA among the users.
|Fairness Strategy||Characteristics||Bandwidth efficiency||Fairness||Complexity||Ref.|
|Ordered power allocation||Allocates more power for weak users||Moderate||Moderate||Low||[36, 89, 37, 110]|
|Max-min rate fairness||Absolutely fairness for users||Low||High||High||[79, 138, 93]|
|Proportional fairness||Maximizes users’ geometric mean||Moderate||Moderate||Low||[164, 158, 159, 165]|
|utility function||Imposes fairness||High||Moderate||Moderate||—|
|Weighted sum rate||Achieves fairness with the aid of MAC layer||High||Low||Low|||
|Jain’s fairness index comparison||Only a fairness performance metric||—||—||—||[103, 163, 108]|
V-A2 Cognitive radio inspired power control
The objective of CR inspired power control relying on NOMA is to guarantee the QoS of weak users by constraining the power allocated to the strong user. Inspired by the CR concept , NOMA can be regarded as a special case of CR networks [24, 167]. More specifically, still considering a downlink scenario supporting two users, Fig. 10 compares conventional CR and CR inspired NOMA. The BS can be viewed as the combination of a primary transmitter (PT) and a secondary transmitter (ST), which transmits the superimposed signals. The strong user (User ) and the weak user (User ) can be regarded as a secondary receiver (SR) and a primary receiver (PR), respectively. By doing so, the strong User becomes capable of accessing the spectrum occupied by the weak User under predetermined interference constraints, which is the key feature of the classic underlay CR. The concept of CR-inspired PA in NOMA was proposed by Ding et al. in , who investigated the PA of user-pairing-based NOMA systems.
The key advantages of cognitive PA are summarized as follows:
Guaranteed QoS: by applying cognitive PA, the QoS requirements of the weak user are guaranteed, which is especially vital in real-time safety-critical applications.
Fairness/throughput tradeoff: cognitive PA is capable of striking a beneficial tradeoff between the overall system throughput and the individual user fairness, where the targeted data rate of the weak user has to be satisfied by appropriate PA.
: cognitive PA offers a high degree of freedom for the BS to explore the opportunistic support of the strong user.
Low complexity: compared to the optimal PA approach, cognitive PA imposes a lower complexity during PA. This becomes particularly useful when the channel ordering and PA constraints are not convex and hence finding an appropriate PA scheme becomes a challenge, especially in multiple antenna aided NOMA scenarios.
Motivated by its advantages mentioned above, the cognitive PA policy was invoked for characterizing MIMO-NOMA systems in [107, 127]. More particularly, in addition to investigating the convectional downlink cognitive PA conceived for MIMO-NOMA scenarios, the authors of  also designed a more sophisticated CR NOMA PA scheme for uplink MIMO-NOMA scenarios. In , in an effort to find a PA strategy suitable for SU-MIMO IoT scenarios, a cognitive PA policy was designed for ensuring that SIC may indeed be carried out at the strong user.
V-B User Scheduling in Dynamic Cluster/Pair Based Hybrid MA Networks
Due to the low-complexity design of NOMA and the new degree of freedom by the power dimension, it is widely accepted both by the academia and industry that NOMA constitutes a convenient an “add-on” technique for establishing spectral efficient hybrid MA networks. In an effort to design hybrid MA networks, the users have to be assigned to different pairs/clusters. By doing so, how to pair/cluster the users becomes an interesting problem, which is valuable to examine. Several excellent contributions have researched the potential issues aiming for obtaining efficient user pairing/clustering strategies with the objective of improving the performance of both a single pair and of the entire networks, as detailed below.
V-B1 A single user pair’s performance
User pairing is capable of beneficially reducing the complexity of the NOMA design, when establishing advanced hybrid MA networks. By focusing on fully exploiting the potential gains of NOMA over conventional OMA from the perspective of a single user pair, Ding et al.  investigated both the sum rate and the individual rates of the two users. It was demonstrated that a higher sum rate gain can be attained by NOMA over OMA, when the channel conditions of the pair of NOMA users are rather different, which is line with our expectation in the context of SIC-aided detection. In , the impact of spatial location on a pair of NOMA users was examined by employing a stochastic geometry model, in conjunction with three different user selection schemes. In , Qin et al. examined the secrecy performance of a specifically selected user pair in large-scale networks and showed that the secrecy diversity order of the user pair was determined by the user having the weaker channel. User pairing was invoked for MIMO-NOMA scenarios in [107, 127]. We note that the user paring techniques of [24, 110, 111, 107, 127] can be further improved by PA, which is hence a promising research direction.
V-B2 User clustering/pairing from the perspective of the overall system’s performance
Note that allocating NOMA users to different orthogonal RBs (e.g. sub-channels/sub-carries/clusters) generally turns out to be a non-deterministic polynomial-time (NP)-hard problem. It is computationally prohibitive to obtain optimal results by performing an exhaustive search, when the number of users and RBs becomes high, especially when the number of user/RBs is dynamically fluctuating. Hence investigating efficient low-complexity user allocation algorithms, which are capable of achieving attractive performance-complexity trade-offs is necessary. Some of the research contributions in the field of resource allocation can be found in [168, 169, 170, 171, 164, 172, 173, 159, 174, 175, 176, 177]. Below we list some of the promising approaches as follows:
Combinatorial relaxation: A popular method of tackling this kind of issue is to relax the constraint of the combinatorial problem by using continuous variable of
instead of a binary variable of, where indicates whether a user is allocated to a RB block. By doing so, the original NP-hard problem is transferred to a convex problem and can be solved by invoking the classic Lagrangian dual method . However, this kind of relaxation will result in a non-trivial duality performance gap between the original problem and the simplified one.
Monotonic optimization: Due to the non-convex nature of many sophisticated resource allocation problems, finding the optimal solution using convex optimization theory is rather challenging. In addition to convexity, the monotonicity is another important property, which can be exploited for efficiently solving non-convex optimization problems [179, 180]. Note that the resource allocation problem of NOMA scenarios is usually non-convex due to its inter-user interference in the same RB. In this context, Sun et al.  invoked the classic monotonic optimization approach for developing an optimal solution for their joint power and subcarrier allocation problem. A low complexity suboptimal approach was also proposed for striking a performance-vs-complexity tradeoff.
Matching theory, as a powerful mathematical modeling tool conceived for solving the combinatorial user allocation problems, is capable of overcoming some of the shortcomings imposed by the widely used game theory, such as the distributed-limited implementation and unilateral equilibrium deviation. As such, matching theory has recently emerged as a promising technique of tackling the resource allocation problem in wireless networks, also in NOMA scenarios [169, 182, 183, 184]. More particularly, Di et al.  invoked many-to-many two-sided matching theory for resource allocation in the downlink of NOMA systems. A potential shortcoming of matching theory is that both the users and resources should have a predefined preference list. However, these preference lists may vary as the channel conditions fluctuate, which hence requires further research.
Heuristic algorithms:Heuristic algorithms are commonly used for solving computationally complex problems. The core idea of heuristic algorithms is to obtain approximate solutions for the original optimization problem at an acceptable computational complexity. Inspired by this, many heuristic algorithms such as meta-heuristics , greedy techniques  and others  have been adopted by researches in NOMA scenarios for allocating resources. Given the diverse nature of heuristic algorithms , they may lead to significantly different performance vs complexity trade-offs.
It is worth pointing out that apart from applying intelligent user scheduling strategies, optimizing PA for each RB/user is capable of further improving the attainable network performance. However, the joint optimization of user scheduling and PA is a non-trivial problem. Except for , which jointly considers the PA as well as user association and obtains the optimal solution, the commonly-adopted approaches rely on decoupling this correlated problem into a pair of sub-problems [169, 171, 170]. As such, the aforementioned PA and user scheduling algorithms can be invoked for finding a sub-optimal solution. However, the existing literature of resource allocation is predominantly focus on maximizing the performance attained, whilst there is a distinct lack of a systematic performance vs computational complexity analysis. Motivated by filling this gap, Lei et al.  characterized the tractability of NOMA resource allocation problems under several practical constraints. A combined Lagrangian duality and dynamic programming algorithm was also proposed in  for solving the joint optimization of the PA and user scheduling problem of NOMA networks.
|Combinatorial relaxation||Convert to convex problem||Existence of duality gap||—|
|Monotonic optimization||Optimal solution||Relatively high complexity|||
|Matching theory||Achieve near-optimal performance||Requires predefined preference list||[169, 172, 173, 183]|
|Heuristic algorithms||Flexible complexity-performance tradeoff||Unstable performance||[170, 171, 164]|
V-C Software-Defined NOMA Network Architecture
Inspired by the concepts of the emerging SDN paradigm , we propose the novel SD-NOMA concept, which provides the desired degree of flexibility for controlling resources. By decomposing the resource allocation and control problem into complex tractable problems, the SD-NOMA concept makes it much easier to create new abstractions in terms of power optimization, interference management, user association and dynamic user clustering/pairing. Before introducing the proposed SD-NOMA strategy, we first review the compelling concept of SDR. The essential idea behind SDR is to implement the baseband signal processing algorithms in software instead of hardware, which hence exhibit a high grade of flexibility and reconfigurability, when designing agile instantaneously adaptive communication systems. In this spirit, a practical open source SDR-based NOMA prototype has been designed for a typical two-user downlink scenario by Xiong et al. , which bridges the theoretical and practical aspects of NOMA. Both the hardware and software architecture of the NOMA prototype systems designed were elaborated on. The link-level simulation results showed that the performance of the SIC procedure was significantly influenced both by the PA as well as by the modulation scheme employed.
In contrast to the SDR-based NOMA, the key idea of our proposed SD-NOMA network architecture is that the SDN controller has a global view of both the available resources and of the tele-traffic across the whole network, as shown in Fig. 11. However, each component may still rely on the SDR-based NOMA concept. In other words, the SD-NOMA network architecture can globally control the SDR-based NOMA components via a central SDN controller. Considering the user association and PA in the context of a cluster-based MIMO-NOMA scheme  as an example, the SDN controller becomes capable of associating the different users with a potential cluster and allocating the most appropriate power levels to different users, whilst at the same time considering the interference arriving not only from the users in the same cluster but also from other clusters. This approach formulates the PA of NOMA as a global optimization problem, since the SDN controller is aware of the entire network’s state. Therefore, SD-NOMA constitutes an attractive 5G network structure.
V-D Discussions and Outlook
The distinctive co-channel interference characteristics of NOMA usually lead to a non-convex optimization problem. The aforementioned research contributions have provided numerous beneficial techniques of dealing with the resource control problem. However, for complexity reasons, most of these techniques opted for decoupling the user scheduling and PA into consecutive subproblems, which usually result in sub-optimal solutions. The problem of finding optimal solutions by jointly considering both the user scheduling and PA is still far from being well understood. Hence advanced optimization techniques requiring low-complexity algorithms are required for solving this problem.
In summary, the design of attractive NOMA solutions hinges on finding the Pareto-optimal solutions, as discussed for example in an ad hoc networking context in , where none of the system characteristics can be improved without degrading at least one of the others. In the interactive 7-mode networking demo a three-component objective function constituted by the BER, the power and the delay was animated.
Vi Compatibility of NOMA with Other Technologies towards 5G and Beyond
As one promising technique in future 5G networks, one of the main challenges of NOMA is that how well it is to be compatible with other emerging techniques for meeting the requirements of 5G. In this section, we survey the existing research contributions considering the co-existence of NOMA with other 5G proposals.
Vi-a NOMA in HetNets
Dense HetNets, as one of the hot 5G technologies , are capable of significantly improving the network capacity. The core idea of HetNets is essentially to move the low-power BSs closer to the served users in order to form small cells under the over-sailing macro cells. However, due to the co-channel nature of macro cells and small cells, the users surfer both from inter-layer interference as well as from intra-layer interference. To intelligently cope with the interference arriving from the other co-channel layers, in  Xu et al. proposed a cooperative NOMA scheme for HetNets and minimized the inter-user interference with the aid of DPC precoding. The effect of distinctive power disparity between the macro BSs and pico BSs was investigated.
Additionally, as a benefit of aiming to take full advantage of both massive MIMO and HetNets techniques including high array gains, reliable BS-user links etc., massive MIMO aided HetNets solutions are promising for the emerging 5G systems . The basic philosophy of massive MIMO assisted HetNets is to install hundreds/thousands of antennas at the macro BSs for offering an unprecedented level of spatial degrees of freedom, whilst using a single antenna at the densely positioned small-cell BSs. In an effort to further enhance the bandwidth efficiency of small cells, a promising NOMA aided and massive MIMO based framework was proposed in , where a massive MIMO system was adopted by the macro cells to simultaneously serve users and then user pairing based NOMA transmissions were adopted by the small cells, as shown in Fig. 12. More specifically, stochastic geometry was invoked for modelling the -tier HetNets considered and to analyze the efficiency attained. The key feature of this framework is that it integrates the potential advantages of both NOMA (e.g., high bandwidth efficiency, faireness/throughput tradeoff, etc.) and of HetNets (low power consumption, spatial spectrum reuse, etc.) whilst simultaneously relying on a sophisticated cluster based MIMO-NOMA precoder design [135, 41, 40, 125, 107, 127].
Vi-B NOMA in Millimeter Wave Communications
MmWave communications have been recognized as a promising technique in 5G networks and beyond due to their large bandwidths in the high-frequency spectrum . The severe propagation path loss of mmWave channels and their low penetration capabilities  necessitates the redesign of MA techniques, especially when aiming to support massive connectivity in dense networks, where hundreds/thousands of users have to be served within a small area. NOMA can be regarded as a potent MA technique capable of co-existing with mmWave networks due to the following reasons:
The highly directional beams used in mmWave communications lead to correlated channels, which may degrade the performance of convectional OMA systems, but they are amenable to NOMA.
The sharp beams of mmWave networks effectively suppress the inter-beam interference among users, which is suitable for supporting NOMA in each beam.
The application of NOMA in mmWave is capable of enhancing the bandwidth efficiency and supporting massive connectivity.
Inspired by this, some initial research contributions examining NOMA in mmWave networks have been disseminated in [113, 192]. In , Ding et al. investigated the co-existence of NOMA and mmWave solutions relying on random beamforming. Due to the potential line-of-sight (LOS) blockages of mmWave systems, a thinning process aided stochastic geometry model was used to evaluate the performance. As a further advance, Cui et al.  investigated the performance of NOMA-mmWave networks relying on partial CSI feedback. More particularly, the user scheduling and PA were jointly considered with the aid of matching theory and Branch-and-Bound approaches. Fig. 13 illustrates the sum rate of NOMA-mmWave versus the SNR at different frequencies. It is demonstrated that the proposed NOMA-mmWave system is capable of outperforming conventional OMA-mmWave systems.
Vi-C NOMA and Cognitive Radio Networks
The 2010s have witnessed the rapidly increasing penetration of mobile devices (e.g., smart phones, tablets and laptops) all over the world, which gave rise to increasing demand for spectral resources. As reported by the Federal Communications Commission (FCC), there are significant temporal and spatial variations in the exploitation of the allocated spectrum. Given this fact, the CR concept—a terminology coined by Mitola—inspired the community to mitigate the spectrum scarcity problem. The basic concept of CR is that at a certain time of the day or in a geographic region, the unlicensed secondary users (SUs) are allowed to opportunistically access the licensed spectrum of primary users (PUs). These CR techniques may be categorized into the interweave, overlay, and underlay paradigms :
Interweave: The interweave CR can be regarded as an interference avoidance paradigm, where the SUs are required to sense the temporary slivers of the space-frequency domain of PUs before they access the channels [194, 195, 196, 197]. The concurrent transmission of SUs and PUs is not allowed under the interweave paradigm.
Overlay: The overlay paradigm essentially constitutes an interference mitigation technique. With the aid of the classic dirty paper encoding technique, overlay CR ensures that a cognitive user becomes capable of transmitting simultaneously with a non-cognitive PU . Additionally, SUs are capable of forwarding the information of PUs’ to the PU receivers, whilst superimposing their own signals as a reward for their relaying services.
Underlay: The underlay CR operates like an intelligent interference control paradigm, where the SUs are permitted to access the spectrum allocated to PUs as long as the interference power constraint at the PUs is satisfied .
Table VIII provides a summary of the interweave, overlay, and underlay paradigms and briefly illustrates the differences among them.
|Paradigm||Concurrent Transmission||Constraints at SU||Interference Management||Complexity||NOMA-CR|
|Underlay||Not allowed||Limited by the interference power constraint||Interference avoiding||Low||[112, 24]|
|Overlay||Allowed||No power constraints||Interference mitigating||High||—|
|Interweave||Allowed||Limited by the range of sensing hole||Interference controlling||Medium||—|
One of the core challenges in both CR and NOMA networks is the interference management, whilst improving the bandwidth efficiency. Hence it is natural to link them for achieving an improved bandwidth efficiency. Liu et al. investigated the application of NOMA in large-scale underlay CR networks by relying on the stochastic geometry model . The diversity order of the NOMA users was characterized analytically in two scenarios. The classic OMA-based underlay CR was also used as a benchmark to show the benefits of the proposed CR-NOMA scheme. As mentioned in Section VI, Ding et al.  proposed a novel PA policy for NOMA, namely the CR-inspired NOMA PA, which constitutes a beneficial amalgam of NOMA and underlay CR.
To the best of our knowledge, CR-NOMA studies only exist in the context of the underlay CR paradigm. Hence both the interweave and overlay CR paradigms have to be investigated in NOMA networks. It is worth pointing out that a significant research challenge of NOMA is to dynamically cluster/pair the NOMA users first, followed by dynamically allocating the clusters/pairs to different orthogonal sub-channels. In the context of the interweave paradigm, intelligent sensing has to be applied first, followed by user clusering/pairing of NOMA users, depending on the specific channel conditions sensed.
Vi-D NOMA-Based Device-to-Device Communication
Due to the recent rapid increase in the demand for local area services under the umbrella of cellular networks, an emerging technique, namely device-to-device (D2D) communication, may be invoked for supporting direct communications amongst devices without the assistance of cellular BSs . The main advantages of integrating D2D communications into cellular networks are: i) low-power support of proximity services for improving the energy efficiency; ii) reusing the frequency of the over-sailing cellular networks in an effort to increase the bandwidth efficiency; and iii) the potential to facilitate new types of peer-to-peer (P2P) services .
Note that one of the common features of both D2D and NOMA is that of enhancing the bandwidth efficiency by managing the interference among users within each RB. Motivated by this, it is desirable to invoke intelligent joint interference management approaches for fully exploiting the potential benefits of both D2D and NOMA. In , Zhao et al. designed a novel NOMA-based D2D communication scheme, where several D2D groups were permitted to share the same RB with the cellular users. In contrast to the conventional D2D pair’s transmission, the novel “D2D group” concept was introduced, where a D2D transmitter was able to simultaneously communicate with multiple D2D receivers with the aid of NOMA. It was demonstrated that the proposed NOMA-based D2D scheme is capable of delivering higher throughput than conventional D2D communication.
Vi-E Discussions and Outlook
The aforementioned techniques are capable of improving the bandwidth efficiency by exploiting NOMA, but they will also pose some challenges. For example, adopting NOMA in HetNets, CR networks and D2D communication scenarios will impose increased co-channel interference on the existing networks. Hence intelligent interference management is desired.
Apart from the above-mentioned solutions, there are other emerging techniques, such as C-RAN, full-duplex, and other solutions. As the extension of , Sun et al.  studied the multiple carrier NOMA resource allocation problem for the scenario, where a full-duplex BS supported several half-duplex users. While the current research contributions have laid a solid foundation, numerous open questions have to be resolved.
Vii Implementation Challenges and Standardization of NOMA
Although NOMA have been recognized as a promising candidate for 5G and beyond, there are still several implementation challenges to be tackled. In this section, we identify some of the implementation issues and point out some potential approaches to solve them. Moreover, the standardization progress of NOMA will also be discussed in this section to show how NOMA paves the way to 5G and beyond.
Vii-a Error Propagation in SIC
SIC is the key technique of user detection in NOMA systems. Nevertheless, a main drawback of implementing SIC is the inter-user error propagation issue, which propagates on as from one user to another, because a decision error results in subtracting the wrong remodulated signal from the composite multiuser signal, hence resulting in residual interference [202, 203]. More specifically, if the messages of previous users are not correctly decoded, the reconstruction of those signals will result in flawed decoding of the remaining users’ messages, which leads the accumulation of the decoding errors. Most existing research contributions in the context NOMA are based on the assumption that the SIC receivers are capable of perfectly cancelling the interference. Actually this assumption cannot be readily satisfied in practice due to the inaccurate PA and imperfect channel decoding. Several researchers have recognized the opacity of error propagation issues and investigated the effect of imperfect SIC on uplink NOMA  systems, on full-duplex NOMA networks  and on C-RAN NOMA networks .
Some recent research contributions have identified several possible techniques for solving the error propagation issues. The first one is to use multistage channel estimation to improve the SIC  at the cost of increasing the complexity. The second possible approach is to apply iterative SIC aided receiver to overcome the error propagation effects, as proposed by Zhang and Hanzo . Another strategy is to take the channel estimation error into considerations when designing the power control algorithms, which was proposed by Buehrer . More particularly, more power is allocated to the users who will carry out SIC later for compensating the residual interferences. Nevertheless, invoking this approach imposes a capacity payoff .
Vii-B Channel Estimation Error and Complexity for NOMA
Channel estimation plays a more significant role in NOMA than in OMA systems, since the channel estimation errors will result in ambiguous user ordering as well as inaccurate power control, which will in turn affect the SIC decoding accuracy. Naturally, perfect CSI cannot obtained in practice. High performance near-optimal conventional channel estimation algorithms impose an unacceptable system overhead and computational complexity on NOMA systems, especially for MIMO-NOMA scenarios. In order to solve those problems, researchers dedicated their efforts mainly to the following three aspects.
The first approach is to propose more effective channel estimation designs for striking a good complexity-performance tradeoff. As mentioned in Section III, CS can be applied as an effective technique of reducing the complexity . The second approach is to rely on partial CSI. This is motivated by the fact that the large scale fading fluctuates less rapidly than the small scale fading. As mentioned in Section II, the use of partial CSI in downlink NOMA was studied in [91, 92, 93]. The third approach is to use limited feedback for reducing the overhead . Finally, iterative joint decision-directed channel estimation and data detection can be invoked as detailed in .
Vii-C Security Provisioning for NOMA
Security issues are of great significance in each generation of networks. The broadcast nature of the wireless medium makes it vulnerable to eavesdropping. Physical layer security (PLS), which was proposed by Wyner as early as 1975 , has become an appealing technique of improving the confidentiality of wireless communications. In contrast to the traditional approaches, which design cryptographic protocols in the upper layers, PLS aims for exploiting the specific characteristics of wireless channels in the physical layer for transmitting confidential messages. The key idea of achieving perfect secrecy in wiretap channels is to ensure that the capacity of the desired channel is higher than that of the eavesdropper’s channel. Triggered by the rapid development of wireless networks, PLS has been considered in diverse scenarios [209, 210, 211, 212, 213].
Motivated by the security concerns of wireless communications, PLS measures have also been proposed for NOMA networks in order to combat eavesdropping [111, 139, 214, 139, 215, 216]. In , Qin et al. examined the PLS of single-antenna NOMA in large-scale networks by invoking stochastic geometry, where the BS communicates with randomly distributed NOMA users. A protected zone may be adopted around the BS, where the intended users benefit from a high capacity in order to establish an eavesdropper-exclusion area to enhance the PLS with the aid of careful channel-ordering of the NOMA users. As a further development, Liu et al.  investigated the PLS of multiple-antenna NOMA scenarios, where artificial noise was generated at the BS for degrading the channels of eavesdroppers. Zhang et al.  investigated the PLS of SISO-NOMA networks, where the secrecy sum rate was maximized and the optimal PA was characterized in closed-form expressions.
Vii-D Maintaining the Sustainability of NOMA with RF Wireless Power Transfer
One of the key objectives of future 5G networks is to maximize the energy efficiency and to support energy-constrained wireless devices. Energy consumption is a critical factor in maintaining the sustainability of wireless networks, especially for the devices, which invoke a high cost of replacing the batteries. EH is an effective technique of extending the battery recharge period. Hence it has recently received remarkable attention [217, 218, 219, 220, 221, 222]. However, the traditional EH techniques relying on solar-wind-vibration-and thermoelectric-effects, which depend on the location, environment, time of the day, etc. In contrast to the conventional EH techniques, radio-frequency (RF) wireless power transfer (WPT) provides a more flexible approach for powering energy-constrained devices. Another motivation behind this approach lies in the fact that most devices are surrounded by ubiquitous RF signals. As a consequence, even interfering signals can be regarded as the potential EH sources.
To elaborate, NOMA relying on RF WPT techniques in wireless networks has been studied in [223, 110, 108, 224]. More particularly, in  the application of WPT to NOMA networks was investigated, where the users are randomly located. As a further development, in , a new cooperative simultaneous wireless information and power transfer (SWIPT) based NOMA protocol was proposed. In order to elaborate on the impact of user association, three user selection schemes based on the user distances from the base station were proposed in . The analytical results of  confirmed that invoking SWIPT techniques did not degrade the diversity gain compared to that of conventional NOMA. In , the uplink of NOMA transmission was considered in the context of energy constrained users, who can harvest energy from the BS by adopting the “harvest-then-transmit” protocol. The results demonstrated that NOMA is also capable of providing considerable throughput, fairness and energy-efficiency improvements.
Vii-E State-of-the-art for Standardization of NOMA
NOMA has recently been included into LTE-A, terms MUST . More specifically, at the 3GPP meeting in May 2015, it was decided to include MUST into LTE Advanced. Afterwards, at the 3GPP meeting in August 2015, 15 different forms of MUST have been proposed by Huawei, Qualcomm, NTT DOCOMO, Nokia, Intel, LG Electronics, Samsung, ZTE, Alcatel Lucent, etc. Finally, at the 3GPP meeting in December 2015, NOMA has been included into LTE Release 13 . It is worth noting that the MUST technique may be made compatible with the existing LTE structure. In other words, NOMA allows two users to be served at the same OFDM subcarrier without changing the current structure. Various non-orthogonal transmission schemes have been proposed for the MUST items [226, 225], which can be generally classified into three categories , namely, 1) superposition transmission with an adaptive power ratio on each component constellation and non-Gray-mapped composite constellation; 2) Superposition transmission with an adaptive power ratio on component constellations and Gray-mapped composite constellation; 3) Superposition transmission with a label-bit assignment on composite constellation and Gray-mapped composite constellation. The examples of transmitter processing candidate can be found in Figure 6 of . The NOMA-like MUST architecture works as follows. The coded bits of near users and far users are first separately input in a bit converter then modulated with the aid of quadrature amplitude modulation (QAM) or quadrature phase shift keying mapper (QPSK). The modulated symbols are superposed with allocating appropriate powers to transmit. Actually, the first category can be regarded as a special case of the second category, since coded bits in the first category are modulated directly to mappers without inputting into the bit converter. Both of these two categories are capable of supporting flexible power partition among users . For the third category, it is a bit-partition-based scheme which is in contrast to the power partition scheme adopted in the first and second categories. Regarding the detailed differences among the mentioned three schemes, interested readers may refer [23, 228] to identify the transmit structures of the three schemes. Regarding receivers, interference cancelation is required to carried out. The interference scenarios are different between network assisted interference cancellation system (NAICS) and MUST since the receivers of NAICS and MUST are employed by different groups of users. More particularly, for a two-user case which consists of a cell-edge user and a cell-center user, NAICS receivers are typically used for cell-edge users while MUST is typically used for cell-center users. By doing so, the network performance can be enhanced.
In addition to LTE-A, NOMA had also been included in the forthcoming digital TV standard, by the Advanced Television Systems Committee (ATSC) 3.0 , termed as layered division multiplexing (LDM) for providing significant improvements in terms of service reliability, system flexibility, and spectrum efficiency. This standard will generate significant impact on digital TV industry. Moreover, in the white paper of NTT DOCOMO, NOMA has been identified as a key technique for 5G. The system-level performance of NOMA has also been demonstrated by NTT DOCOMO. It is worth pointing out that the key challenges of implementing NOMA in industry is the decoding complexity increases at receivers as the number of users increase. Another potential challenge is that the security and privacy of far users should be protected at near user side due to the characteristic of SIC, which may depend on key generations from upper layer. Although NOMA is reviewed as a promising candidate for 5G and beyond, there are various forms of NOMA (which will be detailed in the following section). The standardization process for NOMA is still ongoing.
Vii-F Discussions and Outlook
In addition to the aforementioned implementation issues, there are also other imperfections to be dealt with for NOMA. Since NOMA relies on MA at different power levels, the strength of the received signals is deliberately different, which bring about new challenges for accurate analog-to-digital (A/D) conversion. On the one hand, for strong signals, a large voltage range is needed. On the other hand, for weak signals, high-resolution ADCs are required for supporting accurate quantization at small levels. In practice, considering the cost and system complexity, it is impossible to apply ADCs, which have both in large voltage range as well as a high resolution. The quantization errors are unavoidable. It is important to seek a good performance-complexity tradeoff.
Accurate synchronization is another significant issue in NOMA, which is to a degree neglected in the existing literature. Actually, perfect synchronous transmissions cannot be achieved in practice due to the dynamic mobile environment of users, especially for uplink NOMA transmission. In order to solve the synchronization issues, two possible approaches can be adopted. The first one is to propose accurate pilot design for reducing the time synchronization errors. The second approach is to investigate novel asynchronous communication schemes. Haci et al.  proposed a new IC scheme for asynchronous NOMA aided OFDM systems. It was demonstrated that the system performance largely depends on the relative time offset among the interfering users. Other imperfections such as the impact of filtering distortion between transmitters and receivers on the performance degradation of NOMA systems are still unknown, which is a promising future direction to consider.
Viii Practical Forms of NOMA
In the previous sections, power-domain NOMA has been investigated from diverse perspectives, including multi-antenna techniques, CR NOMA, the resource management problems of NOMA and the co-existence of NOMA as well as other 5G solutions. In practice, NOMA can be implemented in various forms, such as code-domain and power-domain NOMA, as summarized in this section. We may classify the practical forms of NOMA also into single-carrier and multiple-carrier NOMA. Their advantages and disadvantages will be discussed in this section.
Viii-a Single-Carrier NOMA
We commence our discussions from the single-carrier NOMA design, which will lay the foundations for the multi-carrier NOMA design in the next subsection.
The key idea of the IDMA scheme relies on a unique user-specific chip-interleaver for distinguishing the signals of different users . Hence IDMA may be viewed as chip-interleaved CDMA, which has the benefit of a high diversity gain, because if one or two chips are corrupted, the corresponding spreading sequence could still be recovered with the aid of low-complexity chip-by-chip iterative multi-user detection (IMD) strategy. A comprehensive comparison of IDMA and CDMA was presented in  in terms of its performance vs complexity.
LDS based CDMA constitutes an enhanced version of CDMA , which is inspired by the investigations on the low-density parity check (LDPC) codes . For conventional CDMA, one possible solution is to assign orthogonal spreading sequences for each user, and hence low-complexity receiver can be invoked at receivers for eliminating interference. Nonetheless, this orthogonal spreading code design is only capable of supporting equal number of users and chips, which motivates the development of non-orthogonal spreading code design. So-called sparse spreading sequences are employed instead of the dense spreading sequences of conventional CDMA, such as orthogonal variable spreading factor (OVSF) codes. However, such design requires sophisticated multi-user decoding at receivers. For LDS-CDMA, a message passing algorithm (MPA) based the muti-user detection technique can be applied at the receiver, which is capable of achieving the near maximum likelihood (ML) detection performance.
Lattice partition based multiple access (LPMA) is a new downlink non-orthogonal multi-user superposition transmission scheme, which was proposed by Fang et al. . LPMA achieves a beneficial multiplexing gain both in the power domain and in the code domain. More explicitly, power-domain multiplexing has the potential of increasing the throughput by superimposing different-power streams. By contrast, code-domain multiplexing superimposes several streams by exploiting that the linear combination of lattice codes also results in a lattice code. More specifically, LPMA encodes the information of users by applying lattice coding at the transmitters and invokes SIC at the receivers for detection. It is worth pointing out that a specific advantage of LPMA is that it has the potential of circumventing a specific impediment of power-domain NOMA, namely that the performance gain attained relies on the channel quality difference of users. However, LPMA imposes a higher encoding and decoding complexity than power-domain NOMA.
Viii-B Multi-Carrier NOMA
Given the remarkable advantages of OFDM, this mature wave form design is likely to be incorporated in 5G networks. Explicitly, one of the main benefits of multi-carrier techniques is that instead of the short dispersion-sensitive symbols of serial modems, many parallel long-duration dispersion-resistant symbols are transmitted over dispersive channels. Hence these long-duration symbols are only mildly affected by the same CIR and can be readily equalized by a single-tap frequency-domain equalizer. The NOMA techniques are expected to coexist with OFDM. In this subsections, several forms of multi-carrier NOMA designs are discussed.
LDS-OFDM  is essentially a combination of LDS-CDMA and OFDM, which can be regarded as an advanced variant of LDS-CDMA in a multi-carrier form. Therefore, the same sparse spreading sequences are applied at the transmitters and the same MPA based detection is adopted at the receivers. The data-stream mapping process consists of two steps: 1) Each bit of the data streams is first spread by the low density spreading sequences; and 2) The data streams are then transmitted over different subcarriers by applying an OFDM modulator. There are several techniques of mapping the spreading sequences to OFDM, each having different pros and cons. For example, each chip may be mapped to a different subcarrier for achieving frequency-domain diversity. Alternatively, each subcarrier may convey a spread low-rate stream. However, this design results in a higher complexity due to the application of the MPA detection compared to a conventional OFDMA design.
SCMA  also relies on sparse spreading codes for ensuring that each RB can support more than one user with the aid of low density spreading, hence resulting in a scheme similar to LDS-CDMA and LDS-OFDM. Considering an example of six users and four sub-carriers, a typical signature matrix can be illustrated as follows:
It is worth noting that for in (9), each column has only two non-zero entries, which implies that each user is only allowed to occupy two sub-carriers. This is one of the key characteristics of SCMA. In addition to these sparse spreading sequences, SCMA also relies on multi-dimensional constellations for generating its codebooks in order to achieve a so-called constellation shaping gain. More particularly, SCMA allows the employment of fewer constellation points to be used at a given throughput. For example, the four-level quadrature amplitude modulation (4-QAM) constellation can be reduced to a smaller constellation, because some bits can be conveyed in the sparse-code domain. However, this requires sophisticated codebook design [238, 239, 240]. SCMA relies on the joint encoding of the signals of multiple sub-carriers, hence joint decoding is required at the receivers. For this large joint alphabet MPA based detection is capable of achieving near-ML performance at a fraction of the ML complexity.
PDMA is another form of sparse signature matrix based multi-carrier NOMA . Again, we use the previous example of six users and four subcarriers relying on the pattern matrix of:
At the transmitter side, In contrast to the matrix design of SCMA in (9), where the number of users in each RB has to be the same, PDMA allows a variable number of users to be mapped to each RB. For example, the first user in (10) is seen to activate all the subcarriers for transmission, while the sixth user only activates a single subcarrier. Another main difference between PDMA and SCMA is that PDMA does not aim for achieving a constellation shaping gain, which beneficially avoids the complex multi-dimensional constellation design of SCMA. At the receiver side, the MPA may also be adopted for joint decoding, which is similar to LDS-CDMA and SCMA. Moreover, other MPA-SIC detection strategies or the turbo detection design of  can also be used for improving the decoding performance.
|Paradigm||Carrier||Spreading||Modulation||Flexibility||Complexity||Decoding||Key Advantages||Main Challenges|
|PD-NOMA||SC||Not used||Separated||High||Low||SIC||High Spectral Efficiency||Error Propagation|
|IDMA||SC||Low-rate||Separated||Medium||Low||IMD||High Diversity Gain||Interleaver Design|
|LDS-CDMA||SC||Sparse||Separated||High||Medium||MPA||CSI is not required||Coding Redundancy|
|LPMA||SC||Lattice||Separated||Medium||Medium||SIC||Gain benefits PD and CD||Specific Channel Coding|
|LDS-OFDM||MC||Sparse||Integrated||Low||Medium||MPA||Wideband Signals Suitable||Coding Redundancy|
|SCMA||MC||Sparse||Integrated||Low||High||MPA||Enhanced Diversity than LDS||Codebook Design|
|PDMA||MC||Sparse||Separated||Medium||High||MPA-SIC||Multi-dimension Diversity||Patterns Design|
Viii-C Discussions and Outlook
While we have provided a detailed introduction to the most popular power-domain NOMA variants, there are also other NOMA schemes, such as multiuser superposition transmission (MUST) scheme of , the MUSA arrangement of , etc. Table IX compares their key characteristics at a glance, where “SC” refers to single-carrier and “MC” refers to multi-carrier schemes. Note that each form has its own advantages and disadvantages. For example, SCMA is an open-loop grant-free access scheme, which is suitable for uplink transmission, and it relies both on sophisticated codebook design as well as on joint MPA detection. MUST is capable of enhancing the bandwidth efficiency but it can only be used for downlink transmission. As a consequence, a unified NOMA framework is sought, which is capable of supporting the access of numerous users in general scenarios. This is a promising future problem for researchers to contribute to. Additionally, more research contributions are also needed on the following aspects: 1) Optimal codebook/coding designs for SCMA and PDMA; 2) Hybrid MPA-SIC designs are sought for low-complexity decoding; 3) The joint designs of new modulation and MA schemes.
Ix Summary and Conclusions
In this article, the recent literature of power-domain multiplexing aided NOMA proposed for 5G systems has been surveyed with an emphasis on the following aspects: the basic principles of NOMA, the amalgams of multiple antenna techniques and NOMA, the interplay of NOMA and cooperative communications, the resource control of NOMA, its co-existence with other key 5G techniques, and the implementation challenges and standadization. Apart from surveying the existing NOMA contributions, we have highlighted the key advantages of NOMA itself as well as the inherent features of other techniques in Section II. Investigating the inherent integration of multiple-antenna aided and cooperative techniques with NOMA is particularly important, since they are capable of providing extra spatial diversity, either with the aid of centralized or distributed beamforming designs. It is worth pointing that when designing centralized beamformers, the most influential factor is the appropriate ordering of the matrix based channels. Design guidelines were provided both for multiple-antenna aided and cooperative NOMA in Sections III and IV, respectively.
Bearing in mind that NOMA multiplexes users associated with different power levels with the aid of superposition coding techniques, the power sharing among the users should be carefully optimized for each scenario. For example, in practical scenarios, a laptop displaying high-definition online video may share a RB with low-rate wireless sensors. Clearly, these applications have very different target rates, and processing capabilities. More particularly, high-capability laptops and smart phones can readily carry out SIC, but this is quite the contrary for sensors. As such, intelligent resource control including PA and user scheduling should be investigated by taking into account the recommendations listed in Section V. What is also worth emphasizing is that the proposed software-defined NOMA strategy is capable of dealing with all the above-mentioned issues from a global perspective for the sake of holistically optimizing the performance of the entire network.
The benefits of invoking NOMA in combination with the emerging large-scale MIMO, cooperative transmission, wireless power transfer, HetNets, etc were discussed. However, given the fact that NOMA imposes extra intra-user interference on the system, it brings about a range of open challenges, especially those related to sophisticated interference management. This problem would become more challenging in CR, D2D, and HetNets scenarios. Indeed, the related research of NOMA relying on sophisticated interference coordination is still in its infancy and hence has to be more deeply investigated, as recommended in Section VI.
The implementation issues of NOMA such as error propagation, channel estimation errors, security issues, etc. were discussed in Section VIII. Moreover, the standardization progress of NOMA was also discussed. It was noting that there are still several gaps between research and implementation to fill with, which require more efforts on this field, as described in Section VIII.
Apart from power-domain NOMA, other NOMA schemes have also been advocated both by the industry and academia, as described in Section VIII. All NOMA schemes discussed in this treatise share the same spirits, of non-orthogonal transmissions to enhance the attainable bandwidth efficiency and to provide connectivity for numerous users within the limited number of RBs. Naturally, the problem of designing a unified NOMA framework would be beneficial for supporting 5G scenarios.
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