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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. X, NO. X, MONTH 2016 1 Quadrature Amplitude Modulation Division for Multiuser MISO Broadcast Channels Zheng Dong, Yan-Yu Zhang, Jian-Kang Zhang, Senior Member, IEEE and Xiang-Chuan Gao Abstract—This paper considers a discrete-time multiuser can be significantly simplified, since it has only one antenna multiple-input single-output (MISO) Gaussian broadcast chan- and the system still enjoys the multi-antenna diversity and nel (BC), in which channel state information (CSI) is available multiuser diversity. BC was first introduced by Cover [1], who at both the transmitter and the receivers. The flexible and explicit design of a uniquely decomposable constellation group demonstrated the idea of superposition coding for both binary- (UDCG) is provided based on pulse amplitude modulation (PAM) symmetric and Gaussian BC. Since then, great efforts have and rectangular quadrature amplitude modulation (QAM) con- been devoted to obtaining the capacity regions of different stellations. With this, a modulation division (MD) transmission BCs and to seeking for the optimal transmission strategies scheme is developed for the MISO BC. The proposed MD scheme under various constraints. Although the capacity region for enables each receiver to uniquely and efficiently detect their desired signals from the superposition of mutually interfering the general discrete memoryless broadcast channel (DM-BC) cochannel signals in the absence of noise. In our design, the is still unknown, much progress has been made since [1]. In optimal transmitter beamforming problem is solved in a closed- particular, the achievability and converse of the capacity region form for two-user MISO BC using max-min fairness as a design for the degraded DM-BC were proved by Bergmans [2] and criterion. Then, for a general case with more than two receivers, Gallager [3], respectively. Surveys of the literature on the BC we develop a user-grouping-based beamforming scheme, where the grouping method, beamforming vector design and power can be found in [4]–[6]. On the other hand, if the transmitter allocation problems are addressed by using weighted max-min and/or receiver nodes are allowed to have more than a single fairness. It is shown that our proposed approach has a lower antenna, there will be a Gaussian vector channel in which probability of error compared with the zero-forcing (ZF) method much higher spectral efficiency (through spatial multiplexing) when the Hermitian angle between the two channel vectors is and reliability (by multi-path diversity) can be achieved by small in a two-user case. In addition, simulation results also reveal that for the general channel model with more than two exploiting the scattering medium between the transmitter and users, our user-grouping-based scheme significantly outperforms receiver antenna arrays [7], [8]. Specifically for the MISO the ZF, time division (TD), minimum mean-square error (MMSE) BCs, the achievable throughput was developed in [9] based and signal-to-leakage-and-noise ratio (SLNR) based techniques on Costa’s writing on dirty paper approach [10] that achieves in moderate and high SNR regimes when the number of users the sum-capacity for a two-user case with a single transmitting approaches to the number of base station (BS) antennas and it degrades into the ZF scheme when the number of users is far less antenna. Then, the sum-capacity for a general multiuser MISO than the number of BS antennas in Rayleigh fading channels. BC was established in [11]–[14] by exploiting the uplink- downlink duality between the multiaccess channel (MAC) Index Terms—Broadcast channels (BCs), MISO, modulation division, uniquely decomposable constellation group (UDCG), and the corresponding BC. By using more practical finite- grouping, non-orthogonal multiple access (NOMA). alphabet constellations rather than Gaussian input signals, the transmission schemes that maximize the mutual information between the BS and all the receivers of the multi-user BC are I. INTRODUCTION considered in [15]–[18]. arXiv:1609.02107v1 [cs.IT] 7 Sep 2016 ULTIUSER systems in a downlink, also known as The aforementioned information-theoretic analyses serve as M broadcast channels, have long been the main building a guideline for a general system design. For a transmitter block of modern wireless communication systems such as design, non-linear precoding techniques such as the dirty paper cellular system, telephone conference and digital TV broad- coding (DPC) method can be used to approach the sum rate casting. In this paper, we concentrate on MISO BC, where of the MISO BC [12], [13]. It was shown in [9] that a one multi-antenna access point serves several single-antenna successive interference cancellation procedure, namely the ZF- receivers at the same time. Hence, the design of the receiver DPC, can be performed at the transmitter side to completely remove mutual interference between receivers. Given the com- The work of J.-K. Zhang is funded in part by NSERC. Z. Dong would plexity of DPC, the Tomlinson-Harashima precoding (THP) like to thank the support of the China Scholarship Council (CSC) and X.-C. Gao is funded by China National 863 Project (2014AA01A705), Outstanding method [19]–[22] serves as a suboptimal but practical ap- Young Talent Research Fund of ZZU (1521318003). proximation of DPC by introducing a modulo operation to Z. Dong and J.-K. Zhang are with the Department of Electrical and transmitted symbols. Despite the fact that there is a modulo Computer Engineering, McMaster University, Hamilton, Ontario, Canada. (emails: [email protected], [email protected].) loss [23], the transmitted symbols are guaranteed to have a Y.-Y. Zhang is with National Digital Switching System Engineering and finite dynamic range. All these precoding methods were pri- Technological Research Center (NDSC), Zhengzhou (450000), China (email: marily devoted to improving the sum rate of multiuser MISO [email protected]) X.-C. Gao is with the School of Information and Engineering, Zhengzhou BCs. On the other hand, practical transmitter designs may also University, Zhengzhou (450001), China (e-mail: [email protected]) aim to improve signal quality at the receiver side. Among IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. X, NO. X, MONTH 2016 2 such transmitter designs, linear precoding techniques receive UDC was investigated in a complex number domain to extract tremendous attention because of their potential and simplicity. the desired signal from the superposition of the signal and Using signal-to-noise ratio (SNR) as a design criterion, it cochannel interferences [56]–[58]. In addition, the concept of was shown that transmitter beamforming can increase the UDC was also exploited to design variety of multi-resolution received SNR in the multiuser MISO channel by performing modulation schemes for BC and it was shown that they not optimization on the beamformer design and the power allo- only outperform the frequency division scheme by properly cation scheme [24]–[26]. In addition, by employing MMSE designing the resulting constellation [59]–[62], but also reduce as a performance measure, an optimal precoder was proposed the transmission delay of the network at the cost of increased in [27] with regularized channel inversion, which outperforms transmitting power for fading channels [61]. Recently, a pair the ZF scheme when the channel condition number is large. By of uniquely decodable constellations was designed to study maximizing SLNR for all users simultaneously, a closed-form the capacity region of a two user Gaussian multi-access beamforming method was given in [28]. Even so, however, it channel [63]. was demonstrated that the ZF beamforming technique, which Indeed, it is the above aforementioned factors that greatly is simple to implement, can achieve most of the capacity in motivate and enlighten us to look into interference from moderdate and high SNR regimes [29], [30]. Comprehensive the perspective of signal processing. In this paper, we are comparisons of these schemes can be found in [31]. interested in exploring a novel signal processing technique to As we can see, interference has long been the central manage interference for BC, which allows strongly interfered focus for meeting the ever increasing requirements on quality user signals to cooperate with each other as a common desired of service in modern and future wireless communication sum signal from which each individual user signal is able to systems. The key to the understanding of multiuser com- be uniquely and efficiently decoded. Specifically, our main munications is the understanding of interference. Traditional contributions of this paper can be summarized as follows: approaches, which treat interference as a detrimental phe- 1) An explicit construction of UDCG, which can be con- nomenon are, therefore, to suppress or eliminate it. The sidered as a UDC in the complex domain for a mul- classical information-theoretic study on the two-user Gaussian tiuser case, for general PAM and rectangular QAM interference channel [32] suggests us that we should treat the constellations for any number of users is proposed. interference as noise when it is weak and that the optimal The main difference between our UDCG design and all strategy is to decode the interference when it is very strong. In currently available UFC designs in literature is that in addition, when the level of interference is of the same order of our UDCG design, the sum-constellation and all the user the power of a desired signal, one good strategy is to suppress constellations are PAM and QAM constellations with all the undesired interferences into a smaller space that has different scales. It is because of this nice geometric no overlap with the signal space [33]–[35]. However, some structure that once the sum signal is received, each recent innovative approaches, which consider interference as individual user signal can be efficiently and uniquely a useful resource, are, thus, to make use of it for developing decoded (see Algorithms 1 and 2).

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