On Optimal Beamforming Design for Downlink MISO NOMA Systems

Abstract

This work focuses on the beamforming design for downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) systems. The beamforming vectors are designed by solving a total transmission power minimization (TPM) problem with quality-of-service (QoS) constraints. In order to solve the proposed nonconvex optimization problem, we provide an efficient method using semidefinite relaxation. Moreover, for the first time, we characterize the optimal beamforming in a closed form with quasi-degradation condition, which is proven to achieve the same performance as dirtypaper coding (DPC). For the special case with two users, we further show that the original nonconvex TPM problem can be equivalently transferred into a convex optimization problem and easily solved via standard optimization tools. In addition, the optimal beamforming is also characterized in a closed form and we show that it achieves the same performance as the DPC. In the simulation, we show that our proposed optimal NOMA beamforming outperforms OMA schemes and can even achieve the same performance as DPC. Our solutions dramatically simplifies the problem of beamforming design in the downlink MISO NOMA systems and improve the system performance.

Is NOMA Efficient in Multi-Antenna Networks? A Critical Look at Next Generation Multiple Access Techniques

“…The following two precoder optimization problems are solved in the simulation for the K-user MISO NOMA system 32 Another detail missing and misleading in the comparison between NOMA and DPC is that the whole capacity region is achieved with DPC and timesharing between the precoding orders [12]. In the NOMA literature [44], the optimality of NOMA is only shown with respect to one fixed precoding order in DPC. The true capacity is achieved with time-sharing between the precoding orders and is larger.…”

“…MISO NOMA with G = 1 never achieves an MMF multiplexing gain higher than 1-layer RS. Corollary 6: The MMF multiplexing gain comparison between MISO NOMA with G > 1 and 1-layer RS is summarized in (44). MISO NOMA with G > 1 never achieves an MMF multiplexing gain larger than 1-layer RS.…”

“…Nevertheless, recall that our analysis relies on having the concatenated matrix of the user channels being full rank, or in other words that the user channels are not aligned, as per footnotes 11 and 16. Whenever the channels are aligned (though aligned channels are unlikely to occur in real wireless settings) and CSIT is perfect, NOMA can achieve the same performance as DPC, and could therefore be used as an alternative to DPC 32 in that outlier scenario [41], [42], [44]. This should not appear as a surprise since a multi-antenna setting with aligned channel vectors can effectively be seen as a SISO setting where users are distinguished only based on their channel strengths.…”

“…Thus, throughout the paper we assume user channels are not aligned. This matter is further discussed in Section VIII-E schemes [1]- [5], [18]- [44] (and references therein). Although there are a few contributions comparing NOMA with MU-LP schemes, such as Zero-Forcing Beamforming (ZFBF) or DPC [29], [41]- [44], much emphasis is put on comparing (single/multi-antenna) NOMA and OMA, and showing that NOMA outperforms OMA.…”

“…This matter is further discussed in Section VIII-E schemes [1]- [5], [18]- [44] (and references therein). Although there are a few contributions comparing NOMA with MU-LP schemes, such as Zero-Forcing Beamforming (ZFBF) or DPC [29], [41]- [44], much emphasis is put on comparing (single/multi-antenna) NOMA and OMA, and showing that NOMA outperforms OMA. But there is a lack of emphasis on contrasting multi-antenna NOMA to other multi-user multiantenna baselines developed for the multi-antenna BC, such as MU-LP (or other forms of multi-user MIMO techniques) and Rate-Splitting Multiple Access (RSMA) [45].…”