In recent years, the multiple-input multiple-output (MIMO) non-orthogonal multiple-access (NOMA) systems have attracted a significant interest in the relevant research communities. As a potential precoding scheme, the generalized singular value decomposition (GSVD) can be adopted in MIMO-NOMA systems and has been proved to have high spectral efficiency. In this paper, the performance of the GSVD-based MIMO-NOMA communications with Rician fading is studied. In particular, the distribution characteristics of generalized singular values (GSVs) of channel matrices are analyzed. Two novel mathematical tools, the linearization trick and the deterministic equivalent method, which are based on operator-valued free probability theory, are exploited to derive the Cauchy transform of GSVs. An iterative process is proposed to obtain the numerical values of the Cauchy transform of GSVs, which can be exploited to derive the average data rates of the communication system. In addition, the special case when the channel is modeled as Rayleigh fading, i.e., the line-of-sight propagation is trivial, is analyzed. In this case, the closed-form expressions of average rates are derived from the proposed iterative process. Simulation results are provided to validate the derived analytical results.

翻译：近年来，多输入多输出（MIMO）非正交多址接入（NOMA）系统已引起相关研究领域的广泛关注。作为潜在预编码方案，广义奇异值分解（GSVD）可应用于MIMO-NOMA系统，并被证明具有高频谱效率。本文研究了基于GSVD的MIMO-NOMA通信系统在Rician衰落下的性能。特别地，分析了信道矩阵广义奇异值（GSV）的分布特性。利用基于算子值自由概率理论的线性化技巧与确定性等效方法两种新型数学工具，推导了GSV的柯西变换。提出了一种迭代算法以获取GSV柯西变换数值解，进而推导通信系统的平均数据速率。此外，分析了信道建模为Rayleigh衰落的特殊情形（即视距传播可忽略），在此情形下，基于所提迭代算法推导了平均速率的闭式表达式。仿真结果验证了所推导解析表达式的有效性。