This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular probability distribution model for fading channels (which is typically Gaussian), our approach merely relies on the first and second moments of fading channels. For the stochastic precoding problem, a naive idea is to directly apply the fractional programming (FP) method to the data rate inside the expectation; it does not work well because the auxiliary variables introduced by FP are then difficult to decide. To address the above issue, we propose using a lower bound to approximate the expectation of data rate. This lower bound stems from a nontrivial use of the matrix FP, and outperforms the existing lower bounds in that it accounts for generalized fading channels whose first and second moments are known. The resulting approximate problem can be efficiently solved in closed form in an iterative fashion. Furthermore, for large-scale MIMO, we improve the efficiency of the proposed algorithm by eliminating the large matrix inverse. Simulations show that the proposed stochastic precoding method outperforms the benchmark methods in both Gaussian and non-Gaussian fading channel cases.

翻译：本文旨在为多输入多输出（MIMO）网络中最大化长期平均加权和速率寻求一种高效的随机预编码算法。与许多现有工作假设衰落信道服从特定概率分布模型（通常为高斯分布）不同，我们的方法仅依赖于衰落信道的一阶矩和二阶矩。对于随机预编码问题，一种朴素的想法是直接将分数规划（FP）方法应用于期望内部的数据速率；这种方法效果不佳，因为FP引入的辅助变量难以确定。为解决上述问题，我们提出使用下界来近似数据速率的期望。该下界源于矩阵分数规划的非平凡应用，其优势在于能够适用于一阶矩和二阶矩已知的广义衰落信道，且性能优于现有下界。由此得到的近似问题可通过迭代方式以闭式解高效求解。此外，针对大规模MIMO场景，我们通过消除大矩阵求逆运算提升了所提算法的效率。仿真结果表明，所提出的随机预编码方法在高斯与非高斯衰落信道条件下均优于基准方法。