This is the first treatise on multi-user (MU) beamforming designed for achieving long-term rate-fairness in fulldimensional MU massive multi-input multi-output (m-MIMO) systems. Explicitly, based on the channel covariances, which can be assumed to be known beforehand, we address this problem by optimizing the following objective functions: the users' signal-toleakage-noise ratios (SLNRs) using SLNR max-min optimization, geometric mean of SLNRs (GM-SLNR) based optimization, and SLNR soft max-min optimization. We develop a convex-solver based algorithm, which invokes a convex subproblem of cubic time-complexity at each iteration for solving the SLNR maxmin problem. We then develop closed-form expression based algorithms of scalable complexity for the solution of the GMSLNR and of the SLNR soft max-min problem. The simulations provided confirm the users' improved-fairness ergodic rate distributions.

翻译：本文首次系统研究了全维多用户大规模多输入多输出（m-MIMO）系统中实现长期速率公平性的多用户波束赋形设计。具体而言，基于可预先获知的信道协方差，我们通过优化以下目标函数解决该问题：采用信漏噪比最大最小优化（SLNR max-min optimization）、信漏噪比几何均值（GM-SLNR）优化以及信漏噪比软最大最小优化（SLNR soft max-min optimization）来提升用户信漏噪比。针对SLNR最大最小问题，我们提出了一种基于凸优化求解器的算法，该算法在每次迭代中调用一个时间复杂度为三次方的凸子问题。随后，针对GM-SLNR和SLNR软最大最小问题，我们分别推导了具有可扩展复杂度的闭式表达式算法。仿真结果验证了所提方法在用户遍历速率分布公平性方面的改善效果。