This paper is concerned with the proportional fairness (PF) of the spectral efficiency (SE) maximization of uplinks in a cell‐free (CF) massive multiple‐input multiple‐output (MIMO) system in which a large number of single‐antenna access points (APs) connected to a central processing unit (CPU) serve many single‐antenna users. To detect the user signals, the APs use matched filters based on the local channel state information while the CPU deploys receiver filters based on knowledge of channel statistics. We devise the maximization problem of the SE PF, which maximizes the sum of the logarithm of the achievable user rates, as a jointly nonconvex optimization problem of receiver filter coefficients and user power allocation subject to user power constraints. To handle the challenges associated with the nonconvexity of the formulated design problem, we develop an iterative algorithm by alternatively finding optimal filter coefficients at the CPU and transmit powers at the users. While the filter coefficient design is formulated as a generalized eigenvalue problem, the power allocation problem is addressed by a gradient projection (GP) approach. Simulation results show that the SE PF maximization not only offers approximately the achievable sum rates as compared to the sum‐rate maximization but also provides an improved trade‐off between the user rate fairness and the achievable sum rate.

中文翻译：

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无小区大规模MIMO系统中上行频谱效率的比例公平性

本文涉及无小区（CF）大规模多输入多输出（MIMO）系统中上行链路的频谱效率（SE）最大化的比例公平（PF），其中大量单天线接入连接到中央处理器（CPU）的单点（AP）为许多单天线用户提供服务。为了检测用户信号，AP使用基于本地信道状态信息的匹配过滤器，而CPU根据信道统计信息部署接收器过滤器。我们设计了SE PF的最大化问题，该问题将可达到的用户速率的对数的总和最大化，作为受用户功率约束的接收机滤波器系数和用户功率分配的联合非凸优化问题。为了解决与制定的设计问题的非凸性相关的挑战，我们通过在CPU上找到最佳滤波器系数并在用户处传输功率来开发迭代算法。虽然滤波器系数设计被公式化为广义特征值问题，但功率分配问题通过梯度投影（GP）方法解决。仿真结果表明，与总和最大化相比，SE PF最大化不仅提供大约可实现的总和，而且在用户费率公平性和可实现的总和之间提供了更好的折衷。