In this paper, we investigate duplex mode selection and transceiver design for cell-free massive multiple-input multiple-output (MIMO) with network-assisted full duplexing (NAFD), where the remote antenna units (RAUs) simultaneously serve both uplink and downlink users on the same time-frequency resource, and the joint transmission and reception are done at the central processing unit. We consider that each antenna can operate in three modes, i.e., uplink reception, downlink transmission and sleep. In particular, we model the problem as a mixed-integer optimization problem to maximize the aggregated spectral efficiency (SE) of downlinks and uplinks, where the quality-of-service constraints and power budget constraints are considered. Since the uplinks and downlinks are highly coupled, to address the design problem, we resolve the combinatorial problem by a series of nonconvex-convex approximate methods, such as equivalent formulations, iterative success convex approximations, and binary relaxations. In particular, a two-stage strategy is proposed to solve the optimization problem. In the first stage, we fix the mode selection vectors and then obtain the optimal transceivers with such a fairness strategy. In the second stage, with the transceiver parameters obtained from the first stage, we further optimize the duplex mode of each antenna. The algorithms of the two stages will alternately run in several loops until convergence. Numerical results indicate that the proposed solution can obtain SE performance that is close to the optimal exhaustive search solution and yields a higher SE gain compared with the traditional fixed-mode duplex scheme.

在本文中，我们研究了具有网络辅助全双工 (NAFD) 的无蜂窝大规模多输入多输出 (MIMO) 的双工模式选择和收发器设计，其中远程天线单元 (RAU) 同时为上行链路和下行链路提供服务同一时频资源上的用户，在中央处理单元进行联合发送和接收。我们认为每个天线可以工作在三种模式，即上行接收、下行发送和休眠。特别是，我们将该问题建模为混合整数优化问题，以最大化下行链路和上行链路的聚合频谱效率 (SE)，其中考虑了服务质量约束和功率预算约束。由于上下行高度耦合，为了解决设计问题，我们通过一系列非凸-凸近似方法来解决组合问题，例如等效公式、迭代成功凸近似和二元松弛。特别地，提出了一种两阶段策略来解决优化问题。在第一阶段，我们固定模式选择向量，然后通过这种公平策略获得最佳收发器。在第二阶段，利用第一阶段获得的收发器参数，我们进一步优化每个天线的双工模式。两个阶段的算法将在几个循环中交替运行，直到收敛。数值结果表明，与传统的固定模式双工方案相比，所提出的解决方案可以获得接近最优穷举搜索解决方案的 SE 性能，并产生更高的 SE 增益。