Max-min Fairness of K-user Cooperative Rate-Splitting in MISO Broadcast Channel with User Relaying

Cooperative Rate-Splitting (CRS) strategy, relying on linearly precoded rate-splitting at the transmitter and opportunistic transmission of the common message by the relaying user, has recently been shown to outperform typical Non-cooperative Rate-Splitting (NRS), Cooperative Non-Orthogonal Multiple Access (C-NOMA) and Space Division Multiple Access (SDMA) in a two-user Multiple Input Single Output (MISO) Broadcast Channel (BC) with user relaying. In this work, the existing two-user CRS transmission strategy is generalized to the $K$ -user case. We study the problem of jointly optimizing the precoders, message split, time slot allocation, and relaying user scheduling with the objective of maximizing the minimum rate among users subject to a transmit power constraint at the base station. As the user scheduling problem is discrete and the entire problem is non-convex, we propose a two-stage low-complexity algorithm to solve the problem. Both centralized and decentralized relaying protocols based on selecting $K_{1}$ ( $K_{1} ) strongest users are first proposed followed by a Successive Convex Approximation (SCA)-based algorithm to jointly optimize the time slot, precoders and message split. Numerical results show that by applying the proposed two-stage algorithm, the worst-case achievable rate achieved by CRS is significantly increased over that of NRS and SDMA in a wide range of network loads (underloaded and overloaded regimes) and user deployments (with a diversity of channel strengths). Importantly, the proposed SCA-based algorithm dramatically reduces the computational complexity without any rate loss compared with the conventional algorithm in the literature of CRS. Therefore, we conclude that the proposed $K$ -user CRS combined with the two-stage algorithm is more powerful than the existing transmission schemes.