Joint Beamforming Design and Stream Allocation for Non-Coherent Joint Transmission in Cell-Free MIMO Networks

We consider joint beamforming and stream allocation to maximize the weighted sum rate (WSR) for non-coherent joint transmission (NCJT) in user-centric cell-free MIMO networks, where distributed access points (APs) are organized in clusters to transmit different signals to serve each user equipment (UE). We for the first time consider the common limits of maximum number of receive streams at UEs in practical networks, and formulate a joint beamforming and transmit stream allocation problem for WSR maximization under per-AP transmit power constraints. Since the integer number of transmit streams determines the dimension of the beamformer, the joint optimization problem is mixed-integer and nonconvex with coupled decision variables that is inherently NP-hard. In this paper, we first propose a distributed low-interaction reduced weighted minimum mean square error (RWMMSE) beamforming algorithm for WSR maximization with fixed streams. Our proposed RWMMSE algorithm requires significantly less interaction across the network and has the current lowest computational complexity that scales linearly with the number of transmit antennas, without any compromise on WSR. We draw insights on the joint beamforming and stream allocation problem to decouple the decision variables and relax the mixed-integer constraints. We then propose a joint beamforming and linear stream allocation algorithm, termed as RWMMSE-LSA, which yields closed-form updates with linear stream allocation complexity and is guaranteed to converge to the stationary points of the original joint optimization problem. Simulation results demonstrate substantial performance gain of our proposed algorithms over the current best alternatives in both WSR performance and convergence time.