  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.
