Joint Beamforming and Data Stream Allocation for Non-Coherent Joint Transmission

This paper addresses the joint beamforming and data stream allocation (DSA) optimization problem for non-coherent joint transmission (NCJT). A critical yet neglected issue in NCJT beamforming is the tightly related DSA, which involves determining the number of streams transmitted from access points (APs) to their serving user equipments (UEs) according to the channel quality, so that the weighted sum-rate (WSR) can be maximized. However, since the integer number of streams directly determines the dimensions of beamformers, the joint optimization problem is mixed-integer and nonconvex with tightly coupled decision variables, making it NP-hard. To solve this problem, we first fix the DSA variables and propose a distributed and reduced weighted minimum mean square error (WMMSE) beamforming algorithm, called distributed RWMMSE, by leveraging the low-dimensional subspace property of the beamformer obtained by the traditional WMMSE. The distributed RWMMSE achieves the same WSR as the traditional WMMSE but with significantly lower computational complexity (scaling linearly with the number of AP antennas) and reduced interaction cost. Building on this, a joint beamforming and DSA optimization algorithm, named RWMMSE-LSA, is proposed by decoupling the decision variables through introduced stream indicator matrices. The RWMMSE-LSA optimizes beamformers and DSA via the distributed RWMMSE and linear programming, respectively, both of which have closed-form solutions. Simulations validate substantial performance gain of our proposed algorithms over existing alternatives in computational and interaction costs.