A Practical Weighted Sum Rate Maximisation for Multi-stream Cellular MIMO Systems

The problem of weighted sum-rate maximisation in a multi-cell multi-user downlink system is NP-hard and complicated to solve even for Multiple Input Single Output scheme (MISO). In this work, a low complexity suboptimal distributed algorithm is proposed for joint optimisation of beamforming and power allocation. The algorithm is based on two independent phases. In the first one, Regularised Block-Diagonalisation beam-forming is proposed (multi-stream transmission). In the second phase an approximated Dual decomposition and sub-gradient methods are used. Where the objective problem transformed into a sequence of successive convex approximations. Then, using Broadcast/Multiple access channel duality (BC/MAC), each base station computes optimal values of its local variables (virtual uplink power and beamforming) for fixed virtual noise levels (complicating variable). The Alternating-Direction Method of Multipliers (ADMM) is used for updating the virtual noise vectors once the per base station optimisations are finished. Base station optimisations and the sub-gradient method are carried out in an iterative approach for a fixed number of iterations. Finally, power can be allocated by leveraging optimal virtual uplink Signal-to-Interference plus Noise Ratio (SINR). Numerical results prove that the process can converge to a steady-state with in limited number of iterations and the network sum rate is closed to (only 1bpsk/Hz difference at 15dB SINR) the centralised scheme performance.