Sparse beamforming design for network MIMO system with per-base-station backhaul constraints

This paper considers the joint beamforming and clustering design problem in a downlink network multiple-input multiple-output (MIMO) setup, where the base-stations (BSs) are connected to a central processor with rate-limited backhaul links. We formulate the problem as that of devising a sparse beamforming vector across the BSs for each user, where the nonzero beamforming entries correspond to that user's serving BSs. Differing from the previous works, this paper explicitly formulates the per-BS backhaul constraints in the network utility maximization framework. In contrast to the traditional utility maximization problem with transmit power constraint only, the additional backhaul constraints result in a discrete ℓ0-norm formulation, which makes the problem more challenging. Motivated by the compressive sensing literature, we propose to iteratively approximate the per-BS backhaul constraints using a reweighted ℓ1-norm technique and reformulate the backhaul constraints as weighted per-BS power constraints. This allows us to solve the weighted sum rate maximization problem through a generalized weighted minimum mean square error (WMMSE) approach. To reduce the computational complexity of the proposed algorithm within each iteration, we propose two additional techniques, iterative link removal and iterative user pool shrinking, which dynamically decrease the potential BS cluster size and user scheduling pool. Numerical results show that the proposed algorithm can significantly improve the system throughput as compared to the naive BS clustering strategy based on the channel strength.