Scalable Long-Term Beamforming for Massive Multi-User MIMO

Fully digital massive MIMO systems with large numbers (1000+) of antennas offer dramatically increased capacity gains from spatial multiplexing and beamforming. Designing digital receivers that can scale to these array dimensions presents significant challenges regarding both channel estimation overhead and digital computation. In the massive MIMO setting, long-term beamforming is widely-used since it offers significant reductions in both computation and channel estimation overhead. Long-term beamforming operates by projecting the data onto a low-dimensional subspace that can be tracked at a relatively slow time-scale from the long-term channel parameters. In this setting, we show how to optimally compute the projection matrix to maximize a capacity upper-bound using a matrix inverse square root. Computationally efficient methods are then presented to perform the matrix computation. The methods can be realized with matrix-matrix multiplies, making them amenable to systolic array implementations in hardware. Error analysis bounds on the degradation in the SINR for users are derived. Ray tracing simulations in a realistic rural uplink setting show minimal loss relative to complete instantaneous MMSE beamforming while offering significant overhead and computational gains.