Hybrid Beamforming for Sum Rate Maximization in Wideband Multi-User MIMO Relay Systems

Hybrid precoding has a great potential to achieve near-optimal performance with few radio-frequency (RF) chains in comparison to the number of antennas. This paper proposes a novel hybrid beamforming solution for sum rate maximization in a wideband multi-user multi-input multi-output (MU-MIMO) relay system. The problem at hand is non-convex and hence mathematically intractable due to the constant modulus constraints associated with the analog beamforming design at communicating nodes shared by all sub-carriers. Furthermore, relaying in MU-MIMO systems under frequency-selective channels is also a challenging task as it requires complicated signal processing. To address this problem, source analog beamformer, relay RF combiner and phase-only processing component at each destination are obtained by deriving the common RF processing matrix which enables beamforming gain over all sub-carriers. This process involves reconstruction loss minimization for designing the required analog beamforming vectors having ability to maximize end-to-end signal-to-interference plus noise ratio (SINR). The relay analog precoder is designed by maximizing the received power at each destination through gain maximization of the equivalent baseband channel over the allocated frequency spectrum. To reduce the computational complexity of the iterative approach used to find the relay RF precoding matrix, the closed form expression is derived for achieving the desired objective. Finally, digital baseband processing components are obtained from the equivalent baseband channels by suppressing the interference among transmitted signals indirectly. Simulation results for different system configurations reveal that the proposed algorithm can achieve near-optimal performance.