Spatial Filter for MIMO Repeaters with First-Hop Channel State Information and End-to-End SNR

A repeater is a device that improves the rate-coverage performance of a system by amplifying and forwarding its received signal. When multiple antennas are deployed on a repeater, spatial signal processing becomes possible for better performance. In this paper we propose a spatial filter for such a multi-antenna repeater. This filter is designed based on first-hop channel state information (CSI) and end-to-end signal-to-noise ratio (SNR). The optimal filter matrix is proved to be a product of a diagonal matrix and the conjugate transpose of the left singular matrix of the first-hop channel matrix. The diagonal matrix is obtained by maximizing an upper bound of the ergodic channel capacity. Simulation results indicate that the proposed filter outperforms that without filtering in end-to-end channel capacity, especially when the number of repeater antennas is greater than that of the source antennas. As the first-hop CSI and the end-to-end SNR can be obtained without any modification of the source or the destination, a repeater with the proposed spatial filter can be easily implemented in a current system.