In this study, we consider multi-pair user frequency division duplexing massive MIMO relay systems and design a two-stage combining and beamforming (TSCB) scheme based on statistical channel state information (S-CSI). By leveraging S-CSI to co-design the pre-combining matrix and the pre-beamforming matrix, the scheme reduces the equivalent channel matrix dimensions, thereby cutting the pilot overhead. In the first stage, the two matrices are constructed through a selection of beams from a discrete Fourier transform codebook and mathematically cast as a multivariate optimization problem. An alternative optimization algorithm is proposed by splitting it into three sub-problems. The first two are 0–1 integer programming problems solved by iterative beam selection, while the third is a convex problem that is solved using a convex optimization algorithm. In the second stage, the reduced-dimension equivalent matrices are then estimated with low overhead, and a digital precoding matrix is then designed using zero-forcing algorithms. Simulations confirm the TSCB scheme’s superior ESE performance over that of existing methods.
Ge et al. (Sat,) studied this question.