Joint Hybrid Tx–Rx Design for Wireless Backhaul With Delay-Outage Constraint in Massive MIMO Systems

This paper studies joint design of mixed-timescale hybrid precoding and combining to maximize the effective capacity for wireless backhaul in massive multiple-input multiple-output (MIMO) systems. Specifically, radio frequency (RF) analog processing is adaptive to statistical channel state information (CSI) while digital baseband processing is updated with instantaneous effective CSI. Equipped with traditional MIMO solutions at the baseband, the issue of RF design for both unconstrained-modulus and constant-modulus elements is addressed. Under the jointly correlated channel model, the objective function does not have a closed-form expression. In the unconstrained case, we derive the optimal RF solution structures, which lead to a combinatorial eigenmode selection formulation. Such an NP-hard problem is solved to near-optimality by semi-definite relaxation. In view of the additional difficulty posed by the non-convex modulus constraint, we exploit the problem structure to construct the constant-modulus design from the unconstrained-modulus solution which is cast as a problem of joint matrix approximation and solved by low-complexity Jacobi-like algorithms. Numerical results show that under loose and stringent delay-outage constraints, the mixed-timescale hybrid designs deliver effective rates comparable with other perfect CSI-based state-of-the-art baselines.