Discrete Phase Shifters-based Hybrid Precoding for Full-Duplex mmWave Relaying Systems

This paper considers the hybrid precoding design with quantized phase shifters (PSs) for full-duplex millimeter-wave relaying systems, in which the relay node is equipped with PSs of different resolution levels. The joint optimization of relay hybrid precoding and discrete PSs is a high-dimensional non-convex problem with both higher-order polynomial and modulus constraints. To solve this challenging problem, the optimization function under the imperfect channel state information (CSI) is reformulated into a low-complexity norm-minimization form equation. Then, a relaxed algorithm based on the alternating direction method of multipliers and quantization steps is proposed to obtain the coupling approximate solutions for the above optimized equation. And the optimality of analytical solutions is guaranteed based on the imposed termination criterion and necessary conditions. Furthermore, given the requirement of arbitrary quantization, the trade-off between spectral efficiency (SE) and energy efficiency (EE) is investigated under the imperfect CSI. Numerical results verify that the hybrid precoding with low-resolution PSs can achieve excellent SE close to the full-resolution one but with a considerably lighter burden of energy consumption. Moreover, the transmission power plays a positive role in compensating quantization loss, but the excessive value will bring the reduction of EE.