Robust and Low-Overhead Hybrid Beamforming Design With Imperfect Phase Shifters in Multi-User Millimeter Wave Systems

Phase shifters, often applied for analog beamforming in hybrid millimeter wave systems, are usually imperfect with random phase and gain errors brought by manufacture imperfections. Due to the uncertainty and nonreciprocity of random phase and gain errors, the digital precoder cannot eliminate the inter-user interference, which leads to system performance degradation. In our previous works [1], [2], we have analyzed the degradation of the achievable sum rate caused by imperfect phase shifters. The results show that the impact of random phase and gain errors is indeed very severe and they lead to performance ceiling. In this paper, we propose a novel channel estimation and Hybrid BeamForming (HBF) design method considering the structures both with and without switches. More specifically, we apply the discrete Fourier transform interpolation algorithm to estimate the downlink angle-of-departure of the strongest path, which avoids the exhaustive search of the narrow beam codebook and greatly saves the training overhead. Then, the downlink equivalent channel is estimated at the users and fed back for the digital precoder design, which guarantees the robustness against imperfect phase shifters. Finally, we derive a closed-form expression to make a better tradeoff between the estimation performance and training overhead. We show that our proposed method outperforms other state-of-the-art beam training methods with much less training overhead both theoretically and numerically.