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

Abstract

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.INDEX TERMS Millimeter wave massive Multiple-Input Multiple-Output (MIMO), multi-user, imperfect phase shifters, random phase and gain errors, channel estimation, HBF design method.

Hybrid beam-forming techniques for multi-cell massive MIMO

“…However, hardware impairment, Kalman beam-former, and multi-cell system have not been considered. In [34], a novel channel estimate and hybrid beam-forming design method while considering switches and non-ideal phase shifters have been considered. However, the multi-cell cell scenario has not been discussed in this research.…”

Channel Estimation and Hybrid Precoding for Millimeter Wave Communications: A Deep Learning-Based Approach

“…As the two NNs are trained with the assumption of perfect phase shifters, there is mismatch between the perfect phase shifters in the offline training stage and the imperfect ones in practical implementation in the online deployment. Unlike the quantization error, random phase and gain errors are neither known nor reciprocal [42]. Therefore, it is meaningful to explore the robustness of the DL-based HBF NNs to imperfect phase shifters with random phase and gain errors.…”

“…Therefore, it is meaningful to explore the robustness of the DL-based HBF NNs to imperfect phase shifters with random phase and gain errors. According to [42], an imperfect phase shifter can be modeled as γe j(φ−δ) , where j = √ −1, φ is the ideal phase shift, δ denotes the phase error satisfying a Gaussian distribution with zero mean and variance σ 2 δ , i.e., δ ∼ N 0, σ 2 δ , and γ ∼ N 1, σ 2 γ denotes the non-ideal gain of the phase shifter. According to [43] and [44], a typical σ δ is set to 0.1rad and a typical σ γ is set to 0.2.…”

A Study on the Effect of Phase Shifter Quantization Error on the Spectral Efficiency Using Neural Network

“…Beamforming (BF) techniques play an important role in all communication and sensing systems. These are usually implemented with phase shifters (PS) network with constant amplitude constraint [1]. One of the implementation ways of the PSs is using digital technology with N b -bit resolution discrete phase [1], [2].…”

“…These are usually implemented with phase shifters (PS) network with constant amplitude constraint [1]. One of the implementation ways of the PSs is using digital technology with N b -bit resolution discrete phase [1], [2]. The important specification of these PSs, which concern a system designer, is quantization error.…”