Joint Pilot Design and Channel Estimation Using Deep Residual Learning for Multi-Cell Massive MIMO Under Hardware Impairments

In multi-cell massive multiple-input multiple-output (MIMO) systems, channel estimation is deteriorated by pilot contamination and the effects of pilot contamination become more severe due to hardware impairments. In this paper, we propose a joint pilot design and channel estimation based on deep residual learning in order to mitigate the effects of pilot contamination under the consideration of hardware impairments. We first investigate a conventional linear minimum mean square error (LMMSE) based channel estimator to suppress the interference caused by pilot contamination. After that, a deep learning based pilot design is proposed to minimize the mean square error (MSE) of LMMSE channel estimation, which is utilized to the joint pilot design and channel estimator for transfer learning approach. For the channel estimator, we use a deep residual learning which extracts the features of interference caused by pilot contamination and eliminates them to estimate the channel information. Simulation results demonstrate that the proposed joint pilot design and channel estimation method can effectively reduce the effect of pilot contamination as well as outperforms the conventional approach in multi-cell massive MIMO scenarios. Moreover, the joint pilot design and channel estimation method using transfer learning further enhances the estimation performance when the prior knowledge of pilot contamination cannot be exploited.

I. Introduction

Massive multiple-input multiple-output (MIMO) has been attracted considerable attention in wireless communications to meet the high data rate requirements and improve the link reliability [1], [2]. In addition, massive MIMO has the advantages of multiplexing gain, simple signal processing, and cost reduction in radio frequency (RF) hardware components [3]. In order to achieve the benefits of massive MIMO, the accurate channel estimation technique is of vital importance. However, channel estimation is challenging in massive MIMO systems since pilot length for downlink channel estimation in frequency division duplex (FDD) is proportional to the number of antennas as the base station (BS). In contrast, the pilot overhead which is proportional to the number of user equipments (UEs) can be significantly reduced by exploiting the channel reciprocity in time-division duplex (TDD) mode [1]. Despite the use of TDD mode, the pilot overhead in multi-cell scenario has to be proportional to the number of all UEs in all the cells for allocating orthogonal pilots to UEs [4]. In practical systems, however, the allocated pilot sequences are no longer orthogonal between UEs in adjacent cells since the pilot length needs to be limited by coherence time. As a result, it leads to pilot contamination which is a fundamentally limiting factor degrading the channel estimation performance [5]–[7]. Furthermore, the pilot contamination induces inter-cell interference due to the reuse of pilot sequences in multi-cell environments, which deteriorates the system throughput [8].