End-to-End Deep Learning for Multipair Two-Way Massive MIMO with PA Impairments

Abstract

Multipair (MP) massive multiple-input–multiple-output (MIMO) two-way relaying system is a promising solution that is able to provide excellent spectral efficiency performance. It consists in multiple pairs ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2K$</tex-math></inline-formula> ) of single-antenna user terminals that exchange information through of a relay using a large number of antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M_{t}\gg 2K$</tex-math></inline-formula> . The relay is equipped with a large number of energy-efficient power amplifiers (PAs) and ensure the multipair two-way forwarding. In this article, we first present an analytical study focused on the effects of PAs on the considered system over block fading Rayleigh channel. We derive closed-form expressions for the symbol error rate. Then, we develop a new efficient distributed learning approach for MP two-way massive MIMO. Specifically, we design the MP two-way massive MIMO system by leveraging the concept of the autoencoder, whereas the end-to-end communication system is designed using one deep neural network (NN). Interestingly, the proposed scheme, referred to as AE-MP-mMIMO, is suited for varying block fading Rayleigh channel scenarios. Indeed, we propose to adopt one stage precoder/decoder for each UE and two-stage precoding scheme for the relay: 1) an NN-Tx is used to address the PA nonlinearity and 2) a linear zero-forcing precoder is adopted to remove the multiuser interference. The NN-Tx and the UE's precoder/decoder are trained off-line and when the channel varies, only the zero-forcing precoder changes on-line. Numerical simulations show the capability of the proposed approach to achieve competitive performance with a significantly lower complexity compared to existing literature.