Message Passing Based Two-Timescale Bayesian Deep Learning for Joint Channel and Hardware Impairments Estimation

In time division duplex (TDD) massive MIMO systems, the multiple antenna BS suffers severe hardware impairments such as power amplifier nonlinearity, crosstalk and in-phase/quadrature (IQ) imbalance, which significantly degrade the uplink channel estimation performance, especially for hybrid analog-digital beamforming (HBF) systems. Though polynomial and neural network (NN) have been proposed to compensate for the impairments, there are few works consider online joint channel and hardware impairments estimation at the receiver based on pilot signals, which is necessary when impairments varies slowly over time, leading to model mismatch. In this work, we model the impairments using a ResNet and propose a two-timescale Bayesian framework for joint short-term channel tracking and long-term hardware impairments estimation, where the parameters both in the channel model and the ResNet follow a time-evolving Markov prior, while the transition probabilities are set at different timescales. To obtain the marginal posterior distributions of the parameters, we propose a message passingbased two-timescale Bayesian deep learning (MP-TTBDL) algorithm: the messages w.r.t. the channel are computed via turbo orthogonal approximate message passing (Turbo-OAMP), while the messages within the ResNet are computed via deep approximate message passing (DAMP). Such a two-timescale joint estimation scheme can better track the fast-varying wireless channel and slow-varying impairments. Simulations show that the proposed scheme outperforms various baseline schemes under practical scenarios when the impairments and the channel vary at different timescales.