This paper considers a joint scattering environment sensing and data recovery problem in an uplink integrated sensing and communication (ISAC) system. To facilitate joint scatterers localization and multi-user (MU) channel estimation, we introduce a three-dimensional (3D) location-domain sparse channel model to capture the joint sparsity of the MU channel (i.e., different user channels share partially overlapped scatterers). Then the joint problem is formulated as a bilinear structured sparse recovery problem with a dynamic position grid and imperfect parameters (such as time offset and user position errors). We propose an expectation maximization based turbo bilinear subspace variational Bayesian inference (EM-Turbo-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse MU channel by exploiting the joint sparsity, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. Two methods are introduced to greatly reduce the complexity with almost no sacrifice on the performance and convergence speed: 1) a subspace constrained bilinear variational Bayesian inference (VBI) method is proposed to avoid any high-dimensional matrix inverse; 2) the multiple signal classification (MUSIC) and subspace constrained VBI methods are combined to obtain a coarse estimation result to reduce the search range. Simulations verify the advantages of the proposed scheme over baseline schemes.

We investigate a joint scattering environment sensing, channel estimation, and data recovery problem in an uplink integrated sensing and communication (ISAC) system. Based on a three-dimensional (3D) location-domain sparse channel model, the joint problem is formulated as a bilinear sparse recovery problem with a dynamic position grid and imperfect parameters. We propose an expectation maximization based bilinear subspace variational Bayesian inference (EM-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse channel and transmitted data, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. In particular, the BiSVBI algorithm in the E-step avoids the high-dimensional matrix inverse by a subspace constrained approach while ensuring convergence to a stationary solution of the Kullback-Leibler divergence minimization problem. Simulations verify the advantages of the proposed method over baselines.

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.