IRS-Enhanced Cell-Free mMIMO-OTFS Systems: Learning-Based Channel Estimator and SE Analysis

We estimate the channel and analyze the spectral efficiency (SE) of an uplink cell-free (CF) massive multiple-input multiple-output (mMIMO) intelligent reflecting surface (IRS) aided orthogonal time frequency space (OTFS) system. We introduce two novel pilot frames, which significantly reduce the pilot overhead by enabling each access point (AP) to estimate channels of all IRS elements in a single OTFS frame. We show that the delay-Doppler (DD) domain cascaded user-IRS-AP channel can be expressed as the twisted convolution of the user-IRS and IRS-AP DD channels. The cascaded DD channel exhibits twisted convolutional sparsity and common sparsity due to the shared DD profile across IRS elements. We propose a novel convolutional prior to capture these sparsities, and then develop a convolutional Bayesian learning (ConvBL) algorithm, which employs expectation-maximization (EM) procedure to calculate the channel posterior distribution in the E step, and natural gradient descent algorithm to calculate the prior parameters in the M step. We also derive a closed-form SE lower bound for our CF mMIMO IRS-OTFS system. We numerically show that the ConvBL algorithm has a much lower normalized mean squared error than other Bayesian and non-Bayesian algorithms. The algorithm also provides significant SE gains over them.