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.

We propose a novel channel estimator for an uplink cell-free intelligent reflective surface (IRS)-aided orthogonal time frequency space (OTFS) system by introducing a pilot frame that reduces pilot overhead by enabling each access point (AP) to estimate the channels of all IRS elements in a single OTFS frame. The cascaded user-IRS-AP delay-Doppler (DD) channel is modeled as a twisted convolution of the user-IRS and IRS-AP DD channels, which now exhibits twisted convolutional sparsity, and common sparsity due to the shared DD profile across IRS elements. We develop a convolutional Bayesian learning (ConvBL) algorithm, which uses expectation-maximization for calculating channel posterior distribution, and natural gradient descent for optimizing prior parameters. We show that ConvBL vastly outperforms Bayesian and non-Bayesian algorithms.

Orthogonal time-frequency space (OTFS) transmission is a promising multi-carrier modulation scheme for high-mobility communication scenarios. We consider a novel multiple frame-based superimposed pilot (SP)-OTFS system, which exhibits two-dimensional (2-D) delay-Doppler domain channel sparsity. We design a multiple-frame-based coupled prior sparse Bayesian learning (M-CPSBL) algorithm to exploit the 2-D channel sparsity while estimating it. This algorithm, however, inverts a large-dimensional matrix in each iteration with a high complexity. We next design its low-complexity version, which works on a smaller dimensional problem. The two proposed algorithms are used for SP-OTFS systems, which superpose low-powered pilots on to data signals. The combination of M-CPSBL and SP-OTFS frameworks is shown to outperform existing OTFS systems in terms of channel estimation normalized mean squared error, and spectral efficiency (SE). We derive a closed-form expression to optimize pilot and data powers to maximize the signal-to-interference-plus-noise ratio of SP-OTFS systems. We numerically show that optimal power allocation reduces the bit error rate, and increases the SE.

For a reflecting intelligent surface (RIS)-aided orthogonal time-frequency space (OTFS) system, we propose a two-dimensional off-grid sparse channel estimation model that exploits the fact that delay-Doppler (DD) locations of non-zero channel gains in a cascaded RIS-OTFS channel are sum of non-zero DD locations in the base station-RIS and RIS-user channels. Using this model, we estimate channel by considering multiple OTFS frames, which results in a block sparse DD domain channel. The multiple frames allow us to model the temporal correlation in a multi-frame OTFS system. We propose a novel correlated coupled prior to capture the DD sparsity of the channel, and estimate it by developing a sparse Bayesian framework. We maximize the achievable rate for our RIS-OTFS system by developing a gradient descent method, which has a high complexity. We also propose a low-complexity dimension-wise sinusoidal maximization (DSM)-based DD domain channel power maximization to obtain sub-optimal phase shifts. We show that the proposed channel estimation and phase optimization algorithms provide substantial gain over their existing counter-parts. We also show the robustness of an RIS-OTFS system over its non-RIS counterpart in a high-mobility scenario.

We propose a novel coupled prior-based sparse Bayesian framework for superimposed pilot (SP)-aided OTFS systems. The SP-OTFS system, wherein low-powered pilot signals are superimposed on to data signals, reduces the large pilot overhead, which is common in the existing OTFS systems. In the proposed coupled prior, sparsity of each channel gain is controlled not only by its own sparsity, but by also that of all other channel gains. OTFS channel has an inherent two-dimensional sparsity which can be exploited to increase its estimation accuracy. Using the proposed prior, we design a multiple received frame-based coupled prior sparse Bayesian learning (M-CPSBL) OTFS channel estimation algorithm, which is shown to outperform its state-of-the-art counterparts.