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.

We estimate the uplink channel in a multi-user millimeter wave system, which uses a hybrid architecture with low-resolution analog-to-digital converters and low-quality hardware-impaired radio frequency (RF) chains. We propose a hardware-impairment-aware correlated sparse Bayesian learning (HA-CSBL) channel estimation algorithm, which exploits the channel structured sparsity and its correlation by constructing a novel Gaussian prior model. The HA-CSBL algorithm also estimates the statistics of hardware impairments to mitigate their effect. We show that the HA-CSBL algorithm provides i) a lower normalized mean squared error (NMSE) than the existing algorithms in different practical sparsity scenarios. These improvements are due to the better prior design, and the hardware-impairment-awareness of the HA-CSBL algorithm.

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.

We consider the problem of estimating channel in reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) systems. We propose two variational expectation maximization (VEM) based channel estimation algorithms, which exploit the angular domain sparsity of RIS-assisted mmWave channel. To fully capture this sparsity, both within and across UEs, we construct a novel column-wise coupled Gaussian prior. The first proposed structured-mean-field-based VEM (SMF-VEM) algorithm uses the proposed prior, and calculates the posterior distribution of the unknown channel by assuming that it belongs to a set of multivariate distributions. This algorithm inverts a high-dimensional matrix in its posterior update, and consequently does not scale well for a large number of RIS elements and base station antennas, which are commonly used in practical systems. The second proposed fast mean field-based VEM (FMF-VEM) algorithm reduces complexity by assuming a fully-factorized posterior. It also bounds the variational objective to remove the residue coupling between the channel and phase matrices. Using extensive numerical investigations for a practical RIS mmWave system, and by using multiple metrics, we show that the proposed i) SMF- and FMF-VEM algorithms outperform several of their state-of-the-art counterparts; and ii) FMF-VEM has a much lower time complexity than SMF-VEM.

We estimate the uplink channel of an extra large-scale multiple-input-multiple-output (XL-MIMO) system, with the base station (BS) consisting of multiple antenna sub-arrays. The BS has a decentralized processing architecture, wherein each sub-array is connected to a local processing unit (LPU), which performs its signal processing tasks. The non-stationarity in XL-MIMO channel causes it to become sparse. We design a decentralized channel estimation algorithm to exploit this sparsity. In this algorithm, each LPU decentrally estimates the channel of a sub-array by exchanging information with other LPUs. This exchange is required to exploit the XL-MIMO sparsity. This decentralized algorithm is designed in two steps. The first step designs a centralized sub-array-based variational Bayesian learning (cS-VBL) algorithm. The second step extends this centralized design to a decentralized S-VBL (dS-VBL) implementation, which converts the centralized hyperparameter updates in cS-VBL algorithm to equivalent decentralized optimization problems. Each LPU decentrally solves this problem using asynchronous alternating direction method of multipliers. We show that the proposed i) cS-VBL and dS-VBL algorithms exploit the XL-MIMO channel sparsity, and outperform their existing centralized and decentralized counterparts; and ii) dS-VBL algorithm is robust to LPU failures, and has a lower complexity than cS-VBL algorithm.

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.

We consider the problem of detecting active devices and estimating their channels in the uplink of a massive machine type communication (mMTC) network. The base station (BS) in this mMTC system is equipped with massive multiple input multiple output (mMIMO) technology, and the channels across its antennas are correlated, an aspect ignored by most of the existing mMTC works. We propose three Bayesian learning algorithms which exploit channel spatial correlation, and comprehensively outperform several existing state-of-the-art algorithms, which do not exploit it. The proposed algorithms perform better in terms of the normalized mean squared error, activity error rate, and spectral efficiency (SE). The first correlated vector approximate message passing (AMP) algorithm has the best performance, but fails when the BS does not have knowledge of channel large scale fading and device activity probability. The second block sparse Bayesian learning (B-SBL) algorithm overcomes these limitations, but has a high complexity. The third combined AMP-BSBL algorithm retains the advantages of B-SBL, but with a much reduced complexity. We show that all three channel estimators can be represented as plug-in linear minimum mean squared estimators. This crucially helps us in deriving a common lower bound on the SE of mMIMO mMTC systems.

We consider the problems of active user detection (AUD) and channel estimation (CE) in the uplink of massive machine type communication (mMTC) network. We propose a coupled prior sparse Bayesian learning algorithm that exploits the sporadic user activity and variable-sized block channel sparsity. We first design a novel coupled hierarchical Gaussian prior model which captures the variable size block-sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization-minimization technique. We extensively investigate the proposed algorithm performance and show that it, due to its generic prior, outperforms the existing ones.

We consider the problem of estimating channel and detecting active users in the uplink of a massive machine type communication (mMTC) network. We propose a centralized coupled prior based sparse Bayesian learning (cCP-SBL) algorithm that exploits the sporadic user activity and variable-sized block mMTC channel sparsity in the virtual angular domain. To achieve this objective, we first design a generalized coupled hierarchical Gaussian prior which captures this variable-sized block sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization minimization framework. We next design a decentralized CP-SBL (dCP-SBL) algorithm for the emerging base station architectures with multiple processing units. The dCP-SBL algorithm converts the centralized hyperparameter cCP-SBL updates to an equivalent optimization problem, and solves it decentrally using asynchronous alternating direction method of multipliers. We also theoretically analyze the convergence of the dCP-SBL algorithm. We show using extensive numerical investigations that the i) proposed cCP- and dCP-SBL algorithms outperform several existing state-of-the-art designs; and ii) dCP-SBL algorithm is robust to processing unit failures and has a lower time complexity than the cCP-SBL algorithm.