Variational Bayesian learning (VBL)-based sparse channel state information (CSI) estimation is conceived for multiple input multiple output (MIMO) orthogonal time frequency space (OTFS) and for orthogonal time sequence multiplexing (OTSM)-based systems relying on low-resolution analog-to-digital convertors (ADCs). First, the CSI estimation model is developed for MIMO-OTFS systems considering quantized outputs. Then a novel VBL technique is developed for exploiting the inherent DD domain sparsity. Subsequently, an end-to-end system model is derived for MIMO-OTSM systems, once again, using only finite-resolution ADCs. Similar to OTFS systems, it is demonstrated that the channel is sparse in the delay-sequency (DS)-domain. Thus the sparse CSI estimation problem of the MIMO-OTSM system can also be solved using the VBL technique developed for its OTFS counterpart. A bespoke minimum mean square error (MMSE) receiver is developed for data detection, which unlike the conventional MMSE receiver also accounts for the quantization error. Finally, finite-resolution ADCs emerge as a solution, offering reduced costs and energy consumption amid the growing challenge posed by energy-intensive high-resolution ADCs in Next-Generation (NG) systems. The efficacy of the proposed techniques is validated by simulation results, surpassing the state-of-the-art and signalling a transition towards more sustainable communication technologies.

Multi-dimensional sparse channel state information (CSI) acquisition is conceived for Orthogonal time frequency space (OTFS) modulation-based millimetre wave (mmWave) multiple input and multiple output (MIMO) systems. A comprehensive end-to-end relationship is derived in the delay-Doppler (DDA) domain by additionally considering the angular parameters and a hybrid beamforming (HB) architecture. A time-domain pilot model tailored for CSI estimation (CE) in the DDA-domain is proposed, which exploits the inherent multi-dimensional (4D) sparsity that emerges in the DDA-domain during the CE process. An efficient low-complexity Bayesian learning (LC-BL) technique is conceived to fulfil the objective of CSI estimation in such systems. Subsequently, a comprehensive examination of the complexity of the algorithm under consideration is also provided. It is worth noting that the complexity of the BL scheme designed is similar to that of popular orthogonal matching pursuit (OMP), but significantly lower than that of the traditional expectation-maximization (EM) based BL technique. Moreover, a single-stage transmit precoder (TPC) and receiver combiner (RC) design is proposed. This procedure aims for maximizing the directional gain of the RF TPC/RC pair by optimizing their weights. Additionally, a series of comprehensive simulations are conducted which incorporate the use of a practical channel model and fractional Doppler shifts. In light of the inherent trade-offs between complexity and estimation algorithm performance, our proposed scheme, LC-BL, appears suitable, especially considering the substantial enhancement in the performance of CE compared to the existing benchmarks.

In this paper, adaptive channel state information (CSI) estimation techniques are conceived for intelligent reflective surface (IRS)-assisted single input and single output (SISO) and multiple input multiple output (MIMO) systems. Initially, the input-output system model is derived for an IRS-assisted SISO system, and the block least mean square (BLMS) and block recursive least square (BRLS) techniques are proposed for adaptive CSI estimation. Subsequently, the system model is also determined for IRS-assisted MIMO systems, and the adaptive CSI estimation schemes described above are also extended to this scenario. Convergence analysis is presented and the asymptotic mean square error (MSE) of estimation expressions are determined for the BLMS and BRLS algorithms. Finally, the simulation results are presented to demonstrate the performance and also validate the analytical results derived for the above adaptive CSI estimation schemes for IRS-assisted SISO and MIMO systems.

Online Bayesian learning-assisted channel state information (CSI) estimation schemes are conceived for single input single output (SISO) and multiple input multiple output (MIMO) orthogonal time frequency space (OTFS) modulated systems. To begin with, an end-to-end system model is derived in the delay-Doppler (DD)-domain, followed by an online CSI estimation (CE) framework for SISO-OTFS systems. Next, the sequential minimum mean square error (MMSE) estimator is derived for this model which utilizes expectation maximization (EM) based sparse Bayesian learning (SBL) for initialization of the online estimation procedure. Additionally, a low-complexity detection technique is developed for the system under consideration, which is accomplished via an analogous time-frequency (TF)-domain system model that leads to a block-diagonal TF-domain channel matrix. The paradigm designed for online CE is subsequently extended to MIMO-OTFS systems. The corresponding DD-domain CSI is shown to be simultaneously row and group sparse. Hence a novel EM-based row and group sparse Bayesian learning scheme is developed for determining the initialization parameters for the above online algorithm. As a further continuation, a low-complexity detector is also proposed for MIMO-OTFS systems based on an iterative block matrix inversion technique. Furthermore, time-recursive Bayesian Cramer-Rao lower bounds (BCRLBs) are derived to benchmark the MSE performance of the proposed schemes for both the systems. Finally, simulation results are presented to demonstrate the efficiency of the proposed online estimation techniques.

An orthogonal affine-precoded superimposed pilot (AP-SIP)-based architecture is developed for the cyclic prefix (CP)-aided single input single output (SISO) and multiple input multiple output (MIMO) orthogonal time frequency space (OTFS) systems relying on arbitrary transmitter-receiver (Tx-Rx) pulse shaping. The data and pilot symbol matrices are affine-precoded and superimposed in the delay Doppler (DD)-domain followed by the development of an end-to-end DD-domain relationship for the input-output symbols. At the receiver, the decoupled pilot and data symbol are extracted by employing orthogonal precoder matrices, which eliminates the mutual interference. Furthermore, a novel pilot-aided Bayesian learning (PA-BL) technique is conceived for the channel state information (CSI) estimation of SISO OTFS systems based on the expectation-maximization (EM) technique. Subsequently, a data-aided Bayesian learning (DA-BL)-based joint CSI estimation and data detection technique is proposed, which beneficially harnesses the estimated data symbols for improved CSI estimation. In this scenario our sophisticated data detection rule also integrates the CSI uncertainty of channel estimation into our the linear minimum mean square error (LMMSE) detectors. The AP-SIP framework is also extended to MIMO OTFS systems, wherein the DD-domain input matrix is affine-precoded for each transmit antenna (TA). Then an EM algorithm-based PA-BL scheme is derived for simultaneous row-group sparse CSI estimation for this system, followed also by our data-aided DA-BL scheme that performs joint CSI estimation and data detection. Moreover, the Bayesian Cramer-Rao bounds (BCRBs) are also derived for both SISO as well as MIMO OTFS systems. Finally, simulation results are presented for characterizing the performance of the proposed CSI estimation techniques in a range of typical settings along with their bit error rate (BER) performance in comparison to an ideal system having perfect CSI.