This paper presents delay alignment modulation (DAM) toward utilizing the high spatial gain and multipath sparsity of millimeter wave (mmWave) multiuser (MU) multiple-input multiple-output (MIMO) systems for cancelling the inter-symbol interference (ISI), which eliminates the need for traditional schemes such as multi-carrier transmission or channel equalization. We design a partially-connected transmit precoder (PCTPC) at the base station (BS), where each RF chain is connected to a subset of the BS antennas, followed by developing a novel DAM-based hybrid precoding scheme that introduces the delay pre-compensation and per-tap beamforming. The analog domain RF TPC is designed to maximize the array gain and the baseband TPC employs the minimum mean-squared error (MMSE) beamformer to mitigate ISI as well as inter-user interference (IUI). An advantage of the procedure is that the MMSE beamformer does not suffer from noise enhancement, which is otherwise prevalent in zero-forcing (ZF) beamforming. Simulation results depict the superiority of the proposed MU DAM system in comparison to a conventional multi-carrier MU OFDM system. We also demonstrate that the proposed precoding scheme is able to perform accurately both in perfect and imperfect channel state information (CSI) scenarios.

This paper investigates the reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system, wherein an ISAC base station (BS) serves multiple users with the aid of an RIS and detects multiple radar targets (RTs), simultaneously. Specifically, we consider the geometric mean (GM) rate as the communication performance metric to achieve both rate fairness among users and a high sum rate. To this end, we formulate the optimization problem for jointly designing the transmit precoder (TPC) and RIS phase shift matrix, aiming to maximize the GM rate of the users while ensuring minimum radiated power towards the RTs for their sensing, Additionally, the problem incorporates the maximum transmit power at the ISAC BS and unity modulus (UM) constraints on the elements of the RIS phase shift matrix. To solve this highly non-convex problem, we propose a majorization and minimization (MM)-based block coordinate descent (BCD) algorithm. In this algorithm, we first decouple the tightly coupled optimization variables and formulate the sub-problems via the BCD approach. Subsequently, each sub-problem is efficiently solved via employing the MM technique. Finally, the simulation results are presented and compared with benchmark schemes, which demonstrates the efficacy of the proposed algorithm in improving GM rate performance.

A data-aided (DA) framework is proposed for joint wireless channel and bistatic target parameter estimation in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) integrated sensing and communication (ISAC) systems. The framework begins with the formulation of a multi-measurement vector (MMV)-based sparse reconstruction problem for beamspace communication channel estimation. To solve this, a pilot-aided MMV-based Bayesian learning (PA-MBL) algorithm is developed, enabling efficient estimation of the beamspace channel. These channel estimates provide coarse target parameters, including the direction of arrival (DoA), direction of departure (DoD), range, and reflection coefficient. While DoA and DoD are obtained from a predefined angular grid, a specialized approach is designed to estimate the range in a continuous domain. Furthermore, the proposed sensing-assisted communication method estimates the communication channel across all subcarriers while requiring only a small number of pilot subcarriers, enhancing spectral efficiency. A subsequent DA scheme is introduced to jointly refine the estimation of target parameters and data, leading to further improvements in accuracy. Extensive simulations validate the effectiveness of the proposed framework, demonstrating significant performance gains in terms of normalized mean squared error (NMSE), bit error rate (BER), and 2D imaging.

A three-dimensional (3D) sparse signal recovery problem formulation is conceived for delay, Doppler, and angular (DDA) domain target parameter estimation in millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM)-based integrated sensing and communication (ISAC) systems relying on a hybrid beamforming architecture. Subsequently, a 3D-sparse Bayesian learning (3D-BL) algorithm is proposed to jointly estimate the angular, range, velocity, and radar cross-section (RCS) parameters of the targets. Furthermore, an uplink beamformer is designed for the user equipment (UE) to alleviate the complexity of uplink parameter estimation at the dual-functional radar-communication (DFRC) base station (BS) by eliminating the need for angle of departure (AoD) estimation. Additionally, a Bayesian alternating minimization (BAT-MIN) algorithm is constructed for the designing of a DFRC waveform, enabling the simultaneous generation of beams toward both the radar targets and the UE. Furthermore, the sparse Bayesian learning lower bound (SBL-LB) and the Bayesian Cramér-Rao lower bound (BCRLB) are derived to serve as benchmarks for estimation performance. Finally, simulation results are presented to showcase the enhanced performance of the proposed methodologies in terms of multiple performance metrics when contrasted both to the existing sparse recovery techniques and to conventional non-sparse parameter estimation algorithms. The simulation outcomes unequivocally demonstrate the commendable performance of the proposed 3D-BL estimation methodology, approaching closely to the SBL-LB. Notably, this approach exhibits a substantial gain of at least 5 dB when compared to alternative techniques. Additionally, the introduced BAT-MIN beamformer emerges as a highly competitive solution, closely approximating the capabilities of a fully digital beamformer while maintaining a noteworthy minimum advantage over its contemporaries. These findings underscore the significance and efficacy of the proposed techniques in the context of advanced signal processing and beamforming.

In this work, we conceive novel robust hybrid beamformer design schemes for millimeter-wave (mmWave) multi-cell multi-user (MCMU) systems in the presence of channel state information (CSI) uncertainty, that relies on base station (BS) coordination and minimization of total transmit power while ensuring compliance to practical signal-to-interference-noise ratio (SINR) constraints for each user. We consider a scenario where some of the users are located close to the cell boundary and thus desire to receive the signal of interest transmitted by multiple BSs while ensuring the quality-of-service (QoS) constraint. Initially, a Bayesian learning (BL) framework is developed for estimating the sparse mmWave channel of each user in the system. Next, a semidefinite relaxation (SDR) based technique has been proposed for a centralized MCMU system toward designing the fully digital beamformer (FDBF) in the presence of stochastic uncertainty in the estimated channel. Subsequently, a BL technique is employed to split the FDBF into its analog and digital constituents toward obtaining a hybrid transmit precoder (TPC). However, the centralized TPC design requires global CSI, resulting in a high signaling overhead. Next, a distributed coordinated hybrid TPC utilizing the alternating direction method of multipliers (ADMM) algorithm is developed for the mmWave MCMU system in the presence of cell-edge (CE) users. The distributed TPC design solely relies on CSI and only requires a limited exchange of information between the BSs, consequently eliminating the need for the high signaling overheads that come along with the centralized method. Our simulation results illustrate the superior performance of the proposed centralized and distributed robust TPC design methods in comparison to non-coordinated systems.

This paper proposes an integrated sensing and communication (ISAC) framework based on the orthogonal time-frequency space (OTFS) modulation scheme for millimeter wave (mmWave) multiple-input multiple-output (MIMO) dual functional radar and communication (DFRC) systems. Initially, we derive the delay-Doppler (DD)-domain end-to-end input-output model for a phased-array ISAC (PA-ISAC) system, which employs a single RF chain (RFC) both at the DFRC base station (BS) and at the user equipment (UE). Furthermore, a Bayesian learning (BL) based two-stage procedure is developed for transceiver design followed by radar target parameter and channel estimation in PA-ISAC systems, which efficiently exploits the sparsity of the signal scattering environment. Next, the transceiver design, parameter learning, and channel estimation procedures are extended to an OTFS-aided mmWave MIMO ISAC (mM-ISAC) system, wherein multiple RFCs are employed at the DFRC BS and UE, leading to improved sensing and enhanced data rates. Furthermore, it is demonstrated that the radar target parameter and DD-domain channel estimation exhibit block sparsity for mM-ISAC systems. Subsequently, the block-sparse BL (B-BL) scheme is proposed to leverage the block sparsity for improved results. Analytical expressions are derived for the Bayesian Cramér-Rao lower bounds (BCRLB), which serve as benchmarks for the mean squared error (MSE) of both the target parameter and channel estimates. Finally, our simulation results illustrate the superior performance of the proposed transceiver designs, parameter and channel estimation techniques for both PA-ISAC and mM-ISAC systems.

Sparse Bayesian learning (SBL)-aided target localization is conceived for a bistatic mmWave MIMO radar system in the presence of unknown clutter, followed by the development of an angle-Doppler (AD)-domain representation of the target-plus-clutter echo model for accurate target parameter estimation. The proposed algorithm exploits the three-dimensional (3D) sparsity arising in the AD domain of the scattering scene and employs the powerful SBL framework for the estimation of target parameters, such as the angle-of-departure (AoD), angle-of-arrival (AoA) and velocity. To handle a practical scenario where the actual target parameters typically deviate from their finite-resolution grid, a super-resolution-based improved off-grid SBL framework is developed for recursively updating the parameter grid, thereby progressively refining the estimates. We also determine the Cramér-Rao bound (CRB) and Bayesian CRB for target parameter estimation in order to benchmark the estimation performance. Our simulation results corroborate the superior performance of the proposed approach in comparison to the existing algorithms, and also their ability to approach the bounds derived.

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.

Pareto optimal solutions are conceived for radar beamforming error (RBE) and sum rate maximization in short-packet (SP) millimeter-wave (mmWave) integrated sensing and communication (ISAC). Our ultimate goal is to realize ultra-reliable low-latency communication (uRLLC) and real-time sensing capabilities for 6G applications. The ISAC base station (BS) transmits short packets in the downlink (DL) to serve multiple communication users (CUs) and detect multiple radar targets (RTs). We investigate the performance trade-off between the sensing and communication capabilities by optimizing both the radio frequency (RF) and the baseband (BB) transmit precoder (TPC), together with the block lengths. The optimization problem considers the minimum rate requirements of the CUs, the maximum tolerable radar beamforming error (RBE) for the RTs, the unit modulus (UM) elements of the RF TPC, and the finite transmit power as the constraints for SP transmission. The resultant problem is highly non-convex due to the intractable rate expression of the SP regime coupled with the non-convex rate and UM constraints. To solve this problem, we propose an innovative two-layer bisection search (TLBS) algorithm, wherein the RF and BB TPCs are optimized in the inner layer, followed by the block length in the outer layer. Furthermore, a pair of novel methods, namely a bisection search-based majorizer and minimizer (BMM) as well as exact penalty-based manifold optimization (EPMO) are harnessed for optimizing the RF TPC in the inner layer. Subsequently, the BB TPC and the block length are derived via second-order cone programming (SOCP) and mixed integer programming methods, respectively. Finally, our exhaustive simulation results reveal the effect of system parameters for various settings on the RBE-rate region of the SP mmWave ISAC system and demonstrate a significantly enhanced performance compared to the benchmarks.

A hybrid beamformer (HBF) is designed for integrated sensing and communication (ISAC)-aided millimeter wave (mmWave) systems. The ISAC base station (BS), relying on a limited number of radio frequency (RF) chains, supports multiple communication users (CUs) and simultaneously detects the radar target (RT). To maximize the probability of detection (PD) of the RT, and achieve rate fairness among the CUs, we formulate two problems for the optimization of the RF and baseband (BB) transmit precoders (TPCs): PD-maximization (PD-max) and geometric mean rate-maximization (GMR-max), while ensuring the quality of services (QoS) of the RT and CUs. Both problems are highly non-convex due to the intractable expressions of the PD and GMR and also due to the non-convex unity magnitude constraints imposed on each element of the RF TPC. To solve these problems, we first transform the intractable expressions into their tractable counterparts and propose a power-efficient bisection search and majorization and minimization-based alternating algorithms for the PD-max and GMR-max problems, respectively. Furthermore, both algorithms optimize the BB TPC and RF TPCs in an alternating fashion via the successive convex approximation (SCA) and penalty-based Riemannian conjugate gradient (PRCG) techniques, respectively. Specifically, in the PRCG method, we initially add all the constraints except for the unity magnitude constraint to the objective function as a penalty term and subsequently employ the RCG method for optimizing the RF TPC. Finally, we present our simulation results and compare them to the benchmarks for demonstrating the efficacy of the proposed algorithms.

Automatic modulation classification (AMC) is essential in non-orthogonal multiple access (NOMA) systems, since it enables dynamic adaptation of modulation schemes to optimize spectral efficiency and reduce inter-user interference. To address the AMC of the interference users in NOMA downlink systems, a lightweight Dual-Pool convolutional neural network (Dual-Pool CNN) algorithm is proposed, which leverages the power of the pooling layers in CNNs for better classification accuracy. It synergistically combines max-pooling and average-pooling to extract both general as well as sharp features from the distorted, faded, and superposed constellation diagrams. Our extensive experimentation demonstrates that the proposed model can classify the signals of four different modulation schemes with an accuracy score of more than 90% at an SNR of 14 dB and above. Moreover, this higher accuracy is obtained at lower computational complexity using the superposed constellation density grid (SCDG) approach followed by lightweight Dual-Pool CNN architecture.

This work conceives a novel sparse Bayesian learning (SBL)-based extended target parameter estimation scheme for an orthogonal frequency division multiplexing (OFDM) wave-form based-mmWave MIMO joint radar and communication (JRC) system. The proposed framework also incorporates the intercarrier interference (ICI) effect arising due to the Doppler shift together with radar clutter. The proposed algorithms are based on the hybrid mmWave MIMO architecture that requires a significantly fewer number of radio frequency (RF) chains in comparison to the number of antennas. A range, Doppler and angular (RDA)-domain representation of the target-plus-clutter echo is conceived toward target parameter estimation. The SBL framework is developed that exploits the 3-dimensional (3D)-sparsity arising in the RDA domain, given the limited number of targets and clutter, to jointly estimate the angles, range, velocity and radar cross-section (RCS) coefficients of an extended target. Simulation results demonstrate the imaging and accuracy of estimation of the target parameters in comparison to other existing techniques.

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.

This paper presents an innovative scheme for estimating the channel impulse response (CIR) in sparse multipath conditions for asymmetrically clipped direct current-biased op-tical OFDM (ADO-OFDM) visible light communication (VLC) systems, utilizing Bayesian learning (BL) techniques. We derive a multipath CIR model capturing both specular and diffusive reflections within the VLC system. Subsequently, we present a novel scheme for estimating the CIR in sparse multipath scenar-ios using the BL paradigm, which leverages the inherent sparsity of the multipath CIR in the delay domain. This scheme neces-sitates a constrained set of pilot subcarriers, thereby reducing pilot overhead when juxtaposed with traditional state-of-the-art channel estimation (CE) techniques. To assess the performance of the proposed BL-based paradigm for estimation, we compute the Oracle-MMSE (O-MMSE) along with the Bayesian Cramer Rao lower bound (BCRLB). Our extensive simulations reveal that even with a lower pilot overhead, the suggested BL method surpasses other conventional and sparse CE techniques across key metrics such as bit error-rate (BER) and normalized mean-square-error (NMSE).

This paper conceives a hybrid beamforming (HBF) design that maximizes the energy efficiency (EE) of an integrated sensing and communication (ISAC)-enabled millimeter wave (mmWave) multiple-input multiple-output (MIMO) system. In the system under consideration, an ISAC base station (BS) with the hybrid MIMO architecture communicates with multiple users and simultaneously detects multiple targets. The proposed scheme seeks to maximize the EE of the system, considering the signal-to-interference and noise ratio (SINR) as the user's quality of service (QoS) and the sensing beampattern gain of the targets as constraints. To solve this non-convex problem, we initially adopt Dinkelbach's method to convert the fractional objective function to subtractive form and subsequently obtain the sub-optimal fully-digital transmit beamformer by leveraging the principle of semi-definite relaxation. Subsequently, we propose a penalty-based manifold optimization scheme in conjunction with an alternating minimization method to determine the baseband (BB) and analog beamformers based on the designed fully-digital transmit beamformer. Finally, simulation results are given to demonstrate the efficacy of our proposed algorithm with respect to the benchmarks.

Hybrid precoder and combiner designs are conceived for decentralized parameter estimation in millimeter wave (mmWave) multiple-input–multiple-output (MIMO) wireless sensor networks (WSNs). More explicitly, efficient pre- and post-processing of the sensor observations and received signal are proposed for the minimum mean square error (MMSE) estimation of a parameter vector. The proposed techniques exploit the limited scattering nature of the mmWave MIMO channel for formulating the hybrid transceiver design framework as a multiple measurement vectors (MMVs)-based sparse signal recovery problem. This is then solved using the iterative appealingly low-complexity simultaneous orthogonal matching pursuit (SOMP). Tailor-made designs are presented for WSNs operating under both total and per-sensor power constraints, while considering ideal noiseless as well as realistic noisy sensors. Furthermore, both the Bayesian Cramer–Rao lower bound and the centralized MMSE bound are derived for benchmarking the proposed decentralized estimation schemes. Our simulation results demonstrate the efficiency of the designs advocated and verify the analytical findings.

Bayesian learning aided massive antenna array based THz MIMO systems are designed forspatial-widebandandfrequency-widebandscenarios, collectively termed as thedual-widebandchannels. Essentially, numerous antenna modules of the THz system result in a significant delay in the transmission/ reception of signals in the time-domain across the antennas, which leads to spatial-selectivity. As a further phenomenon, the wide bandwidth of THz communication results in substantial variation of the effective angle of arrival/ departure (AoA/ AoD) with respect to the subcarrier frequency. This is termed as thebeam squint effect, which renders the channel state information (CSI) estimation challenging in such systems. To address this problem, initially, a pilot-aided (PA) Bayesian learning (PA-BL) framework is derived for the estimation of the Terahertz (THz) MIMO channel that relies exclusively on the pilot beams transmitted. Since the framework designed can successfully operate in an ill-posed model, it can verifiably lead to reduced pilot transmissions in comparison to conventional methodologies. The above paradigm is subsequently extended to additionally incorporate data symbols to derive a Data-Aided (DA) BL approach that performs joint data detection and CSI estimation. We will demonstrate that it is capable of improving the dual-wideband channel’s estimate, despite further reducing the training overhead. The Bayesian Cramér-Rao bounds (BCRLBs) are also obtained for explicitly characterizing the lower bounds on the mean squared error (MSE) of the PA-BL and DA-BL frameworks. Our simulation results show the improved normalized MSE (NMSE) and bit-error rate (BER) performance of the proposed estimation schemes and confirm that they approach their respective BCRLB benchmarks.

Cooperative hybrid transmit precoder (TP) and receive combiner (RC) design algorithms are conceived for cell-free millimeter wave (mmWave) multiple-input multiple-output (MIMO) networks, operating in the face of asynchronous interference (ASI). To begin with, a Wiener filtering-based optimal hybrid TP/RC (WHB-U) design is proposed for unicast scenarios that minimizes the normalized mean squared error (NMSE) between the received signal and the desired signal subject to user-specific power constraints. Next, a signal-to-leakage plus noise ratio (SLNR) maximization-based hybrid TP/RC design (SHB-U) is conceived, which reduces the interference engendered by the signal transmission targeted towards a specific user, rather than focuses on the interference at a particular user. Next, a multicast transmission scenario is considered, wherein the users belonging to a particular multicast group request identical information. Toward this, the WHB-M and SHB-M hybrid TP/RC schemes are designed for mitigating both the inter-user and inter-group interference. Subsequently, we also develop a Bayesian learning (BL)-based framework for jointly designing the RF and baseband (BB) TPs/RCs for both unicast and multicast scenarios, which does not require the full knowledge of mmWave MIMO channel components. Finally, the efficiency of the proposed TP/RC schemes is extensively evaluated by simulations both in terms of their ability to mitigate the ASI, and the spectral efficiency attained.

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.

Hybrid transceivers are designed for linear decentralized estimation (LDE) in a mmWave multiple-input–multiple-output (MIMO) IoT network (IoTNe). For a noiseless fusion center (FC), it is demonstrated that the mean squared error (MSE) performance is determined by the number of RF chains used at each IoT node (IoTNo). Next, the minimum-MSE RF transmit precoders (TPCs) and receiver combiner (RC) matrices are designed for this setup using the dominant array response vectors, and subsequently, a closed-form expression is obtained for the baseband (BB) TPC at each IoTNo using Cauchy’s interlacing theorem. For a realistic noisy FC, it is shown that the resultant MSE minimization problem is nonconvex. To address this challenge, a block-coordinate descent-based iterative scheme is proposed to obtain the fully digital TPC and RC matrices followed by the simultaneous orthogonal matching pursuit (SOMP) technique for decomposing the fully digital transceiver into its corresponding RF and BB components. A theoretical proof of the convergence is also presented for the proposed iterative design procedure. Furthermore, robust hybrid transceiver designs are also derived for a practical scenario in the face of channel state information (CSI) uncertainty. The centralized MMSE lower bound has also been derived that benchmarks the performance of the proposed LDE schemes. Finally, our numerical results characterize the performance of the proposed transceivers as well as corroborate our various analytical propositions.

Linear hybrid beamformer designs are conceived for the decentralized estimation of a vector parameter in a millimeter-wave (mmWave) multiple-input–multiple-output (MIMO) Internet of Things Network (IoTNe). The proposed designs incorporate both total IoTNe and individual IoT node power constraints, while also eliminating the need for a baseband receiver combiner at the fusion center (FC). To circumvent the nonconvexity of the hybrid beamformer design problem, the proposed approach initially determines the minimum mean-square error (MMSE) digital transmit precoder (TPC) weights followed by a simultaneous orthogonal matching pursuit (SOMP)-based framework for obtaining the analog RF and digital baseband TPCs. Robust hybrid beamformers are also derived for the realistic imperfect channel state information (CSI) scenario, utilizing both the stochastic and norm ball CSI uncertainty frameworks. The centralized MMSE bound derived in this work serves as a lower bound for the estimation performance of the proposed hybrid TPC designs. Finally, our simulation results quantify the benefits of the various designs developed.

Robust linear decentralized tracking of a time-varying sparse parameter is studied in a multiple-input–multiple-output (MIMO) wireless sensor network (WSN) under channel state information (CSI) uncertainty. Initially, assuming perfect CSI availability, a novel sparse Bayesian learning-based Kalman filtering (SBL-KF) framework is developed in order to track the time-varying sparse parameter. Subsequently, an optimization problem is formulated to minimize the mean-square error (MSE) in each time slot (TS), followed by the design of a fast block coordinate descent (FBCD)-based iterative algorithm. A unique aspect of the proposed technique is that it requires only a single iteration per TS to obtain the transmit precoder (TPC) matrices for all the sensor nodes (SNs) and the receiver combiner (RC) matrix for the fusion center (FC) in an online fashion. The recursive Bayesian Cramer–Rao bound (BCRB) is also derived for benchmarking the performance of the proposed linear decentralized estimation (LDE) scheme. Furthermore, for considering a practical scenario having CSI uncertainty, a robust SBL-KF (RSBL-KF) is derived for tracking the unknown parameter vector of interest followed by the conception of a robust transceiver design. Our simulation results show that the schemes designed outperform both the traditional sparsity-agnostic Kalman filter and the state-of-the-art sparse reconstruction methods. Furthermore, as compared to the uncertainty-agnostic design, the robust transceiver architecture conceived is shown to provide improved estimation performance, making it eminently suitable for practical applications.

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.

Hybrid transceiver design in multiple-input multiple-output (MIMO) Tera-Hertz (THz) systems relying on sparse channel state information (CSI) estimation techniques is conceived. To begin with, a practical MIMO channel model is developed for the THz band that incorporates its molecular absorption and reflection losses, as well as its non-line-of-sight (NLoS) rays associated with its diffused components. Subsequently, a novel CSI estimation model is derived by exploiting the angular-sparsity of the THz MIMO channel. This is followed by designing a sophisticated Bayesian learning (BL)-based approach for efficient estimation of the sparse THz MIMO channel. The Bayesian Cramer-Rao Lower Bound (BCRLB) is also determined for benchmarking the performance of the CSI estimation techniques developed. Finally, an optimal hybrid transmit precoder and receiver combiner pair is designed, which directly relies on the beamspace domain CSI estimates and only requires limited feedback. Finally, simulation results are provided for quantifying the improved mean square error (MSE), spectral-efficiency (SE) and bit-error rate (BER) performance for transmission on practical THz MIMO channel obtained from the HIgh resolution TRANsmission (HITRAN)-database.

This paper presents low-complexity decision rules as well as the pertinent analysis for data fusion in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) wireless sensor networks (WSNs). The proposed framework considers both unknown and known parameter scenarios, and the spatial correlation arising due to close proximity of the sensors for both the centralized MIMO (C-MIMO) and distributed MIMO (D-MIMO) antenna configurations. The resulting detection performance is characterized by determining the closed-form expressions of probabilities of detection and false alarm for both antenna configurations. The optimal sensor gains are also determined for both the D-MIMO and C-MIMO architectures to further improve the detection performance. Additionally, asymptotic analysis is presented for both antenna configurations to determine the power scaling laws for the mmWave massive MIMO WSN, which lead to an improved sensor battery life without sacrificing the system performance. Furthermore, decision rules are also derived along with the pertinent analysis for a practical scenario with uncertainty in the channel state information (CSI) at the fusion center, wherein CSI of the mmWave massive MIMO channel is estimated using the novel sparse Bayesian learning (SBL) framework. Simulation results are presented to illustrate the performance of the proposed schemes and to validate the analytical results.

Novel hybrid beamformer designs are conceived for a multi-user multi-cell (MUMC) mmWave system relying on base station (BS) coordination and total transmit power minimization subject to realistic signal-to-interference-plus-noise ratio (SINR) constraints at each mobile station (MS). Initially, a semidefinite relaxation (SDR)-based approach is developed for a centralized MUMC system to determine the fully digital beamformer having perfect CSI. Subsequently, a Bayesian learning (BL) technique is harnessed for decomposing the fully-digital (FD) solution into its analog and digital components for constructing a hybrid transceiver. Next, an alternating direction method of multipliers (ADMM) based distributed hybrid beamformer is designed for the same system, which requires only local CSI and limited information exchange among the BSs, thus avoiding the excessive signalling overheads required by the centralized approach. Then we further extend both the centralized and the above distributed hybrid designs to construct robust beamformers that minimize the worst-case transmit power with imperfect CSI. Our robust beamforming techniques leverage the S-lemma, which is eminently suitable for the infinitely many constraints arising from the associated CSI uncertainty. Finally, our simulation results demonstrate the improved performance of the proposed centralized and distributed methods over the system having no coordination.

Sparse Bayesian learning (SBL)-based channel state information (CSI) estimation schemes are developed for filter bank multicarrier (FBMC) systems using offset quadrature amplitude modulation (OQAM). Initially, an SBL-based channel estimation scheme is designed for a frequency-selective quasi-static single-input single-output (SISO)-FBMC system, relying on the interference approximation method (IAM). The IAM technique, although has low complexity, is only suitable for channels exhibiting mild frequency-selectivity. Hence, an alternative time-domain (TD) model based sparse channel estimation framework is developed for highly frequency-selective channels. Subsequently, the Kalman filtering (KF)-based IAM and its TD counterpart are developed for sparse doubly-selective CSI estimation in SISO-FBMC systems. These schemes are also extended to FBMC-based multiple-input multiple-output (MIMO) systems, for both quasi-static and doubly-selective channels, after demonstrating the special block and group-sparse structures of the IAM and TD-based models respectively, which are the characteristic features of such channels. The Bayesian Cramér-Rao lower bounds (BCRLBs) and the time-recursive BCRLBs are derived for the proposed quasi-static as well as doubly-selective sparse CSI estimation models, respectively. Our numerical results closely match the analytical findings, demonstrating the enhanced performance of the proposed schemes over the existing techniques.

A sparse channel state information (CSI) estimation model is proposed for reducing the pilot overhead of orthogonal time frequency space (OTFS) modulation aided multiple-input multiple-output (MIMO) systems. Explicitly, the pilots are directly transmitted over the time-frequency (TF)-domain grid for estimating the delay-Doppler (DD)-domain CSI that leads to a reduction of the pilot overhead, training duration and pre-processing complexity. Furthermore, it completely avoids placing multiple DD-domain guard intervals corresponding to each transmit antenna within the same OTFS frame, while keeping the training duration flexible, hence increasing the bandwidth efficiency. A unique benefit of the proposed CSI estimation model is that it can efficiently handle fractional Dopplers also. The resultant DD-domain CSI becomes simultaneously row and group (RG)-sparse. To exploit this compelling property, an orthogonal matching pursuit (OMP)-based RG-OMP technique is developed, conveniently complemented by an enhanced Bayesian learning (BL)-based RG-BL framework, both of which substantially outperform the state-of-the-art methods. Furthermore, low-complexity linear detectors are designed for the ensuing data detection phase, which directly employ the estimated DD-domain sparse CSI, without assuming any further knowledge concerning the number of dominant multipath components. Finally, simulation results are provided to demonstrate performance improvement of the proposed BL-based schemes over the OMP and the state-of-the-art schemes.

Orthogonal time frequency space (OTFS) waveform based millimeter wave (mmWave) MIMO systems are capable of achieving high data rates in high-mobility scenarios. Hence, transceivers are designed for both analog beamforming (AB) and hybrid beamforming (HB), where we commence by deriving the delay-Doppler (DD)-domain input-output relationship considering a delay-Doppler-angular domain channel model. Subsequently, a novel two-stage procedure is developed for transmit beamformer (TBF)/ precoder (TPC) and receiver combiner (RC) design, and for estimating the DD-domain’s equivalent channel state information (CSI). The key feature of the proposed framework is that the RF TBF/ TPC and RC design maximizes the directional beamforming gains. It is also demonstrated that the low-dimensional baseband CSI of the DD-domain becomes sparse for mmWave-AB MIMO OTFS systems, and block-sparse for mmWave-HB MIMO OTFS systems. Subsequently, Bayesian learning (BL) and block-sparse BL (BS-BL) solutions are developed for improved CSI estimation. We also derive the Bayesian Cramer-Rao lower bounds (BCRLB) for benchmarking the mean-squared-error (MSE) of the CSI estimates. Finally, our simulation results demonstrate the improved efficacy of the proposed transceiver designs and confirm the enhanced CSI estimation performance of the BL-based schemes over other competing sparse signal recovery schemes.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relying on realistic imperfect channel estimates over the benchmarks.

Sparse, group-sparse and online channel estimation is conceived for millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We exploit the angular sparsity of the mmWave channel impulse response (CIR) to achieve improved estimation performance. First a sparse Bayesian learning (SBL)-based technique is developed for the estimation of each individual subcarrier's quasi-static channel, which leads to an improved performance versus complexity trade-off in comparison to conventional channel estimation. Then a novel group-sparse Bayesian learning (G-SBL) scheme is conceived for reducing the channel estimation mean square error (MSE). The salient aspect of our G-SBL technique is that it exploits the frequency-domain (FD) correlation of the channel's frequency response (CFR), while transmitting pilots on only a few subcarriers, thus it has a reduced pilot overhead. A low complexity (LC) version of G-SBL, termed LCG-SBL, is also developed that reduces the computational cost of the G-SBL significantly. Subsequently, an online G-SBL (O-SBL) variant is designed for the estimation of doubly-selective mmWave MIMO OFDM channels, which has low processing delay and exploits temporal correlation as well. This is followed by the design of a hybrid transmit precoder and receive combiner, which can operate directly on the estimated beamspace domain CFRs, together with a limited channel state information (CSI) feedback. Our simulation results confirms the accuracy of the analysis.

We design and analyse filter bank multicarrier (FBMC) offset quadrature amplitude modulation (OQAM)-based millimeter wave (mmWave) hybrid multiple-input multiple-output (MIMO) systems. Furthermore, a novel channel estimation model is conceived for quasi-static mmWave hybrid MIMO-FBMC-OQAM (mmH-MFO) systems that reconfigures the radio-frequency (RF) circuitry during the transmission of zero symbols. Subsequently, a Bayesian learning (BL) technique is proposed for sparse channel estimation, which relies on multiple measurement vectors combined with selective subcarrier grouping for enhanced estimation. Additionally, an online BL based Kalman filter (OBL-KF) is designed for sparse channel tracking in doubly-selective mmH-MFO systems. Then the Bayesian Cramér-Rao lower bounds (BCRLBs) are derived for characterizing the performance of the proposed frequency-selective and doubly-selective channel estimation techniques. Finally, a limited feedback based algorithm relying on beamspace channel estimates is proposed for hybrid precoder/combiner design. The accuracy of our analytical results is confirmed by our simulation results.

This paper designs a novel multiple measurement vector (MMV)-based sparse Bayesian learning (MSBL) technique for wideband channel estimation in single-carrier (SC) mmWave hybrid multiple input multiple output (MIMO) systems. The notable features of the proposed technique are that it leverages the simultaneous sparsity innate in the beamspace channel matrix across subcarriers, which has hitherto been unexplored by approaches that perform decoupled estimation of the individual sparse channel at each subcarrier. Furthermore, the framework developed also incorporates the effect of colored noise due to radio-frequency (RF)-combining, which has been ignored in other similar works. The realization of the frequency-domain (FD) simultaneous-sparse channel state information (CSI) acquisition model is rendered possible via the transmission of zero-padded (ZP) training blocks using a suitable choice of pilot symbols, followed by the overlap-and-sum processing module at the receiver. The Bayesian Cramér-Rao lower bound (BCRLB) is also derived to characterize the lower bound for the mean-squared-error (MSE) of channel estimation, which is achieved by a genie estimator with known channel support. Our simulation results demonstrate the enhanced performance of the proposed MMV-based MSBL approach over the conventional single measurement vector (SMV)-based SBL and the existing OMP techniques, which is also close to various benchmarks.

Semi-blind (SB) channel estimation is conceived for millimeter wave (mmWave) analog-beamforming (AB) and hybrid-beamforming (HB)-based multiple-input multiple-output (MIMO) systems, which also exploits the data symbols for improving the estimation accuracy. A novel aspect of the proposed framework is that it directly estimates the analog beamformer/ combiner weights without necessitating the estimation of the entire mmWave MIMO channel matrix. By involving powerful matrix perturbation theoretic techniques, a closed-form expression is derived for the mean-squared-error (MSE) of the mmWave-AB-SB algorithm. As a further novelty, our mmWave-HB-SB technique relies on the decomposition of the channel matrix as the product of a decorrelating and a unitary matrix. Subsequently, the former is estimated purely relying on the unknown data symbols, whereas the latter is estimated exclusively from the training vectors. A lower bound on the MSE of the proposed mmWave-HB-SB technique is derived using the constrained Cramér-Rao lower bound (CRLB) framework. Furthermore, the performance gain of our mmWave-HB-SB technique over the conventional purely training-based scheme is also quantified analytically. Our simulation results demonstrate the superiority of the techniques advocated over the existing solutions and also verify the accuracy of our analytical findings.

Hierarchical Bayesian Kalman filter (HBKF) based schemes are conceived for doubly-selective sparse channel estimation in orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless systems. Initially, a pilot based multiple measurement vector (MMV) model is formulated for estimating the OSTBC MIMO-OFDM channel. This is followed by the development of a low-complexity, online pilot-based HBKF (P-HBKF) scheme for tracking the sparse time-varying frequency-selective channel. The salient advantages of the proposed P-HBKF technique are that it requires significantly lower number of pilot subcarriers, while also exploiting the inherent sparsity of the wireless channel. Subsequently, data detection is also incorporated in the proposed framework, leading to the development of a procedure for joint sparse doubly-selective channel estimation and symbol detection. Recursive Bayesian Cramér-Rao bounds and closed form expressions are also obtained for the asymptotic mean square error (MSE) based on the solution of the Riccati equation for the KF for benchmarking the performance. Simulation results are presented for validating the theoretical bounds and for comparing the performance of the proposed and existing techniques.