In this paper, we investigate a covert communication system based on a hybrid active and passive reconfigurable intelligent surface (HAPRIS), where each RIS element can be dynamically configured to operate in either active or passive mode. By dynamically configuring the operational mode of each element, the system can effectively harness the high-gain benefits of the active RIS while simultaneously preserving the low power consumption and enhanced covertness properties offered by the passive RIS. Then, we formulate an energy efficiency maximization problem by jointly optimizing the active/passive mode selection vector, transmit beamforming vector and reflect coefficient matrix subject to the power, covertness and hardware constraints. To evaluate the detection performance of the warden, we further derive a tractable expression of the covertness constraint for the multi-antenna warden. To solve the mixed-integer non-convex problem, we propose a penalty dual decomposition (PDD) scheme utilizing the block coordinate descent method to decompose the original problem into several sub-problems, which are subsequently solved via the Lagrangian multiplier method and the interior-point method. In addition, we investigate a comparative scenario considering the position error of warden. Specifically, we first derive an expression for the estimation error of channel state information (CSI) based on the position error. We then propose a successive convex approximation method to obtain an upper bound on the CSI error, enabling us to formulate a worst-case covertness constraint. Finally, we extend the proposed PDD scheme to such a scenario with the CSI error. Simulation results demonstrate the effectiveness of the proposed schemes.

Simultaneous wireless information and power transfer (SWIPT) has emerged as a cornerstone technology for sustainable connectivity in sixth-generation (6G) space–air–ground integrated networks (SAGIN). This paper proposes a unified signal design framework that jointly supports radio-frequency (RF) coherent reception and noncoherent energy detection with colocated or separated deployments of information/energy receivers (IR/ER), thereby bridging RF and intensity-modulation/direct-detection (IM/DD) optical links. Guided by reliability, spectral efficiency, and harvested power metrics, we develop a generalized signal design framework based on a refined sphere-packing aimed at constructing high-dimensional symbols across space-time-frequency resources subject to symbol-level wireless power transfer constraints and an average power budget. The resulting nonconvex quadratically constrained quadratic program (QCQP) is efficiently solved using an alternating semidefinite programming–linear programming (ASDP–LP) method and an augmented Lagrangian dual-ascent (ALDA) algorithm. Analytical and simulation results confirm that the proposed approach achieves significant gains in communication-power trade-offs compared with conventional schemes, providing a foundation for sustainable RF–optical SWIPT in future 6G integrated networks.

Hybrid beamforming structure is widely used in mmWave massive MIMO due to the low hardware complexity. However, its performance is severely degraded by beam squint effects in wideband multiuser mmWave massive MIMO resulting from the non-frequency-specific analog beamforming. To overcome this issue, we develop an integrated user grouping, subcarrier allocation, and hybrid beamforming (IUSH) scheme to compensate for the beam squint effects and maximize the multiuser sum-rate. First, we investigate the time-division and frequency-division analog beamforming for the single radio frequency (RF) chain cases to gain useful insights regarding user grouping and subcarrier allocation. The frequency-division approach achieves superior performance by leveraging the correlations between analog beamforming and user channels, and utilizing subcarrier allocation to dynamically align them. To this end, for multiple RF chain cases, we propose a wideband user grouping strategy that clusters users with close physical channel angles to strengthen the correlations, thereby facilitating efficient subcarrier allocation among users. Then, we develop an alternating minimization-based joint subcarrier allocation and hybrid beamforming (AM-JSH) algorithm to maximize the sum-rate of grouped users. The AM-JSH algorithm alternates between subcarrier allocation and hybrid beamforming, where the subcarrier allocation is formulated as an assignment problem to be solved using the classic Hungarian algorithm, and the hybrid beamforming is implemented with the developed penalty-based two-loop hybrid beamforming algorithm. Simulation results show that the developed IUSH scheme significantly outperforms the existing ones.

In this paper, we propose a quantized penalty gradient (QPG) detection algorithm for massive multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs). To tackle the challenges of maximum likelihood (ML) detection under discrete constraints, we reformulate the detection problem into an unconstrained optimization by introducing two customized penalty functions that promote alignment between the estimated signals and target constellation set. Based on this, the QPG algorithm is developed to efficiently solve the resulting problem, achieving competitive detection performance with only second-order computational complexity. We further provide a theoretical analysis establishing the Lipschitz continuity of the objective function, which guarantees the monotonic descent property of QPG and ensures its convergence. Moreover, we prove that QPG efficiently finds the local minima with an accessible linear convergence rate, thus leading to an explicit trade-off between detection performance and computational complexity. Finally, simulation results confirm the significant performance gains of QPG over the conventional quantized detectors across various channel conditions, while maintaining low computational complexity.

Pinching antennas (PAs), a special class of leaky-wave antennas (LWAs), have recently emerged as a promising technology to mitigate blockage and reduce large-scale path loss. However, PAs suffer from performance limitations due to their passive radiation characteristics and mechanical actuation. To overcome these limitations, we introduce reconfigurable LWAs (RLWAs), which enable RLWA beamforming through electronic control of both radiation amplitudes and phases. By integrating RLWAs into the existing PA systems (PASS), we propose a hybrid PASS (H-PASS) architecture, which combines mechanically reconfigurable PA beamforming with electronically reconfigurable RLWA beamforming. Given that PAs in H-PASS can be deployed in discrete-position or continuous-position manners, H-PASS comes in two variants accordingly, and we formulate weighted sum-rate maximization problems for them, respectively. For the discrete-position case, we propose a penalty-based two-loop joint analog and digital beamforming algorithm. For the continuous-position case, we propose an alternating-minimization-based joint position optimization and beamforming algorithm. Simulation results demonstrate that H-PASS can increase the sum-rate of the existing PASS by up to 33%, reduce the performance loss caused by phase quantization in discrete-position PAs by up to 69%, and mitigate the performance loss caused by position errors in continuous-position PAs by up to 90%. Overall, H-PASS significantly improves the performance of existing PASS by leveraging the strengths of RLWAs while mitigating the limitations of PAs.

In this paper, we investigate near-field wideband channel estimation with block sparsity. First, we propose an on-grid total variation-regularized block sparse Bayesian learning (TV-BSBL) algorithm. By constructing sparse representations of near-field wideband channels, we show that the sparse coefficient vectors exhibit both common sparsity across subcarriers and block sparsity in the surrogate distance-angle domain. To promote common sparsity, a Gamma prior combined with subcarrier-adaptive factors is utilized. To encourage block sparsity, TV regularization is incorporated into the prior model. The channel estimation is formulated as a maximum a posteriori (MAP) problem and solved via an expectation-maximization (EM) algorithm. Then, in the M-step, we further propose a primal-dual hybrid gradient-based signal hyperparameter update algorithm, which admits simple primal and dual updates and guarantees convergence to the global optimum. Moreover, we propose an off-grid TV-BSBL algorithm for near-field wideband channel estimation. We introduce additional variables to characterize the deviations between the true channel parameters and their quantized grids. These deviation variables are then integrated into the MAP estimation framework and refined via gradient descent. Simulation results demonstrate that the proposed on-grid and off-grid TV-BSBL algorithms achieve superior estimation performance under various conditions.

For millimeter wave communications, beams used to transmit synchronization signal blocks (SSBs) affect both base station coverage and beam training overhead. We therefore consider fair SSB codebook design, formulated as an optimization problem, aiming to maximize the minimum average signal-to-interference-plus-noise ratio (SINR) across user clusters. This problem is challenging due to the non-smoothness of the objective function, arising from the optimal beam-pair selection function and the minimum operator. To address this, we propose a double-loop framework, where the outer loop constructs approximations for the selection function with iteratively reduced error, and the inner loop solves the resulting approximate problems. In each inner-loop iteration, the objective function of the approximate problem is smoothed with iteratively reduced smoothness, enabling gradient derivation. This gradient is then estimated using variance-reduced estimators based on samples from users, and the result is used to update codebooks. Following this framework, we develop both first-order (FO) and zeroth-order (ZO) oracle schemes. The FO scheme requires full channel state information samples for gradient estimation while the ZO scheme only requires SINR samples. Simulation results show that in given scenarios, both schemes achieve SINR fairness comparable to or better than that of discrete Fourier transform codebooks, but with fewer beams.

In this paper, we propose a tri-hybrid beamforming (THBF) architecture based on the radiation-center (RC) reconfigurable antenna array (RCRAA), including the digital beamforming, analog beamforming, and electromagnetic (EM) beamforming, where the EM beamformer design is modeled as RC selection. Aiming at spectral efficiency (SE) maximization subject to the hardware and power consumption constraints, we propose a tri-loop alternating optimization (TLAO) scheme for the THBF design, where the digital and analog beamformers are optimized based on the penalty dual decomposition in the inner and middle loops, and the RC selection is determined through the coordinate descent method in the outer loop. Aiming at energy-efficiency (EE) maximization, we develop a dual quadratic transform-based fractional programming (DQTFP) scheme, where the TLAO scheme is readily used for the THBF design. To reduce the computational complexity, we propose the Lagrange dual transform-based fractional programming (LDTFP) scheme, where each iteration has a closed-form solution. Simulation results demonstrate the great potential of the RCRAA in improving both SE and EE. Compared to the DQTFP scheme, the LDTFP scheme significantly reduces the computational complexity with only minor performance loss.

Energy efficiency (EE) is an important metric of both the communication and sensing systems, which has not been studied in the reconfigurable intelligent surface (RIS) assisted integrated sensing and communication (ISAC) system with partial blocked direct links. In this paper, we consider the EE optimization of the RIS assisted ISAC system with multiple users and targets in a new and common scenario where the direct links between the base station (BS) and targets are blocked. Through analyzing the expression of the EE and signal relation, the EE maximization is modeled as an optimization problem with the constraints of sensing mutual information, transmit power of the BS, and the reflecting coefficients restrict of the passive RIS. The problem can be solved by finding out the optimal beamforming matrix and RIS phase shift. As the problem is a complex non-convex optimization problem and optimization variables are coupled, an effective approximation algorithm based on the alternating optimization is proposed to maximize the EE of the communication part. The original problem is first decomposed into two subproblems. And then, by using the sequential convex approximation and Dinkelbach algorithm, these two subproblems are alternately solved, and the beamforming matrix and the RIS phase shift are alternately optimized accordingly. The simulation results show that the proposed algorithm can converge to the optimized value rapidly and significantly improve the EE performance.

This paper investigates the beamforming for the reconfigurable intelligent surface (RIS)-aided millimeter wave integrated sensing and communication system. We propose a fractional programming (FP) and alternating optimization-based hybrid beamforming (HBF) scheme. The weighted sum of the signal-to-clutter-and-noise-ratio at the radar receiver and the smallest signal-to-interference-plus-noise ratio among all communication users is maximized under the hardware constraints. Since it is difficult to directly obtain a solution for this non-convex FP problem, it is divided into three sub-problems that are alternately solved. Two sub-problems optimizing the digital transceiving beamforming at the base station (BS) are transformed into typical convex quadratic constraint quadratic programming ones using quadratic transformation. The other sub-problem optimizing the RIS passive beamforming is transformed into a manifold optimization one using Dinkelbach transformation. In addition, we consider the HBF structure at the BS through substituting the fully digital beamformer by the digital and analog ones. To reduce the computational complexity, a low-complexity HBF scheme based on Rayleigh quotient, zero-forcing and discrete Fourier transform codewords is proposed with closed-form expressions. Simulation results verify the effectiveness of two proposed schemes.

The hybrid beamforming structure is widely used in terahertz (THz) communications due to the low hardware complexity. However, its performance is severely degraded by beam squint effects in wideband THz communications resulting from the non-frequency-specific analog beamforming. To overcome this issue, in this paper, we investigate THz multiuser communications and propose a joint subcarrier allocation and hybrid beamforming (JSH) algorithm to compensate for the beam squint effects and maximize the sum-rate of users. The JSH algorithm alternates between subcarrier allocation and hybrid beamforming. Given the hybrid beamforming, the subcarrier allocation is formulated as an assignment problem and solved using the classic Hungarian algorithm. Given the subcarrier allocation, the hybrid beamforming is solved by developing a penalty-based two-loop hybrid beamforming algorithm. Simulation results show that the proposed JSH algorithm can effectively compensate for the beam squint effects and outperforms the existing ones in terms of the multiuser sum-rate.

Reconfigurable antenna arrays have advantages in increasing design degrees-of-freedom for future wireless communications. In this paper, we propose a tri-hybrid multipleinput multiple-output architecture based on a radiation-center reconfigurable antenna array (RCRAA). To maximize the sumrate of multiuser millimeter wave communications subject to the hardware and transmit power constraints, we propose a tri-loop alternating optimization scheme for tri-hybrid beamforming, including the digital beamforming, analog beamforming, and electromagnetic (EM) beamforming, where the EM beamformer design is modeled as a radiation-center selection problem. In the inner and middle loops, the analog and digital beamformers are optimized based on the alternating direction method of multipliers. In the outer loop, the optimal radiation-center selection are determined through a coordinate descent method. Simulation results verify the advantages of RCRAA in improving the sum-rate and enhancing the adaptability to complex channel conditions.

In millimeter wave communications, the initial access stage involves a trade-off between beam sweeping overhead and base station coverage. To balance this, we consider site-specific fair synchronization signal block codebook design, formulated as an optimization problem, aiming to maximize the minimum average signal-to-noise ratio (SNR) across user clusters, subject to constant modulus constraints. To solve this, we propose a double-loop framework, where the outer loop relaxes the original problem into sub-problems using an augmented Lagrangian (AL) algorithm, and the inner loop solves these sub-problems using a hybrid variance-reduced (HVR) stochastic gradient descent (SGD) algorithm. In each inner iteration, the non-smooth objective function of the sub-problem, comprising numerous user-wise SNR functions, is approximated by a differentiable function, with its gradient estimated using HVR estimators. The estimated gradient is then used to update the codebook. Simulation results demonstrate the efficiency of the proposed AL-HVR-SGD scheme.

We investigate hybrid beamforming design for covert millimeter wave multiple-input multiple-output systems with finite-resolution digital-to-analog converters (DACs), which impose practical hardware constraints not yet considered by the existing works and have negative impact on the covertness. Based on the additive quantization noise model, we derive the detection error probability of the warden considering finite-resolution DACs. Aiming at maximizing the sum covert rate (SCR) between the transmitter and legitimate users, we design hybrid beamformers subject to power and covertness constraints. To solve this nonconvex joint optimization problem, we propose an alternating optimization (AO) scheme based on fractional programming, quadratic transformation, and inner majorization-minimization methods to iteratively optimize the analog and digital beamformers. To reduce the computational complexity of the AO scheme, we propose a vector-space based heuristic (VSH) scheme to design the hybrid beamformer. We prove that as the number of antennas grows to be infinity, the SCR in the VSH scheme can approach the channel mutual information. Simulation results show that the AO and VSH schemes outperform the existing schemes and the VSH scheme can be used to obtain an initialization for the AO scheme to speed up its convergence.

For near-field multiuser communications based on hybrid beamforming (HBF) architectures, high-quality effective channel estimation is required to obtain the channel state information (CSI) for the design of the digital beamformer. To simplify the system reconfiguration and eliminate the pilot overhead required by effective channel estimation, we consider an analog-only beamforming (AoBF) architecture in this study. AoBF is designed to maximize the sum rate, it is transformed into a problem maximizing the power transmitted to the target user equipment (UE) and meanwhile minimizing the power leaked to the other UEs. To solve this problem, we use beam focusing and beam nulling and propose two AoBF schemes based on the majorization–minimization algorithm. First, the AoBF scheme based on perfect CSI is proposed, with the focus on beamforming performance and regardless of CSI acquisition. Then, the AoBF scheme based on imperfect CSI is proposed, where low-dimensional imperfect CSI is obtained by beam sweeping based on a near-field codebook. Simulation results demonstrate that the two AoBF schemes can approach HBF schemes in terms of the sum rate and outperform HBF schemes in terms of energy efficiency.

This paper proposes a dual-band reconfigurable antenna array (DBRAA), enabling wireless capabilities in both sub-6 GHz (sub-6G) and millimeter wave (mmWave) bands using a single array. For the sub-6G band, we propose a reconfigurable antenna selection structure, where each sub-6G antenna is formed by multiplexing several mmWave antennas, with its position dynamically adjusted using PIN diodes. For the mmWave band, we develop a reconfigurable hybrid beamforming structure that connects radio frequency chains to the antennas via phase shifters and a reconfigurable switch network. We then investigate integrated sensing and communications (ISAC) in sub-6G and mmWave bands using the proposed DBRAA and formulate a dual-band ISAC beamforming design problem. This problem aims at maximizing the mmWave communication sum-rate subject to the constraints of sub-6G communication quality of service and sensing beamforming gain requirements. The dual-band ISAC beamforming design is decoupled into sub-6G beamforming design and mmWave beamforming design. For the sub-6G beamforming design, we develop a fast search-based joint beamforming and antenna selection algorithm. For the mmWave beamforming design, we develop an alternating direction method of multipliers-based reconfigurable hybrid beamforming algorithm. Simulation results demonstrate the effectiveness of the proposed methods.

This paper investigates reconfigurable pixel antenna (RPA)-based electronic movable antennas (REMAs) for multiuser communications. First, we model each REMA as an antenna with a set of predefined and discrete selectable radiation positions within the radiating region. Considering the trade-off between performance and cost, we propose partially-connected and fully-connected RPA-based electronic movable-antenna arrays (PC/FC-REMAA). Then, we formulate a multiuser sum-rate maximization problem subject to the power and hardware constraints of the PC/FC-REMAA. To solve this problem, we propose a two-step multiuser beamforming and antenna selection scheme. In addition, we revisit mechanical movable antennas (MMAs) to establish a benchmark for evaluating the performance of REMA-enabled multiuser communications. Finally, we analyze the performance gap between REMAs and MMAs. Based on Fourier analysis, we derive the maximum power loss of REMAs compared to MMAs for any given position interval. Specifically, we show that REMAs lose at most 3.25% power relative to MMAs when the position interval is one-tenth of the wavelength. Simulation results demonstrate the effectiveness of the proposed methods.

In this paper, we investigate super-resolution angle estimation (SRAE) for reconfigurable intelligent surface (RIS)-aided mmWave communications. For the RIS-aided narrowband system, based on beam sweeping using a wide-beam codebook, we propose a two-step SRAE (TS-SRAE) scheme. In the first step, the selected optimal wide beam is refined to a narrow beam. In the second step, we develop an angle quantization error correction method. Then, for the RIS-aided wideband system, we propose an adaptive codebook design scheme, where the angle domain is divided into two regions, including the central region and the edge region, regarding the beam squint effect. Based on the beam sweeping using the adaptive codebook, we propose a two-region SRAE (TR-SRAE) scheme. In the central region, we extend the TS-SRAE scheme for angle estimation. In the edge region, we formulate the angle estimation as a maximum-a-posteriori problem, which is then solved by our developed Bayesian inference method. Simulation results demonstrate that both TS-SRAE and TR-SRAE schemes can effectively reduce the training overhead and improve the achievable rate.

In this paper, we investigate channel estimation and tracking for wideband millimeter wave (mmWave) satellite communications (SatComs) with reconfigurable intelligent surface (RIS). Different from the existing schemes that separately estimate the uplink channels from the user to the RIS and from the RIS to the satellite, we directly estimate the cascaded channel by proposing two schemes. In the first scheme with two stages, we power off different antennas in each stage and estimate the channels based on the estimating-signal-parameter-via-rotational-invariance-techniques (ESPRIT). In the second scheme based on the null space projection (NSP), we estimate the equivalent channel matrix through projecting the dictionary steering vectors to the null space of the received signal covariance matrices. The NSP-based scheme does not power off any antenna and needs only one stage. In addition, we propose a gradient descent (GD)-based channel tracking scheme for the moving user. We first obtain a rough estimation of the user channel based on geometry relationships and then make channel refinement using the GD. Simulation results show that the NSP-based scheme needs fewer pilots than the ESPRIT-based scheme but at the cost of some performance sacrifice. The GD-based channel tracking scheme outperforms the existing schemes.

In this paper, we propose the decentralized likelihood ascent search (DLAS)-aided detection for the distributed large-scale multiple-input multiple-output (MIMO) systems to achieve more remarkable performance gains. With the help of DLAS, traditional distributed iterative methods are able to achieve better performance than the linear detection schemes such as ZF and MMSE. According to analysis, we derive the equivalent noise and the post-processing SNR for DLAS. More importantly, based on them, we demonstrate that the proposed DLAS-aided detection achieves the full received diversity. To further facilitate its implementation in practice, we design the decentralized effective ring (DER) architecture with significantly reduced bandwidth requirement and better parallel computation. Finally, simulation results demonstrate that the proposed DLAS-aided detection attains the same received diversity as ML detection while surpassing state-of-the-art decentralized schemes in terms of BER performance, with reduced complexity and bandwidth costs.

For high-speed train (HST) millimeter wave (mmWave) communications, the use of narrow beams with small beam coverage needs frequent beam switching, while wider beams with small beam gain leads to weaker mmWave signal strength. In this paper, we consider beam switching based beam design, which is formulated as an optimization problem aiming to minimize the number of switched beams within a predetermined railway range subject to that the receiving signal-to-noise ratio (RSNR) at the HST is no lower than a predetermined threshold. To solve this problem, we propose two sequential beam design schemes, both including two alternately-performed stages. In the first stage, given an updated beam coverage according to the railway range, we transform the problem into a feasibility problem and further convert it into a min-max optimization problem by relaxing the RSNR constraints into a penalty of the objective function. In the second stage, we evaluate the feasibility of the beamformer obtained from solving the min-max problem and determine the beam coverage accordingly. Simulation results show that compared to the first scheme, the second scheme can achieve 96.20% reduction in computational complexity at the cost of only 0.0657% performance degradation.

We investigate hybrid beamforming design for covert multiple-input multiple-output communications with finite-resolution digital-to-analog converters (DACs), which im-pose practical hardware constraints not yet considered by the existing works and have negative impact on the covertness. Based on the additive quantization noise model, we derive the detection error probability of the warden considering finite-resolution DACs. Aiming at maximizing the sum covert rate (SCR) between the transmitter and legitimate users, we design hybrid beamformers subject to the power and covertness constraints. To solve this nonconvex joint optimization problem, we propose an alternating optimization (AO) scheme based on fractional programming, quadratic transformation, and inner majorization-minimization methods to iteratively optimize the analog and digital beamformers. Simulation results verify the performance gain provided by the proposed AO scheme.

In this paper, we propose a fractional programming (FP)-based alternating optimization scheme to jointly design the transceiver beamforming at the integrated sensing and communication (ISAC) base station (BS) and the passive beamforming at the reconfigurable intelligent surface (RIS) for the RIS-aided ISAC system. The weighted sum of the signal-to-clutter-and-noise-ratio at the radar receiver of the BS and the smallest signal-to-interference-plus-noise ratio among all the communication users is maximized under the hardware constraints. Since it is difficult to directly obtain a solution for this non-convex FP problem, it is divided into three sub-problems that are alternately solved. The two sub-problems optimizing the transceiving beamforming at the BS are transformed into typical convex quadratic constraint quadratic programming ones using quadratic transformation. The other sub-problem optimizing the RIS passive beamforming is transformed into a manifold optimization one using Dinkelbach transformation. Simulation results verify the effectiveness of the proposed scheme.

In this paper, we investigate beam training for multiuser millimeter wave massive MIMO. To reduce the training overhead, a super-resolution wide-beam training scheme including three stages is proposed. In the first stage, we perform beam sweeping based on a wide-beam codebook, where a multipath detection method based on extreme point detection is proposed to generate candidate wide-beam pairs for multiuser beam allocation. In the second stage, we propose a narrow-beam prediction method to refine the allocated wide-beam pair. In the third stage, a super-resolution angle estimation method which can break through the resolution limitation is proposed to further calibrate the channel angle-of-arrival and angle-of-departure of the predicted narrow-beam pair. Simulation results demonstrate that the proposed scheme can approach the performance of the existing beam sweeping with only a quarter of the training overhead.

This paper investigates an integrated sensing and communication (ISAC) system with reconfigurable intelligent surface (RIS). Our simultaneous beam training and target sensing (SBTTS) scheme enables the base station to perform beam training with the user terminals (UTs) and the RIS, and simultaneously to sense the targets. Based on our findings, the energy of the echoes from the RIS is accumulated in the angle-delay domain while that from the targets is accumulated in the Doppler-delay domain. The SBTTS scheme can distinguish the RIS from the targets with the mixed echoes from the RIS and the targets. Then we propose a positioning and array orientation estimation (PAOE) scheme for both the line-of-sight channels and the non-line-of-sight channels based on the beam training results of SBTTS by developing a low-complexity two-dimensional fast search algorithm. Based on the SBTTS and PAOE schemes, we further compute the angle-of-arrival and angle-of-departure for the channels between the RIS and the UTs by exploiting the geometry relationship to accomplish the beam alignment of the ISAC system. Simulation results verify the effectiveness of the proposed schemes.

This paper investigates beam training for extremely large-scale multiple-input multiple-output systems. By considering both the near field and far field, a triple-refined hybrid-field beam training scheme is proposed, where high-accuracy estimates of channel parameters are obtained through three steps of progressive beam refinement. First, the hybrid-field beam gain (HFBG)-based first refinement method is developed. Based on the analysis of the HFBG, the first-refinement codebook is designed and the beam training is performed accordingly to narrow down the potential region of the channel path. Then, the maximum likelihood (ML)-based and principle of stationary phase (PSP)-based second refinement methods are developed. By exploiting the measurements of the beam training, the ML is used to estimate the channel parameters. To avoid the high computational complexity of ML, closed-form estimates of the channel parameters are derived according to the PSP. Moreover, the Gaussian approximation (GA)-based third refinement method is developed. The hybrid-field neighboring search is first performed to identify the potential region of the main lobe of the channel steering vector. Afterwards, by applying the GA, a least-squares estimator is developed to obtain the high-accuracy channel parameter estimation. Simulation results verify the effectiveness of the proposed scheme.

In this paper, beam training and beam tracking are investigated for extremely large-scale multiple-input-multiple-output communication systems with partially-connected hybrid combining structures. Firstly, we propose a two-stage hybrid-field beam training scheme for both the near field and the far field. In the first stage, each subarray independently uses multiple far-field channel steering vectors to approximate near-field ones for analog combining. To find the codeword best fitting for the channel, digital combiners in the second stage are designed to combine the outputs of the analog combiners from the first stage. Then, based on the principle of stationary phase and the time-frequency duality, the expressions of subarray signals after analog combining are analytically derived and a beam refinement based on phase shifts of subarrays (BRPSS) scheme with closed-form solutions is proposed for high-resolution channel parameter estimation. Moreover, a low-complexity near-field beam tracking scheme is developed, where the kinematic model is adopted to characterize the channel variations and the extended Kalman filter is exploited for beam tracking. Simulation results verify the effectiveness of the proposed schemes.

Since hybrid beamforming (HBF) can approach the performance of fully-digital beamforming (FDBF) with much lower hardware complexity, we investigate the HBF design for beam-hopping (BH) low earth orbit (LEO) satellite communications (SatComs). Aiming at maximizing the sum-rate of totally illuminated beam positions during the whole BH period, we consider joint beamforming and illumination pattern design subject to the HBF constraints and sum-rate requirements. To address the non-convexity of the HBF constraints, we temporarily replace the HBF constraints with the FDBF constraints. Then we propose an FDBF and illumination pattern random search (FDBF-IPRS) scheme to optimize illumination patterns and fully-digital beamformers using constrained random search and fractional programming methods. To further reduce the computational complexity, we propose an FDBF and illumination pattern alternating optimization (FDBF-IPAO) scheme, where we relax the integer illumination pattern to continuous variables and after finishing all the iterations we quantize the continuous variables into integer ones. Based on the fully-digital beamformers designed by the FDBF-IPRS or FDBF-IPAO scheme, we propose an HBF alternating minimization algorithm to design the hybrid beamformers. Simulation results show that the proposed schemes can achieve satisfactory sum-rate performance for BH LEO SatComs.

Beam refinement is a key technology to overcome the problem of limited resolution in beam training. However, most existing works on beam refinement are not suitable for the emerging extremely large-scale multiple-input-multiple-output (XL-MIMO) due to the differences in the channel characteristics. To fill in the gap, in this paper, beam refinement for XL-MIMO systems is investigated. Inspired by the similarities between the Taylor series of the Gaussian function and that of the beam gain, we propose to approximate the beam gain by the Gaussian function. Then, a low-complexity beam refinement based on the Gaussian approximation (BRGA) scheme, which quantizes the narrowed intervals after beam training into several samples and performs additional channel tests on the quantized grids, is proposed to improve the estimation accuracy of the beam training. Based on the measurements in the beam refinement stage, the BRGA-based least square (BRGA-LS) estimator is developed for high-resolution channel parameter estimation. To avoid the noise amplification effects of the BRGA-LS, the BRGA-based weighted least square (BRGA-WLS) estimator is further developed. Simulation results verify the effectiveness of the proposed scheme and show that the proposed BRGA scheme can greatly improve the accuracy of beam training with only a few additional channel tests.

Millimeter wave (mmWave) communications can achieve high data-rate transmission for high-speed trains (HSTs). However, the rapid change in path loss during the fast movement of HSTs poses a significant challenge to the mm Wave beamforming design. In this paper, a two-stage beam-forming (TSB) scheme is proposed to address this challenge for downlink HST mmWave communications. In the first stage, an algorithm based on semi-definite relaxation (SDR) and alternating minimization (AM) is proposed to stabilize the instantaneous receive signal-to-noise ratio (SNR) above a predefined threshold when the HSTs travel along the railway. In the second stage, the coverage of each beam used by the base station (BS) is widened to reduce the number of beam switches. Simulation results demonstrate that the proposed scheme requires fewer BS beams to cover the same railway range than the existing schemes while keeping the instantaneous receive SNR of the HSTs above the predefined threshold.

Since the hybrid beamforming (HBF) can approach the performance of fully-digital beamforming (FDBF) with much lower hardware complexity, we investigate the HBF design for beam-hopping (BH) low earth orbit (LEO) satellite communications (SatComs). Aiming at maximizing the sum-rate of totally illuminated beam positions during the whole BH period, we consider joint beamforming and illumination pattern (BIP) design subject to the HBF constraints and sum-rate requirements. To address the nonconvexity of the HBF constraints, we temporarily replace the HBF constraints with the FDBF constraints. Then a joint FDBF and illumination pattern design scheme is proposed using random search and fractional programming (FP) methods. Based on the designed illumination patterns, we optimize the digital beamformers with the constrained analog beamformers by utilizing the FP methods, where a sum-rate maximization HBF scheme is proposed. Simulation results show that the proposed schemes can achieve satisfactory sum-rate performance for BH LEO SatComs.

In this paper, simultaneous beam training and target sensing for reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) systems is investigated. The sensing ability of base station (BS) is exploited to acquire the channel state information of the RIS-aided ISAC. Based on our findings that the energy of the echoes from the RIS can be accumulated in the angle-delay domain while the energy of the echoes from the targets can be accumulated in the Doppler-delay domain, we can distinguish the RIS from the targets. Then we propose a simultaneous beam training and target sensing scheme, which enables the BS to perform the beam training with the RIS and to sense the targets simultaneously based on the mixed echoes from the RIS and the targets, and also enables the user equipment (UE) to perform collaborative sensing to figure out their position. Moreover, the beam alignment between the BS and the UE via the RIS can be directly computed without additional beam training overhead. Simulation results verify the effectiveness of the proposed scheme and show that it outperforms the existing schemes with much smaller training overhead, which benefits from the integration of the sensing units.

In this paper, radar-aided multiuser beam tracking and target detection are investigated for integrated sensing and communication (ISAC). A multiuser beam tracking scheme based on the collaboration of radar sensing and uplink communication is proposed. It is first proved that the echoes of each communication signal can be extracted from the mixed echoes of multiple communication signals, by performing point-wise division and two-dimensional discrete Fourier transform. Based on it, the scheme enables the road side unit (RSU) to perform multiuser beam tracking and target detection with only two radio frequency chains, no matter how many users are served by the RSU. To distinguish the users from the targets and further improve the beam tracking by extended Kalman filtering, uplink pilots from the users to the RSU are employed. Then the digital beamformer can be designed to mitigate the multiuser interference. Simulation results show that the proposed scheme outperforms the conventional beam tracking scheme and can approach the performance of independent beam tracking of each user.

In this paper, we consider a cooperative mobile edge computing (MEC) network where both the user equipments (UEs) and the MEC server can help with the task computing. Multiple heterogeneous tasks of different sizes for each UE are separately offloaded to the nearby UEs and MEC server’s central processing unit and graphics processing unit for processing. Tasks of the same type are transmitted sequentially so that the waiting latency is required for offloading transmission and computation. We aim to minimize the maximum latency of UEs for processing all the tasks while ensuring that all tasks are successfully transmitted and processed. To solve the formulated non-convex problem, an iterative algorithm named directed mutation process based on discrete differential evolution is proposed. Simulation results are presented to verify the performance gain provided by the proposed algorithm.

Time-domain channel estimation for wideband millimeter wave (mmWave) MIMO OFDM systems is considered. To mitigate the overfitting of the existing time-domain channel estimation exploiting block sparsity (TDCEBS) scheme, we propose a block sparse channel estimation exploiting residual difference (BSCERD) scheme, where we first compute the difference of the residual power for every two adjacent iterations, and then determine a threshold to indicate the convergence of the iterations. Moreover, to improve the global optimality and reduce the time overhead of compressive sensing, a block sparse channel estimation based on deep learning (BSCEDL) scheme is proposed to determine the indices of the nonzero blocks simultaneously. We exploit the QuaDRiGa to assess the efficacy of the schemes proposed. Simulation results show that both BSCERD and BSCEDL outperform TDCEBS, while BSCEDL is better than BSCERD in performance and can achieve much lower time overhead.

Beam allocation is considered for wideband multiuser mmWave massive MIMO systems. By introducing the interference-free achievable rate, the analog precoder and the digital precoder is decoupled for the beam allocation problem. Then the beam allocation is treated as a multi-label classification problem and a deep learning-based beam allocation (DLBA) scheme is proposed, where a convolutional neural network is trained offline using the simulated environments to predict the beam allocation for all the users. In order to avoid the beam conflict and maximize the sum-rate, a rule to avoid the beam conflict is also proposed. Simulation results demonstrate that the DLBA scheme can substantially reduce the computational complexity with a marginal sacrifice of sum-rate performance, compared to the existing schemes.

We address the image retrieval problem for a wireless system including an edge server and an edge device. The query image is first compressed by the edge device, and then transmitted into wireless channel, while the edge server retrieves the received image. Different from conventional schemes directly compressing features via unsupervised learning regardless of the database semantic distribution, we design a deep semantic coding (DSC) scheme by integrating the inverted semantic index structure of the database into the coding process, which can utilize the prior semantic information of the database to reduce the bandwidth. We extract the feature vectors from the images via a convolutional neural network and generate the semantic guided code head, which is followed by the product quantization. The experimental results verify the effectiveness of the DSC scheme in reducing the bandwidth as well as improving the performance of wireless image retrieval.

In this paper we investigate the uplink collaborative sensing in the mmWave MIMO integrated sensing and communication system. Since the vehicles periodically transmit pilot sequences to the road side unit (RSU) and the pilot sequences are a priori knowledge of the RSU, the RSU can perform collaborative sensing and parameter estimation for the vehicles. A two-dimensional fast Fourier transform (FFT) and estimating-signal-parameter-via-rotational-invariance-techniques (ESPRIT)-based scheme is proposed for parameter estimation in the RSU, where the FFT is used to estimate the distance and relative radial velocity, and the ESPRIT is used to estimate the angle-of-arrival and angle-of-departure of the channel line-of-sight path. Then these estimated parameters are exploited by an extended Kalman filtering model to achieve the efficient beam tracking. Simulation results verify the effectiveness of the proposed scheme and show that it can save the estimation resources while ensuring the estimation accuracy.

A variable-phase-shifter (VPS) architecture with hybrid precoding for mixture use of phase shifters and switches, is proposed for millimeter wave massive multiple-input multiple-output communications. For the VPS architecture, a hybrid precoding design (HPD) scheme, called VPS-HPD, is proposed to optimize the phases according to the channel state information by alternately optimizing the analog precoder and digital precoder. To reduce the computational complexity of the VPS-HPD scheme, a low-complexity HPD scheme for the VPS architecture (VPS-LC-HPD) including alternating optimization in three stages is then proposed, where each stage has a closed-form solution and can be efficiently implemented. To reduce the hardware complexity introduced by the large number of switches, we consider a group-connected VPS architecture and propose a HPD scheme, where the HPD problem is divided into multiple independent subproblems with each subproblem flexibly solved by the VPS-HPD or VPS-LC-HPD scheme. Simulation results verify the effectiveness of the propose schemes and show that the proposed schemes can achieve satisfactory spectral efficiency performance with reduced computational complexity or hardware complexity.

Rather than considering only one legitimate user as in the existing works, we investigate multiple legitimate users served by Alice using multicast millimeter wave communications in this paper. Hybrid beamformers for the max-min fairness problem are designed to maximize the minimum covert rate between Alice and the legitimate users subject to the power constraint for confidential signal (CS) and the covertness constraint. In particular, the fully-digital beamformers for the CS and jamming signal are designed by temporarily neglecting the hardware constraints from the constant envelop for phase shifters and the limited number of RF chains, where a semi-definite programming-based method and a successive convex approximation (SCA)-based method are proposed. To approach the fully-digital beamformers, hybrid beamformers are designed subject to the hardware constraints, where an alternating minimization method is proposed to iteratively optimize the analog and digital beamformers. Simulation results show that the proposed methods can achieve better covert communication performance than the existing methods.

To reduce the number of phase shifters for analog precoding in millimeter wave massive multiple-input multiple-output communications, we investigate the hybrid use of expensive phase shifters and low-cost switches. Different from the existing fixed phase shifter (FPS) architecture where the phases are fixed and independent of the channel state information, we consider variable phase shifter (VPS) whose phases are variable and subject to the hardware constraint. Based on the VPS architecture, a hybrid precoding design (HPD) scheme named VPS-HPD is proposed to optimize the phases according to the channel state information. Specifically, we alternately optimize the analog precoder and the digital precoder, where the former is converted into several subproblems and each subproblem further includes the alternating optimization of the phase matrix and switch matrix. Simulation results show that the spectral efficiency of the VPS-HPD scheme is very close to that of the fully digital precoding, higher than that of the existing MO-AltMin scheme for the fully-connected architecture with much fewer phase shifters, and substantially higher than that of the existing FPS-AltMin scheme for the FPS architecture with the same number of phase shifters.

In this paper, a land mobile satellite (LMS) multiple-input multiple-output (MIMO) is considered, where two satellites simultaneously communicate with a mobile user terminal (UT). Spatial degree of freedom brought by the two satellites is introduced in the channel modeling, aside of other channel parameters including time correlation, shadowing, multipath fading and Doppler effect. Then an algorithm table using Markov multiple-state transition is provided to generate the LMS MIMO channels. Based on the modeled LMS MIMO channels, signal transmission between two satellites and the UT using space-time block coding is considered. Simulation results show that compared to the single satellite communications, the dual-satellite MIMO communications can achieve better bit error rate performance under the same signal-to-noise-ratio condition. In particular, the performance of dual-satellite single-polarization communications is slightly worse than that of single-satellite dual-polarization communications, since the spatial correlation is stronger than the polarization correlation.

We consider an mmWave satellite communication system with a reconfigurable intelligent surface (RIS) to enhance the signal coverage, where both the satellite and the served users are equipped with phased arrays. Different from the existing methods that separately estimate the uplink channel from the user to the RIS and that from the RIS to the satellite, we directly estimate the cascaded channel by proposing two schemes. In the first scheme with two stages, we power off the last antennas of the satellite, user and the RIS in the first stage and then transceive some pilot symbols, while in the second stage we power off the first antennas of the satellite, user and the RIS and then transceive the same pilot symbols. Then we perform the channel estimation based on the estimating-signal-parameter-via-rotational-invariance-techniques (ESPRIT) method. In the second scheme that does not power off any antenna and needs only one stage, we propose a null space projection (NSP) algorithm, where the equivalent channel matrix is estimated through projecting the dictionary steering vectors to the null space of the received signal covariance matrices. Simulation results show that the NSP scheme needs much fewer pilots and much lower hardware complexity than the ESPRIT scheme but with some sacrifice in channel estimation performance.

Different from the existing hierarchical beam training schemes which typically require a feedback in each layer of the codebook to indicate the best codeword for the base station (BS), beam training in this work only needs two feedbacks in total. The proposed beam training scheme includes two stages and requires only one feedback in each stage by using the designed hierarchical codebook. In the first stage, beam training for the top layer of our designed codebook is performed to narrow the search range of the channel angle of departure (AoD). In the second stage, based on the feedback information from the first stage, beam training for the other layers of our designed codebook is performed, where the BS can obtain an estimate of the channel AoD. Simulation results show that the performance of the proposed beam training scheme with limited feedback can approach that of time-division multiple access (TDMA) hierarchical beam training scheme with much fewer feedbacks.

Different from the existing predefined hierarchical codebook before the beam training, we design a computation-aided adaptive codebook and propose a beam training algorithm based on it. At each layer of the hierarchical codebook, we first estimate the channel angle of arrival (AOA) or angle of departure (AOD) according to the beam training results from the previous layers and then adaptively design a codeword in the current layer to align with the estimated AOA or AOD. Benefiting from the computation resources used for the adaptive codebook design and beam alignment, the proposed algorithm can improve the success rate of beam training as well as reducing the training overhead comparing with the existing algorithms. Simulation results verify the effectiveness of the proposed algorithm.

Channel estimation and hybrid precoding are considered for multi-user millimeter wave massive multi-input multi-output system. A deep learning compressed sensing (DLCS) channel estimation scheme is proposed. The channel estimation neural network for the DLCS scheme is trained offline using simulated environments to predict the beamspace channel amplitude. Then the channel is reconstructed based on the obtained indices of dominant beamspace channel entries. A deep learning quantized phase (DLQP) hybrid precoder design method is developed after channel estimation. The training hybrid precoding neural network for the DLQP method is obtained offline considering the approximate phase quantization. Then the deployment hybrid precoding neural network (DHPNN) is obtained by replacing the approximate phase quantization with ideal phase quantization and the output of the DHPNN is the analog precoding vector. Finally, the analog precoding matrix is obtained by stacking the analog precoding vectors and the digital precoding matrix is calculated by zero-forcing. Simulation results demonstrate that the DLCS channel estimation scheme outperforms the existing schemes in terms of the normalized mean-squared error and the spectral efficiency, while the DLQP hybrid precoder design method has better spectral efficiency performance than other methods with low phase shifter resolution.

In this paper, we develop two high-resolution channel estimation schemes based on the estimating signal parameters via the rotational invariance techniques (ESPRIT) method for frequency-selective millimeter wave (mmWave) massive MIMO systems. The first scheme is based on two-dimensional ESPRIT (TDE), which includes three stages of pilot transmission. This scheme first estimates the angles of arrival (AoA) and angles of departure (AoD) and then pairs the AoA and AoD. The other scheme reduces the pilot transmission from three stages to two stages and therefore reduces the pilot overhead. It is based on one-dimensional ESPRIT and minimum searching (EMS). It first estimates the AoD of each channel path and then searches the minimum from the identified mainlobe. To guarantee the robust channel estimation performance, we also develop a hybrid precoding and combining matrices design method so that the received signal power keeps almost the same for any AoA and AoD. Finally, we demonstrate that the proposed two schemes outperform the existing channel estimation schemes in terms of computational complexity and performance.

In this article, multiuser beam training based on hierarchical codebook for millimeter wave massive multi-input multi-output is investigated, where the base station (BS) simultaneously performs beam training with multiple user equipments (UEs). For the UEs, an alternative minimization method with a closed-form expression (AMCF) is proposed to design the hierarchical codebook under the constant modulus constraint. To speed up the convergence of the AMCF, an initialization method based on Zadoff-Chu sequence is proposed. For the BS, a simultaneous multiuser beam training scheme based on an adaptively designed hierarchical codebook is proposed, where the codewords in the current layer of the codebook are designed according to the beam training results of the previous layer. The codewords at the BS are designed with multiple mainlobes, each covering a spatial region for one or more UEs. Simulation results verify the effectiveness of the proposed hierarchical codebook design schemes and show that the proposed multiuser beam training scheme can approach the performance of the beam sweeping but with significantly reduced beam training overhead.

In this paper, a simultaneous multiuser hierarchical beam training scheme for multiuser mmWave massive MIMO systems is proposed based on the designed adaptive hierarchical codebook. Different from the existing work sequentially performing the beam training for different users with the same hierarchical codebook, in our work the hierarchical codebook is designed in an adaptive manner, where the codewords in the current layer are designed according to the beam training results of the previous layer. In particular, multi-mainlobe codewords are designed for simultaneously beam training with all the users, where each mainlobe of the multi-mainlobe codeword covers a spatial region that one or more users are probably in. Except for the bottom layer, there are only two codewords at each layer in the designed adaptive hierarchical codebook, which only requires two times of simultaneous beam training for all the users no matter how many users the BS serves. Simulation results verify the effectiveness of our scheme and show that our scheme can approach the performance of the beam scanning but with considerable reduction in training overhead.

Aiming at maximizing the sum-rate of multiuser multibeam satellite communications, user grouping algorithms are studied. Different users are divided into several groups, where the users in the same group are simultaneously served by the satellite via space division multiple access (SDMA) and different groups of users are served in different time slots via time division multiple access (TDMA). A sum-rate maximization user grouping (SMUG) algorithm is proposed. Given the number of total time slots, the SMUG algorithm sequentially selects users one by one from the candidate users to maximize the current sum-rate and to guarantee the increase of sum-rate in each time slot. Simulation results verify the effectiveness of our work and show that the proposed SMUG algorithm outperforms the existing algorithms.

Channel estimation for frequency-selective millimeter wave (mmWave) massive MIMO system is investigated. To overcome the frequency-selective fading, orthogonal frequency division multiplexing (OFDM) is employed. First, the channel structure of frequency-selective channel is analyzed to show that all the OFDM subcarriers share the same angles of arrival (AoA) and angles of departure (AoD). Then a two dimensional ESPRIT (TDE)-based channel estimation scheme is proposed, where the super-resolution estimation of AoA and AoD can be obtained by utilizing the rotation invariance of the channel steering vectors. Finally the AoA and AoD are paired to reconstruct the channel. Simulation results show that the proposed TDE-based channel estimation scheme outperforms the existing schemes at high SNR region.

In this paper multiuser beam allocation for millimeter wave (mmWave) massive MIMO systems is investigated, based on an improved hybrid precoding design framework. The framework includes two stages. In the first stage, an orthogonal pilot (OP) based beam training scheme is proposed, where all users can simultaneously perform the beam training with the base station (BS) and all the RF chains at the BS are fully utilized. In the second stage, a channel estimation method based on the results from the beam training is presented without transmitting any pilot sequences. Note that users close in geographical may share the same beam from the base station (BS) and cause the beam conflict. To mitigate the multiuser interference caused by beam conflicts, a quality of service (QoS) constrained beam allocation scheme is proposed, with the objective to maximize the equivalent channel gain for the users satisfying QoS constraints as well as maximizing the number of users satisfying QoS constraints on the premise of no beam conflict for all users. Simulation results verify the effectiveness of the proposed schemes and show that the QoS constrained beam allocation scheme can achieve higher spectral efficiency than existing schemes.

In this paper, we investigate the downlink transmission for cache-enabled fog radio access networks aiming at maximizing the delivery rate under the constraints of fronthaul capacity, maximum transmit power, and size of files. To reduce the delivery latency and the burden on fronthaul links and make full use of the local cache and baseband signal processing capabilities of enhanced remote radio heads (eRRHs), a two-level transmission scheme including cache-level and network-level transmission is proposed. In cache-level transmission, only requested files cached at the local cache are transmitted to the corresponding users. The duration of cache-level transmission is the delay caused by the transfer between the baseband unit (BBU) and eRRHs as well as the signal processing at the BBU. The remaining requested files are jointly transmitted to the corresponding users at network-level transmission. For cache-level transmission, a centralized optimization algorithm is first presented and then a decentralized optimization algorithm is provided to avoid the exchange of signaling among eRRHs. Meanwhile, another centralized optimization algorithm is presented to tackle the optimization problem for network-level transmission. All presented algorithms are proved to converge to the Karush-Kuhn-Tucker solutions of the problems. Numerical results are provided to validate the effectiveness of the proposed transmission scheme as well as evaluating the system performance.

We investigate beam training and allocation for multiuser millimeter wave massive MIMO systems. An orthogonal pilot-based beam training scheme is first developed to reduce the number of training times, where all users can simultaneously perform the beam training with the base station (BS). As the number of users increase, the same beam from the BS may point to different users, leading to beam conflict and multiuser interference. Therefore, a quality-of-service (QoS) constrained (QC) beam allocation scheme is proposed to maximize the equivalent channel gain of the QoS-satisfied users, under the premise that the number of the QoS-satisfied users without beam conflict is maximized. To reduce the overhead of beam training, two partial beam training schemes, an interlaced scanning (IS)-, and a selection probability (SP)-based schemes, are proposed. The overhead of beam training for the IS-based scheme can be reduced by nearly half, while the overhead for the SP-based scheme is flexible. The simulation results show that the QC-based beam allocation scheme can effectively mitigate the interference caused by the beam conflict and significantly improve the spectral efficiency, while the IS-based and SP-based schemes significantly reduce the overhead of beam training at the cost of sacrificing spectral efficiency, a little.

In this paper, beam design for millimeter wave (mmWave) massive MIMO systems is studied regarding quantized phase shifters and different number of RF chains. Given the objective beam, the beam design problem is formulated as a hybrid optimization problem involving continuous variables as well as discrete variables. To reduce the difficulty in solving this problem, it is converted into several discrete optimization subproblems. Then beam design methods are proposed for the system with only one RF chain and two RF chains, respectively. For the general system with more than two RF chains, the parameter estimation is incorporated into the random search. Based on these findings, a partial random search (PRS) based beam design algorithm is proposed. To further improve the convergence speed, a fast search (FS) based beam design algorithm is proposed. Simulation results verify the effectiveness of the proposed algorithms and show that the beam pattern using the proposed PRS and FS based algorithm can well approach the objective beam with much less RF chains than OMP.

Beamspace channel estimation for millimeter wave (mmWave) massive MIMO system is investigated. An identity matrix approximation (IA)-based beamspace channel estimation scheme is proposed, including the design of hybrid precoding and combining matrix as well as searching the largest entry of over- sampled beamspace receiving matrix. The design of hybrid combining and hybrid precoding is formulated as two optimization problems. By decoupling the design of analog combining and digital combining, closed-form solutions are obtained. Then an algorithm based on bisection search is proposed to search the largest entry of the over-sampled beamspace receiving matrix. Additionally, computational complexity is compared between the proposed scheme and the existing channel estimation schemes. Simulation results show that the proposed IA-based beamspace channel estimation scheme outperforms the existing schemes.

Deep clipping is beneficial for the optical orthogonal frequency division multiplexing (O‐OFDM) system, since it can lower the peak‐to‐average power ratio, reduce the direct current requirement in light emitting diodes (LEDs), and relax the bit‐resolution requirement in digital‐to‐analogue converters (DACs). However, it is accompanied by more signal distortions. In this study, a deep clipping noise mitigation scheme using iterative shrinkage/thresholding algorithm (ISTA) with three steps is proposed to improve bit error rate (BER) performance of the LED‐based DCO‐OFDM systems. In the first step, the estimated observation interference is eliminated from the received symbols to minimise the negative effect of channel noise. In the second step, two strategies are presented to generate the specified observations thus reduce the component of measurement noise in the whole observation vector. In the last step, combining the generalised cross validation and the estimation of observation interference, the appropriate regularisation parameter are calculated for ISTA to improve the robustness of the sparse recovery performance. They use simulations to show that the proposed scheme can correct the deep clipping noise with favourable reconstruction quality, which significantly improves the BER performance and therefore assist the LED non‐linearity mitigation.

In massive MIMO systems, different wireless channels starting from the same user antenna to different base station (BS) antennas usually share a common channel support. In this paper, Bayesian channel estimation is studied to jointly recover uplink channels sharing common support in massive MIMO systems. Since wireless channel is usually modeled as a mixed Bernoulli-Gaussian random process, it is employed as a prior knowledge for Bayesian estimation. A group Bayesian sparse channel estimation algorithm is proposed by enhancing the posterior probability of common support after jointly processing the received signal at BS. To reduce the computational complexity of Bayesian estimation, the genuine support set of uplink channels is approximated by a main support set. Moreover, the estimation of channel sparsity is also derived. Simulation results show that the proposed group Bayesian algorithm performs much better than the existing sparse recovery algorithms.

Analog beamforming at transmitter and analog combining at receiver can be designed based on a hierarchical codebook, which consists of a small number of low-resolution codewords covering wide angle at top level and a large number of high-resolution codewords offering high directional beamforming gain at bottom level. Although high- resolution codewords are preferred, it takes more time for channel training. In this paper, weighted sum-rate maximization for millimeter wave (mmWave) massive MIMO communications is investigated by jointly considering the duration for channel training and the receiving signal-to-noise ratio (SNR). An algorithm is proposed to design the analog beamforming and analog combining based on the hierarchical codebook. At each iteration, the channel gain of the dominant path is estimated. The level of the hierarchical codebook achieving the weighted sum-rate maximization is predicted and then fed back to the transmitter. If the predicted level is reached, the transmitter and the receiver stop channel training and begin data transmission using the designed analog beamforming and analog combining. Simulation results show that the proposed algorithm outperforms multi-sectional search, where the former can achieve the weighted sum-rate almost twice of the latter at certain length of transmission block when the channel SNR is 20dB.

The selection of nonzero taps for sparse linear equalizer under the criterion of minimum mean square error (MMSE) is investigated. In some applications such as underwater acoustic communications, the computational resource in terms of the number of nonzero channel taps is given in existing channel equalizers. In this context, the joint determination of positions and weights of nonzero taps of sparse equalizer is considered and then formulated as a subset selection problem. A fast algorithm that uses two levels of loops is proposed to iteratively update each entry of the subset. The computational complexity of the proposed algorithm is analyzed. To make the work comprehensive, the sparse equalizer design where the number of nonzero taps is not given is also investigated. Simulation results show that around 60% equalizer taps can be saved with no more than 1dB of performance loss. Moreover, compared to the OMP algorithm, the proposed algorithm can save 33% equalizer taps achieving the same bit error rate (BER) of 0.001.

This paper studies joint beamforming and power allocation for multicell multiuser multi‐antenna systems with the objective of maximising the minimum signal‐to‐interference‐plus‐noise ratio (max–min SINR). The authors first consider developing an iterative algorithm to achieve the optimal performance by extending the uplink–downlink duality for finite‐scale wireless communication systems. The solution is then generalised to achieve the asymptotically optimal multicell beamforming with the aim to reduce the overhead of signalling exchange between coordinated base stations based on large dimension random matrix theory. Based on that, an efficient multicell beamforming algorithm is proposed to asymptotically achieve the max–min SINR. To further solve the complexity issue of large dimensional matrix inversion involved in the calculation of beamforming vectors, they propose a low‐complexity beamforming calculator based on truncated polynomial expansion approach. Numerical results validate the effectiveness of the authors’ proposed algorithms and show that they can achieve the optimal or asymptotically optimal performance in a massive multi‐input multi‐output system with low complexity and small backhaul overhead.

The sparse channel estimation which sufficiently exploits the inherent sparsity of wireless channels, is capable of improving the channel estimation performance with less pilot overhead. To reduce the pilot overhead in massive MIMO systems, sparse channel estimation exploring the joint channel sparsity is first proposed, where the channel estimation is modeled as a joint sparse recovery problem. Then the block coherence of MIMO channels is analyzed for the proposed model, which shows that as the number of antennas at the base station grows, the probability of joint recovery of the positions of nonzero channel entries will increase. Furthermore, an improved algorithm named block optimized orthogonal matching pursuit (BOOMP) is also proposed to obtain an accurate channel estimate for the model. Simulation results verify our analysis and show that the proposed scheme exploring joint channel sparsity substantially outperforms the existing methods using individual sparse channel estimation.

In this paper, a wavelet-based underwater acoustic (UWA) communication system is proposed. The convolutional structure of the UWA channel is exploited and the pilot assisted channel estimation is formulated as a sparse recovery problem. Then the restricted isometry property (RIP) of the measurement matrix is investigated via eigenvalue analysis and Gersgorin circle theorem. It's proved that the sparse recovery of the wavelet-based UWA channel satisfies the RIP. With the above setup, comparisons of channel estimation for OFDM-based and wavelet-based UWA communication systems are deployed. Simulation results show that the wavelet-based system achieves more accurate channel estimation performance than the OFDM-based system under the same conditions of bandwidth, duration, data rate and channel profile.

Underwater acoustic (UWA) channel is typically sparse. In this paper, a complex Homotopy algorithm is presented and then applied for UWA OFDM channel estimation. Two enhancements that exploit UWA channel temporal correlation for the compressed-sensing(CS)-based channel estimators are proposed. The first one is based on a first-order Gauss-Markov (GM) model which uses the previous channel estimate to assist current one. The other is to use the recursive least-squares (RLS) algorithm together with the CS algorithms to track the time-varying UWA channel. Simulation results show that the Homotopy algorithm offers faster and more accurate UWA channel estimation performance than other sparse recovery methods, and the proposed enhancements offer further performance improvement.

Due to multipath delay spread and relatively high sampling rate in OFDM systems, the channel estimation is formulated as a sparse recovery problem, where a hybrid compressed sensing algorithm as subspace orthogonal matching pursuit (SOMP) is proposed. SOMP first identifies the channel sparsity and then iteratively refines the sparse recovery result, which essentially combines the advantages of orthogonal matching pursuit (OMP) and subspace pursuit (SP). Since SOMP still belongs to greedy algorithms, its computational complexity is in the same order as OMP. With frequency orthogonal random pilot placement, the technique is also ex tend to MIMO OFDM systems. Simulation results based on 3GPP spatial channel model (SCM) demonstrate that SOMP performs better than OMP, SP and interpolated least square (LS) in terms of normalized mean square error (NMSE).

In order to reduce the pilot number and improve the spectral efficiency, recently emerged compressed sensing (CS) technique is applied for digital broadcast channel estimation. According to the six channel profiles of the ETSI digital radio mondiale (DRM) standard, the subspace pursuit (SP) algorithm is employed for the delay spread and attenuation estimation of each path in the case where the channel profile is identified and the multipath number is known beforehand. The stop condition for SP is that the estimated sparsity equals the multipath number. For the case where the multipath number is unknown, the orthogonal matching pursuit (OMP) algorithm is employed for channel estimation, while the stop condition is that the estimation satisfies the level of the noise variance. Simulation results show that with the same number of pilots, CS algorithms with randomly placed pilots outperform traditional cubic-spline-interpolation-based least square (LS) channel estimation. SP is also demonstrated to be better than OMP when the multipath number is known as a priori.

Compressed sensing (CS) has recently been applied for pilot-aided sparse channel estimation. However, the design of the pilot placement has not been considered. In this letter, we propose a scheme using the modified discrete stochastic approximation to optimize the pilot placement in OFDM systems. The channel data is employed to offline search the near-optimal pilot placement before the transmission. Meanwhile we also get a criterion to select CS algorithms based on the mean squared error (MSE) minimization. Simulations using a sparse wireless channel model have validated the effectiveness of the proposed scheme, which is demonstrated to be much faster convergent and more efficient than the exhaustive search. It has been shown that substantial performance improvement can be achieved for OMP and YALL1 based channel estimation, where YALL1 is preferred.