Energy efficiency has become increasingly pivotal for sustainable wireless communications, driving the exploration of innovative technologies to enhance performance while minimizing energy consumption. Movable antenna (MA) technology emerges as a promising paradigm in this pursuit, introducing enhanced spatial degrees of freedom by dynamically adjusting antenna positions at the base station (BS). In this paper, we investigate the energy-efficient design problem for downlink communication systems, where the BS is equipped with MAs and serves multiple single-antenna users.We develop a comprehensive energy efficiency model that integrates the communication sum rate with the power consumption associated with both MA movements and signal transmissions. We aim to maximize the energy efficiency by jointly optimizing the transmit beamforming and antenna positions at the BS, subject to practical constraints including the transmit power budget, minimum inter-antenna distance, and maximum movement range. To address this non-convex problem, we propose an efficient alternating optimization algorithm that iteratively solves the beamforming and MA position optimization subproblems using successive convex approximation and particle swarm optimization methods, respectively. Extensive simulations show that the proposed MA-aided system achieves significantly higher energy efficiency than conventional fixed-position antenna systems and hybrid analog/digital array systems with the same number of radio frequency chains.

In recent years, physical layer security (PLS) techniques have been paid considerable attention due to its high-security level and strong compatibility. However, the request of the superior legitimate channel is the Achilles’ Heel of PLS. A significant challenge exists in ensuring information confidentiality when the eavesdropper locates at user’s direction in the multi-antenna system. To overcome this limitation, we propose a novel framework to achieve secure communication via distributed split single sideband (SSB) time modulated array (TMA). By strategically dividing the I/Q paths of the transmitted signals into geographically separated subarrays, we establish the non-aliasing zone to achieve error-free communication for legitimate user (LU), while the eavesdropper positioned in the aliasing zone receives irrecoverably disturbed waveform. To assess performance, we adopt the encoder-decoder-based deep neural network to optimize the time-switching sequence, ensuring the subarrays’ spatial radiation areas overlap exclusively at the LU. A specialized loss function is formulated to enhance the interference-to-signal ratio by increasing the −1stto the +1stharmonic power ratio in non-LU regions. Furthermore, the joint optimization improves security by focusing energy on the LU while generating interference in non-LU areas. The bit error rate (BER) is used as the metric, and the simulation results validate the effectiveness of the proposed method, ensuring reliable transmission and increasing Eve’s BER to approximately 0.5, thereby compromising her ability to intercept the communication.

For two-dimensional direction-of-arrival (2-D DOA) estimation, the uniform planar arrays (UPAs) can offer satisfactory estimation performance among various sensor array configurations, but is prone to be affected by the unknown mutual coupling effects. Existing 2-D DOA estimation algorithms accounting for the mutual coupling effects calibration either suffer from low estimation resolution or high computational complexity. To deal with this problem, we propose a tensor-based 2-D DOA estimation algorithm for UPAs in the presence of unknown mutual coupling. Specifically, by exploiting the block banded symmetric Toeplitz structure of the mutual coupling matrix, we construct a calibration matrix to relieve the mutual coupling effect. Then, the received signals are reformulated into a tensor format admitting the canonical polyadic decomposition, where the factor matrices incorporate the azimuth and elevation angles. By exploiting the inherent Vandermonde structure of the equivalent steering matrix, we develop an algebraic-based factor matrix estimation method without the necessity of iteration, followed by the azimuth and elevation angles extraction from the estimated factor matrices. In addition, the closed-form solutions of the mutual coupling coefficients are obtained based on the estimated angles. On this basis, we mathematically investigate the uniqueness condition of the tensor decomposition and the maximum number of resolvable targets. Moreover, we derive the Cramér-Rao bound to evaluate the performance limit for the considered 2-D DOA estimation problem with mutual coupling effects, and the computational complexity. Simulation results corroborate the superiority of the proposed tensor-based 2-D DOA estimation algorithm over competing methods in terms of complexity and resolution.

Movable Antenna (MA) technology is emerging as a promising advancement with the potential to significantly enhance the performance of future wireless communication and sensing systems. In this paper, we address two-dimensional (2D) direction of arrival (DOA) estimation via joint shape-position optimization. Specifically, we formulate an optimization problem aimed at minimizing the Cram´er-Rao Bound (CRB) based on a 2D DOA estimation model for MA systems. To tackle the highly non-convex nature of this CRB minimization, we investigate the spatial utilization of the movable region (MR) under minimum antenna spacing constraints. By demonstrating that an equilateral triangle yields the minimum overlap area, we strategically design an equilateral triangular MR. This specific geometric configuration enables the exploitation of structural symmetry to simplify the geometric constraints, which effectively reduces the complexity of solving the optimization problem. Subsequently, we derive the optimal MA positions by selecting the candidate locations farthest from the centroid of MR. The results demonstrate that the proposed joint shape-position optimization substantially enhances 2D DOA estimation performance.

Movable antenna (MA)-enabled multiple-input multiple-output (MIMO) systems offer a promising enhancement for integrated sensing and communication (ISAC) applications. Unlike conventional MIMO systems with fixed-position antenna (FPA) arrays, MAs can flexibly adjust their positions within a given region, enabling reconfiguration of both communication and sensing channels with additional spatial degrees of freedom. In this paper, we propose a unified mutual information (MI) framework for MA-enabled MIMO ISAC systems, where MI characterizes communication performance as reliably conveyable information and sensing performance as extractable target information in cluttered environments. We formulate an optimization problem to maximize the weighted sum of communication and sensing MI by jointly optimizing the transmit beamforming matrix under a transmit power constraint and the MA positions under practical constraints, with a weighting coefficient characterizing their trade-off. To tackle the non-convexity arising from the log-det objective, position constraints, and the nonlinear coupling between optimization variables, we develop an alternating optimization-based algorithm that iteratively updates the transmit beamforming matrix and the MA positions. Specifically, with the fixed MA positions, we optimize the beamforming by approximating the objective function using weighted mean square error and majorization-minimization methods, yielding a closed-form solution. Moreover, with fixed beamforming, the MA positions are sequentially refined by decomposing the position optimization into simpler subproblems, resulting in an efficient suboptimal solution. Numerical results show that the unified MI framework with MAs significantly outperforms conventional FPA systems in both communication and sensing. Channel amplitude heatmap visualizations further illustrate how MA positioning strategies exploit spatial flexibility in array geometry to enhance overall system performance.

Phased array (PA) has received considerable attention as a representative multiantenna technique due to its inherent advantages of superior directionality, spatial multiplexing capabilities, and robust anti-jamming characteristics. However, PA suffers from relatively high hardware complexity and power consumption. As a low-complexity array technology with excellent beamforming capability, time modulated array (TMA) has attracted much attention in recent years. In this article, we exploit a TMA for enhancing the Age of Information (AoI) of covert communication. Specifically, we first propose the transmitter structures and the corresponding beamforming methods for the TMA scheme and the PA scheme as a benchmark. Subsequently, the closed-form expressions of the Kullback-Leibler (KL) divergence is derived to serve as the quantitative measure of communication covertness under both schemes, based on which the average covert AoI (CAoI) is derived to jointly characterize the covertness and timeliness performance. Then, to minimize the average CAoI, the optimization problems of the block-length and beamforming parameters for both the TMA and PA schemes are formulated and solved. Finally, the numerical results are provided to show that the proposed TMA scheme surpasses the PA scheme in terms of both the convergence rate and the average CAoI.

Integrated sensing and massive multiple-input-multiple-output (MIMO) communication (mMIMO-ISAC) at terahertz (THz) bands can provide vast spatial degrees of freedom and abundant bandwidth resources. However, the employment of a massive number of antennas will pose prominent challenges to both target sensing and channel training in THz-mMIMO-ISAC. In this article, our goal is to integrate the target sensing functionality into the channel estimation stage and develop a channel-training-aided target sensing framework to facilitate the efficient resource sharing of THz-mMIMO-ISAC. Specifically, by exploiting the sparse characteristics of THz mMIMO channels, we build up the intrinsic connection between the channel parameters and the target parameters in angular, delay, and Doppler dimensions. Then, we propose a shared channel training pattern accommodating the hybrid architecture constraints of THz transceiver. Both the channel estimation and the target sensing can be formulated as two structured tensor decomposition problems and then concurrently addressed at the UE and BS sides, respectively. Next, we propose a tensor-based parameter estimation algorithm to acquire the target and channel parameters, where the associated angles of arrival/departure, time delays, Doppler shifts, and coefficients can be extracted from the estimated factor matrices. In addition, we present the detailed derivation of the Cramér-Rao bound (CRB) for the considered parameter estimation problem in THz-mMIMO-ISAC. Numerical results demonstrate that the proposed algorithm can achieve the target parameters estimation performance close to their corresponding CRB, and recover the high-dimensional THz mMIMO channels with substantially reduced training overhead.

Extremely large-scale multiple-input multiple-output (XL-MIMO) with orthogonal frequency division multiplexing (OFDM) transmission can provide unprecedented improvement in spectral efficiency and data rate. Dynamic metasurface antennas (DMAs) have been proposed as a cost-effective and power-efficient solution for realizing XL-MIMO systems. However, the extremely large number of antennas in XL-MIMO-OFDM with DMAs poses critical challenges in acquiring accurate channel state information. To address this issue, we propose in this paper a tensor-based channel estimation method for frequency-selective XL-MIMO-OFDM systems with DMAs. We first characterize the configurable property of DMAs and propose a microstrip-sequential channel training method with quasi-dynamically adjustable metamaterial elements, by representing the received frequency-domain training signals as a fourth-order tensor which admits the canonical polyadic decomposition. Then, by exploiting the sparsity of XL-MIMO channels, we propose a two-stage tensor decomposition-based channel estimation algorithm, where the four coupling factor matrices are obtained without the need of iterative refinement, and the channel multipath parameters can be extracted for reconstructing the entire high-dimensional channel matrix. In addition, we analyze the uniqueness condition for the proposed tensor-based channel estimation method, which reveals that the required channel training overhead is only proportional to the number of channel multipaths, instead of that of metamaterial elements and microstrips. Numerical results demonstrate the superior performance of our proposed design with significantly reduced training overhead as compared to various benchmark schemes.

In the cellular Internet of Things (CIoT), it is crucial to ensure the information freshness for status update applications. Considering the centralized access methods could cause large access delay and hamper timely status updates, this paper exploits the random access method and studies decentralized status update schemes to minimize the average age of information (AoI) for CIoT. However, due to the non-cooperation among machine type communication devices (MTCDs) in random access, packet collisions are inevitable, which makes it tricky to improve the AoI performance. In this regard, we design novel age-based status update schemes to control the transmission behavior of MTCDs, where the AoI at the MTCDs and the base station (BS) is used. We first model the AoI minimization problem as a Markov decision process. Then, through variable substitution and linear programming, we get a slightly more computationally complex status update scheme, where the dual threshold structure of the scheme is proved theoretically. To facilitate system design and reduce computational complexity, we further design a low-complexity scheme, where the age thresholds at both the MTCDs and BS are optimized. Simulation results verify that the proposed schemes significantly outperform the common access scheme.

Benefitting from the vast spatial degrees of freedom, the amalgamation of integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO) is expected to simultaneously improve spectral and energy efficiencies as well as the sensing capability. However, a large number of antennas deployed in massive MIMO-ISAC raises critical challenges in acquiring both accurate channel state information and target parameter information. To overcome these two challenges with a unified framework, we first analyze their underlying system models and then propose a novel tensor-based approach that addresses both the channel estimation and target sensing problems. Specifically, by parameterizing the high-dimensional communication channel exploiting a small number of physical parameters, we associate the channel state information with the sensing parameters of targets in terms of angular, delay, and Doppler dimensions. Then, we propose a shared training pattern adopting the same time-frequency resources such that both the channel estimation and target parameter estimation can be formulated as a canonical polyadic decomposition problem with a similar mathematical expression. On this basis, we first investigate the uniqueness condition of the tensor factorization and the maximum number of resolvable targets by utilizing the specific Vandermonde structure. Then, we develop a unified tensor-based algorithm to estimate the parameters including angles, time delays, Doppler shifts, and reflection/path coefficients of the targets/channels. In addition, we propose a segment-based shared training pattern to facilitate the channel and target parameter estimation for the case with significant beam squint effects. Simulation results verify our theoretical analysis and the superiority of the proposed unified algorithms in terms of estimation accuracy, sensing resolution, and training overhead reduction.

Integrated sensing and communications (ISAC), supported by massive multiple-input multiple-output (MIMO), can provide simultaneously improvement of sensing capability and communication capacity. However, employing the conventional fully digital beamforming architecture with a large-scale antenna array will incur the prohibitively high hardware cost and power consumption. In this paper, we propose a hybrid beamforming design with the overlapped subarrays (OSA)-based hybrid architecture for massive MIMO-ISAC systems. We design the analog and digital beamformers by jointly optimizing the spectral efficiency of communication and beampattern mean squared error of sensing under the specific constraints of OSA structures, power budget, and constant modulus. To tackle the resulting non-convex problem, we relax it as a weighted summation minimization problem, where the Euclidean distance between the designed hybrid beamformers and the optimal communication/desired sensing beamformers is minimized. We further decompose the formulated problem into three subproblems and develop an effective alternating minimization algorithm. Numerical simulations demonstrate the effectiveness and flexibility of the proposed OSA-based hybrid beamforming design in terms of spectral efficiency and sensing beampattern performance.

With the proliferation of marine activities, underwater Internet of Things (UIoT), which integrates various techniques for supporting smart ocean, has attracted more research interest. The trend is that one desires to use computationally efficient and widely applicable algorithms for source localization. For fulfilling the above requirements, this paper proposes a novel unitary quaternion (UQ) model, which is applied to widespread centro-symmetric arrays. The estimation and decomposition of the corresponding covariance matrix can be executed in the real number field, thus benefiting from low complexity. Moreover, we analyze the physical implication of the proposed model and associate it with the emerging quaternion-based attitude estimation and control, which reveals the potential advantages of the UQ model in UIoT. In the simulations, we test the algorithm performance in several realistic underwater scenarios, demonstrating the flexibility and applicability of the UQ model.

Massive multiple-input multiple-output (MIMO) integrated with millimeter-wave (mmWave) can provide unprecedented performance improvement for realizing future wireless communications. However, acquiring accurate channel state information in wideband mmWave massive MIMO systems with hybrid transceiver architectures is even challenging, especially in high-mobility scenarios with severe Doppler effects. In this paper, we propose a tensor decomposition-based method to estimate the time-varying and frequency-selective (TVFS) mmWave MIMO channels. Specifically, by exploiting the sparse scattering nature of TVFS channels, we model the frequency-domain received signal as a third-order tensor that admits a canonical polyadic (CP) decomposition format. Then, we analyze the uniqueness condition of the proposed CP decomposition-based channel estimation problem and propose a novel estimator to acquire TVFS channel parameters including angle of departure/arrival (AoD/AoA), time delay, path gain, and the Doppler shift. To address the sophisticated coupling among unknown parameters, we further propose a joint AoD and Doppler shift estimation (JADE) algorithm that provides reliable initial and iteratively refined estimates. The derived analysis and simulation results verify that the proposed JADE algorithm achieves higher estimation accuracy and guarantees the superiority of the proposed TVFS channel estimator over existing schemes.

Ultra-dense network (UDN) is emerging as a promising solution to meet the 1000-fold wireless traffic volume increment in wireless communication systems. In order to inspire system design and evaluate performance, this paper develops a tractable analysis framework of multi-antenna UDNs over Nakagami-m fading channels, in which the base stations (BSs) of each tier are distinguished by spatial densities, transmit powers and numbers of antennas. Resorting to stochastic geometry model, we derive the closed-form expression of coverage probability. The analytical expression reveals the signal-to-interference-plus-noise ratio (SINR) invariance property of UDNs with Rayleigh fading only holds in some special case of Nakagami-m fading scenario. In order to observe intuitively the effects of system parameters on coverage probability, the asymptotic results are also given, which are verified to be almost accurate when the SINR threshold is greater than 6 dB. The area spectral efficiency (ASE) is also provided. Furthermore, an effective algorithm is proposed to design the optimal active BSs densities, maximizing the ASE with appropriate requirements of coverage probability.

Ultra-dense network (UDN) is emerging as a promising technology to satisfy the explosive data traffic requirement in the fifth generation wireless communication systems. In order to facilitate system design and evaluate performance, this paper develops a tractable analysis framework of K-tier UDNs over Nakagami-m fading channels, in which the base stations (BSs) of each tier have a particular spatial density and transmit power. Using stochastic geometry, we derive the closed-form expression of coverage probability for a typical user. The analytical expression reveals the signal-to-interference-plus-noise ratio (SINR) invariance property of UDNs with Rayleigh fading also holds in Nakagami-m fading scenario when each tier has the same fading parameter. The asymptotic expression with a simple form is also provided, from which it is convenient to observe the effects of system parameters on the coverage probability. The simulation results verify the asymptotic form is very accurate for moderate SINR targets, e.g., above 5 dB. The average outage rate of a typical user is also provided. Furthermore, an effective algorithm is proposed to find the optimal SINR threshold, maximizing the average outage rate with appropriate requirements of coverage probability.

Phase noise (PN) introduced by the oscillator at the base station and user side severely degrades the channel estimation performance. This paper investigates the impact of PN on downlink compressive channel estimation in massive multiple-input multiple-output (MIMO) systems. Particularly, the downlink compressive channel estimation with PN is modeled as a sparse signal recovery problem with additive correlated perturbation on the pilot matrix, which is a general formulation for both non-synchronous and synchronous PN. Based on this signal model, the performance of the equivalent sensing matrix is analyzed by invoking restricted isometry property (RIP) in compressive sensing. In addition, the upper bound for $l_{1}$ -minimization based channel estimation method and tight channel estimation bound are derived in the framework of RIP and Oracle least square methodology, respectively. Finally, we propose a PN-aware sparse Bayesian learning (PNA-SBL) algorithm to improve the channel estimation performance in the presence of synchronous PN. Simulation results demonstrate our analysis and superiority of the proposed PNA-SBL algorithm.

Compared with ordinary linear antenna arrays or planar antenna arrays, space conformal antenna array has many advantages, such as the flexibility and accuracy of the beam. However, conventional algorithms cannot be applied to the designing of conformal antenna arrays, so the weighted minimum mean square error algorithm is proposed. In this paper, a new iterative phase correction algorithm is presented to improve the weighted minimum mean square error (MMSE) algorithm. By using the new algorithm, the shape of the beam can be controlled more flexibly, and more interferences can be resisted compared with the weighted minimum mean square error algorithm. The simulation results show an improved performance in beamforming.

Acquisition of accurate channel state information (CSI) at transmitters results in a huge pilot overhead in massive multiple input multiple output (MIMO) systems due to the large number of antennas in the base station (BS). To reduce the overwhelming pilot overhead in such systems, a structured joint channel estimation scheme employing compressed sensing (CS) theory is proposed. Specifically, the channel sparsity in the angular domain due to the practical scattering environment is analyzed, where common sparsity and individual sparsity structures among geographically neighboring users exist in multi-user massive MIMO systems. Then, by equipping each user with multiple antennas, the pilot overhead can be alleviated in the framework of CS and the channel estimation quality can be improved. Moreover, a structured joint matching pursuit (SJMP) algorithm at the BS is proposed to jointly estimate the channel of users with reduced pilot overhead. Furthermore, the probability upper bound of common support recovery and the upper bound of channel estimation quality using the proposed SJMP algorithm are derived. Simulation results demonstrate that the proposed SJMP algorithm can achieve a higher system performance than those of existing algorithms in terms of pilot overhead and achievable rate.

To improve physical (PHY) layer security of a wireless relay system in the presence of an eavesdropper, a two-phase cooperative relaying scheme is investigated in this paper. In phase I, the source transmits confidential message, simultaneously, it cooperates with the friendly jammers and destination to create jamming signal at the eavesdropper without affecting the forwarding relay which is preselected. In phase II, the forwarding relay retransmits the decoded signal, meanwhile, the particular relay cooperates with the friendly jammers to create jamming signal at the eavesdropper without affecting the destination. We focus on the investigation of optimal power allocation for maximizing achievable secrecy rate subject to a total power constraint. Optimal relay selection and suboptimal relay selection schemes are also proposed. It is shown that as the number of relays increases, both secrecy rate and the performance of suboptimal relay selection scheme improve significantly. Numerical results are presented to validate the derived analytical results and compare them to existing work.