Movable antenna (MA) has been recognized as a promising technology to enhance communication network performance by adjusting the antenna position within a confined region. In this paper, we consider an energy-efficient MA-enabled multiple-input multiple-output (MIMO) network with the hybrid analog-digital transceiver, where energy consumption induced by the MA movement is additionally considered to accurately evaluate the system energy efficiency (EE) performance. Under both fully-connected and partially-connected transceiver structures, we aim to maximize the system EE by jointly optimizing the hybrid beamformers and antenna positions, subject to the unit-modulus constraints and the minimum MA distance constraints. To tackle these two highly non-convex problems effectively, we propose an efficient two-layer successive convex approximation (SCA) based iterative algorithm, where we aim to iteratively update the achievable EE in the outer layer and alternately optimize the hybrid beamformers and antenna positions in the inner layer. Furthermore, considering the asymptotically low-SNR and high-SNR regimes, we respectively develop two low-complexity algorithms by leveraging the structural properties of their corresponding optimal fully-digital beamformers. Simulation results validate the superior EE performance and low-complexity advantage of our proposed algorithms over the existing benchmark schemes.

The evolution of communication systems shows a trend toward multifunctional integration, thus the joint design of training sequence and precoder for multifunctional purposes is of great significance. In this paper, we investigate the joint optimization of training sequence and precoder matrices for dual-functional multiple-input multiple-output (MIMO) systems under per-antenna power constraints, which considers the performance metrics of channel estimation, data transmission and target estimation simultaneously. A general fusion framework under per-antenna power constraints is established, where multiple linear constraints are transformed into a single weighted-sum constraint, and a modified subgradient algorithm is proposed to address it. Then, based on the fusion of positive semi-definite matrix-valued signal-to-noise ratios (SNRs), training sequence is optimized to strike a trade-off between channel estimation accuracy and sensing performance, and the optimal pilot based on the fusion structure is derived. The proposed algorithm solves mean square error minimization and mutual entropy maximization problems, achieving a balance between system performance and algorithm complexity. Based on the optimized training sequence, channel estimation error model is derived, and the corresponding precoder matrix is designed, which takes into account the performance of both data transmission and target estimation. Finally, numerical results are provided for demonstrating the performance of the proposed algorithms.

In contrast to conventional fixed-position antennas (FPAs), movable antennas (MAs) are capable of actively exploiting the spatial channel variations to enhance the performance of wireless systems. In this paper, we investigate a movable antenna (MA) aided integrated sensing and covert communication (ISACC) system, where the MA movable regions are quantized into practical discrete positions. We aim to maximize the covert sum rate by jointly optimizing the BS transmit beamformers, the positions of both BS- and user-side MAs, and the radar receive equalizer, subject to constraints on radar echo signal-to-clutter-plus-noise ratio (SCNR) and covertness. To effectively tackle this problem, an efficient successive convex approximation (SCA) based alternating optimization (AO) algorithm is proposed, where the complicated log-fractional objective function is handled by fractional programming (FP) technique, and the discrete MA position variables are optimized by employing the penalty strategy. To obtain useful insights, we then focus on a simple single-user single-target (SUST) scenario, and demonstrate that the optimal Tx MA positions aim to de-correlate the BS-target and BS-Willie channels, whereas the optimal Tx MA positions can be flexibly chosen. Furthermore, we extend our work into the practical imperfect CSI scenario, in which a conservative approximation of the covertness constraint is derived, based on which the proposed AO algorithm is still applicable after some slight modifications. Numerical results demonstrate the superior performance of our proposed algorithms under both perfect CSI and imperfect CSI.

Target encirclement by heterogeneous swarms composed of uncrewed aerial vehicles (UAVs) and uncrewed ground vehicles (UGVs) represents a significant application in multi-agent cooperative operations. With the unified kinematic model for the air-ground heterogeneous multi-agent system (HMAS) established, a finite-time distributed target observer (FTDTO) is first developed to address the issue that not all individuals in the swarm can obtain complete target information. An extended state observer (ESO) is then designed to simultaneously estimate both the agent’s own state and external disturbances, effectively handling uncertainties arising from sensor measurement noise and nonlinear model dynamics. Furthermore, considering the inherent communication challenges and bandwidth limitations in complex air-ground cooperative networks, a dynamic event-triggered mechanism (DETM) is employed. Based on this DETM, an HMAS encirclement control law is developed with adaptive radius contraction capability to prevent target escape. Theoretical analysis demonstrates the stability of the proposed ESO, FTDTO, and control law, and shows that Zeno behavior can be avoided. Simulation experiments are conducted to compare the proposed method with existing approaches, verifying the effectiveness of the proposed method and the target tracking capability with adaptive encirclement formation.

Reconfigurable intelligent surface (RIS) has emerged as a promising technology for greatly enhancing communication performance of future wireless networks. To overcome the multiplicative fading effect of passive RIS and high energy consumption of active RIS, we propose a novel dynamic subarray-based hybrid active-passive RIS (HRIS) architecture by dividing all reflecting elements into multiple sub-RISs, each of which can flexibly switch between active and passive modes. Therefore, the proposed subarray-based HRIS is anticipated to achieve optimal system performance with minimal cost and energy consumption. In this paper, we aim to maximize the energy efficiency (EE) for the subarray-based HRIS assisted multi-user multiple-input single-output (MISO) system, where the transmit beamforming vectors at the base station (BS), the mode switching matrix, and the reflection matrices of active and passive sub-RISs are jointly optimized subject to individual user rate constraints. To tackle this intractable problem, we firstly explore the feasible region of the minimum rate threshold among all users, and then develop an efficient two-layer successive convex approximation (SCA) based iterative algorithm. Considering a simplified single-user scenario, we also derive some interesting insights into the optimal active-passive sub-RISs allocation for maximizing EE. It is revealed that for a small BS transmit power, deploying more active sub-RISs in the subarray-based HRIS is preferred to attain the maximum EE. Conversely, under a high BS transmit power and a small HRIS reflection power, more sub-RISs should be switched to the passive mode. Numerical simulation results verify the superior EE performance of the proposed dynamic subarray-based HRIS over the traditional active and passive RISs.

In this paper, we propose a general energy efficiency (EE) optimization framework for the hybrid analog-digital transceivers design in multi-hop communication systems. The analog and digital beamforming matrices are jointly optimized considering two kinds of practical power constraint models, i.e., sum power with box eigenvalue constraints (SPBECs) and multiple weighted power constraints (MWPCs), and unit-modulus constraints on analog beamforming matrices. For both the SPBECs and MWPCs cases, to tackle the challenging problem involving highly-coupled variables, an effective decoupling approach is first proposed. Specifically, a set of auxiliary variables are introduced to equivalently transform the original problem into a decoupled form with respect to the variables of each node. Then, for each node, we propose an efficient two-stage analog and digital beamforming optimization algorithm. To be specific, we optimize the analog beamforming matrices in the first stage by jointly exploiting the matrix-monotonic optimization framework and channel-alignment strategy. Then, we optimize the digital beamforming matrices in the second stage based on the multi-node water-filling methodology. Furthermore, in order to compute the parameters involved in the multi-node water-filling solutions for the SPBECs case, we propose two novel strategies, i.e., the Dinkelbach based strategy and the per-node penalty based strategy, which derive the parameters in closed-forms and offer clear physical interpretations. Moreover, the per-node penalty based strategy is effectively extended to the MWPCs case by additionally employing the Lagrangian duality theory. Simulation results demonstrate the superior performance and high efficiency of our proposed algorithms.

Movable antenna (MA) has emerged as a promising technology for enhancing communication performance over conventional fixed position antenna (FPA) by exploiting spatial channel variations. In this paper, we propose a general energy efficiency (EE) optimization framework for the MA-aided multi-user multiple-input multiple-output (MU-MIMO) downlink communications. We jointly optimize the precoding matrices and the positions of transmit and receive MAs considering two different types of power constraint models, i.e., the sum power constraint (SPC) and multiple weighted power constraints (MWPCs), and various physical constraints on MA positions. In both the SPC case and the MWPCs case, we optimize the MA positions by jointly employing the weighted minimum mean square error (WMMSE) and successive convex approximation (SCA) methodologies. As for the precoding matrices optimization, by exploiting the uplink-downlink duality of MU-MIMO systems, we transform the downlink EE optimization into their virtual uplink EE optimization counterparts. Then, we derive the optimal structures of the precoding matrices, where the involved optimal power allocations take the multi-user water-filling solutions. To compute the parameters of the multi-user water-filling solutions, by taking advantage of the underlying algebraic monotonicity of the problem, we propose three novel design strategies, i.e., the direct Dinkelbach based design, the modified Dinkelbach based design, and the bound-ware penalty based design. In contrast to conventional fractional programming (FP) based EE optimization methods, the proposed algorithms offer significantly lower computational complexities and explicit physical insights. Moreover, the simulation results demonstrate the superior performance and high efficiency of our proposed EE optimization algorithms.

Reconfigurable intelligent surface (RIS) assisted cell-free multiple-input multiple-output (MIMO) systems have emerged as a promising paradigm for future wireless communications. To overcome the multiplicative fading effect inherent in the passive RIS, a novel active RIS equipped with reflection-type power amplifiers has been proposed, which however is confronted with high hardware cost and power consumption under the fully-connected architecture. To address this issue, we consider a cost-and power-efficient sub-connected active RIS assisted cell-free system in this paper, where the whole active RIS is divided into multiple sub-RISs, each being connected to a dedicated power amplifier. We aim to maximize the system sum rate under imperfect channel state information (CSI) by jointly optimizing the AP transmit beamforming matrices and the RIS reflection coefficient matrix. Since the traditional centralized beamforming scheme may lead to a high computational burden at the central processing unit (CPU), we propose a two-stage distributed iterative algorithm to efficiently find high-quality suboptimal solutions. Specifically, in stage 1, users apply the classical weighted minimum mean-square error (WMMSE) method to optimize their local variables in parallel. Then in stage 2, APs optimize their respective transmit beamforming matrices, the RIS reflection phase shift vector and the RIS reflection amplification vector sequentially. The corresponding semi-closed-form optimal solutions are available by jointly leveraging the Lagrange duality theory, majorization minimization (MM) and symmetric alternating direction method of multiplier (S-ADMM) techniques. Moreover, we develop a simplified distributed algorithm to further reduce system communication overhead. Numerical results demonstrate that the two proposed distributed algorithms can achieve comparable sum rate performance to the centralized scheme while attaining lower computational overhead.

Energy efficiency (EE) optimization has attracted significant research attention for implementing green communications. With cost-effective and low-power advantages, intelligent reflecting surface (IRS) and hybrid analog-digital transceiver have recently emerged as two promising technologies of next-generation green wireless systems. In this paper, we propose a comprehensive framework for EE optimization in four types of IRS-aided hybrid analog-digital multiuser multiple-input multiple-output communication systems, including the uplink (UL) systems under the sum power and box eigenvalue constraints as well as the per-radio-frequency chain power constraints (PRPCs), and the downlink (DL) systems under the sum power constraint and the PRPCs. This framework proposes a unified design methodology to these four considered systems by separating the optimization of analog and digital matrix variables. Specifically, for the UL EE maximization problems, we firstly propose a channel alignment based algorithm to separately optimize the analog precoders at users, the analog combiner at the base station and the IRS reflecting matrix, whose computational complexity is significantly reduced as compared with the traditional alternating optimization algorithm. Then, by introducing the auxiliary variables and exploiting the Karush-Kuhn-Tucker conditions based algorithm, the optimal digital precoders at users are obtained in closed forms. Furthermore, the intractable DL EE optimization can be equivalently transformed into its virtual UL counterpart using the DL-UL duality, leading to the general applicability of the proposed framework. Extensive simulations reveal that the proposed algorithm attains the almost identical EE performance to the traditional benchmarks with a lower computational complexity.

This paper investigates joint device identification, channel estimation, and symbol detection for cooperative multi-satellite-enhanced random access, where orthogonal time-frequency space modulation with the large antenna array is utilized to combat the dynamics of the terrestrial-satellite links (TSLs). We introduce the generalized complex exponential basis expansion model to parameterize TSLs, thereby reducing the pilot overhead. By exploiting the block sparsity of the TSLs in the angular domain, a message passing algorithm is designed for initial channel estimation. Subsequently, we examine two cooperative modes to leverage the spatial diversity within satellite constellations: the centralized mode, where computations are performed at a high-power central server, and the distributed mode, where computations are offloaded to edge satellites with minimal signaling overhead. Specifically, in the centralized mode, device identification is achieved by aggregating backhaul information from edge satellites, and channel estimation and symbol detection are jointly enhanced through a structured approximate expectation propagation (AEP) algorithm. In the distributed mode, edge satellites share channel information and exchange soft information about data symbols, leading to a distributed version of AEP. The introduced basis expansion model for TSLs enables the efficient implementation of both centralized and distributed algorithms via fast Fourier transform. Simulation results demonstrate that proposed schemes significantly outperform conventional algorithms in terms of the activity error rate, the normalized mean squared error, and the symbol error rate. Notably, the distributed mode achieves performance comparable to the centralized mode with only two exchanges of soft information about data symbols within the constellation.

Reconfigurable intelligent surface (RIS) has gained much attention as a cost-effective solution to enhance connectivity and coverage in massive machine-type communication. However, the passive nature of RIS poses fundamental challenges to decoupling and estimating base station (BS)-RIS and RIS-device channels, as well as identifying active devices. To effectively tackle this issue, we cast the joint channel estimation and activity detection for RIS-assisted Internet-of-Things networks as a tensor-based two-layer problem by exploiting the channel sparsity and a multi-frame pilot training structure. The first layer involves the Canonical Polyadic (CP) decomposition of a third-order tensor observation, while the second layer addresses compressive sensing (CS)-based simple measurement vector (SMV) and multiple measurement vector (MMV) problems. Then, by leveraging the Bayesian inference framework, we propose a tensor-based approximate message passing (TAMP) algorithm to estimate one-hop BS-RIS channel, one-hop RIS-device channels, and active IoT devices simultaneously. Furthermore, we conduct the state evolution (SE) analysis of TAMP to theoretically characterize its MSE. Numerical results corroborate the superior estimation and detection performance of TAMP and demonstrate that our SE analysis perfectly predicts the actual MSE.

Reconfigurable intelligent surface (RIS) has recently emerged as a promising solution to significantly enhance the security of wireless communication systems. By combining the advantages of the conventional fully-active and fully-passive RISs, a novel hybrid active-passive RIS has been anticipated to achieve the excellent communication performance at a low cost. In this paper, we aim to maximize the secrecy rate in a hybrid active-passive RIS assisted multi-input single-output multi-antenna Eve (MISOME) system, where both fixed and dynamic hybrid RIS architectures are considered. To tackle this intractable problem, we jointly optimize the transmit covariance matrix at the base station (BS), the reflection matrices of active and passive sub-RISs, as well as the element allocation matrix for the dynamic hybrid RIS. Specifically, we firstly explore the rank-1 structure of the optimal BS transmit covariance matrix. Then, for the fixed hybrid RIS, we develop an efficient two-loop successive convex approximation (SCA) based iterative algorithm, where the optimal semi-closed-form solution to each subproblem can be obtained. For the dynamic RIS, this proposed algorithm is still applicable by relaxing the binary active/passive elements allocation variables into exponent-based continuous ones. Simulation results validate the superior secrecy performance of the proposed designs over the existing fully-active and fully-passive RIS designs. Moreover, it is demonstrated that the dynamic hybrid RIS is able to strike a good balance between the passive beamforming gain and the power amplification gain to adapt to the varying propagation environment.

Holographic metasurface antenna (HMA) has been envisioned as a new antenna paradigm anticipated to realize massive multiple-input multiple-output (MIMO) capability with greatly reduced hardware cost and power consumption. In this paper, we develop a framework for the energy efficiency (EE) optimization in the HMA-assisted uplink (UL) multiuser MIMO (MU-MIMO) system. We consider two types of power constraints, namely, the sum power and box eigenvalue constraints (SPBECs) and the multiple weighted power constraints (MWPCs). In this framework, we firstly formulate a general EE maximization problem subject to SPBECs and propose a novel EE-oriented water-filling algorithm by jointly exploring the quasi-concave property of the EE function and introducing an actual power consumption factor. Based on this, we then develop a low-complexity two-stage algorithm to separately optimize the HMA weighting matrix and the transmit covariance matrix. Specifically, in the first stage, two different algorithms, i.e., the channel alignment based algorithm and the weighted minimum mean square error (WMMSE) based algorithm, are proposed to optimize the HMA weighting matrix. In the second stage, we apply the proposed novel EE-oriented water-filling algorithm to optimize the transmit covariance matrix by respectively introducing per-user and all-user power consumption factors. Moreover, this two-stage algorithm is applicable to the EE optimization under MWPCs by leveraging duality theory to integrate multiple power constraints into a single one. Finally, numerical simulations validate that the proposed algorithms can achieve comparable EE performance to traditional benchmark schemes with significantly reduced computational complexities.

Future mobile networks are projected to support integrated sensing and communications in high-speed communication scenarios. Nevertheless, large Doppler shifts induced by time-varying channels may cause severe inter-carrier interference (ICI). Frequency domain shows the potential of reducing ISAC complexity as compared with other domains. However, parameter mismatching issue still exists for such sensing. In this paper, we develop a novel sensing scheme based on sparse Bayesian framework, where the delay and Doppler estimation problem in time-varying channels is formulated as a 3D multiple measurement-sparse signal recovery (MM-SSR) problem. We then propose a novel two-layer variational Bayesian inference (VBI) method to decompose the 3D MM-SSR problem into two layers and estimate the Doppler in the first layer and the delay in the second layer alternatively. Subsequently, as is benefited from newly unveiled signal construction, a simplified two-stage multiple signal classification (MUSIC)-based VBI method is proposed, where the delay and the Doppler are estimated by MUSIC and VBI, respectively. Additionally, the Cramér-Rao bound (CRB) of the considered sensing parameters is derived to characterize the lower bound for the proposed estimators. Corroborated by extensive simulation results, our proposed method can achieve improved mean square error (MSE) than its conventional counterparts and is robust against the target number and target speed, thereby validating its wide applicability and advantages over prior arts.

Integrated sensing and communication (ISAC) has been envisioned as a prospective technology to enable ubiquitous sensing and communications in next-generation wireless networks. In contrast to existing works on reconfigurable intelligent surface (RIS) aided ISAC systems using conventional phased arrays (PAs), this paper investigates a frequency diverse array (FDA)-enabled RIS-aided ISAC system, where the FDA aims to provide a distance-angle-dependent beampattern to effectively suppress the clutter, and RIS is employed to establish high-quality links between the BS and users/target. We aim to maximize sum rate by jointly optimizing the BS transmit beamforming vectors, the covariance matrix of the dedicated radar signal, the RIS phase shift matrix, the FDA frequency offsets and the radar receive equalizer, while guaranteeing the required signal-to-clutter-plus-noise ratio (SCNR) of the radar echo signal. To tackle this challenging problem, we first theoretically prove that the dedicated radar signal is unnecessary for enhancing target sensing performance, based on which the original problem is much simplified. Then, we turn our attention to the single-user single-target (SUST) scenario to demonstrate that the FDA-RIS-aided ISAC system always achieves a higher SCNR than its PA-RIS-aided counterpart. Moreover, it is revealed that the SCNR increment exhibits linear growth with the BS transmit power and the number of BS receive antennas. In order to effectively solve this simplified problem, we leverage the fractional programming (FP) theory and subsequently develop an efficient alternating optimization (AO) algorithm based on symmetric alternating direction method of multipliers (SADMM) and successive convex approximation (SCA) techniques. Numerical results demonstrate the superior performance of our proposed algorithm in terms of sum rate and radar SCNR.

Integrated sensing and communication (ISAC) technology effectively enables spectrum and hardware sharing between radar and communication. This paper investigates the dual-functional (DF) constant modulus waveform design for simultaneously transmitting and reconfigurable intelligent surface (STAR-RIS)-aided ISAC, in which the channel information can be used as semantic information. To investigate the performance trade-off, the weighted sum of multi-user interference (MUI) energy and waveform discrepancies is minimized via jointly optimizing the transmit waveform and the reflection and transmission coefficient matrices at STAR-RIS. Furthermore, a practical case of coupled phase shifts at STARRIS is investigated. We first formulate the optimization problem as a Markov decision process, employing a twin delayed deep deterministic policy gradient (TD3)-based deep reinforcement learning approach to address it. Simulation results verify the effectiveness of the proposed scheme.

We study a semi-passive intelligent reflecting surface (IRS) enabled ISAC, where IRS is employed to assist the secure communication and perform target sensing. Specifically, we model two types of targets, namely point targets and extended targets. The direction-of-arrival (DoA) of the former and the complete target response matrix of the latter should be estimated. We derive the Cramér-Rao bound (CRB) as the performance metric of target estimation. To achieve the performance tradeoff, we design a weighted optimization problem that balances maximizing the secrecy rate and minimizing the CRB, via jointly optimizing the transmit beamforming and phase shifts of IRS. Then, we employ the alternating optimization, successive convex approximation and semi-definite relaxation to tackle the non-convex problems for the two target cases. Simulation results show the effectiveness of the proposed schemes.

In this article, we investigate the analog–digital hybrid transceiver optimization for multiple-input–multiple-output (MIMO) Internet of Things (IoT) systems, aiming at maximizing the sum rate of multiple IoT devices in downlink communications. We first derive the downlink–uplink duality for the MIMO communications with analog–digital hybrid structures. Based on this, the intractable MIMO downlink sum-rate maximization is equivalently transferred into an easier-to-handle virtual uplink counterpart. In order to solve the nonconvex virtual uplink problem effectively, we resort to decouple the involved digital and analog matrix variables. On the one hand, we propose two kinds of algorithms for the analog matrices optimizations, namely, the joint design and the separate design. Specifically, the joint design optimizes the analog precoder and equalizer matrices in an alternating manner. In each iteration, an element-wise optimization algorithm is utilized to optimize the analog matrix variables under constant modulus constraints. For the separate design, the analog precoder and equalizer matrices are optimized separately via the elaborately designed space alignments with lower computational complexities. On the other hand, the digital precoders can be computed with fixed analog matrix variables, in which a modified iterative water-filling algorithm is proposed. Finally, numerical results demonstrate the superior performance advantages of the proposed algorithms over several benchmark algorithms.

The simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has been a promising enabler for the future wireless network due to its full-space coverage capability. In this article, we investigate the STAR-RIS assisted hybrid mmWave multiple-input-multiple-output system, where the two practical operating protocols, i.e., energy splitting (ES) and mode switching (MS), and the coupled transmission and reflection (T&R) phase-shift model for the STAR-RIS are considered. For each operating protocol, we aim to maximize the system weighted sum rate (WSR) by jointly optimizing the passive T&R coefficients at the STAR-RIS and the hybrid analog-digital precoder/combiners, subject to the discrete phase shift constraints. Specifically, we propose an efficient weighted minimum mean-square error based alternating optimization (AO) algorithm to address this highly coupled nonconvex problem. By leveraging the special ordered set of type 1 under the MS protocol, the optimization of both the discrete T&R coefficients and analog precoder/combiners can be equivalently transformed into the standard binary quadratic programming, which can be effectively solved by the mathematical programming with the equilibrium constraints-based exact penalty algorithm. The proposed penalty-based AO algorithm is also applicable to the WSR maximization under the ES protocol. In addition, to avoid high-complexity iterative process wherever possible, we develop a separate analog-digital beamforming scheme, where a fast projection-based gradient descent algorithm is applied to successively optimize discrete T&R coefficients and analog precoder/combiners to maximize the effective channel gain, and then the optimal digital precoder/combiners are obtained in semi-closed forms. Numerical simulation results demonstrate the superior WSR performance and complexity advantage of the proposed algorithms over the existing benchmark schemes.

Reconfigurable intelligent surface (RIS) has evolved into a promising approach to significantly improve both spectral and energy efficiencies of wireless communications. Different from the traditional fully-passive and fully-active RISs, a novel hybrid RIS composed of both active and passive reflecting elements has recently emerged, which can leverage their combined advantages to effectively mitigate the RIS-induced multiplicative path loss. In this paper, we investigate a hybrid active-passive RIS assisted wireless system from a rate-maximization perspective. Specifically, we firstly consider the multi-antenna multi-user system and aim to maximize the system weighted sum rate (WSR) by jointly optimizing the transmit precoding matrices and the active-passive RIS reflection matrix. The optimal semi-closed-form solution to each subproblem is obtained by jointly exploring the activeness of constraints and leveraging the majorization-minimization (MM) technique. To gain more useful insights into the rate maximization, we also study the special single-antenna single-user scenario, in which it is revealed that both the optimal transmit beamsteering direction and the optimal phase shifts at the hybrid RIS are independent of actual reflection amplitudes of the hybrid RIS. Numerical results demonstrate the lower complexity and superior rate performance of our proposed algorithms as compared to the existing schemes adopting the fully-passive RIS. Moreover, it is revealed that the hybrid RIS can strike a flexible balance between the square-order beamforming gain of the fully-passive RIS and the power amplification gain of the fully-active RIS by adjusting the active/passive element allocation.

Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including diagonal structure constraints and constant modulus constraints, both of which are closely related to the state-of-the-art wireless applications. Specifically, for diagonal structure constraints mostly considered in the uplink multi-user single-input multiple-output (MU-SIMO) system and the amplitude-adjustable intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system, the capacity maximization problem, the mean-squared error (MSE) minimization problem and their variants are rigorously investigated. By leveraging complex matrix derivatives, the optimal solutions of these problems are directly obtained in closed forms. Nevertheless, for constant modulus constraints with the intrinsic nature of element-wise decomposability, which are often seen in the hybrid analog-digital MIMO system and the fully-passive IRS-aided MIMO system, we firstly explore inherent structures of the element-wise phase derivatives associated with different optimization problems. Then, we propose a novel alternating optimization (AO) algorithm with the aid of several arbitrary feasible solutions, which avoids the complicated matrix inversion and matrix factorization involved in conventional element-wise iterative algorithms. Numerical simulations reveal that the proposed algorithm can dramatically reduce the computational complexity without loss of system performance.

Extremely large-scale multiple-input multiple-output (XL-MIMO) communications and ultra-high frequency bands are both potential enablers for satisfying extreme performance requirements of future wireless systems. Thanks to low hardware cost and power consumption, holographic metasurface antennas (HMAs) operating at high frequencies have recently emerged as an effective realization of large-scale antenna arrays, leading to greatly enlarged near-field region. In this paper, we investigate a power-efficient HMA-based near-field downlink multiuser system, where three different HMA-based arrays are considered. Specifically, we aim to minimize the total transmit power for each HMA-based array while maintaining the signal to interference plus noise ratio (SINR) constraint of each user by jointly optimizing the digital transmit precoder and the analog HMA weighting matrix. In the special single-user scenario, we validate that the original optimization problem can be decomposed into several independent subproblems each corresponding to a single HMA microstrip, whose optimal solution can be obtained by the successive convex approximation (SCA) based method. It is also revealed that the HMA-based array is capable of achieving near-field beam focusing. In the general multiuser scenario, we develop an efficient SCA-alternating direction method of multipliers (ADMM) based alternating optimization (AO) algorithm to tackle the intractable optimization problem, where the digital precoders and the HMA weighting matrix are iteratively optimized in an alternating manner. Numerical results demonstrate the superior performance of our proposed algorithms over existing benchmark schemes. It is also shown that the HMA-based array attains lower hardware overhead and power consumption as compared to the conventional hybrid array.

Aiming at providing wireless communication systems with environment-perceptive capacity, emerging integrated sensing and communication (ISAC) technologies face multiple difficulties, especially in balancing the performance trade-off between the communication and radar functions. In this paper, we introduce a reconfigurable intelligent surface (RIS) to assist both data transmission and target detection in a dual-functional ISAC system. To formulate a general optimization framework, diverse communication performance metrics have been taken into account including famous capacity maximization and mean-squared error (MSE) minimization. Whereas the target detection process is modeled as a general likelihood ratio test (GLRT) due to the practical limitations, and the monotonicity of the corresponding detection probability is proved. For the single-user and single-target (SUST) scenario, the minimum transmit power for sensing has been revealed. By exploiting the optimal conditions, we validate that the optimal BS satisfies the maximum power allocation criterion and derive the optimal BS precoder in a semi-closed form. Moreover, an alternating direction method of multipliers (ADMM) based RIS design is proposed to address the non-convex radar constraint. For the sake of enhancing computational efficiency, a low-complexity RIS design is also developed based on the manifold optimization theory. Furthermore, the ISAC transceiver design for the multiple-users and multiple-targets (MUMT) scenario is also investigated, where a zero-forcing (ZF) radar receiver is adopted to cancel the interference signals from different targets. Then optimal BS precoder is derived under the maximum power allocation scheme, and the RIS phase shifts can be optimized by extending the proposed ADMM-based RIS design algorithm. Finally, the ISAC transceiver design with imperfect in-band full-duplex transceivers is also discussed and two radar receive beamformer designs have been proposed to mitigate the performance loss. Numerical simulation results verify the convergence and superior communication/sensing performance of our proposed transceiver designs.

Both the reconfigurable intelligent surface (RIS) and the hybrid analog-digital antenna array have been envisioned as two cost-effective and promising technologies for achieving various types of functionality enhancement of future wireless systems. In this paper, we develop a framework for the multi-functional optimization in the RIS-aided hybrid analog-digital multiple-input multiple-output (MIMO) system, where a board of performance metrics related to diverse system functionalities are considered, such as capacity and mean square error (MSE) for information transmission (IT), Cramer-Rao bound (CRB) for radar sensing, harvested energy for energy harvesting (EH) and so on. Under this framework, we focus on two types of multi-functional optimization problems, namely, the multi-objective multi-functional optimization and the single-objective optimization subject to multi-functional constraints, and propose a unified low-complexity algorithm by separately optimizing analog and digital matrix variables. Specifically, for the multi-objective optimization, we firstly propose the numerical quadratic optimization based (QuaOpt-based) algorithm and the low-complexity channel alignment based algorithm to separately optimize analog matrices, including the RIS reflecting matrix, the analog precoder and the analog equalizer. Then, for the optimization of digital precoder, the numerical semidefinite programming (SDP)-based algorithm and the QuaOpt-based algorithm are proposed to iteratively solve the digital precoder optimization problem, while the matrix-monotonic optimization based algorithm derives the optimal closed-form solution in low computational complexity. Whereas for the single-objective optimization, the above proposed algorithms are still applicable by applying the Lagrangian duality theory to tackle the multi-functional constraints. Numerical simulation results reveal that the proposed low-complexity algorithm can achieve comparable performance to numerical algorithms.

Reconfigurable intelligent surface (RIS) has emerged as a cost-effective solution for green communications in 6G. However, its further extensive use has been greatly limited due to its fully passive characteristics. Considering the appealing distribution gains of distributed antenna systems (DAS), a flexible reconfigurable architecture called reconfigurable distributed antenna and reflecting surface (RDARS) is proposed. RDARS encompasses DAS and RIS as two special cases and maintains the advantages of distributed antennas while reducing the hardware cost by replacing some active antennas with low-cost passive reflecting surfaces. In this paper, we present a RDARS-aided uplink multi-user communication system and investigate the system transmission reliability with the newly proposed architecture. Specifically, in addition to the distribution gain and the reflection gain provided by the connection and reflection modes, respectively, we also consider the dynamic mode switching of each element which introduces an additional degree of freedom (DoF) and thus results in a selection gain. As such, we aim to minimize the total sum mean-square-error (MSE) of all data streams by jointly optimizing the receive beamforming matrix, the reflection phase shifts and the channel-aware placement of elements in the connection mode. To tackle this nonconvex problem with intractable binary and cardinality constraints, we propose an inexact block coordinate descent (BCD) based penalty dual decomposition (PDD) algorithm with the guaranteed convergence. Since the PDD algorithm usually suffers from high computational complexity, a low-complexity greedy-search-based alternating optimization (AO) algorithm is developed to yield a semi-closed-form solution with acceptable performance. Numerical results demonstrate the superiority of the proposed architecture compared to the conventional fully passive RIS or DAS. Furthermore, some insights about the practical implementation of RDARS are provided.

Integrated sensing and communication (ISAC) has evolved into an influential technique to ameliorate energy and spectrum scarcity via co-designing these two functionalities. However, the target can be a potential eavesdropper aiming at wiretapping the information transmitted to the communication user. This paper studies a semi-passive intelligent reflecting surface (IRS) enabled ISAC system, where the IRS is employed to assist the secure communication and simultaneously perform the target sensing based on the echo signals received by the dedicated sensor at the IRS. Specifically, we model two types of targets, namely point targets and extended targets. The direction-of-arrival (DoA) of the former and the complete target response matrix of the latter should be estimated. Under this configuration, we derive the Cramér-Rao bound (CRB) as the performance metric of target estimation. To achieve an optimal performance trade-off, we formulate a weighted optimization problem that balances maximizing the secrecy rate and minimizing the CRB, via jointly optimizing the transmit beamforming and the phase shifts of IRS. Then, we employ the alternating optimization, successive convex approximation and semi-definite relaxation to tackle the proposed non-convex problems for the two target cases. Simulation results show the effectiveness of the proposed schemes compared with benchmarks.

Integrated sensing and communication (ISAC) technology effectively enables spectrum and hardware sharing between radar and communication. Moreover, ISAC outperforms traditional separate radar and communication systems in terms of both power consumption and spectral efficiency. This paper investigates the dual-functional (DF) constant modulus waveform design for simultaneously transmitting and reconfigurable intelligent surface (STAR-RIS)-aided ISAC. To investigate the performance trade-off, the weighted sum of multi-user interference (MUI) energy and waveform discrepancies is minimized via jointly optimizing the transmit waveform and the reflection and transmission coefficient matrices at STAR-RIS. Furthermore, both cases of independent and coupled phase shifts at STAR-RIS are investigated. For independent phase shifts, we develop an alternating direction method of multipliers (ADMM)-based algorithm to decouple the original problem into several tractable subproblems that facilitates the derivation of a closed-form solution to each subproblem. In the scenario with the coupled phase shifts, we first formulate the optimization problem as a Markov decision process, employing a twin delayed deep deterministic policy gradient (TD3)-based deep reinforcement learning approach to address it. Simulation results verify the effectiveness of the proposed schemes, demonstrating STAR-RIS’s superiority over conventional RIS. Moreover, the adopted protocol of STAR-RIS can maintain an excellent balance between performance and complexity.

Stochastic partial differential equations (SPDEs) are crucial for modelling dynamics with randomness in many areas including economics, physics, and atmospheric sciences. Recently, using deep learning approaches to learn the PDE solution for accelerating PDE simulation becomes increasingly popular. However, SPDEs have two unique properties that require new design on the models. First, the model to approximate the solution of SPDE should be generalizable over both initial conditions and the random sampled forcing term. Second, the random forcing terms usually have poor regularity whose statistics may diverge (e.g., the space-time white noise). To deal with the problems, in this work, we design a deep neural network called \emph{Deep Latent Regularity Net} (DLR-Net). DLR-Net includes a regularity feature block as the main component, which maps the initial condition and the random forcing term to a set of regularity features. The processing of regularity features is inspired by regularity structure theory and the features provably compose a set of basis to represent the SPDE solution. The regularity features are then fed into a small backbone neural operator to get the output. We conduct experiments on various SPDEs including the dynamic $\Phi^4_1$ model and the stochastic 2D Navier-Stokes equation to predict their solutions, and the results demonstrate that the proposed DLR-Net can achieve SOTA accuracy compared with the baselines. Moreover, the inference time is over 20 times faster than the traditional numerical solver and is comparable with the baseline deep learning models.

In view of the nonideality of communication links in the Internet of Things (IoT) originating from transceiver hardware impairments, in this article, we introduce a general framework for hardware impairments-aware multiantenna transceiver design, which considers different availabilities of CSI at the transmitter (CSIT) and the receiver (CSIR). The well-known Kronecker model is applied to characterize stochastic channel state information (CSI) errors. For each case, we aim to minimize the (average) total mean square error (MSE) of all data streams subject to the practical per-antenna power constraints. To address the nonconvexity of the formulated problem, we propose an efficient majorization–minimization (MM)-based iterative algorithm to transform the original problem into a series of convex subproblems with semiclosed-form optimal solutions. For low-complexity implementation, we also develop an alternative scheme for directly finding a high-quality suboptimal solution by considering both worst case hardware impairments and worst case CSI errors. In particular, since an explicit expression of the average total MSE for the perfect CSIR and imperfect CSIT case is hard to derive, we instead optimize its effective upper and lower bounds. The prospective applications of our work in the two currently popular multiple-input–multiple-output (MIMO) IoT scenarios are then discussed. Furthermore, we fundamentally reveal the MSE floor effect caused by both hardware distortion and CSI imperfection in the high-SNR regime. Numerical results illustrate the excellent average total MSE and average bit error rate (BER) performance of our proposed algorithms over the adopted benchmark schemes.

Reconfigurable intelligent surface (RIS) has been envisioned as an innovative technology to assist millimeter wave (mmWave) communications. Thanks to both advantages of low hardware cost and low power consumption, the hybrid transceiver structure also becomes an integral component of mmWave systems. However, due to practical limitations of hardware components, the RIS-assisted mmWave communications usually suffer unavoidable hardware impairments (HWIs). In this paper, we aim to minimize the (sum) MSE and maximize the average rate of the hardware-impaired RIS-assisted point-to-point mmWave MIMO system, respectively, by jointly optimizing the hybrid transceiver and RIS reflection coefficients under the realistic discrete phase shift constraints. We firstly consider the single-antenna user case and propose efficient alternating optimization (AO) algorithms to solve the two intractable problems. A binary-oriented exact penalty (BEP) method is developed for the involved discrete optimization, which is able to strike a good trade-off between performance and complexity. Moreover, we analyze the optimality of AO algorithms under the cascaded line-of-sight (LoS) channel condition, and reveal both the MSE floor effect and average rate saturation effect in the high-SNR regime. The above studies are then extended to the general multi-antenna user case, where a low-complexity two-phase scheme with the aim of creating the favorable RIS-cascaded channel in the first phase and enhancing system performance in the second phase is proposed. This two-phase scheme is also demonstrated to attain the optimal performance in the LoS scenario. Numerical results validate our theoretical analysis and illustrate superior performance of the proposed algorithms over various benchmark schemes.

In many core problems of signal processing and wireless communications, Karush-Kuhn-Tucker (KKT) conditions based optimization plays a fundamental role. Hence we investigate the KKT conditions in the context of optimizing positive semidefinite matrix variables under nonconvex rank constraints. More explicitly, based on the properties of KKT conditions, we optimize a reconfigurable intelligent surface (RIS) aided multi-user multi-input multi-output (MU-MIMO) network. Specifically, we consider the capacity maximization and sum mean square error (MSE) minimization problems of both the RIS-aided MU-MIMO uplink (UL) and downlink (DL) under multiple weighted power constraints and rank constraints. As for the RIS-aided MU-MIMO UL, the optimal structures of the signal covariance matrices are derived based on the KKT conditions. Furthermore, an efficient procedure is designed for solving the capacity maximization and sum mean square error (MSE) minimization problems. Then the UL-DL dualities are exploited for solving the capacity maximization and MSE minimization problems of the RIS-aided MU-MIMO DL based on the results of the UL optimization. Hence in the proposed framework, the phase shifting matrix of the RIS is jointly optimized with the signal covariance matrices for both the UL and DL. Our simulation results demonstrate the performance advantages of the proposed framework.

Reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) communications has been envisioned as a prominent technology for future wireless networks, since it is capable of simultaneously providing abundant spectrum resources and favorable propagation environments. The small wavelength at mmWave bands also enables the widespread use of large antenna arrays, of which the hybrid beamforming structure has emerged as a cost-effective solution. In this paper, we aim to minimize the sum-mean-square-error (sum-MSE) in the RIS-assisted mmWave multiuser multiple input multiple output (MU-MIMO) system by jointly optimizing the hybrid analog-digital precoders and the RIS reflection matrix. We demonstrate that the role of RIS in assisting mmWave communications can be completely replaced by a large-scale Kronecker-structured hybrid array. Moreover, an accelerated Riemannian gradient algorithm using majorization minimization technique is proposed to tackle the unit-modulus constrained analog precoder/RIS design. Under the assumption of perfect channel state information (CSI), we firstly consider the single-user MIMO (SU-MIMO) setup and propose an effective alternating minimization (AM) procedure to characterize the system performance limit. Moreover, a two-stage scheme is developed for low-complexity implementation. This AM procedure is then extended to the general MU-MIMO scenario. In addition, we develop a novel enhanced regularized zero-forcing (ERZF) scheme for simultaneously combating strong noise in the low-SNR regime and mitigating multi-user interference (MUI) in the high-SNR regime. The optimality of our proposed algorithms is validated for some simplified practical scenarios. Numerical results illustrate that the proposed algorithms outperform existing benchmark schemes in terms of the actual complexity and performance.

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

In this paper, we propose a general framework on the hybrid analog-digital transceiver design for multi-hop communications. For the inclusive purpose, a transceiver model unifying both linear and nonlinear transceivers has been taken into account. Various performance metrics, including the most representative capacity and weighted mean-squared error (MSE), have been investigated in a unified manner. In particular, to meet practical needs for the quality of services (QoS), a general eigenvalue power constraint model is introduced, which contains a sum power constraint and box eigenvalue constraints as special cases. Specifically, by carefully designing the auxiliary analog and digital beamformers, the multi-hop transceiver optimization is decomposed into a series of independent sub-problems, where the analog beamformers for different hops are completely decoupled. Based on that, this framework establishes a majorization-minimization (MM) based analog beamformer design algorithm, which is able to handle the complicated weighted unit-modulus matrix optimizations by finding their semi-closed-form solutions. Furthermore, an efficient waterfilling algorithm is proposed for the digital beamformer designs to deal with the difficulties of optimizations subject to the multiple eigenvalue power constraints. The numerical results are provided to demonstrate the performance advantages of the proposed framework.

In order to reduce computational complexity and hardware cost for reconfigurable intelligent surface (RIS)-aided multiple-input–multiple-output (MIMO) systems, in this article, the subarray partition algorithm designs at RIS are investigated. Without instantaneous channel state information (CSI) of the RIS-related links, the subarray partition algorithms aim at minimizing the number of subarrays while keeping a minimum sum rate requirement. In nature, the subarray partition optimization problem is a combinatorial optimization and NP-hard because of many discrete optimization variables. Three kinds of subarray partition algorithms are proposed. The first one is named as a fixed pattern subarray partition algorithm, in which subarray is arranged in a predefined manner. This algorithm is easy to implement but its performance is far from optimal. To reap the benefits of RIS as much as possible, two dynamic pattern subarray partition algorithms are given as well. The first dynamic pattern algorithm is the greedy dynamic pattern subarray partition algorithm that is more complicated than the fixed pattern one but benefits much better performance. To reduce complexity, the relaxation-based dynamic pattern algorithm is given, which has almost the same performance as the greedy dynamic algorithm but has a much lower complexity. At the end of the whole work, numerical results are given to access the performance of the proposed algorithms.

In this article, we investigate the training optimization for multiple-input–multiple-output (MIMO)-aided Internet of Things (IoTs) systems that employ subarray-based intelligent reflecting surface (IRS). In order to overcome the nonlinear relationship between two cascaded channel matrices, the IRS can be divided into a series of subarrays, for which only an equivalent cascaded channel matrix should be estimated in each subarray. Correspondingly, the training sequence should be divided into multiple segments. By sufficiently utilizing the available statistical channel state information (CSI), either mean-square error (MSE) minimization or mutual information (MUI) maximization can be taken as the performance metric for optimizing the training sequence. A variety of fairnesses among different subarray channel estimations has been taken into account. Furthermore, in order to reduce the hardware cost of the power amplifier, we propose a two-stage training sequence structure, including a fully digital filter and a constant modulus sequence. To further reduce computational complexity, various low-complexity water-filling solutions are proposed. Numerical results demonstrate the accuracy and efficiency of the proposed solutions.

Intelligent reflecting surface (IRS) is an emerging cost-efficient technology to enhance communication performance by implementing a large number of passive reflecting elements with tunable phases in wireless systems. In this paper, we propose a general framework for the IRS-aided MIMO system designs under both single-user and multi-user setups, in which the diverse performance metrics including weighted mutual information and weighted MSE, and the realistic multiple weighted power constraint are taken into consideration. Leveraging the alternating optimization approach, the optimal IRS phase shifts are obtained in semi-closed forms. Specifically, based on the matrix-monotonic optimization theory, it is found that optimizing IRS phase shifts is essentially equivalent to tuning the eigenvalues and the corresponding eigenvectors of the MSE matrix. Then the proposed general framework is extended to a multi-user system by introducing a majorization-minimization (MM)-based method for IRS phase shift optimization. Simulation results show that our proposed optimal design brings significant enhancement on the chosen performance metric compared to the traditional MIMO systems without the IRS, and also significantly outperforms various benchmark designs in both single-user and multi-user systems.

Hybrid energy supply composed of batteries and radio frequency (RF) signals has been anticipated to be a prominent solution for balancing the reliability and self-sustainability of future IoT networks. The newly emerging reconfigurable intelligent surface (RIS) is also capable of greatly enhancing spectral and energy efficiencies. In this paper, by considering an asynchronous transmission protocol among all energy receivers (ERs) and assuming the perfect self-interference cancellation (SIC) at the hybrid access point (HAP), we aim to maximize sum throughput in the RIS-aided hybrid powered communication networks (HPCNs) by jointly optimizing the transmit covariance matrices of the HAP and all ERs, the RIS reflection matrix and the downlink/uplink (DL/UL) time allocation. Generally, this optimization problem is intractable to solve due to strongly coupled variables and nonconvex unit-modulus constraints. To draw more insights into this joint design, we firstly carry out feasibility analysis on this problem, and then develop a 2-block alternating optimization algorithm, which consists of the semi-closed-form solution based iterative algorithm for deriving the optimal MIMO transceivers together with the DL/UL time allocation and the alternating direction method of multipliers (ADMM) based algorithm for the RIS design. To avoid the potential high complexity of alternating optimization, we also propose a two-stage scheme, where the RIS design is independent of the others and aims to create favorable DL/UL channels. The extension of our proposed algorithms to the practical imperfect SIC case is then discussed. Numerical results illustrate the superior performance of our proposed algorithms over the baselines in terms of the achievable sum throughput, and their time effectiveness in solving large-scale problems.

Wireless powered sensor networks (WPSNs) have evolved as a promising paradigm for energy-efficient communications. Recently, the proliferation of reconfigurable intelligent surface (RIS) has further been envisioned as a cost-effective solution for improving wireless power transfer (WPT) efficiency. In this paper, from the practical perspective of balancing the network sustainability and reliability, we consider a RIS-enhanced partially WPSN that composed of wireless-powered energy receivers (ERs) and battery-powered information receivers (IRs). Assuming the partially WPSN operates in time division multiple access (TDMA) mode, the joint optimization of covariance matrices, downlink/uplink (DL/UL) time allocation and RIS reflecting coefficients are investigated under the minimum DL rate constraint among all IRs for maximizing the achievable UL sum rate. Specifically, the single-IR single-ER (SISE) case is first studied based on the assumption of separate DL/UL RIS reflecting coefficients, in which an alternating optimization algorithm is proposed with semi-closed-form optimal solutions. In order to reduce the hardware overhead and signal processing complexity, we also investigate the case of identical DL/UL RIS reflecting coefficients, in which an iterative optimization algorithm is developed to tackle the coupled DL/UL transmissions. Then, we extend our work to the multiple-IRs multiple-ERs (MIME) case, where both the optimization problems corresponding to separate and identical DL/UL RIS reflecting schemes become more challenging to solve. To circumvent this intractability, we propose a successive convex relaxation (SCA) based alternating optimization algorithm and a low-complexity two-step algorithm. Finally, numerical results demonstrate the superior UL sum rate performance of our proposed algorithms over the adopted benchmarks.

Intelligent reflecting surface (IRS) is capable of constructing the favorable wireless propagation environment by leveraging massive low-cost reconfigurable reflect array elements. In this article, we investigate the IRS-aided multiple-input-multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) for Internet-of-Things (IoT) networks, where the active base station (BS) transmits beamforming and the passive IRS reflection coefficients are jointly optimized for maximizing the minimum signal-to-interference-plus-noise ratio (SINR) among all information decoders (IDs), while maintaining the minimum total harvested energy at all energy receivers (ERs). Moreover, the IRS with practical discrete phase shifts is considered, and thereby the max-min SINR problem becomes an NP-hard combinatorial optimization problem with a strong coupling among optimization variables. To explore the insights and generality of this max-min design, both the single-ID single-ER (SISE) scenario and the multiple-IDs multiple-ERs (MIME) scenario are studied. In the SISE scenario, the classical combinatorial optimization techniques, namely, the special ordered set of type 1 (SOS1) and the reformulation-linearization (RL) technique, are applied to overcome the difficulty of this max-min design imposed by discrete optimization variables. Then, the optimal branch-and-bound algorithm and suboptimal alternating optimization algorithm are, respectively, proposed. We further extend the idea of alternating optimization to the MIME scenario. Moreover, to reduce the iteration complexity, a two-stage scheme is considered aiming to separately optimize the BS transmit beamforming and the IRS reflection coefficients. Finally, numerical simulations demonstrate the superior performance of the proposed algorithms over the benchmarks in both the two scenarios.

In this article, we investigate the analog–digital hybrid transceiver optimization for distributed Internet-of-Things (IoT) sensing networks consisting of a multiantenna fusion center (FC) and several multiantenna sensor nodes. Analog–digital hybrid transceiver is an economic way to realize tradeoffs between hardware cost and performance for multiantenna communications. Under the nonconvex unit modulus constraints and transmit power constraint at each sensor, two synchronization schemes are considered for the hybrid linear minimum mean-square error (LMMSE) transceiver optimization. First, a centralized algorithm is proposed, in which the hybrid transceivers are computed at the FC. Based on the framework of alternating direction method of multipliers (ADMMs), the unit modulus constraints can be satisfied by projecting the elements of analog transceivers onto the unit modulus circle. However, the centralized algorithm usually suffers from strict synchronous requirements and high communication overhead. In order to accommodate the inevitable computing and communication delays in distributed IoT sensing networks, an asynchronous distributed ADMM (AD-ADMM) algorithm is proposed. By using the aged information, the hybrid transceivers are computed at the sensors without the coordination of the FC. Thus, the AD-ADMM algorithm can greatly reduce the computation overhead of the FC and improve the scalability of IoT sensing networks. Simulation results are presented to show that both the centralized ADMM and AD-ADMM algorithms perform closely to the fully digital counterpart.

A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at the source. In this paper, a unified MIMO optimization framework based on the Karush-Kuhn-Tucker (KKT) conditions is proposed. In this framework, with the aid of matrix optimization theory,Theorem 1presents a generic optimal transmit covariance matrix for MIMO systems with diverse objective functions subject to various power constraints and different levels of channel state information (CSI). Specifically,Theorem 1fundamentally reveals that for a diverse family of MIMO systems, the optimal transmit covariance matrices associated with different objective functions under various power constraints can be derived in a unified generic water-filling-like form. When applyingTheorem 1to the case of multiple general power constraints, we firstly equivalently transform multiple power constraints into a single counterpart by introducing multiple weighting factors based on Pareto optimization theory. The optimal weighting factors can be found by the proposed modified subgradient method. On the other hand, for the imperfect MIMO system with statistical CSI errors, we firstly address the non-convexity of the robust optimization problem by following the idea of alternating optimization. Finally, our numerical results verify the optimal solution structure inTheorem 1and the global optimality of the proposed modified subgradient method, as well as demonstrate the performance advantages of the proposed alternating optimization algorithm.

Data aggregation is a promising technology in the Internet-of-Things (IoT) network for a wide range of applications, e.g., environmental monitoring, traffic control, and real-time surveillance. In order to meet the high requirement of transmission rate for data aggregation, we investigate the transceiver optimization to improve the spectral efficiency. As a tradeoff between the system complexity and performance, hybrid transceivers are adopted for data aggregation in the IoT network. We first present the optimal structures of digital precoders and unconstrained analog transceivers to maximize the spectral efficiency. Then, we propose two different kinds of iterative algorithms to optimize the analog transceivers under nonconvex unit-modulus constraints. The first algorithm is based on the framework of the alternating direction method of multipliers (ADMM). The second one is the steepest descent (SD) algorithm based on the Riemannian geometry, which has lower computational complexity than the first one. For both algorithms, closed-form solutions are derived in each iteration. Finally, numerical results demonstrate that the performance of the proposed algorithms in the hybrid transceiver design is very close to the fully digital solution but with less hardware complexity and power consumption.

In this work, we investigate in depth the two timescale robust system energy efficiency (EE) precoding design for the multiuser dual-polarized multiple-input multiple-output (MIMO) system. To achieve good performance, low feedback overhead as well as low implementation complexity, the dual-structured linear precoding scheme is adopted, which is based on the two timescale channel state information (CSI) and the dual-polarized antenna structure. The subgrouping technique, which is based on polarization, is also utilized to divide spatially grouped users into co-polarized subgroups to further reduce channel feedback overhead. The proposed robust system EE precoding design can achieve the maximization of the worst-case system EE, with the norm-bounded channel errors of all users. This robust EE optimization is naturally decomposed into two parts. In the first part, based on the polarized spatial correlation information, the block diagonalization is utilized to design the preprocessing matrix. In the second part, based on the relationship between the mean square error and the signal-to-interference-plus-noise ratio, the linear precoding matrix can be optimized by utilizing the sign-definiteness lemma and the fractional programming technique. Specifically, the corresponding nonconvex EE fractional optimization problem is converted to a series of semidefinite programming problems, which are solved by the convex optimization method efficiently. Simulation results indicate that the proposed two timescale based dual-structured precoding has many advantages on the robust system EE performance in the dual-polarized multiuser MIMO system.

The new paradigm of wirelessly powered two-tier heterogeneous networks (HetNets) is considered in this paper. Specifically, the femtocell base station (FBS) is powered by a power beacon (PB) and transmits confidential information to a legitimate femtocell user (FU) in the presence of a potential eavesdropper (EVE) and a macro base station (MBS). In this scenario, we investigate the secrecy beamforming design under three different levels of FBS-EVE channel state information (CSI), namely, the perfect, imperfect and completely unknown FBS-EVE CSI. Firstly, given the perfect global CSI at the FBS, the PB energy covariance matrix, the FBS information covariance matrix and the time splitting factor are jointly optimized aiming for perfect secrecy rate maximization. Upon assuming the imperfect FBS-EVE CSI, the worst-case and outage-constrained SRM problems corresponding to deterministic and statistical CSI errors are investigated, respectively. Furthermore, considering the more realistic case of unknown FBS-EVE CSI, the artificial noise (AN) aided secrecy beamforming design is studied. Our analysis reveals that for all above cases both the optimal PB energy and FBS information secrecy beamformings are of rank-1. Moreover, for all considered cases of FBS-EVE CSI, the closed-form PB energy beamforming solutions are available when the cross-tier interference constraint is inactive. Numerical simulation results demonstrate the secrecy performance advantages of all proposed secrecy beamforming designs compared to the adopted baseline algorithms.

In this paper, we propose a superimposed training based two-phase robust channel estimation scheme for the unmanned aerial vehicle (UAV) assisted cellular communication system, in which various unitarily-invariant channel statistics errors are considered. Specifically, in the first phase, mobile station (MS) estimates the UAV-MS channel via the UAV training sequence, of which the robust design can be solved based on convex-concave theory. While in the second phase, the superimposed training scheme is considered at the ground base station (GBS) to improve spectrum efficiency. Then the robust GBS training sequence, the information signal power and the UAV amplifying factor are jointly optimized for the partially cascaded GBS-UAV-MS channel estimation subject to GBS and UAV transmit power constraints as well as the required information signal strength at the MS. To tackle this NP-hard problem, the optimal structures of involved variables are firstly derived, based on which the robust superimposed training design is simplified and proved to be quasi-convex in the UAV amplifying factor. Particularly, for Spectral norm and Nuclear norm bounded errors, the optimal training sequence can be obtained via convex-concave theory and Golden section searchWhile for Frobenius norm bounded error, a tractable upper-bounding scheme is proposed for the robust superimposed training design. Furthermore, we extend our work into the more general probabilistic path loss scenario of UAV-ground channels, and analyze the impacts of the probabilistic path loss and RicianK-factor on channel estimation performance. Numerical results illustrate the excellent performance of the proposed superimposed training based two-phase channel estimation scheme.

Channel estimation is conceived for hybrid multiple-input multiple-output (MIMO) communication systems. Both mean square error minimization and mutual information maximization are used as our performance metrics and a pair of low-complexity channel estimation schemes are proposed. In each scheme, the training sequence and the analog matrices of the transmitter and receiver are jointly optimized. We commence by designing the optimal training sequences and analog matrices for the first scheme. Upon relying on the resultant optimal structures, the training optimization problems are substantially simplified and the nonconvexity resulting from the analog matrices can be overcome. In the second scheme, the channel estimation and data transmission share the same analog matrices, which beneficially reduces the overhead of optimizing the associated analog matrices. Therefore, a composite channel matrix is estimated instead of the true channel matrix. By exploiting the statistical optimization framework advocated, the analog matrices can be designed independently of the training sequence. Based on the resultant analog matrices, the training sequence can then be efficiently designed according to diverse channel statistics and performance metrics. Finally, we conclude by quantifying the performance benefits of the proposed estimation schemes.

We investigate the energy efficiency (EE) of multiple-input-multiple-output (MIMO) amplify-and-forward relaying networks relying on the realistic imperfect channel state information (CSI). Specifically, the relay jointly optimizes the source covariance and relay beamforming matrices by maximizing the EE under additive or multiplicative relay-destination CSI errors. The optimal channel-diagonalizing structure is derived for the source covariance and relay beamforming matrices under the spectral-norm constrained additive or multiplicative CSI error. Then, the existence of a saddle point is proved, which shows that the channel-diagonalizing transmission strategy is optimal in the robust EE maximization under these two types of CSI errors, and the original matrix-valued fractional robust EE problem is transformed into a scalar fractional problem. We propose the Dinkelbach method-based alternating optimization scheme for this transformed robust EE problem, which is capable of finding a locally optimal solution of the original robust EE problem efficiently, and show that the semi-closed-form solution to each of the two associated subproblems can be obtained. We then prove that the channel-diagonalizing transmission strategy remains optimal when the statistically imperfect source-relay channel is additionally imposed. We also extend our work into multi-hop MIMO relaying scenarios and prove that the channel-diagonalizing structure is optimal for the source covariance matrix and the multiple relay beamforming matrices.

In this paper, we investigate the linear transceiver optimization for multiple-inputmultiple-output (MIMO) interference networks, where multiple pairs of multi-antenna source and destination nodes communicate simultaneously. Different from most of existing works, we jointly consider three critical issues of the linear transceiver optimization for MIMO interference networks based on multi-objective optimization theory, i.e., signal transmission, energy and security. Specifically, using the modified weighted Tchebycheff method, we investigate three kinds of multi-objective optimization problems (MOOPs): 1) sum mean square error minimization and harvested energy maximization; 2) transmit power minimization and energy harvesting efficiency maximization; 3) transmit power minimization, energy harvesting efficiency maximization, and physical layer security. Based on the Charnes-Cooper transformation and penalty function method, the formulated MOOPs are transformed into convex optimization problems and thus can be effectively solved. The resulting Pareto optimal solutions set reveals the complicated but important relationships among these involved single objective optimization problems, which are usually individually investigated in the literature. Finally, numerical simulation results demonstrate the performance advantages of the proposed algorithm and corroborate the theoretical analysis.

We design novel transmission strategies to maximize the energy efficiency (EE) of the uplink multi-user multipleinput and multiple-output relay channel. In this channel, K multi-antenna users communicate with a multi-antenna base station (BS) through a multi-antenna relay. To achieve the goal of EE maximization, we propose new iterative algorithms to jointly optimize the multi-user precoder and the relay precoder under transmit power constraints for two cases. In the first case, the perfect global channel state information (CSI) is available, while in the second case, the CSI between the relay and the BS is imperfect. To surmount the non-convexity of our formulated EE optimization problems in both cases, we introduce the parameter subtractive function into the proposed algorithms. Then, the EE parameter in the parameter subtractive function is updated by Dinkelbach's algorithm in the perfect CSI case, and by the bisection method in the imperfect CSI case. Moreover, in the perfect CSI case, the relay precoder is optimized by the diagonalization operation and the multi-user precoder is optimized based on the weighted minimum mean square error method. Differently, in the imperfect CSI case, we apply the sign-definiteness lemma to promote the semidefinite programming formulation of the EE optimization problem. Furthermore, we present the numerical results to demonstrate that our proposed iterative algorithms have a good convergence rate in both cases. In addition, we show that our proposed iterative algorithms achieve a higher EE performance than the existing algorithms in both CSI cases.

Owing to the wireless signal power received by the energy harvesting (EH) node is generally higher than that of the information decoding (ID) node in simultaneous wireless information and power transfer (SWIPT) system, the confidential information becomes vulnerable to be wiretapped. Motivated, in this paper, we aim at realizing secure communications for two-user MIMO interference channel with SWIPT. Unfortunately, the formulated secrecy rate maximization problem is non-convex with respect to the covariance matrices of two transmitters, thus an alternative algorithm is proposed to solve the nonconvex optimization problem. Firstly, the orthogonal-projection-based optimization algorithm is performed to completely suppress the interference to ID receiver, then by applying the Taylor series expansion, the covariance matrix of information transmitter is optimized based on the dual optimization. Finally, numerical experiments are conducted to validate the security performance of the proposed algorithm.

Thanks to gigahertz unlicensed spectrum, the millimeter wave (mmWave) communication becomes an important enabling technology to meet the increasing data rate demands of future communication systems. It is also well-known that wireless communications are susceptible to security threatening, especially for wireless two-way relaying networks. Hence, in this work, we propose two secrecy beamforming schemes for large mmWave two-way relaying networks. Firstly, the secrecy rate maximization problem is considered with the constraint of relay power. Then the relay transmit power is optimized to satisfy the secrecy rate requirement of network. Owing to the nonconvexity of original optimization problem, the null-space beamforming is utilized to transform both problems into the standard SOCP problem, which can be solved effectively with the convex optimization technique. Finally, numerical experiments are conducted to show the superior security performance and high energy efficiency of the two proposed secrecy beamforming schemes, respectively.