This paper investigates channel estimation for holographic MIMO (HMIMO) systems that achieve continuous electromagnetic aperture synthesis through ultra-dense configurations of antenna elements within constrained spatial dimensions. We aim to exploit the inherent sparsity characteristics of the HMIMO generated by ultra-dense antenna configurations, thereby reducing the error and complexity caused by the large number of antennas in channel estimation process. Unlike previous algorithms that rely solely on sparsity, the proposed algorithm considers the block sparse structure of the channel, thereby yielding more accurate channel estimation performances. Specifically, we first establish the block sparse representation in the wavenumber domain of the channel for HMIMO systems. Subsequently, the channel estimation problem is formulated as the block sparse matrix recovery problem, incorporating an l2,1norm term in the objective function to promote block sparse structure. The block sparse-based gradient descent (BSBGD) algorithm is proposed to solve the formulated problem. Simulation results show that channel estimation results obtained by the proposed algorithm are more accurate.

In this article, we propose a hybrid-field-aware two-stage beamforming (HFA-TSB) scheme for extremely large-scale MIMO (XL-MIMO) systems. The HFA-TSB scheme can reduce the high pilot overhead associated with channel estimation by leveraging statistical channel state information (SCSI). Utilizing our derived ergodic spectral efficiency (SE), which relies solely on SCSI, we can eliminate the interference resulting from the nonorthogonality of near-field polar domain codewords. Specifically, the HFA-TSB scheme comprises two stages: 1) pre-beamforming and 2) precoding. In the pre-beamforming stage, we use SCSI to design the pre-beamforming matrix, focusing on eliminating interference among asymptotically orthogonal channels. This can establish an equivalent reduced-dimensional channel matrix, which can be estimated using less pilot overhead. Additionally, to address the interference caused by the nonorthogonality of near-field codewords, we derived an ergodic SE that relies solely on SCSI. Using this as an optimization objective, the pre-beamforming matrix design problem is formulated as a 0-1 integer nonlinear programming problem, which is challenging to solve. To address this, we propose a constraint-driven two-phase greedy beam selection algorithm for identifying effective beams. In the precoding stage, we design the precoder based on the estimated equivalent sparse channel to effectively mitigate any residual interuser interference. Simulations validate the superior performance of our proposed HFA-TSB scheme in terms of net SE.

As a potential technology to support the extreme requirements of next-generation communications, holographic multiple-input multiple-output (H-MIMO) refers to arrays with a large number of individually controlled and densely deployed antennas. An important challenge to realize this innovative concept is the need to integrate information theory, electromagnetic theory and circuit theory in modeling, which is also required for electromagnetic information theory (EIT). This paper aims to connect information theory and electromagnetic theory using circuit theory to provide electromagnetically consistent and mutual coupling-aware near-field communication models for H-MIMO systems. Specifically, first, the considered H-MIMO system model is given and represented as a linear multiport network in circuit theory. Unlike the mainstream models that only consider the wireless propagation environment, the circuit-based model is physically consistent and considers the radio frequency components, mutual coupling between different antenna elements, noise, etc. Second, the mutual coupling and propagation effects are represented in the circuit model by the impedance, which requires relating the quantities of the circuit to the fields generated by the antenna. The relationship between the quantities of the circuit and the fields generated by the antenna is given according to the reciprocity and reaction theorems. Furthermore, the method of moments (a computational electromagnetic method) is introduced to calculate the impedance in the line-of-sight case. Finally, the integration of the physical model with the digital model provides a framework for the design of H-MIMO. In the numerical simulations, the H-MIMO performance is provided using the proposed model.

User clustering presents a significant design challenge when implementing non-orthogonal multiple access (NOMA) in multiple-input multiple-output (MIMO) systems. To fully exploit the potential of power domain multiplexing and achieve better performance of NOMA, users must possess significant variations in their channel gains. Consequently, it becomes necessary to cluster users based on their distinct channel gain characteristics. However, using random user clustering often leads to suboptimal outcomes, while the exhaustive search method is burdened with exorbitant complexity. To achieve the balance between system performance and complexity, this paper proposes a user clustering scheme that relies on Jaccard coefficient, which is a measure of differences in user channels, ranging from 0 to 1. A value of 0 indicates complete dissimilarity, while a value of 1 indicates complete similarity. By calculating the Jaccard coefficient, we can identify users who are dissimilar to the centroid as a cluster. Additionally, a new power allocation algorithm is developed to maximize the sum spectral efficiency by employing successive convex approximations (SCA), taking into account both spectral efficiency and user quality of service. The simulation results demonstrate that the algorithm proposed for maximizing the sum spectral efficiency exhibits a higher convergence rate and can substantially enhance the sum spectral efficiency in comparison to the full power control (FPC) scheme.

This paper investigates hybrid-field channel estimation for extremely large-scale MIMO (XL-MIMO) systems. Different from the previous algorithms based on sparsity, the proposed algorithm considers both the low-rank structure and the sparsity of the channel, leading to a more accurate estimation performance. Particularly, we formulate the estimation problem of the hybrid-field channel as a sparse matrix recovery problem with a fixed-rank constraint. However, this problem encounters two challenges: the non-smooth$\ell_{1}-\mathbf{norm}$term and the non-convex fixed-rank matrix constraint. To address these challenges, we employ the proximal operator to handle the non-smooth$\ell_{1}-\mathbf{norm}$term and consider the set of matrices with a fixed rank as the fixed-rank matrix manifold. Then a fixed-rank matrix manifold-based proximal gradient (FRM-PG) algorithm is proposed to smoothly search the solution on the fixed-rank matrix manifold, where the descent direction is derived in each iteration. Simulation results demonstrate that the proposed algorithm outperforms the classical channel estimation algorithms.

Abstract This paper proposes a two‐stage beamforming and combining scheme in frequency division duplex (FDD) massive multiple‐input multiple‐output (MIMO) systems with multi‐antenna users. Specifically, the proposed scheme is a two‐stage scheme, where the pre‐beamforming matrix and pre‐combining matrix are designed using the channel covariance matrix (CCM) in the first stage. The problem of the pre‐beamforming matrix and pre‐combining matrix design are formulated as an 0–1 quadratic integer programming problem. To solve this problem, it is further transformed into an 0–1 mixed linear integer programming problem. In the second stage, the sparse code multiple access and multi‐user precoding and combining are adopted to mitigate the inter‐user interference. Different from the previous transmission scheme using CCM, the proposed scheme consider the multi‐antenna user system, and uses the CCM to design both the pre‐beamforming and pre‐combining matrices to sparsify the effective channel matrix, such that the overhead of pilot and feedback can be reduced. Moreover, the sparse code multiple access can help to better reduce the inter‐user interference. Simulation results validate the good performance of the proposed scheme.

This article proposes a two-stage beamforming (TSB) scheme with user scheduling for FDD massive MIMO. The developed TSB scheme designs the analog prebeamformer and schedules the users using statistical channel state information (S-CSI), reducing the overhead of the pilot and the feedback. Particularly, in the one-ring local scattering channel model, the prebeamformer design and user scheduling problem is formulated as a 0–1 quadratic constrained quadratic programming (QCQP), which is further linearized to a mixed integer linear programming (MILP). In the multiple scattering clusters channel model, we design the prebeamformer and schedule the users based on graph theory, where the chromatic number of the equivalent matrix represents the minimum number of orthogonal pilots. Then, we propose an iterative beam selection and user scheduling (I-BSUS) scheme that approximates the minimum pilot constraint by the maximum vertex degree. Moreover, the net spectrum efficiency (NSE) is improved using a multiuser digital precoder, which depends on the effective instantaneous CSI (EI-CSI). Simulation results validate the superiority of the proposed scheme in enhancing the NSE over the existing schemes.

The escalating growth of the Internet of Things (IoT) has intensified the demand for dependable and efficient communication networks to accommodate the massive data volumes produced by interconnected devices. Satellite networks have emerged as a promising alternative, particularly in remote and underserved regions where terrestrial communication infrastructures are inadequate. Nevertheless, guaranteeing secure uplink communications in satellite-based IoT networks is a daunting task due to similar satellite channels and limited resources at IoT nodes. In this article, we explore the potential of unmanned aerial vehicle (UAV) to improve the secrecy performance of uplink transmissions in satellite-supported IoT networks. Specifically, we first introduce a framework for UAV-aided secure uplink communications, presuming a secure UAV-to-satellite connection. To mitigate the risks of ground eavesdroppers intercepting uplink transmissions, we develop a max–min secrecy rate optimization problem with uplink power constraints. To address this nonconvex problem, a streamlined two-stage optimization approach is proposed. In the inner stage, we combine uplink power allocation and UAV beamforming and propose a successive convex approximation (SCA)-based joint optimization algorithm to address them. In the outer stage, we propose a synergized bisection and coordinate descent algorithm to optimize UAV positioning. Convergence is attained by alternating iterations between these two stages. Particularly, the secrecy fairness among IoT users is reached by solving the max–min problem. Additionally, we offer a complexity analysis of the proposed algorithm and validate the efficacy of the presented approach through comprehensive simulation results.

This paper proposes a manifold optimization-based tensor recovery algorithm for channel estimation (MO-TRACE) in reconfigurable intelligent surface (RIS)-assisted millimeter wave (mmWave) MIMO-OFDM systems. Specifically, considering the inherent sparse scattering characteristics of mmWave channels, the multidimensional cascaded channel in the angular-delay domain is represented by a sparse and low-rank tensor, and we formulate the channel estimation problem as a sparse and low-rank tensor recovery problem. Then, we use the canonical polyadic (CP) decomposition technique to decompose the tensor into multiple factor matrices, where the factor matrices are related to the channel parameters. To account for the sparse factor matrices, we add the sparse regularization terms of the factor matrices to the optimization objective, which can also reduce the number of nonzero columns in factor matrices, i.e., the rank of the tensor. As the concatenation of multiple factor matrices can be seen as a point on a product manifold, we apply MO algorithms to search for the optimal sparse point with enhanced convergence speed. The proposed MO-TRACE algorithm provides a more precise description of channels and ensures that the iteration point always remains within the feasible domain, thereby enhancing solution accuracy. Simulation results validate the superiority of the proposed MO-TRACE in terms of estimation accuracy.

Abstract In this paper, a transmission scheme based on multi‐agent reinforcement learning for intelligent reflecting surface (IRS)‐assisted multiple unmanned aerial vehicles (UAVs) systems is proposed. The proposed scheme is based on reinforcement learning and alternating optimization algorithm, which can effectively improve communication quality and ensure fairness. The scheme is divided into two parts. In the first part, the multi‐UAV cooperation problem is modeled as a markov decision process. The objective of each UAV is to maximize the minimum user channel gain. To achieve stable strategies for all agents, the Multi‐agent Deep Deterministic Policy Gradient (MADDPG) algorithm is applied to train UAVs trajectories to reach the Nash equilibrium. The MADDPG algorithm is centralized trained at the base station and executed in a distributed manner by each UAV, ensuring efficient and effective coordination among agents. In the second part, an alternating optimization algorithm is formulated to optimize active and passive beamforming. Considering the non‐convexity of the fairness objective, by using auxiliary variables and semi‐definite relaxation method, the problem of maximizing the minimum user achievable rate is transformed into a feasibility problem. Simulation results show that the proposed scheme can effectively train UAVs trajectories and improve the communication performance of all users fairly.

In this paper, we investigate the secure transmission of multi-resource heterogeneous radio access networks (RANs) in space-air-ground integrated network (SAGIN) from the perspective of physical layer security. Considering the network heterogeneity, resource constrain, and channel similarity, it is challenging to implement the physical layer security in SAGIN. Particularly, digital twin (DT) is considered in the cyberspace of SAGIN to reflect the physical network entities (i.e., satellite, unmanned aerial vehicle (UAV), and terrestrial base station), which is assumed to comprehensively control and manage the heterogeneous RANs’ resources. To ensure secure transmissions of multi-tier heterogeneous downlink communications in SAGIN, a multi-point symbiotic security scheme is proposed through DT-assisted multi-dimensional domain synergy precoding, where the co-channel interference due to spectrum sharing among these heterogeneous RANs is recast to unevenly corrupt the main and wiretap channels of each legitimate user. Specifically, to realize the multi-point symbiotic security, a max-min problem is formulated to maximize the minimum secrecy rate of three heterogeneous downlinks. Since this problem is non-convex and challenging, a list of mathematical reformulations is derived and the successive convex approximation (SCA) based multi-dimensional domain synergy precoding algorithm is proposed to solve it. Moreover, the computational complexity of our proposed approach is analyzed and meaningful discussions are made. In addition, extensive simulations are carried out to evaluate the secrecy rate performance and verify the efficiency of our proposed approach.

In frequency division duplex (FDD) massive multi-input multi-output (MIMO), the two-stage beamforming (TSB) using channel covariance matrices significantly reduces the downlink training length (DTL) and channel feedback. Nevertheless, most of the TSB methods focus on the one-ring channel. In this paper, we consider the multiple scatterer clusters (MSC) channel in massive MIMO systems and propose a TSB method based on cluster group. To reduce the channel state information (CSI) feedback, for each cluster we use a cluster-group-based eigen-prebeamformer to sparsify the effective channel matrix. The DTL is also reduced by a graph-based downlink training design. We further develop a multi-user beamformer to mitigate the inter-user interference. To further reduce the DTL, two other methods are also proposed based on the vertex and edge deletion. Simulation results confirm the efficiency of the proposed schemes in improving the effective spectral efficiency.

In this study, the authors investigate the joint design problem of interference alignment (IA) and power splitting (PS) in simultaneous wireless information and power transfer (SWIPT) networks. The existing joint design method is generally divided into two steps. First, IA is performed, and then the PS ratio is optimised. To obtain IA and SWIPT, a new joint design multi‐objective alternating optimisation (MOAO) algorithm is proposed. Different from the existing joint design method, the proposed MOAO algorithm not only maximises the sum harvested power after PS, but also maximises the sum signal‐to‐intereference‐plus‐noise ratio (SINR) by jointly designing the transmitting precoding matrices, the receiving interference suppression matrices, and the PS ratio. For this multi‐objective optimisation problem, a weighted optimisation method is proposed, which compromises between maximising the sum harvested power and maximising the sum SINR. Simulation validates that the sum achievable rate and sum harvested power of the proposed MOAO algorithm are significantly superior to those of the current scheme under the reasonable weighting coefficients.

Millimeter wave (mmWave) massive multiple‐input multiple‐output (MIMO) is a promising technology for next generation wireless communications. The utilisation of traditional full digital precoding techniques for mmWave massive MIMO systems is too costly. Fortunately, the hybrid (analogue/digital) precoding is a better choice. In this study, the authors investigate a near‐optimal iterative approximation hybrid precoding algorithm via cost‐efficient sub‐connected structure for mmWave massive MIMO systems. Based on the minimum mean square error (MSE) criterion, the optimal design of the proposed hybrid precoders is non‐convex. The original problem is reformulated as two optimisation sub‐problems, where one of the sub‐problems is convex and another is non‐convex. First, the authors convert the non‐convex sub‐problem into a convex problem by relaxing the constant modulus constraint from beampattern with interference control method, and eliminating the block diagonal constraint from vector operation with the properties of Kronecker product. Then the two convex sub–problems are solved iteratively. The proposed algorithm can achieve a highly approximate optimal solution, which can be theoretically demonstrated to converge to a Karush‐Kuhn‐Tucker point of the original problem. Simulation results show that the proposed algorithm via both sub–connected and fully connected structure gets favourable performance in terms of MSE and achievable rate.

In this paper, we propose a joint spatial division and multiplexing (JSDM) beamforming based on a neighbor scheme for frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems. The neighbor-based JSDM (N-JSDM) can fully utilize signal space, leading to higher spectral efficiency over the conventional JSDMs. The reason is that for the neighbor scheme, neighbors and non-neighbors are classified adaptively by the angles of departure (AoD), and the prebeamformer is designed to mitigate the non-neighbors' interference by the statistical channel state information. The effective channel matrix after the prebeamformer then becomes a band matrix, from which the downlink training length (DTL) and the channel feedback length are much smaller than the number of antennas. Moreover, an optimal prebeamformer which is proved to be able to achieve the same system capacity as the full CSI system is proposed, followed by a suboptimal prebeamformer with constrained DTL, and a DFT-based prebeamformer. On the other hand, the neighbors' interference is mitigated using the banded channel state information. Simulation results validate the good performance of the proposed N-JSDM.

Interference coordination can effectively suppress interference to improve communication quality and is one of the fundamental problems in three-dimension multiple-input multiple-output (3D MIMO) wireless communication systems, especially in multi-cell multi-user multiple-input multiple-output (MIMO) systems. Previous works on interference coordination only consider system spectral efficiency, which may result in departmental users' throughput approaching zero. In this paper, we design an efficient transmission scheme to suppress the interference in multi-cell multi-user 3D MIMO downlink system, taking both the spectral efficiency and fairness into account. In this scheme, cell-center user and cell-edge user specific downtilts and power are jointly optimized and each user can reach an acceptable sum rate. The target problem is a combinatorial non-convex optimization problem that cannot be solved by the traditional KKT-based (Karush-Kuhn-Tucker) Lagrangian algorithm, here the improved quantum bacterial foraging optimization (IQBFO) algorithm is used to solve it due to its fast convergence. Finally, simulation results show that the proposed scheme has a larger system throughput when considering the user fairness, i.e., all of the users can transmit at an acceptable rate. Moreover, our IQBFO algorithm has a fast convergence.

Lens-based millimeter-wave massive MIMO technologies could reduce the number of required radio frequency chains at the base station without a loss of performance, but require the beamspace channel information, which is often costly to obtain. In this paper, a low-complexity scheme to estimate the channel for lens-based 3D millimeter wave massive MIMO systems is proposed. Beamspace analysis shows that the main entries of the channel matrix form a dual crossing (DC) shape. Existing DC-based channel estimation algorithms have a very high computational complexity. The proposed algorithm eliminates the process of repeatedly selecting the main row and column that is required in existing algorithms, and provides a solution even when certain entries exceed the matrix boundary. It thus has a much lower computational complexity than existing algorithms. Additionally it achieves a smaller normalized mean-squared error of the channel estimates than existing DC-based algorithms.

Recently, lattice reduction (LR)‐aided linear detectors (LDs) are shown to be very effective in multi‐input–multi‐output systems for low‐complexity and small bit‐error‐rate (BER) performance. However, the LR algorithms in the previous LR‐aided LDs mainly aim to improve the orthogonality of the channel matrix where only channel state information is used. In this study, the authors design a novel LR algorithm to enhance the BER performance of the LR‐aided LDs. Unlike the previous LR algorithms, the proposed LR algorithm aims to decrease the modified Euclidean distance (MED) in the LR‐aided LDs, whereas the MED utilises the received signal as well as the channel matrix. Note that the MED is directly related to the BER performance of the LR‐aided LDs, thus decreasing the MED in the LR‐aided LDs can help to reduce the BER of the LR‐aided LDs. In the proposed LR algorithm, the partial column addition operation is used. The simulation results indicate that their LR‐aided LDs exhibit smaller BER than the previous LR‐aided LDs. Moreover, the computational complexity is also shown in the simulation results.

Lattice reduction (LR) is a powerful technique for improving the performance of linear multiple‐input–multiple‐output detection methods. The efficient LR algorithms can largely improve the performance of the linear detectors (LDs). Note that the ordered successive interference cancellation (OSIC) system can decrease the interference between antennas and provide performance gain of the LDs. In this paper, a novel LR‐aided algorithm called NLR‐OSIC improving the performance of the OSIC system has been proposed. Most existing LR algorithms are designed to improve the orthogonality of channel matrices, which is not directly related to the error performance of the OSIC system. While the authors’ algorithm maximises the signal‐to‐interference‐plus‐noise ratio (SINR) of the detected symbol in each stage of the OSIC system, thus exhibiting improved error rate than the previous LR‐aided LDs and their corresponding OSIC algorithms. In each stage, the authors verify that maximising the SINR of the detected symbol can be formulated as a shortest vector problem which is solved by a suboptimal algorithm in this study. In the end of this study, the error rate performance of the proposed algorithm as well as the required complexity has been demonstrated through extensive computer simulations.

Lattice reduction (LR) is a powerful technique for improving the performance of linear MIMO detection methods. The efficient LR algorithms can largely improve the performance of the linear detectors (LDs). However, there are two problems involved in the LR-aided detection algorithms. One is that, the reduced basis is still not orthogonal, and most existing LR-aided algorithms devote to find a near orthogonal matrix. The other one is that the original constellation is no longer the feasible set of the detected symbol, and the elements of the new symbol vector are correlated. In this paper, an improved LR-aided algorithm (ILRA) considering the feasible set of the new symbol has been proposed. We verify that the feasible set is the integer set in a polyhedron. Eliminating the integer constraint, we simplify the detection to a convex optimization problem. Finally, we get the new detected symbol by solving the convex optimization problem. The simulation results show that our algorithm can achieve significant performance gain over the previous LR-aided LDs, especially in the low-order QAM system.