In this work, we consider a covert communication scenario with multiple friendly interference nodes. The goal is to hide a legitimate communication link from a transmitter to a receiver under a warden’s surveillance. Firstly, we propose a novel strategy for generating artificial noise (AN) signals and formulate a corresponding design problem, aiming to minimize the adverse effects of AN on the legitimate receiver while enhancing communication covertness. Specifically, we optimize the basis matrix for AN signal space using statistical information of the involved channel coefficients, when precise channel state information are unavailable. Secondly, we analyze the geometric structure of the AN basis matrix constraint and transform the nonconvex problem into an unconstrained problem on the complex Stiefel manifold. Additionally, we develop a specialized Riemannian Stochastic Variance Reduced Gradient (R-SVRG) algorithm to tackle the problem. In the algorithm, the problem is solved with lower computational complexity compared to full gradient algorithm. Thirdly, we prove that the customized R-SVRG algorithm is theoretically guaranteed to be converge and that the solution is a stationary point of the optimization problem. In the end, simulation results demonstrate the superiority of the proposed AN signal generation strategy over traditional AN in terms of achieving higher covert communication rate.

In this paper, we investigate secure transmission for intelligent reflecting surface (IRS)-aided wireless communication systems, where the IRS assists Alice in delivering confidential information to the legitimate user while preventing leakage to eavesdroppers. To improve physical layer security (PLS), we jointly optimize transmit beamforming (TB) at Alice and passive beamforming (PB) at the IRS. Due to imperfect channel state information (CSI) related to eavesdroppers, the joint TB and PB problem is formulated as a maximization of the expected minimum secrecy rate problem with constant-modulus constraints for IRS. To solve this problem, we first address the expectation operation in the objective function by employing Jensen’s inequality. Then, the deterministic max-min sum-of-logarithms problem is reformulated as an equivalent minimization weighted minimum mean-square error (WMMSE)problem with a bi-quadratic objective function in terms of TB and PB. This problem is solved by the proposed alternating optimization algorithm, where TB and PB are alternately optimized. Specifically, TB is optimized by solving a convex quadratic constrained quadratic programming (QCQP) subproblem, while PB is optimized by applying the penalty convex-concave procedure (PCCP). Simulation results demonstrate that the proposed algorithm achieves good secrecy performance.

In this paper, we consider a scenario of covert communication assisted by multiple friendly interference nodes, aimed at concealing the legitimate communication link under the surveillance of a warden. Its main content is summarized in the following: firstly, we propose a novel strategy for generating artificial noise signals. Specifically, in the absence of accurate channel information between the friendly interference nodes and the legitimate receiver, the statistical information of channel coefficients is leveraged to formulate an optimization problem to design the basis matrix of the artificial noise signal space. Secondly, we employ the Riemannian optimization framework to analyze the geometric structure of the basis matrix constraint and transform the original non-convex optimization problem to an unconstrained problem on complex Stiefel manifold. Additionally, we utilize the Riemannian Stochastic Variance Reduced Gradient (RSVRG) algorithm on complex Stiefel manifold to solve the problem, which has the advantage of low computational burden. Thirdly, we prove that the customized R-SVRG algorithm is theoretically guaranteed convergent. In the end, simulation results show that under some mild conditions on covertness and jamming power, the designed artificial noise signals can let the system enjoy better covertness and less impact on the legitimate communication link than the traditional artificial noise signals.

Rate Splitting (RS) is a versatile and powerful technique for multi-antenna transmission. In this paper, we study the precoding optimization for RS, which is critically important for improving the system performance but often challenging to address. We first investigate the non-convex sum rate maximization problem under perfect Channel State Information at the Transmitter (CSIT). By constructing a separable structure for the sum-of-functions-of-ratios problem and jointly leveraging the Convex Concave Procedure (CCP) and the Alternating Direction Method of Multipliers (ADMM), we obtain a fast algorithm that substantially reduces the overall computational time through the parallel computation and explicit closed-form solutions. We then investigate the average sum rate maximization problem under imperfect CSIT, which is known as a more challenging non-convex stochastic problem. To obtain a fast algorithm for practical use, we carefully approximate the non-convex stochastic problem to a non-convex deterministic one with acceptable performance loss and tailor the fast algorithm derived from perfect CSIT for imperfect CSIT with modest changes. Numerical results show that compared to the state-of-the-art algorithms, the proposed algorithms achieve comparable sum rates or average sum rates but short computation times for large problem sizes, owing to the unique parallel computation structures and few matrix inverse operations.

In this letter, a new decoder based on a bit-embedding technique for non-binary low-density parity-check (LDPC) codes over Galois fields of characteristic two ($\mathbb {F}_{2^{q}}$) is presented. The main content of this work is summarized in the following: first, we derive the equivalent binary codeword and binary parity-check matrix for non-binary LDPC codes in$\mathbb {F}_{2^{q}}$; second, a customized belief propagation algorithm utilizing a bit-embedding technique is proposed based on the formulated binary-check matrix; in the end, simulations results demonstrate that the proposed approach enjoys significant improvement on computational complexity, but almost similar error-correction performance in comparison with the state-of-the-art non-binary LDPC decoders.

While graph neural networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve these issues by first augmenting the node features and then imposing node-wise functions based on multilayer perceptron (MLP), which are widely referred to as graph-augmented MLP (GA-MLP) models. However, while GA-MLP models enjoy deeper architectures for better accuracy, their efficiency largely deteriorates. Moreover, popular acceleration techniques such as stochastic-version or data-parallelism cannot be effectively applied due to the dependency among samples (i.e., nodes) in graphs. To address these issues, in this article, instead of data parallelism, we propose a parallel graph deep learning Alternating Direction Method of Multipliers (pdADMM-G) framework to achieve model parallelism: parameters in each layer of GA-MLP models can be updated in parallel. The extended pdADMM-G-Q algorithm reduces communication costs by introducing the quantization technique. Theoretical convergence to a (quantized) stationary point of the pdADMM-G algorithm and the pdADMM-G-Q algorithm is provided with a sublinear convergence rate o(1/k) , where k is the number of iterations. Extensive experiments demonstrate the convergence of two proposed algorithms. Moreover, they lead to a more massive speedup and better performance than all state-of-the-art comparison methods on nine benchmark datasets. Last but not least, the proposed pdADMM-G-Q algorithm reduces communication overheads by up to 45% without loss of performance. Our code is available at https://github.com/xianggebenben/pdADMM-G.

In this paper, we present a unmanned aerial vehicles (UAV) relay covert communication scheme assisted by an intelligent reflecting surface (IRS), which is exploited to improve channel quality between transmitter and legitimate user. Specifically, we formulate a nonconvex optimization problem to maximize average covert rate, where trajectory of the UAV, transmit beamforming (TB) at Alice, and passive beamforming (PB) of the IRS under the covert constraint are considered. To tackle the difficult problem, we divide it into trajectory optimization (TO) subproblem, TB optimization subproblem, and PB optimization subproblem and then solve them alternately via successive convex approximation algorithm and semidefinite relaxation technique respectively. Numerical results demonstrate the effectiveness of the proposed approach and provide insights on how covert rate is influenced by the trajectory, TB, and PB.

This paper investigates the secure hybrid beamforming (HB) design in an intelligent reflecting surface (IRS) assisted millimeter-wave (mmWave) system, where an IRS is deployed to help the legitimate transmission from Alice to Bob under the eavesdropping of Eve. To protect the legitimate transmission, Alice employs HB to send both the information signal and the artificial noise, while the IRS employs passive beamforming (PB) to reconstruct the wireless environment. Aiming at the secrecy capacity (SC) maximization, the joint optimization of HB and PB is formulated as a non-convex problem with constant-modulus constraints. To efficiently solve such a challenging problem, the original problem is decomposed into a PB subproblem and an HB subproblem, then these subproblems are sequentially solved by the proposed algorithms. Particularly, for the PB subproblem, we propose a channel information aided PB algorithm, which is proved to converge at a stationary point. With the solution of PB subproblem, two algorithms are proposed for the HB subproblem: 1) near-optimal SC approaching HB algorithm that achieves a near-optimal solution; 2) low-complexity HB algorithm that achieves a slight lower SC with less computational complexity. Simulation results demonstrate the superior performance of proposed algorithms in comparison with the state-of-the-art works.

This paper presents an efficient quadrature amplitude modulation (QAM) signal detector for massive multiple-input multiple-output (MIMO) communication systems via the penalty-sharing alternating direction method of multipliers (PS-ADMM). The content of the paper is summarized as follows: first, we formulate QAM-MIMO detection as a maximum-likelihood optimization problem with bound relaxation constraints. Decomposing QAM signals into a sum of multiple binary variables and exploiting introduced binary variables as penalty functions, we transform the detection optimization model to a non-convex sharing problem; second, a customized ADMM algorithm is presented to solve the formulated non-convex optimization problem. In the implementation, all variables can be solved analytically and in parallel; third, it is proved that the proposed PS-ADMM algorithm converges under mild conditions. Simulation results demonstrate the effectiveness of the proposed approach.

In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two $\left( {{\mathbb{F}_{{2^q}}}} \right)$. Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in ${\mathbb{F}_{{2^q}}}$ to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly $\mathcal{O}\left( {nq} \right)$, where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.

In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code’s length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders.

In this paper, we design two efficient quadrature amplitude modulation (QAM) signal detectors for massive multiple-input multiple-output (MIMO) communication systems via the penalty-sharing alternating direction method of multipliers (PS-ADMM). The content of the paper is summarized as follows: first, we transform the maximum-likelihood detection model to a non-convex sharing optimization problem for massive MIMO-QAM systems, where a high-order QAM constellation is decomposed to a sum of multiple binary variables, integer constraints are relaxed to box constraints, and quadratic penalty functions are added to the objective function to result in a favorable integer solution; second, a customized ADMM algorithm, called PS-ADMM, is presented to solve the formulated non-convex optimization problem. In the implementation, all variables in each vector can be solved analytically and in parallel; and third, in order to solve the penalty-sharing distributively, we improve the proposed PS-ADMM algorithm to a distributed one, named DPS-ADMM. In the end, performance analyses of the proposed two algorithms, including convergence properties and computational cost, are provided. Simulation results demonstrate the effectiveness of the proposed approaches.

Manifold landmarking is the problem of selecting a subset of discrete locations on a continuous manifold for label assignment, in order to reduce interpolation error of subsequent semi-supervised learning. In this paper, we select landmarks to minimize the condition number (λmax/λmin) of a submatrix of an alignment matrix Φ, which is equivalent to minimizing an interpolation error bound. Specifically, we design an efficient greedy scheme, where at each iteration t + 1 we choose one landmark i (thus deleting the corresponding row and column i of Φt) so that the resulting submatrix Φt+1has the smallest condition number. Towards fast landmark selection, at iteration t + 1, we first compute the two extreme eignevectors v1and vNcorresponding to λminand λmaxof Φtvia known methods like LOBPCG. We show that λmin(λmax) of submatrix Φt+1, from deleting the chosen row-column pair, can be approximated by an upper (lower) bound that is an easily computable function of eigen-pair {v1, λmin} ({vN, λmax}) of Φt. The error bounds of the obtained approximations can be numerically computed during the greedy step. Leveraging these proofs, we minimize a bound of the condition number for submatrix Φt+1at each greedy step t + 1. Experiments on synthetic and real-world manifold data demonstrate the superiority of our proposed landmarking algorithm compared to several state-of-the-art schemes.

In this paper, we develop an efficient quadratic programming (QP) decoding algorithm via the alternating direction method of multipliers (ADMM) technique for binary low density parity check (LDPC) codes. Its main content is as follows: first, through transforming the three-variables parity check equation to its equivalent expression, we relax the maximum likelihood decoding problem to a quadratic program. Second, the ADMM technique is exploited to design the solving algorithm of the resulting QP decoding model. Compared with the existing ADMM-based mathematical programming (MP) decoding algorithms, our proposed algorithm eliminates complex Euclidean projection onto the check polytope. Third, we prove that the proposed algorithm satisfies the favorable property of all-zeros assumption. Moreover, by exploiting the inside structure of the QP model, we show that the decoding complexity of our proposed algorithm in each iteration is linear in terms of LDPC code length. Simulation results demonstrate that the proposed QP decoder attains better error-correction performance than the sum-product BP decoder and costs the least amount of decoding time amongst the state-of-the-art ADMM-based MP decoding algorithms.

This paper investigates the hybrid precoding design in millimeter-wave (mmWave) systems with a fully-adaptive-connected precoding structure, where a switch-controlled connection is deployed between every antenna and every radio frequency (RF) chain. To maximally enhance the energy efficiency (EE) of hybrid precoding under this structure, the joint optimization of switch-controlled connections and the hybrid precoders is formulated as a large-scale mixed-integer non-convex problem with high-dimensional power constraints. To efficiently solve such a challenging problem, we first decouple it into a continuous hybrid precoding (CHP) subproblem. Then, with the hybrid precoders obtained from the CHP subproblem, the original problem can be equivalently reformulated as a discrete connection-state (DCS) problem with only 0-1 integer variables. For the CHP subproblem, we propose an alternating hybrid precoding (AHP) algorithm. Then, with the hybrid precoders provided by the AHP algorithm, we develop a matching assisted fully-adaptive hybrid precoding (MA-FAHP) algorithm to solve the DCS problem. It is theoretically shown that the proposed MA-FAHP algorithm always converges to a stable solution with the polynomial complexity. Finally, simulation results demonstrate the superior performance of the proposed MA-FAHP algorithm in terms of EE and beampattern.

Graph sampling with independent noise towards minimum mean square error (MMSE) leads to the known A-optimality criterion, which is computation-intensive to evaluate and NP-hard to optimize. In this paper, we propose a new low-complexity sampling strategy based on Neumann series that circumvents large matrix inversion and eigen-decomposition. We first prove that a DC-shifted A-optimality criterion is equivalent to an objective computed using the inverse of a sub-matrix of an ideal graph low-pass (LP) filter. The LP filter matrix can be approximated efficiently via fast Graph Fourier Transform (FGFT). Using the shifted A-optimality objective as a proxy, we then propose a fast algorithm to greedily select samples one-by-one based on a matrix inversion lemma with simple matrix updates. We show that the obtained solution has a performance upper bound via super-modularity analysis. Simulation results show that our proposed sampling strategy has lower complexity and outperforms several existing deterministic sampling schemes.

Unimodular sequences with good correlation properties are desired in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences and the main content is as follows: first, we formulate the design problem as a quartic polynomial minimization problem with constant modulus constraints. Then, by introducing auxiliary variables, the polynomial minimization problem is equivalent to a nonconvex consensus problem. Second, we develop a low-complexity consensus parallel direction method of multipliers (consensus-PDMM) algorithm, in which all subproblems can be performed in parallel with analytical solutions. Moreover, we prove that consensus-PDMM's output is some stationary point of the original nonconvex problem if it is convergent. Third, two variant PDMM algorithms, based on stochastic block coordinate descent and accelerated gradient descent, are proposed to reduce the computational complexity and speed up the convergence rate. Numerical simulation results show that the proposed algorithm offers better performance than the state-of-the-art approaches.

This paper investigates the hybrid precoding design in millimeter-wave (mmWave) systems. To jointly consider the spectral efficiency and energy consumption, we propose an adaptive hybrid precoding structure, where a switch-controlled connection is deployed between every antenna and every radio frequency (RF) chain. To maximally enhance the spectral-and-energy efficiency under this structure, the joint optimization of the on-off states for switch-controlled connections and the hybrid precoding matrices is formulated as a non-convex problem. To efficiently solve this problem, we first propose an alternative limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) based algorithm to determine the hybrid precoders. Then, using the alternative L-BFGS algorithm, a greedy algorithm is proposed to jointly optimize the hybrid precoders and the on-off states of switch-controlled connections. It is theoretically shown that, this alternative L-BFGS based algorithm always converges to a stationary point. Further, the convergence of proposed greedy algorithm is also theoretically proved and validated by simulations. Simulation results also demonstrate that the proposed hybrid precoding achieves a superior tradeoff between the spectral efficiency and energy consumption.

In this paper, we design constant modulus probing waveforms with low correlation sidelobes for colocated multi-input multi-output (MIMO) radar. Through exploiting the structure of the problem, we formulate it as a non-convex consensus minimization problem. Then a customized alternating direction method of multipliers (ADMM) algorithm is proposed to solve the problem, which is guaranteed convergent to its stationary point. Numerical examples show that the proposed approach offers better performance than the state-of-the-art approaches. Moreover, parallel implementation structure indicates that the proposed ADMM algorithm is suitable for applications involving large dimensionality.

Each user inside the cell of massive multiple- input multiple-output (MIMO) system suffers from severe pilot contamination (PC), which directly decreases the quality of service. To mitigate the PC, this paper proposes an improved soft pilot reuse scheme combined with time-shifted pilot arrangement, named by TS-SPR. First, we divide the users inside the cell into two parts: the center users and the edge users. For the center users, we divide all cells into three groups and implement the time- shifted pilot transmissions in uplink training stage. For the edge users, a filtering approach based on fast Fourier transform (FFT) operation is proposed to extract desired signals from interfering signals by the non-overlapping angle- of-arrivals (AOAs). Simulation results show that the proposed TS-SPR scheme can effectively improve the overall performance of the system without extra cost of pilot resources.

Beamforming with multiple data streams, or named as precoding, plays a significant role in millimeter-wave massive MIMO systems. If properly designed, the precoding can improve spectral efficiency of the system and compensate for the degradation caused by channels. Although the classical full-digital precoding can achieve the optimal performance, it is too expensive for implementation. To reduce cost and power consumption, some hybrid structures of precoding are recently proposed while their precoding schemes have not been extensively studied. In this paper, the mathematical model of the precoding for relay assisted system is reconstructed. The objective function is highly non-convex and has some complex constraints. Especially the block-diagonal constraint and constant-modulus constraint make the classical precoding methods based on singular value decomposition not applicable. We design an algorithm based on alternating direction method of multipliers to optimize the objective function. By deliberating over the iteration order of the variables, we give the convergent condition of the proposed algorithm. This paper focused on sub-connected precoding structures since they have more constraints. Meanwhile, the proposed algorithm can be applied to full-connected structures simply. We present the simulation results which indicate that the proposed algorithm can provide a near optimal solution to the original precoding problem.

Graph signal processing (GSP) studies signals that live on irregular data kernels described by graphs. One fundamental problem in GSP is sampling-from which subset of graph nodes to collect samples in order to reconstruct a bandlimited graph signal in high fidelity. In this letter, we seek a sampling strategy that minimizes the mean square error (MSE) of the reconstructed bandlimited graph signals assuming an independent and identically distributed noise model-leading naturally to the A-optimal design criterion. To avoid matrix inversion, we first prove that the inverse of the information matrix in the A-optimal criterion is equivalent to a Neumann matrix series. We then transform the truncated Neumann series-based sampling problem into an equivalent expression that replaces eigenvectors of the Laplacian operator with a submatrix of an ideal low-pass graph filter. Finally, we approximate the ideal filter using a Chebyshev matrix polynomial. We design a greedy algorithm to iteratively minimize the simplified objective. For signal reconstruction, we propose an accompanied signal reconstruction strategy that reuses the approximated filter submatrix and is provably more robust than conventional least square recovery. Simulation results show that our sampling strategy outperforms two previous strategies in MSE performance at comparable complexity.

In this paper, a multi-cell joint optimization scheme based on pilot allocation is proposed in order to mitigate pilot contamination for multi- cell massive MIMO systems. This method measures interference of each pilot sequence caused by users multiplexing from adjacent cells exploiting the massive MIMO characteristics of fading channels. The scheme takes jointly optimizing a plurality of cells into account to ensure users in poor channel conditions suffering from less interference after the assignment, and improves the system performance with low computational complexity. Simulation results demonstrate the effectiveness of the proposed scheme.

This paper considers a MISO interference channel with simultaneous wireless information and power transfer. We aim to jointly optimizing transmit beamformers and receive power splitting factors to minimize the total transmission power subject to both the signal-to-interference-plus-noise ratio constraints and energy harvesting constraints. We propose relaxation solution to the power minimization problem and provide an easily-checkable sufficient condition to confirm when the relaxation solution is optimum. Moreover, we propose a simple suboptimal solution to the power minimization problem when the sufficient optimality condition does not hold. Simulation results indicate that the proposed solution outperforms the existing suboptimal solution and reaches optimality.

This paper studies minimum mean square error (MMSE)-based training signal design for MIMO channel estimation with correlated disturbance (i.e., interference plus noise). First, we consider training signal design for Kronecker-structured MIMO channel estimation where both channel and disturbance are assumed in Kronecker structures. We prove the optimal training sequence structure for arbitrarily Kronecker-structured MIMO channel estimation. Using the optimal training sequence structure, we show that the MSE minimization problem can be globally solved. Second, we consider the training signal design problem in the case of general channel and disturbance model (i.e., without Kronecker structure assumption). We propose a simple iterative algorithm based on block coordinate descent method which can keep the MSE nonincreasing at each iteration. Finally, simulation results indicate good performance of the proposed iterative algorithm by comparing with the optimal training signal design method.