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

In this paper, we study a sampling-based detection strategy for massive multiple-input multiple-output (MIMO) systems, driven by a modified discrete diffusion model formulated as an analytical, non-learning sampling process. Built upon this framework, the proposed discrete diffusion-based sampling (DDS) algorithm improves decoding performance by leveraging residual-dependent sampling, compared to the independent randomized successive interference cancellation (SIC). Specifically, the modified diffusion model incorporates a shortcut perturbation toward the SIC solution, a forward diffusion step to enhance diversity, and step-wise alignment with the perturbed received signal. Within this framework, the DDS algorithm further adopts one-dimensional discrete Gaussian distribution, involving a reformulated discrete Gaussian noise and an explicitly characterized sampling range, but retains computational complexity amenable to practical deployment. Moreover, we theoretically demonstrate an improved expected decoding radius over randomized SIC. Finally, simulation results based on massive MIMO detection are presented to confirm performance gain of the proposed DDS algorithm.

Intelligent reflecting surface (IRS) emerges as a promising technology to enhance wireless communication in recent years. However, the applications of deep learning algorithms within RIS-aided communication systems often suffer performance degradation under extreme conditions owing to a reliance on manual trial-and-error attempts. In this paper, the proposed beamforming neural network architecture search (BNAS) framework automates the design of of neural networks for the joint optimization of precoding vectors and IRS phase shift vectors. To improve robustness and performance, a specialized search space, incorporating two cascading supernets with selectable channel routes, diverse topological connections, and varied operations, is meticulously crafted for beamforming tasks. Meanwhile, the integration of neural tangent kernel theory, supported by alternative optimization guidance and bayesian optimization, not only enhances interpretability but also improves efficiency, thus enabling a more systematic and insightful search process compared to conventional approaches. Extensive numerical simulations confirm the applicability of BNAS, demonstrating superior performance compared to existing deep learning-based methods and traditional algorithms, particularly in challenging scenarios.

This paper investigates the downlink energy efficiency (EE) optimization for cell-free massive multiple input multiple output (CF-mMIMO) systems subject to ultra-reliable and low-latency communication (URLLC) requirements. To achieve superior performance, we jointly consider the impacts of power allocation, access point (AP)-user association, and AP sleep modes under the finite blocklength (FBL) regime, leading to a challenging mixed-integer (MI) non-convex optimization problem. Utilizing a sequential convex approximation (SCA) framework, we first propose the SCA-Relaxation algorithm to convert the original problem into a series of second-order cone programming (SOCP) sub-problems, which can be efficiently addressed via modern convex programming solvers. Moreover, for further reducing computational complexity, we approximate the original problem as a continuous-variable optimization and tackle it via a combination of the Dinkelbach transformation, penalty functions, as well as an accelerated proximal gradient method with adaptive momentum, resulting in the proposed low complexity EE maximization (LCEE-max) algorithm. Besides, the related convergence and complexity analysis of these two algorithms are also presented in detail. Simulation results demonstrate that compared to the state-of-the-art baseline algorithm, the proposed two algorithms achieve the EE improvements of approximately 40% and 30%, respectively, along with a substantial reduction in complexity, thereby enabling efficient and fast resource allocation in CF-mMIMO-enabled URLLC scenarios.

As the scale of Internet of Things (IoT) grows rapidly, accurate active user detection has emerged as an important problem in massive connectivity scenarios. This paper presents a novel low-complexity expectation propagation (LC-EP) algorithm for massive connectivity. Different from traditional methods that reduce the complexity of EP through channel hardening, LC-EP exploits a new statistical convergence property of the Gram matrix for the complexity reduction. Meanwhile, the decision method is modified from the original log-likelihood ratio (LLR)-based approach to an order-based method for the future performance gain. Simulation results demonstrate that the proposed LC-EP algorithm improves both detection accuracy and efficiency.

This paper proposes a cluster-based low-complexity codebook design scheme for hierarchical near-field beam training in extremely large-scale MIMO(XL-MIMO), referred to as the cluster hierarchical beam training (CHB). Specifically, to reduce the codebook dimensionality while preserving essential angle and distance information, the proposed CHB scheme employs a cluster-based approach to identify cluster centers as new polar-domain sampling points. By doing so, CHB significantly reduces the complexity of codeword generation. The generated codewords are then applied to hierarchical beam training, thereby further decreasing the associated training overhead. Finally, simulation results confirm that CHB reduces complexity while offering comparable or even superior performance to other codebook-based near-field beam training schemes.

In this paper, we consider real-time beamforming design for dynamic wireless environments with different channel state information (CSI) distributions in cell-free systems. Specifically, a sum-rate maximization optimization problem for different CSI distributions is built to model the beamforming design of dynamic wireless environments in cell-free systems. To efficiently solve the optimization problem, we propose a high-generalization network (HGNet). By preserving invariant features and discarding sensitive features for different CSI distributions, HGNet effectively improves the generalization performance of beamforming design for dynamic wireless environments in cell-free systems. Numerical results demonstrate that HGNet achieves a higher sum rate with a lower reflection time for different CSI distributions, thus realizing real-time beamforming design for dynamic wireless environments in cell-free systems.

Next-generation wireless communication systems are unifying massive MIMO and integrated sensing and communication (ISAC) to enhance sensing and communication performance simultaneously. In this paper, the signal detection problem for MIMO-ISAC systems is modeled as a mixed-integer least squares problem (MILSP). To solve it in an efficient way, an iterative algorithm combining alternating direction method of multipliers (ADMM) and neighborhood search (NS) technique is proposed, which is named as NS-ADMM. Specially, at each iteration, the output of ADMM serves for the following neighborhood search to achieve the extra performance gain. Moreover, a flexible mechanism of ADMM iterations is also given for a better estimation of the sensing signals. Finally, simulations demonstrate the proposed NS-ADMM algorithm has significant performance advantages with low computational complexity.

In this paper, we consider real-time beamforming design for dynamic wireless environments with varying channels and different numbers of access points (APs) and users in cell-free systems. Specifically, a sum spectral efficiency (SE) maximization optimization problem is formulated for the beamforming design in dynamic wireless environments of cell-free systems. To efficiently solve it, a high-generalization network (HGNet) is proposed to adapt to the changing numbers of APs and users. Then, a high-generalization beamforming module is also designed in HGNet to extract the valuable features for the varying channels, and we theoretically prove that such a high-generalization beamforming module is able to reduce the upper bound of the generalization error. Subsequently, by online adaptively updating about 3% of the parameters of HGNet, an online adaptive updating (OAU) algorithm is proposed to enable the online adaptive real-time beamforming design for improving the sum SE. Numerical results demonstrate that the proposed HGNet with OAU algorithm achieves a higher sum SE with a lower computational cost on the order of milliseconds.

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the discrete constraint of AP clustering. Through transformations, the intractable simultaneous optimization of continuous and discrete variables is reduced to optimizing only the sparsity of the continuous variables, facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.

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

The Langevin sampling method relies on an accurate score matching while the existing massive multiple-input multiple output (MIMO) Langevin detection involves an inevitable singular value decomposition (SVD) to calculate the posterior score. In this work, a massive MIMO sampling detection strategy that leverages the denoising diffusion model is proposed to narrow the gap between the given iterative detector and the maximum likelihood (ML) detection in an SVD-free manner. Specifically, the proposed score-based sampling detection strategy, denoted as approximate diffusion detection (ADD), is applicable to a wide range of iterative detection methods, and therefore entails a considerable potential in their performance improvement by multiple sampling attempts. On the other hand, the ADD scheme manages to bypass the channel SVD by introducing a reliable iterative detector to produce a sample from the approximate posterior, so that further Langevin sampling is tractable. Customized by the conjugated gradient descent algorithm as an instance, the proposed sampling scheme outperforms the existing score-based detector in terms of a better complexity-performance trade-off.

Hybrid precoding plays an important role in massive MIMO systems for reducing the hardware cost caused by radio frequency (RF) chains. In this paper, an efficient joint hybrid precoding and analog combining (EJHPAC) scheme is proposed for massive MIMO with multiple-antenna user equipment (UE), which applies the phase elimination method to harvest the power gain. Specifically, the problem of analog combining is transformed to a least square problem with constant modulus constraint. Based on it, we adopt the gradient descent projection (GDP) method to the analog combiner and jointly design the related hybrid precoding algorithm, which leads to the proposed EJHPAC algorithm. According to complexity analysis and simulation results, we show that the EJHPAC algorithm has advantages in both spectral efficiency and computational complexity for massive MIMO systems.

The cell-free network (CFN) is a promising technology capable of delivering high-reliability, high-data rate wireless communication services for Metaverse communication. This paper studies a joint optimization problem of user scheduling (US) and beamforming (BF) in CFN, where constraints of per access point (AP) power and the limited number of the scheduled users per AP are considered. In order to reduce the interaction overhead, this problem is investigated using local channel state information (CSI). Since this problem is a mixed-integer nonlinear programming (MINP) program with non-convexity and high complexity, we propose an alternating optimization framework to solve this problem. Specifically, we first adopt the weighted$l_{1}$-norm approximation to transform the discrete variables into the continuous variables. Then, we solve the rest of the problem by fractional programming, and solve the subproblems alternatively. The analysis of complexity and convergence analysis validate the efficiency and accuracy of the proposed algorithm. Numerical results show that the cross-layer design of the US&BF scheme is superior to the separate design of US&BF schemes. In addition, the proposed algorithm with local CSI achieves a comparable data rate to the algorithms with global CSI.

In this paper, a deterministic sampling decoding strategy for multiple-input multiple output (MIMO) systems is studied, which performs probabilistic searching according to a probability threshold in the lattice Gaussian distribution. Motivated by model probabilistic twin (MPT), the randomness in obtaining the target decoding solution is overcome by the proposed probabilistic searching decoding (PSD) algorithm, which brings considerable decoding gains in both performance and complexity. Specifically, the decoding radius of PSD is derived while the decoding complexity in terms of the number of visited nodes during the searching is also upper bounded, leading to an explicit decoding trade-off. Meanwhile, we generalize PSD by the mechanism of candidate protection so that it enjoys a flexible performance between the suboptimal successive interference cancelation (SIC) decoding and the optimal maximum likelihood (ML) decoding by adjusting the initial search size$K$. Methods for further optimization and complexity reduction of the proposed PSD algorithm are also given. Finally, simulation results based on MIMO detection are presented to confirm the tractable and flexible decoding trade-off of the proposed PSD algorithm.

In this paper, the projected-gradient-descent (PGD) -based detector for massive MIMO system, which consists of two basic operations — projection and gradient descent (GD), is studied to achieve the performance improvement. Since the projection and GD step have different loss functions, necessary compromise has to be made to balance them during iterations. For this reason, the generalized PGD (GPGD) method is proposed with flexible choices of projection and GD. Different from performing projection and GD alternatively, we show that implementing projection after every multiple GD steps is a better solution. Meanwhile, the step-size of GD is also investigated for convergence efficiency. After that, by unfolding this proposed GPGD method with deep neural networks (DNN), the self-corrected auto-detector (SAD) is established to achieve better decoding performance, where enhancement by attention mechanism and extension by another iterative method are also given for performance improvement and efficiency.

Accurate channel estimation is an essential prerequisite for achieving significant performance gains in intelligent reflecting surface (IRS)-aided communication systems. Recent studies have shown that deep neural network-based channel estimation holds promise as a competitive alternative to conventional methods. However, existing neural network-based approaches typically involve manual design of network architectures through a trial-and-error process, demanding extensive domain knowledge and human resources. In this paper, we propose an automatic approach to construct a high-performance neural network architecture for channel estimation. Our method, called the channel estimation neural network architecture search (CENAS), utilizes a truncated back-propagation optimization search strategy to explore a neural network tailored for channel estimation. By carefully designing a search space tailored to channel estimation tasks, the automatically constructed network surpasses both conventional and deep learning-based channel estimation algorithms. The convergence of our framework’s network construction process is comprehensively analyzed, providing formal evidence of its convergence properties. Additionally, the proposed framework exhibits good generalization and applicability by allowing flexible adjustment of hyperparameters to generate networks with varying scales. Empirical results show the stability and the improved performance of CENAS framework, validating its effectiveness and desirability.

In this paper, we study low-complexity linear precoding for downlink massive multiple-input multiple-output (MIMO) systems, exploiting a statistical method. In sharp contrast to traditional linear precoding algorithms, our proposed efficient randomized iterative precoding algorithm (ERIPA) not only avoids costly matrix inversion but also considers the complexity reduction of matrix multiplication involved, thus enabling more efficient linear precoding. Additionally, ERIPA is demonstrated to have both exponentially fast and global convergence, making it adaptable to various practical scenarios of massive MIMO. We also investigate the convergence phenomenon of ERIPA in relation to the selection of the sampling distribution during random iterations. After that, the concept of conditional sampling is introduced to ERIPA such that significant system potential can be beneficially exploited in terms of both precoding performance and computational complexity. Finally, simulation results regarding the downlink massive MIMO are presented to confirm the superiorities of the proposed ERIPA.

In this paper, the cross-layer optimization problem of access point selection (APS) and beamforming (BF) in cell-free network (CFN) with local CSI is studied, where constraints of per AP power and the number of active APs are considered. Such a joint APS&BF optimization problem is modeled as a mixed-integer nonlinear programming (MINP) problem aiming at maximizing the sum rate of the whole system. Fractional programming (FP)-based and alternating optimization (AO)-based algorithms with weightedl1-norm approximation are proposed to solve this MINP problem. However, the latter performs better than the former, with higher complexity. A lightweight multi-head single-body graph neural network (MHSB-GNN) algorithm is proposed, where the nodes and structures are innovatively designed. The MHSB-GNN benefits from the different node updating modules for different user equipment (UE), which introduce extra prior information into the graph and mine specific information of different UEs. Moreover, the equivalence between GNN and FP-based algorithm is proved to provide interpretability and theoretical guarantees for MHSB-GNN. The analysis of convergence and complexity validates the accuracy and effectiveness of the FP and AO-based algorithms. Leveraging the existing APS and BF solver, it is shown that the three proposed algorithms guarantee comparable performance as the exhaustive search algorithm in performance and complexity.

In this paper, two ordered iterative detection methods are proposed for better signal detection performance in massive multiple-input multiple-output (MIMO) systems. First of all, in order to reduce error propagation in the traditional iterative detection schemes with sequential order, the ordered iterative detection (OID) algorithm is proposed, which achieves a better detection performance with low complexity. Then, we show that the convergence performance chiefly depends on the residual component during the iterations. Therefore, a dynamic ordering strategy is given for further performance improvement, which leads to the modified ordered iterative detection (MOID) algorithm. After that, we extend the proposed MOID algorithm via deep learning network (DNN), and parameters like relaxation factor are trained to optimal for further performance gain.

In this paper, a cross-layer optimization problem of access point selection (APS) and beamforming (BF) in cell free network (CFN) has been studied, where constraints of per access point (AP) power and per user receiving data streams are considered. Such a cross-layer design of APS&BF problem is modeled as a mixed-integer nonlinear programming (MINP) program. Then, by adopting the weighted l1-norm approximation, the MINP problem is transformed into the sum logarithmic multiple-ratio form. To be specific, a novel and low-complexity mix-integer fractional programming (MIFP) algorithm is proposed to solve the transformed problem effectively. Convergence analysis validates that the proposed MIFP converges to a local optimal solution. Finally, numerical results show that cross-layer design of APS&BF scheme is superior to separate design of APS&BF schemes. In addition, the proposed MIFP has the approximate performance as partial exhaustive search algorithm.

In this paper, rapidly converging low-complexity iterative transmit precoding (TPC) techniques are proposed for the massive multiple-input multiple-output (MIMO) downlink. First of all, the proposed random block-based iterative TPC (RBI-TPC) algorithm performs its iterations by updating multiple rather than a single component at each instant, where the updating order of each block containing multiple components relies on the samples randomly sampled from a discrete distribution. Based on the analytically derived convergence rate, we demonstrate that improved convergence is achieved by the block-based update mechanism conceived since the correlation between multiple components can be beneficially exploited. Then, the random sampling that determines the updating order is studied. By applying conditional random sampling, the updating order is optimized based on the latest updates for attaining more rapid convergence. We also demonstrate that the associated updating order may become deterministic under specific conditions so that a fixed but optimized updating order can be used for facilitating the practical implementations, which paves the way for conceiving the ordered block-based iterative TPC (OBI-TPC) algorithm. Finally, the concept of successive over-relaxation (SOR) is adopted for further convergence improvement and simulations are presented to illustrate the performance improvements of the proposed RBI and OBI TPC algorithms compared to the existing low-complexity iterative TPC schemes.

In this paper, a new randomized iterative detection algorithm (NRIDA) is proposed for uplink large-scale MIMO systems, where the random iterations in it are designed to work for the detection model (denoted by$\mathbf {y}=\mathbf {Hx}+\mathbf {n}$) directly. Different from those traditional iterations designed for the linear system (denoted by$\mathbf {Ax}=\mathbf {b}$with$\mathbf {A}=\mathbf {H}^{H}\mathbf {H}$and$\mathbf {b}=\mathbf {H}^{H}\mathbf {y}$), we show that besides the complexity reduction about the matrix inversion, in the proposed NRIDA the computational complexity of matrix multiplication for the linear detection is also greatly reduced without any performance loss, thus leading to a much lower detection complexity. Meanwhile, according to convergence analysis, we demonstrate that the proposed NRIDA enjoys a globally exponential convergence performance, enabling it well suited to the various detection cases of interest. Besides, further complexity reduction and the choices of the sampling distribution in NRIDA are studied as well in full details. Moreover, in order to achieve a better detection trade-off between performance and complexity, we introduce the concept of the conditional sampling into NRIDA, which brings significant gains in both iteration convergence and efficiency. Finally, simulations with respect to the uplink large-scale MIMO detection are presented to illustrate the remarkable gains of the proposed NRIDA in both performance and complexity.

Abstract We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices$\mathcal {E}_{m}$and$\mathcal {G}_{m}$. By explicitly linking their lattice bases to various forms of$\mathcal {E}_{m}$and$\mathcal {G}_{m}$cosets, we discover the$\mathcal {E}_{m,2}^{+}$lattices, based on which we report the best known lattice quantizers in dimensions 14, 15, 18, 19, 22 and 23. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.

Spectrum mapping has emerged as an important problem in wireless communications, which generates a spectrum map for the spectrum resource analysis and management. Given the constrained transceiver volume and the limited energy consumption, how to effectively reconstruct the spectrum situation by the limited sampling data is a pressing challenge for spectrum mapping. In this paper, by exploiting the sparse nature of spectrum situation, we firstly attempt to solve the three-dimensional (3D) compressed spectrum mapping problem in the way of compressed sensing. Then, we develop a quadrature and right-triangular (QR) pivoting based measurement matrix optimization algorithm. By iteratively selecting new dominant sampling locations, it promotes the recovery accuracy compared to random measurement. After that, we propose a 3D spatial subspace based orthogonal matching pursuit (OMP) algorithm to recover spectrum situation for 3D compressed spectrum mapping. Finally, simulations are presented to show the comparisons in terms of localization, source signal strength recovery, recovery success rate and situation recovery. Results show our proposed 3D spectrum mapping scheme not only effectively reduces the sampling number, but also achieves a high level of spectrum mapping accuracy.

In this paper, the random iterative method is introduced to massive multiple-input multiple-output (MIMO) systems for the efficient downlink linear precoding. By adopting the random sampling into the traditional iterative methods, the matrix inversion within the linear precoding schemes can be approximated statistically, which not only achieves a faster exponential convergence with low complexity but also experiences a global convergence without suffering from the various convergence requirements. Specifically, based on the random iterative method, the randomized iterative precoding algorithm (RIPA) is firstly proposed and we show its approximation error decays exponentially and globally along with the number of iterations. Then, with respect to the derived convergence rate, the concept of conditional sampling is introduced, so that further optimization and enhancement are carried out to improve both the convergence and the efficiency of the randomized iterations. After that, based on the equivalent iteration transformation, the modified randomized iterative precoding algorithm (MRIPA) is presented, which achieves a better precoding performance with low-complexity for various scenarios of massive MIMO. Finally, simulation results based on downlink precoding in massive MIMO systems are given to show the system gains of RIPA and MRIPA in terms of performance and complexity.

Deep learning (DL) has emerged as a powerful tool for signal detection in large-scale multiple-input multiple-output (MIMO) systems. In this paper, the recurrent sparse detection network (RS-Net) is proposed for performance improvement and complexity reduction. First of all, in order to reduce complexity, RS-Net unfolds the projected gradient descent (PGD) method in a modified way, which consists of a projection and a gradient descent (GD) part. Meanwhile, an RNN with the parameter-sharing structure is adopted to its projection, which significantly eases the training burden. Then, to improve the detection performance, we regularize RS-Net by introducing sparse representation. Besides, the step size of iterations in GD part is also investigated for better convergence efficiency. Finally, simulations demonstrate a better decoding trade-off between performance and complexity in RS-Net.

Conventional hybrid precoding and combining based transceivers require a large number of high-resolution radio frequency (RF) phase shifters (PSs), which impose prohibitive hardware costs and power consumption. To address the above issue, both partially connected RF PSs and low-resolution PSs have been proposed. However, the performance limits of these low-cost designs have not been investigated theoretically. Furthermore, there is room for improvement in their spectral efficiency. To fill this knowledge gap, we derive the mean square error performance discrepancy between an optimal precoder/combiner and the hybrid analog-digital precoder/combiner under the constraint of 1-bit PSs relying on lattice theory. Then, by observing that this performance gap can be reduced by deactivating parts of the PSs whilst improving both the spectral and energy efficiency, we develop an adaptive RF PS connection network. To resolve the associated hybrid precoding and combining problems, we appropriately adapt Babai's algorithm from the lattice decoding literature. Our simulation results demonstrate the superiority of the proposed scheme both in terms of its spectral and energy efficiency.

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and decoding while Markov chain Monte Carlo (MCMC) methods from statistics offer an effective way to solve it. In this paper, the sliced lattice Gaussian sampling algorithm is proposed to further improve the convergence performance of the Markov chain targeting at lattice Gaussian sampling. We demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Meanwhile, the convergence rate of the underlying Markov chain is also investigated, and we show the proposed sliced sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. On the other hand, the decoding performance based on the proposed sampling algorithm is analyzed, where the optimization with respect to the standard deviation σ > 0 of the target lattice Gaussian distribution is given. After that, a judicious mechanism based on distance judgement and dynamic updating for choosing σ is proposed for a better decoding performance. Finally, simulation results based on multiple-input multiple-output (MIMO) detection are presented to confirm the performance gain by the convergence enhancement and the parameter optimization.

In this letter, a random sampling strategy is proposed for the non-cooperative spectrum sensing to improve its performance and efficiency in cognitive radio (CR) networks. The proposed refined Metropolis-Hastings (RMH) algorithm generates the desired channel sequence for fine sensing by sampling from the approximated channel availability distributions in an Markov chain Monte Carlo (MCMC) way. The proposal distribution during the sampling is fully exploited and the convergence of the Markov chain is studied in detail, which theoretically demonstrate the superiorities of the proposed RMH sampling algorithm in both sensing performance and efficiency.

In current vector perturbation (VP) precoding architecture, the optimum perturbation vector is found with a closest lattice vector search for a given query point. In this work, we show that the query point should be judiciously chosen such that the effective noise power is minimized. The reduced noise power results in a better error rate performance for VP. The crux in the design is to decode an integer-multiple of lattice point within a modulo lattice architecture, where the integer- multiple can be a prime or a product of primes. Simulations show that around 2 dBs' performance gain can be observed even in the small-scale systems.

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and cryptography. In this paper, the slice sampling from Markov chain Monte Carlo (MCMC) is adopted to lattice Gaussian sampling. Firstly, the slice-based sampling algorithm is proposed to sample from lattice Gaussian distribution. Then, we demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Moveover, the convergence rate of the underlying Markov chain is investigated, and we show the proposed slice sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. Finally, simulation results based on MIMO detection are presented to confirm the performance gain by convergence enhancement.

Sampling from lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, the classic Gibbs algorithm from Markov chain Monte Carlo (MCMC) methods is demonstrated to be geometrically ergodic for lattice Gaussian sampling, which means that the Markov chain arising from it converges exponentially fast to the stationary distribution. Meanwhile, the exponential convergence rate of the Markov chain is also derived through the spectral radius of the forward operator. Then, a comprehensive analysis of the convergence rate is carried out, and two sampling schemes are proposed to further enhance the convergence performance. The first one, referred to as a Metropolis-within-Gibbs (MWG) algorithm, improves the convergence by refining the state space of the univariate sampling. The second is a blocked strategy of the Gibbs algorithm, which performs sampling over multivariates at each Markov move, and is shown to yield a better convergence rate than the traditional univariate sampling. In order to perform blocked sampling efficiently, the Gibbs-Klein (GK) algorithm is proposed, which samples block by block using the Kleins algorithm. Furthermore, the validity of the GK algorithm is demonstrated by showing its ergodicity. Simulation results based on MIMO detections are presented to confirm the convergence gain brought by the proposed Gibbs sampling schemes.

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. First, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding (BDD) using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm in Markov chain Monte Carlo methods is adopted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the limitation of Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, establishes a Markov chain via an independent proposal distribution. We show that the Markov chain arising from this independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is analyzed in terms of the theta series, leading to predictable mixing time. A symmetric Metropolis-Klein algorithm is also proposed, which is proven to be geometrically ergodic.

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the conventional Gibbs sampling algorithm is demonstrated to be geometrically ergodic in tackling with lattice Gaussian sampling, which means its induced Markov chain converges exponentially fast to the stationary distribution. Moreover, as the exponential convergence rate is dominated by the spectral radius of the forward operator of the Markov chain, a comprehensive analysis is given and we show that the convergence performance can be further enhanced by usages of blocked sampling strategy and choices of selection probabilities.

Sampling from a lattice Gaussian distribution is emerging as an important problem in coding and cryptography. This paper gives a further analysis of the independent Metropolis-Hastings-Klein (MHK) algorithm we presented at ISIT 2015. We derive the exact spectral gap of the induced Markov chain, which dictates the convergence rate of the independent MHK algorithm. Then, we apply the independent MHK algorithm to lattice decoding and obtained the decoding complexity for solving the CVP as Õ(e∥Bx-c∥2 / mini ∥b̂i∥2). Finally, the tradeoff between decoding radius and complexity is also established.

As a key sampling scheme in Markov chain Monte Carlo (MCMC) methods, Gibbs sampling is widely used in various research fields due to its elegant univariate conditional sampling, especially in tacking with multidimensional sampling systems. In this paper, a Gibbs-based sampler named as symmetric Metropolis-within-Gibbs (SMWG) algorithm is proposed for lattice Gaussian sampling. By adopting a symmetric Metropolis-Hastings (MH) step into the Gibbs update, we show the Markov chain arising from it is geometrically ergodic, which converges exponentially fast to the stationary distribution. Moreover, by optimizing its symmetric proposal distribution, the convergence efficiency can be further enhanced.

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcomes the restriction on the standard deviation confronted by the Klein algorithm. It is proven that the Markov chain arising from the proposed MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, making it possible to predict the mixing time of the underlying Markov chain.

To be considered for an IEEE Jack Keil Wolf ISIT Student Paper Award. Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm - Klein's algorithm yields a distribution close to the lattice Gaussian only if the standard deviation is sufficiently large. In this paper, we propose the Markov chain Monte Carlo (MCMC) method for lattice Gaussian sampling when this condition is not satisfied. In particular, we present a sampling algorithm based on Gibbs sampling, which converges to the target lattice Gaussian distribution for any value of the standard deviation. To improve the convergence rate, a more efficient algorithm referred to as Gibbs-Klein sampling is proposed, which samples block by block using Klein's algorithm. We show that Gibbs-Klein sampling yields a distribution close to the target lattice Gaussian, under a less stringent condition than that of the original Klein algorithm.

In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic, which brings considerable performance improvement and complexity reduction over to the randomized sampling. Moreover, the upper bound on the sample size K, which corresponds to near-maximum likelihood (ML) performance, is derived. We also find that the proposed algorithm can be used as an efficient tool to implement soft-output decoding in multiple-input multiple-output (MIMO) systems. An upper bound of the sphere radius R in list sphere decoding (LSD) is derived. Based on it, we demonstrate that the derandomized sampling algorithm is capable of achieving near-maximum a posteriori (MAP) performance. Simulation results show that near-optimum performance can be achieved by a moderate size K in both lattice decoding and soft-output decoding.

The sampling decoding algorithm randomly samples lattice points and selects the closest one from the candidate list. Although it achieves a remarkable performance gain with polynomial complexity, there are two inherent issues due to random sampling, namely, repetition and missing of certain lattice points. To address these issues, a derandomized algorithm of sampling decoding is proposed with further performance improvement and complexity reduction. Given the sample size K, candidates are deterministically sampled if their probabilities P satisfy the threshold PK ≥ 1/2. By varying K, the decoder with low complexity enjoys a flexible performance between successive interference cancelation (SIC) and maximum-likelihood (ML) decoding.

In opportunistic spectrum access (OSA), secondary radios (SRs) are allowed to access the channel whenever primary radios (PRs) are not transmitting. The PR's spectrum activities are normally assumed to be a 2-state continuous Markov on-off process which can be modeled as two independent exponential random variables. On the other hand, some simulations prefer using a 2-state discrete Markov chain. As SRs periodically sense the channel to determine its availability before transmitting, maintaining the same false alarm and missed detection probabilities is necessary but still insufficient when discretizing the continuous PR on-off process. Earlier work has shown that type II missed detection error, which is a function of spectrum sensing period, occurs because PR, which is sensed to be inactive in the last sensing duration, can become active before the next spectrum sensing is performed. Hence, it is insufficient to simply perform simulation at the time stamp of spectrum sensing period as information about the type II missed detection error will be lost. This paper looks into the context of spectrum sensing on how we should select the time stamp of the simulation, i.e., the transition probabilities of the 2-state discrete Markov chain, so as to approximate the 2-state continuous Markov process without losing any valuable information. We first derive the expression for type II missed detection error based on the discrete PR on-off model. Then we present the method to decide the time stamp of the simulation so that type II missed detection probability is kept within a given error bound. The same approach can be generalized to other probability distributions of the spectrum activities.