The extremely large reconfigurable intelligent surface (XL-RIS) is an architecture that shows potential in expanding the transmission region to meet high requirements of sixth-generation communication systems. In XL-RIS-assisted scenarios, users transmit signal through spherical-wavefront near-field channel, where the channel estimation presents great challenges. Additionally, XL-RIS elements are prone to failure due to accidental damages or blockages, which further complicates the channel state. To address these issues, we propose a three-stage signal-assisted sparse representation-based channel estimation (SA-SRCE) scheme to robustly recover near-field channel and diagnose RIS failure state with low pilot overhead. The first stage utilizes a double domain filter (DDF) to eliminate noise based on sparse representation in the angle and polar domains. Then, based on the filtered signal, a failure-aware orthogonal matching pursuit (FA-OMP) algorithm is proposed to iteratively reconstruct the channel, as well as eliminate the perturbation invoked by RIS element failures. Moreover, considering the limited availability of pilot, we further exploit the information of compressed signal and propose the signal-assisted failure-aware double-sparsity OMP (FADS-OMP) algorithm as the third stage to improve the estimation performance in FA-OMP. The effectiveness and robustness of our proposed scheme is validated through theoretical analysis and extensive simulations.

Larger antenna arrays, combined with higher transmission frequencies, are prospective in fulfilling the demands of the sixth-generation (6G) communications, enabling a 10-fold increase in overall spectral efficiency. However, such configurations give rise to near-field effects, requiring spherical rather than planar wave modeling. In practical multi-user communications, it is typical that part of the user equippments (UEs) resides in the near-field region, while others are located in the far-field region, thereby leading to a unified near/far-field scenario. Conventional codebooks tailored to either regime alone thus become mismatched, resulting in notable spectral efficiency degradation. In view of this, the ringwise codebook based on the slope-intercept formulation is proposed to address the unified near/far-field communication scenario. Specifically, the slope-intercept domain is first illustrated as the foundation of our codebook design, where the correlation between near/far-field channel steering vectors is exploited by mapping the angle-distance into the slope-intercept parameters. In the slope-intercept domain, the correlation pattern of steering vectors exhibits a dual triangle structure, supported by rigorous analyses on axial symmetry and correlation width, which paves the way for the subsequent codebook development. Secondly, the ringwise codebook is proposed where all UEs coarsely estimate its own slope parameter, based on which ring-wise codebooks composed of orthogonal codewords derived from the slope-intercept domain are constructed for different UEs. The resulting codebooks are then fed back to the base station through specific slope parameters, which are leveraged in the subsequent precoding procedure. Finally, rigorous analysis demonstrates that both the computational complexity and hardware cost of the proposed ringwise codebook design are acceptable, while numerical results validate its effectiveness and feasibility, achieving gains in both spectral efficiency and complexity compared to conventional counterparts.

The rapid development of artificial intelligence has driven smart health with next-generation wireless communication technologies, stimulating exciting applications in remote diagnosis and intervention. To enable a timely and effective response for remote healthcare, efficient transmission of medical data through noisy channels with limited bandwidth emerges as a critical challenge. In this work, we propose a novel diffusion-based semantic communication framework, namely DiSC-Med, for the medical image transmission, where medical-enhanced compression and denoising blocks are developed for bandwidth efficiency and robustness, respectively. Unlike conventional pixel-wise communication framework, our proposed DiSC-Med is able to capture the key semantic information and achieve superior reconstruction performance with ultra-high bandwidth efficiency against noisy channels. Extensive experiments on real-world medical datasets validate the effectiveness of our framework, demonstrating its potential for robust and efficient telehealth applications.

Recent advances in distributed swarm learning (DSL) offer a promising paradigm for edge Internet of Things. Such advancements enhance data privacy, communication efficiency, energy saving, and model scalability. However, the presence of non-independent and identically distributed (non-i.i.d.) data pose a significant challenge for multi-access edge computing, degrading learning performance and diverging training behavior of vanilla DSL. Further, there still lacks theoretical guidance on how data heterogeneity affects model training accuracy, which requires thorough investigation. To fill the gap, this paper first study the data heterogeneity by measuring the impact of non-i.i.d. datasets under the DSL framework. This then motivates a new multi-worker selection design for DSL, termed M-DSL algorithm, which works effectively with distributed heterogeneous data. A new non-i.i.d. degree metric is introduced and defined in this work to formulate the statistical difference among local datasets, which builds a connection between the measure of data heterogeneity and the evaluation of DSL performance. In this way, our M-DSL guides effective selection of multiple works who make prominent contributions for global model updates. We also provide theoretical analysis on the convergence behavior of our M-DSL, followed by extensive experiments on different heterogeneous datasets and non-i.i.d. data settings. Numerical results verify performance improvement and network intelligence enhancement provided by our M-DSL beyond the benchmarks.

To gain panoramic awareness of spectrum coverage in complex wireless environments, data-driven learning approaches have recently been introduced for radio map estimation (RME). While existing deep learning based methods conduct RME given spectrum measurements gathered from dispersed sensors in the region of interest, they rely on the centralized data collected at a fusion center, which unfortunately raises critical concerns on data privacy leakages and high communication overloads. Federated learning (FL) enhances data security and communication efficiency in RME by allowing multiple clients to collaborate in model training without directly sharing local data. However, the performance of the FL-based RME might be hindered by the problem of task heterogeneity across clients located in different environments. To fill this gap, we propose a physicsinspired distributed RME solution for heterogeneous settings in this paper. The key idea is to develop a novel distributed RME framework empowered by leveraging the domain knowledge of radio propagation models. To do so, we design a new distributed learning approach that splits the entire RME deep model into two modules. A global autoencoder module is shared among clients to capture the common pathloss influence on radio propagation patterns, while a client-specific autoencoder module focuses on learning the individual features produced by local shadowing effects from the unique building distributions in local environment. Simulation results show that our proposed method outperforms the benchmarks in achieving higher performance.

Enriching information of spectrum coverage, radiomap plays an important role in many wireless communication applications, such as resource allocation and network optimization. To enable real-time, distributed spectrum management, particularly in the scenarios with unstable and dynamic environments, the efficient transmission of spectrum coverage information for radiomaps from edge devices to the central server emerges as a critical problem. In this work, we propose an innovative physics-enhanced semantic communication framework tailored for efficient radiomap transmission based on generative learning models. Specifically, instead of bit-wise message passing, we only transmit the key “semantics” in radiomaps characterized by the radio propagation behavior and surrounding environments, where semantic compression schemes are utilized to reduce the communication overhead. Incorporating the novel concepts of Radio Depth Maps, the radiomaps are reconstructed from the delivered semantic information backboned on the conditional generative adversarial networks. Our framework is further extended to facilitate its implementation in the scenarios of multi-user edge computing, by integrating with federated learning for collaborative model training while preserving the data privacy. Experimental results show that our approach achieves high accuracy in radio coverage information recovery at ultra-high bandwidth efficiency, which has great potentials in many wireless-generated data transmission applications.

In frequency division duplex (FDD) massive multiple input multiple output (MIMO) systems, reliable downlink channel estimation is essential but requires huge pilot overhead due to hundreds of antennas at base station (BS). In order to reduce pilot overhead without compromising the channel estimation, compressive sensing (CS) has been widely applied for channel estimation by exploiting the inherent sparse structure of massive MIMO channel in angular domain. However, it still suffers from high complexity during the optimization process and the requirement of prior information on the number of spatial paths (PINP). To overcome these challenges, this paper develops a novel hybrid channel estimation scheme by integrating model-driven CS and data-driven deep unrolling techniques. The proposed scheme is composed of a coarse estimation part and a fine correction part, which is implemented in a two-stage manner by exploiting both inter- and intra-frame sparsities of channels in angular domain. Additionally, a threshold function is proposed to eliminate the requirement of the number of spatial paths. Theoretical results are provided to indicate the convergence of both fine correction and coarse estimation. Numerical results demonstrate that our scheme can achieve high accuracy with less pilot overhead and low complexity.

In distributed learning systems, robustness threat may arise from two major sources. On the one hand, due to distributional shifts between training data and test data, the trained model could exhibit poor out-of-sample performance. On the other hand, a portion of working nodes might be subject to Byzantine attacks, which could invalidate the learning result. In this article, we propose a new research direction that jointly considers distributional shifts and Byzantine attacks. We illuminate the major challenges in addressing these two issues simultaneously. Accordingly, we design a new algorithm that equips distributed learning with both distributional robustness and Byzantine robustness. Our algorithm is built on recent advances in distributionally robust optimization (DRO) as well as norm-based screening (NBS), a robust aggregation scheme against Byzantine attacks. We provide convergence proofs in three cases of the learning model being nonconvex, convex, and strongly convex for the proposed algorithm, shedding light on its convergence behaviors and endurability against Byzantine attacks. In particular, we deduce that any algorithm employing NBS (including ours) cannot converge when the percentage of Byzantine nodes is $(1/3)$ or higher, instead of $(1/2)$ , which is the common belief in current literature. The experimental results verify our theoretical findings (on the breakpoint of NBS and others) and also demonstrate the effectiveness of our algorithm against both robustness issues, justifying our choice of NBS over other widely used robust aggregation schemes. To the best of our knowledge, this is the first work to address distributional shifts and Byzantine attacks simultaneously.

This paper studies the decentralized dynamic kernel learning problem where each agent in the network receives continuous streaming local data and works collaboratively to learn a non-linear function "on the fly" in a dynamic environment. We utilize the random feature (RF) mapping method to circumvent the curse of dimensionality issue in conventional kernel methods and reformulate the dynamic kernel learning problem as a dynamic parameter optimization problem, which is then efficiently solved by the Decentralized Dynamic Kernel Learning via ADMM (DDKL) framework. To further improve communication efficiency, we incorporate the quantization and censoring strategies in the communication stage and develop the Quantized and Communication-censored DDKL (QC-DDKL) algorithm. We theoretically prove that QC-DDKL can achieve the optimal sublinear regret $\mathcal{O}(\sqrt T )$ over T time slots. Simulation results also corroborate the learning effectiveness and the communication efficiency of the proposed method.

This paper studies super-resolution harmonic retrieval for strictly non-circular coherent signals. We develop gridless sparse representations of both their covariance and pseudo-covariance matrices over a common matrix-form atom set. This enables the decoupled atomic norm minimization (D-ANM) technique to exploit the sparsity of the covariance and pseudo-covariance matrices jointly. Further, by effectively utilizing the inherent mutual coupling characteristics between the covariance and pseudo-covariance matrices, additional constraints are properly imposed to reflect and enforce desired structure information represented by such matrices and their augmented matrix. It leads to a novel structure-based sparse optimization method, called double decoupled atomic norm minimization (DD-ANM). In addition, performance analysis is provided for the proposed DD-ANM method in practical settings. Simulation results reveal that the proposed DD-ANM outperforms the benchmark methods in terms of lower estimation errors.

Federated learning (FL) is a promising distributed learning framework in terms of privacy protection and communication saving. Most existing FL techniques are developed for independent-and-identically-distributed (IID) datasets, but suffer from performance degradation under Non-IID datasets. To cope with this issue, most existing work designs solutions from data perspectives (e.g., sharing some data samples between local devices) to eliminate the heterogeneity of distributed datasets, which causes extra communication overhead and may expose user privacy that contradicts FL's original intention. Unlike the existing data-based methods, we propose a generative adversarial network (GAN) based FL, named as GANFed, which is designed from a feature perspective. Specifically, we embed a discriminator into the FL network, which works with the shallow layers as a generator to form a GAN in FL. By incorporating such a GAN, the output of the shallow layers tends to present more IID features compared with the original Non-IID input data. These extracted features from the shallow layers are then used to train the deep layers of the FL network. In this way, the proposed GANFed reduces the weight divergence of the local models, and hence improves the performance of FL. Without data exchange, our GANFed avoids the leakage of user privacy and reduces the communication overhead. Experimental results show that our GANFed outperforms the standard FedAvg on Non-IID dataset in terms of improved test accuracy.

The extremely large reconfigurable intelligent surface (XL-RIS) is an architecture that shows potential in expanding the transmission region and meeting the high transmission requirements. With the deployment of XL-RIS, users transmit signals through the spherical-wavefront near-field channel, which presents challenges in channel estimation with low pilot overhead. Additionally, XL-RIS is a non-stationary system whose elements are prone to failure due to accidental damages or blockages, thereby further complicating the channel state. To address these issues, this paper proposes a two-stage sparse representation-based channel estimation (SRCE) scheme to jointly recover the near-field channel state and diagnose RIS element failures with low pilot overhead. The first stage utilizes a proposed double-domain filter (DDF) method to eliminate part of the received noise based on the sparse representation in the angle and polar domain. Then, a robust failure-aware double sparsity orthogonal matching pursuit (FA-OMP) algorithm is proposed by iteratively reconstructing the channel state, as well as eliminating the perturbation invoked by RIS element failures. The efficiency and robustness of our proposed scheme are validated through simulations.

Specific emitter identification (SEI) technology is significant in device administration scenarios, such as self-organized networking and spectrum management, owing to its high security. For nonlinear and non-stationary electromagnetic signals, SEI often employs variational modal decomposition (VMD) to decompose the signal in order to effectively characterize the distinct device fingerprint. However, it has not been well investigated in noisy SEI scenarios. Specifically, the existing VMD algorithms do not utilize the stability of the intrinsic distortion of emitters within a certain temporal span, nor do they consider the vulnerability of this distortion estimates to channel noise, both of which constrain its practical applicability in SEI. In this paper, we propose a joint variational modal decomposition (JVMD) algorithm, which is an improved version of VMD by simultaneously implementing modal decomposition and channel noise estimation on multi-frame signals. The consistency of multi-frame signals in terms of the central frequencies and the inherent modal functions (IMFs) is exploited, which effectively highlights the distinctive characteristics among emitters. In addition, channel noise is estimated during signal decomposition, which improves the ability to stably extract these distinctive characteristics. Additionally, the complexity of JVMD is analyzed, which is proven to be more computational-friendly than VMD. Simulations of both modal decomposition and SEI that involve real-world datasets are presented to illustrate that when compared with other SEI schemes, the JVMD-based scheme improves the accuracy of device classification at low SNRs.

With the rapid development of machine learning technologies, data-driven spectrum prediction enables intelligent dynamic spectrum access to alleviate the bottleneck of spectrum resource scarcity and congestion. However, spectrum prediction still faces some key challenges, including how to exploit the implicit but crucial multi-band correlations in wideband spectrum data, and how to capture the temporal dynamics across different bands. Due to the ignorance of such crucial features inherent from spectrum occupancy patterns, existing learning-based spectrum prediction methods unfortunately suffer from inaccurate prediction performance. To fill this gap, this paper develops a novel model of graph convolutional regression neural network (GCRNN), by introducing efficient graph structure learning (GSL-GCRNN) for dynamic multi-band spectrum prediction. The proposed GSL-GCRNN model is designed to adaptively learn both the multi-band and temporal correlations in dynamic wideband spectrum scenarios. Empowered by the graph structure estimator, graph convolutional networks are fueled to effectively extract the correlations in the frequency domain, followed by gated recurrent unit networks to further extract the temporal correlations of each band. It is worth noting that the graph structure estimator further enables to learn the multi-band correlations across different time periods on-the-fly, enhancing the accuracy of wideband spectrum prediction in dynamic environments. Simulation results verify that our GSLGCRNN approach outperforms the benchmark methods.

For future intelligent communication systems, radiomap estimation (RME) is essential for acquiring panoramic awareness of spectrum spatial distribution in wireless environments. Recently, deep learning-based RME methods have been developed to reconstruct radiomaps from spectrum measurements collected at distributed sensors. However, these methods rely on gathering all input data at a central fusion center, resulting in large communication overheads, high computation costs, and privacy leakage concerns. To address these challenges, this work proposes a FedRME approach that makes federated learning applicable for distributed RME over a large-scale network, accommodating geographically heterogeneous transmitter locations and propagation environments. Specifically, we partition the large area into smaller regions to reduce the model complexity required for learning the radiomap in each region. Meanwhile, we incorporate the landscape map as an auxiliary input to induce a common learning model that adheres to the same propagation physics across all these heterogeneous regions. In doing so, fusion centers in all regions can collaborate through federated learning to enhance the overall RME performance. Simulation results indicate that our proposed method outperforms existing benchmarks, particularly under limited data, achieving higher learning accuracy with reduced model complexity and lower computational cost.

Compressive Sensing (CS) technology, which handles large amounts of data in its low-dimensional form, has been shown to enjoy excellent transmission and storage efficiency. To further improve the stability and robustness of CS-based wireless communication system, Reconfigurable Intelligent Surface (RIS) technology has been introduced to enhance the transmission link connectivity. Current researches generally assume perfect RIS; however, some of its elements may be damaged and fail to work, which degrades the sparse signal recovery. Therefore, this paper establishes a double-sparsity optimization model to jointly recover the sparse signal and diagnose the RIS element failure. For the scenarios with and without Channel State Information (CSI) at the receiver, Double-Sparsity based algorithm (DS), and Atomic norm and Double-Sparsity based algorithm (ADS) exploiting Alternating Direction Method of Multipliers (ADMM) framework are proposed respectively. Additionally, a novel ℓB,B norm is incorporated to further constrain the block and binary characteristics of RIS failures, and the resulting improved versions of DS and ADS are termed as Binary and Block-Sparsity based algorithm (BBS) and Atomic norm, Binary and Block-Sparsity based algorithm (ABBS). Simulations verify the effectiveness and robustness of the proposed algorithms, and show the improved performance of the BBS and ABBS algorithms compared with the DS and ADS algorithms.

Specific emitter identification (SEI) is important to guarantee the security of device administration. Recently, to increase the effectiveness of the recognition, traditional SEI employing only one sensor has been extended to the scenario with multiple sensors. However, the inherent distortion at different sensors impacts the radio frequency fingerprints (RFFs) of the emitter independently, which inevitably leads to the non-universalization of the features extracted at different sensors. Besides, variational modal decomposition (VMD), which is an effective preprocessing in SEI, has not been well investigated in noisy scenarios. To combat the environment noise, this paper proposes two joint VMD (JVMD) algorithms, i.e., JVMD for ignoring the distortions at sensors (I-JVMD) and JVMD for considering the distortions at sensors (C-JVMD). Specifically, I-JVMD exploits the consistency of the central frequencies and intrinsic modal functions (IMFs) of multiple sensors, and C-JVMD further estimates and filters out the phase noise at each sensor that may distort the RFFs of the emitter. Simulations of the proposed JVMD algorithms and their corresponding applications in SEI are provided on two real-world datasets. When compared with the traditional VMD, the proposed ones improve the accuracy of device classification and the robustness towards noise.

This article focuses on online kernel learning over a decentralized network. Each agent in the network receives online streaming data and collaboratively learns a globally optimal nonlinear prediction function in the reproducing kernel Hilbert space (RKHS). To overcome the curse of dimensionality issue in traditional online kernel learning, we utilize random feature (RF) mapping to convert the nonparametric kernel learning problem into a fixed-length parametric one in the RF space. We then propose a novel learning framework, named online decentralized kernel learning via linearized ADMM (ODKLA), to efficiently solve the online decentralized kernel learning problem. To enhance communication efficiency, we introduce quantization and censoring strategies in the communication stage, resulting in the quantized and communication-censored ODKLA (QC-ODKLA) algorithm. We theoretically prove that both ODKLA and QC-ODKLA can achieve the optimal sublinear regret over time slots. Through numerical experiments, we evaluate the learning effectiveness, communication efficiency, and computation efficiency of the proposed methods.

Data-driven machine learning techniques have been advocated for signal detection in complex wireless environments. However, when applied to wideband spectrum sensing scenarios, they face practical challenges including very large data dimensionality, insufficient training data, and implicit inter-band dependencies. Current literature focuses on deep convolutional models, whose inherent model structure is not well suited for representing the diverse spectrum occupancy patterns of practical wideband networks, causing inefficient performance-complexity tradeoff and excessive sensing time. To address these issues, this paper develops a novel Spectrum Transformer with multi-task learning for wideband spectrum sensing at high sample efficiency. Empowered by the multi-head self-attention mechanism, the transformer architecture is designed to effectively learn both the inner-band spectral features and the inter-band spectrum occupancy correlations in the wideband regime. Simulations show that the proposed Spectrum Transformer outperforms the existing methods based on convolutional neural networks especially in the small-data case, by achieving higher sensing accuracy with an 89% reduction in model complexity.

Compressive sensing (CS) technology, which handles large amounts of data in its low-dimensional form, enjoys excellent transmission and storage efficiency. To further improve the stability and robustness of CS-based wireless communication system, reconfigurable intelligent surface (RIS) technology has been introduced to enhance the transmission link connectivity. Current researches generally assume perfect RIS; however, some of its elements may fail to work, which degrades the sparse signal recovery. Therefore, this paper establishes a double-sparsity optimization model to jointly recover the sparse signal and diagnose the RIS element state. A double-sparsity based algorithm (DS) exploiting Alternating Direction Method of Multiplier framework is proposed as the solution. Additionally, a novel$\ell_{B,B}$norm is incorporated to further constrain the block and binary characteristics of RIS failures, and the resulting improved version of DS is termed as the binary and block-sparsity based algorithm (BBS). Simulations verify the effectiveness and robustness of the proposed algorithms, and show the improved performance of the BBS algorithm compared with the DS algorithm.

Massive multiple-input multiple-output (MIMO) enjoys great advantage in 5G wireless communication systems owing to its spectrum and energy efficiency. However, hundreds of antennas require large volumes of pilot overhead to guarantee reliable channel estimation in FDD massive MIMO system. Compressive sensing (CS) has been applied for channel estimation by exploiting the inherent sparse structure of massive MIMO channel but suffer from high complexity. To overcome this challenge, this paper develops a hybrid channel estimation scheme by integrating the model-driven CS and data-driven deep unrolling technique. The proposed scheme consists of a coarse estimation part and a fine correction part to respectively exploit the inter- and intra-frame sparsities of channels to greatly reduce the pilot overhead. Theoretical result is provided to indicate the convergence of the fine correction and coarse estimation net. Simulation results are provided to verify that our scheme can estimate MIMO channels with low pilot overhead while guaranteeing estimation accuracy with relatively low complexity.

This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.

Wideband direction-of-arrival (DoA) estimation is desirable with the ever-increasing data rate in wireless communication systems. In this paper, an iterative coherent signal-subspace method for wideband two-dimensional DoA estimation with a uniform circular array is proposed, which includes three steps in each iteration. The first step selects a subset of frequency points for the subsequent focusing process to avoid unnecessary complexity. The second step realizes the focusing process, where the angle intervals for generating focusing matrices with robust-ness are designed, and then the signal-subspaces at the selected frequency points are focused into a reference frequency. The third step estimates DoAs with the multiple signal classification (MUSIC) algorithm where the range of MUSIC spatial spectrum is constrained by the aforementioned angle intervals, thereby further reducing the complexity. The key parameters of the proposed method in the current iteration are adjusted based on the previous estimation results. The simulation results show that the proposed method enjoys better performance and implementation efficiency when compared with benchmark methods.

In this paper, we study a communication-efficient distributed learning scheme through a holistic integration of federated learning (FL) and particle swarm optimization, called DSL, which is suitable for the implementation of intelligent IoT applications. Since only one selected optimum from all local devices need to report its local model updates to the parameter server, the communication cost of DSL is much reduced compared to its counterpart of standard FL. However, the DSL is vulnerable to adversarial attackers. To achieve Byzantine-resilient DSL, we propose to introduce a shared dataset for scoring local updates to screen attackers. We further provide the convergence analysis to theoretically demonstrate that CB-DSL is superior than the standard FL. Experiment results show that the learning performance of our proposed CB-DSL outperforms the existing benchmarks with only a small amount of globally shared data. It enjoys higher robustness against Byzantine attacks than the vanilla DSL, and has better communication efficiency than the standard FL11Our code can be found at: https://github.com/fuanxiyin/CB-DSL.git..

Federated learning (FL) methods face major challenges including communication bottleneck, data heterogeneity and security concerns in edge IoT scenarios. In this paper, inspired by the success of biological intelligence (BI) of gregarious organisms, we propose a novel edge learning approach for swarm IoT, called communication-efficient and Byzantine-robust distributed swarm learning (CB-DSL), through a holistic integration of AI-enabled stochastic gradient descent and BI-enabled particle swarm optimization. To deal with non-independent and identically distributed (non-i.i.d.) data issues and Byzantine attacks, a very small amount of global data samples are introduced in CB-DSL and shared among IoT workers, which not only alleviates the local data heterogeneity effectively but also enables to fully utilize the exploration-exploitation mechanism of swarm intelligence. Further, we provide convergence analysis to theoretically demonstrate that the proposed CB-DSL is superior to the standard FL with better convergence behavior. In addition, to measure the effectiveness of the introduction of the globally shared dataset, we also evaluate the model divergence by deriving its upper bound. Numerical results verify that the proposed CB-DSL outperforms the existing benchmarks in terms of faster convergence speed, higher convergent accuracy, lower communication cost, and better robustness against non-i.i.d. data and Byzantine attacks11Our code can be found at:https://github.com/fuanxiyin/CB-DSL.git..

Fairness and robustness are two important goals in the design of modern distributed learning systems. Despite a few prior works attempting to achieve both fairness and robustness, some key aspects of this direction remain underexplored. In this paper, we try to answer three largely unnoticed and unaddressed questions that are of paramount significance to this topic: (i) What makes jointly satisfying fairness and robustness difficult? (ii) Is it possible to establish theoretical guarantee for the dual property of fairness and robustness? (iii) How much does fairness have to sacrifice at the expense of robustness being incorporated into the system? To address these questions, we first identify data heterogeneity as the key difficulty of combining fairness and robustness. Accordingly, we propose a fair and robust framework called H-nobs which can offer certified fairness and robustness through the adoption of two key components, a fairness-promoting objective function and a simple robust aggregation scheme called norm-based screening (NBS). We explain in detail why NBS is the suitable scheme in our algorithm in contrast to other robust aggregation measures. In addition, we derive three convergence theorems for H-nobs in cases of the learning model being nonconvex, convex, and strongly convex respectively, which provide theoretical guarantees for both fairness and robustness. Further, we empirically investigate the influence of the robust mechanism (NBS) on the fairness performance of H-nobs, the very first attempt of such exploration.

This paper proposes two novel schemes of wideband compressive spectrum sensing (CSS) via block orthogonal matching pursuit (BOMP) algorithm, for achieving high sensing accuracy in real time. These schemes aim to reliably recover the spectrum by adaptively adjusting the number of required measurements without inducing unnecessary sampling redundancy. To this end, the minimum number of required measurements for successful recovery is first derived in terms of its probabilistic lower bound. Then, a CSS scheme is proposed by tightening the derived lower bound, where the key is the design of a nonlinear exponential indicator through a general-purpose sampling-controlled algorithm (SCA). In particular, a sampling-controlled BOMP (SC-BOMP) is developed through a holistic integration of the existing BOMP and the proposed SCA. For fast implementation, a modified version of SC-BOMP is further developed by exploring the block orthogonality in the form of sub-coherence of measurement matrices, which allows more compressive sampling in terms of smaller lower bound of the number of measurements. Such a fast SC-BOMP scheme achieves a desired tradeoff between the complexity and the performance. Simulations demonstrate that the two SC-BOMP schemes outperform the other benchmark algorithms.

Tomographic SAR technique has attracted remarkable interest for its ability of three-dimensional resolving along the elevation direction via a stack of SAR images collected from different cross-track angles. The emerged compressed sensing (CS)-based algorithms have been introduced into TomoSAR considering its super-resolution ability with limited samples. However, the conventional CS-based methods suffer from several drawbacks, including weak noise resistance, high computational complexity, and complex parameter fine-tuning. Aiming at efficient TomoSAR imaging, this paper proposes a novel and efficient sparse unfolding network based on the analytic learned iterative shrinkage thresholding algorithm (ALISTA) architecture with adaptive threshold, named Adaptive Threshold ALISTA-based Sparse Imaging Network (ATASI-Net). The weight matrix in each layer of ATASI-Net is pre-calculated as the solution of an off-line optimization problem, leaving only two scalar parameters to be learned from data, which significantly simplifies the training stage. Furthermore, the introduction of an adaptive threshold for each azimuth-range pixel permits the threshold shrinkage to be not only layer-varied but also element-wise. Additionally, the final learned thresholds can be visualized and combined with the SAR image semantics for mutual feedback. Finally, extensive experiments on simulated and real data are carried out to demonstrate the effectiveness and efficiency of the proposed method.

For distributed learning among collaborative users, this paper develops and analyzes a communication-efficient scheme for federated learning (FL) over the air, which incorporates 1-bit compressive sensing (CS) into analog-aggregation transmissions. To facilitate design parameter optimization, we analyze the efficacy of the proposed scheme by deriving a closed-form expression for the expected convergence rate. Our theoretical results unveil the tradeoff between convergence performance and communication efficiency as a result of the aggregation errors caused by sparsification, dimension reduction, quantization, signal reconstruction and noise. Then, we formulate a joint optimization problem to mitigate the impact of these aggregation errors through joint optimal design of worker scheduling and power scaling policy. An enumeration-based method is proposed to solve this non-convex problem, which is optimal but becomes computationally infeasible as the number of devices increases. For scalable computing, we resort to the alternating direction method of multipliers (ADMM) technique to develop an efficient implementation that is suitable for large-scale networks. Simulation results show that our proposed 1-bit CS based FL over the air achieves comparable performance to the ideal case where conventional FL without compression and quantification is applied over error-free aggregation, at much reduced communication overhead and transmission latency.

This paper proposes deep kernel learning networks with multiple learning paths (DKL-MLP) for nonlinear function approximation. Leveraging the random feature (RF) mapping technique, kernel methods can be implemented as a two-layer neural network, at drastically reduced workload on weight training. Motivated by the representation power of the deep architecture in deep neural networks, we devise a vanilla deep kernel learning network (DKL) by applying RF mapping at each layer and learn the last layer only. To improve the learning performance of DKL, we add multiple trainable paths to DKL and develop the DKL-MLP method so that some implicit information from earlier hidden layers to the output layer can be learned. We prove that both DKL and DKL-MLP permit universal representation of a wide variety of interesting functions with arbitrarily small error and have no bad local minimum. Numerical experiments on both regression and classification tasks are provided to demonstrate the learning performance and computational efficiency of the proposed methods.

In this paper, we focus on federated learning (FL) over the air based on analog aggregation transmission in realistic wireless networks. We first derive a closed-form expression for the expected convergence rate of FL over the air, which theoretically quantifies the impact of analog aggregation on FL. Based on that, we further develop a joint optimization model for accurate FL implementation, which allows a parameter server to select a subset of edge devices and determine an appropriate power scaling factor. Such a joint optimization of device selection and power control for FL over the air is then formulated as an mixed integer programming problem. Finally, we efficiently solve this problem via a simple finite-set search method. Simulation results show that the proposed solutions developed for wireless channels outperform a benchmark method, and could achieve comparable performance of the ideal case where FL is implemented over reliable and error-free wireless channels.

As a promising distributed learning technology, analog aggregation-based federated learning over the air (FLOA) provides high communication efficiency and privacy provisioning under the edge computing paradigm. When all edge devices (workers) simultaneously upload their local updates to the parameter server (PS) through commonly shared time-frequency resources, the PS obtains the averaged update only rather than the individual local ones. While such a concurrent transmission and aggregation scheme reduces the latency and communication costs, it unfortunately renders FLOA vulnerable to Byzantine attacks. Aiming at Byzantine-resilient FLOA, this article starts from analyzing the channel inversion (CI) mechanism that is widely used for power control in FLOA. Our theoretical analysis indicates that although CI can achieve good learning performance in the benign scenarios, it fails to work well with limited defensive capability against Byzantine attacks. Then, we propose a novel scheme called the best effort voting (BEV) power control policy that is integrated with stochastic gradient descent (SGD). Our BEV-SGD enhances the robustness of FLOA to Byzantine attacks, by allowing all the workers to send their local updates at their maximum transmit power. Under worst-case attacks, we derive the expected convergence rates of FLOA with CI and BEV power control policies, respectively. The rate comparison reveals that our BEV-SGD outperforms its counterpart with CI in terms of better convergence behavior, which is verified by experimental simulations.

This paper proposes an efficient direction of departure (DOD) and direction of arrival (DOA) estimation method for multi-input multi-output (MIMO) systems. For uncorrelated scenarios, the redundancy of the covariance matrix is first exploited by establishing its concise representation through redundancy reduction, which transforms the original large-size covariance matrix into a smaller-size matrix without loss of useful angle information. Then, the resulting transformed matrix, which retains a salient structure, permits efficient two-dimensional (2D) angle estimators working on a reduced-size problem for DOD and DOA estimation. Compared with conventional subspace-based methods, the proposed method incorporating an appropriate 2D angle estimator is more computationally efficient and can achieve higher estimation accuracy for small numbers of snapshots and low signal-to-noise ratios, which are verified by simulation results.

With the rapid growth of data traffic in cellular networks, edge caching has become an emerging technology for traffic offloading. We investigate the caching placement and content delivery in cache-enabling cellular networks. To cope with the time-varying content popularity and user location in practical scenarios, we formulate a long-term joint dynamic optimization problem of caching placement and user association for minimizing the content delivery delay which considers both content transmission delay and content update delay. To solve this challenging problem, we decompose the optimization problem into two sub-problems, the user association sub-problem in a short time scale and the caching placement in a long time scale. Specifically, we propose a low complexity user association algorithm for a given caching placement in the short time scale. Then we develop a deep deterministic policy gradient based caching placement algorithm which involves the short time-scale user association decisions in the long time scale. Finally, we propose a joint user association and caching placement algorithm to obtain a sub-optimal solution for the proposed problem. We illustrate the convergence and performance of the proposed algorithm by simulation results. Simulation results show that compared with the benchmark algorithms, the proposed algorithm reduces the long-term content delivery delay in dynamic networks effectively.

Federated learning (FL) is an attractive paradigm for making use of rich distributed data while protecting data privacy. Nonetheless, non-ideal communication links and limited transmission resources may hinder the implementation of fast and accurate FL. In this paper, we study joint optimization of communications and FL based on analog aggregation transmission in realistic wireless networks. We first derive closed-form expressions for the expected convergence rate of FL over the air, which theoretically quantify the impact of analog aggregation on FL. Based on the analytical results, we develop a joint optimization model for accurate FL implementation, which allows a parameter server to select a subset of workers and determine an appropriate power scaling factor. Since the practical setting of FL over the air encounters unobservable parameters, we reformulate the joint optimization of worker selection and power allocation using controlled approximation. Finally, we efficiently solve the resulting mixed-integer programming problem via a simple yet optimal finite-set search method by reducing the search space. Simulation results show that the proposed solutions developed for realistic wireless analog channels outperform a benchmark method, and achieve comparable performance of the ideal case where FL is implemented over error-free wireless channels.

In cache-enabling cellular networks, we investigate the caching placement and content delivery. To cope with the time-varying content popularity and user location in practical scenarios, we formulate a long-term joint dynamic optimization problem of caching placement and user association for minimizing the content delivery delay. We decompose the optimization problem into two sub-problems, the user association sub-problem in short time-scale and the caching placement in long timescale. Specifically, we propose a low complexity belief propagation based user association algorithm in the short time-scale. Then we develop a deep deterministic policy gradient based caching placement algorithm in the long time-scale. Finally, we propose a joint user association and caching placement algorithm to obtain a sub-optimal solution for the proposed problem. We demonstrate the convergence and performance of the proposed algorithm by simulation results. Simulation results show that compared with the benchmark algorithms, the proposed algorithm reduces the long-term content delivery delay in dynamic networks effectively.

This paper studies the decentralized optimization and learning problem where multiple interconnected agents aim to learn an optimal decision function defined over a reproducing kernel Hilbert space by jointly minimizing a global objective function, with access to their own locally observed dataset. As a non-parametric approach, kernel learning faces a major challenge in distributed implementation: the decision variables of local objective functions are data-dependent and thus cannot be optimized under the decentralized consensus framework without any raw data exchange among agents. To circumvent this major challenge, we leverage the random feature (RF) approximation approach to enable consensus on the function modeled in the RF space by data-independent parameters across different agents. We then design an iterative algorithm, termed DKLA, for fast-convergent implementation via ADMM. Based on DKLA, we further develop a communication-censored kernel learning (COKE) algorithm that reduces the communication load of DKLA by preventing an agent from transmitting at every iteration unless its local updates are deemed informative. Theoretical results in terms of linear convergence guarantee and generalization performance analysis of DKLA and COKE are provided. Comprehensive tests on both synthetic and real datasets are conducted to verify the communication efficiency and learning effectiveness of COKE.

This paper develops an enhanced low-rank structured covariance reconstruction (LRSCR) method based on the decoupled atomic norm minimization (D-ANM), for super-resolution two-dimensional (2D) harmonic retrieval with multiple measurement vectors. This LRSCR-D-ANM approach exploits a potential structure hidden in the covariance by transferring the basic LRSCR to an efficient D-ANM formulation, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. The new LRSCR-D-ANM method builds upon the existence of a generalized Vandermonde decomposition of its solution, which otherwise cannot be guaranteed by the basic LRSCR unless a very conservative condition holds. Further, a low-complexity solution of the LRSCR-D-ANM is provided for fast implementation with negligible performance loss. Simulation results verify the advantages of the proposed LRSCR-D-ANM over the basic LRSCR, in terms of the wider applicability and the lower complexity.

Grant-free non-orthogonal multiple access (NOMA) is considered as one of the most important methodologies for the machine-type communications (MTC). In the field of MTC, compressed sensing based multi-user detection (CS-MUD) has been recognized as an excellent candidate for joint user activity and data detection, since many users sporadically transmit short-size data packets at low rates. This article focuses on the CS-MUD problem in the up-link grant-free NOMA scenario, where users are (in)-active randomly in each time slot yet with high temporal correlation. First, we investigate the CS framework to fully extract the underlying side information in the temporal correlation and propose a novel CS-MUD algorithm. Then, to mitigate the performance degradation due to the imperfect channel estimation in practice, the proposed algorithm is further extended by utilizing the perturbed CS, where the impact of channel estimation errors is modeled as certain perturbation in the measurement matrix. Different from most of the state-of-the-art CS-MUD algorithms, both proposed algorithms can apply even in the absence of prior knowledge on the number of active users. Simulation results indicate that the proposed algorithms achieve better performance than the existing CS-MUD methods. Their convergence and complexity issues are also discussed theoretically and numerically.

This paper aims at accurate channel estimation for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under practical limitations, including an arbitrary array geometry and a hybrid hardware structure. Taking on an angle-based approach, this work adopts a generalized array manifold separation approach via the Jacobi-Anger approximation, which transforms a non-ideal, non-uniform array manifold into a virtual array domain with a desired uniform geometric structure to facilitate super-resolution angle estimation and channel acquisition. Accordingly, structure-based optimization techniques are developed to estimate the channel parameters within a short sensing time. In particular, the difference in time-variation of path angles and path gains is capitalized to design a two-step scheme that can quickly sense fading channels. Theoretical results are provided on the fundamental limits of the proposed technique in terms of sample efficiency. Simulations testify the effectiveness of the proposed approaches.

This paper develops efficient super-resolution spatial channel covariance estimation techniques for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under the hybrid precoding constraint. Two structure-based optimization techniques including low-rank structured covariance reconstruction and dynamic atomic norm minimization are proposed to accurately estimate the channel covariance matrix. For computational efficiency, a fast iterative algorithm is developed via the alternating direction method of multipliers. The extension of this work to the higher-dimensional cases is also discussed. Simulation results verify the effectiveness of the proposed methods in hybrid mmWave massive MIMO systems.

This letter presents a fast algorithm named iterative Vandermonde decomposition and shrinkage-thresholding (IVDST), which offers a low-complexity solution to atomic norm minimization (ANM) in off-grid compressed sensing for line spectral estimation from few measurements. It implements the ANM principle via the accelerated proximal gradient (APG) technique, without invoking computationally expensive semidefinite programming (SDP). To approximate the proximal operator in each APG iteration, Vandermonde decomposition is applied to utilize the Toeplitz structure inherent in the line spectral model, and the low-rank property of the Toeplitz-structured matrix is enforced via a simple shrinkage-thresholding operation. The IVDST algorithm effectively reduces the order of computational complexity compared to SDP-based solutions. It also offers an explicit way to bridge the ANM principle with classic super-resolution line spectral estimation algorithms, such as MUSIC.

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANMin terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy.

In millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, channel estimation in the presence of sparse multipath fading boils down to two-dimensional (2D) direction-of-arrival (DOA) estimation followed by path gain estimation. To achieve super-resolution angle estimation at affordable complexity, this paper develops an efficient channel estimation approach by applying a truncated atomic norm minimization (T-ANM) technique, which is implemented via partial antenna activation during training-based channel estimation. This technique makes use of a key observation that the sparse scattering characteristics of mmWave MIMO channel gives rise to a low-rank two-level Toeplitz structure in the angular domain. Because of the low-rank property, only a subset of the transceiver antennas needs to be activated to save training resources. Meanwhile, the Toeplitz structure enables ANM-based gridless 2D DOA estimation via reduced-size semidefinite programming. Simulation results show that the proposed reduced-size method can achieve comparable spectral efficiency as the full-size benchmark method at much lower computational complexity and shorter sensing time.

In millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, channel estimation is a challenging task in terms of acquiring the instantaneous channel state information (CSI), because both the estimation complexity and the overhead required for pilot symbols and feedback grow drastically as the number of antennas increases. Alternatively, some channel statistics in the form of partial CSI are sufficient for transceiver optimization and noncoherent detection in time-varying wireless environments. To obtain such useful statistical information accurately and efficiently, this paper proposes a new channel statistics estimation method using the compressive covariance sensing technique, which directly estimates the desired second-order statistics of the channel while bypassing the intermediate recovery of the instantaneous channel matrix itself. A diagonal-search orthogonal matching pursuit (DS-OMP) algorithm is developed for fast channel estimation. The proposed algorithm has low computational complexity and reduced overhead in training and feedback, owing to its proper utilization of the joint sparsity structure of the channel covariance matrix.

Compressive sensing (CS) has been applied to reduce the acquisition costs in the task of target localization by deploying a small number of sensors to collect measurements. It is based on a fact that the number of targets is much smaller than all possible positions where the targets could be located. To improve the localization accuracy with noisy measurements, our previous work has proposed a localization approach by solving a row-based least absolute shrinkage and selection operator (RLASSO) formulation, which utilizes the joint sparsity property. However, some practical concerns in localization implementation, e.g., a decrement in power radiated by targets and an enlargement of overall localization region, degrade the localization accuracy seriously. The performance impairment is caused by the common but undesirable limitations that the reduced radiation power and the enlarged field indeed make targets partially unobservable from individual sensor alone. To combat the impacts of such constrains on localization performance, this paper develops a cluster-based multi-target localization approach based on matrix rank minimization (MRM). The solutions representing all the collected measurements from distributed clusters are modeled to possess a low rank property. Capitalizing on this low rank property, a nuclear norm minimization problem is formulated to localize the positions of multiple targets. Simulation results reveal that the proposed localization approach based on MRM outperforms those via RLASSO and direct CS, since the low rank property enables efficient utilization of user diversity in localization even under partial observations.

Prior information is easily obtained in many applications of compressed sensing. This paper considers the sparse signal recovery using certain types of prior information. Our major contribution is proposing two novel reconstruction algorithms with prior information named as logit weight simultaneous orthogonal matching pursuit (LW-SOMP) and logit weight simultaneous orthogonal matching pursuit with amplitude information (LW-SOMP-A) for joint sparsity model of distributed compressed sensing. Simulation results demonstrate improved performance of the proposed algorithms (with respect to the conventional algorithm).

For multi-node networks, a distributed compressed sensing scheme based on one-bit quantization is proposed, where signals at each node consist of common component and innovation component. To reduce the transmission cost, each node derives the measurements as the sign information of the compressed samples by using one-bit quantization. Based on the received sign information from different nodes, two joint recovery algorithms are designed to recover the signal of each node. Simulation results show that the proposed scheme outperforms both the independent reconstruction scheme and the scheme based on multi-bit quantization.

In this paper, we consider the sensor network, where multiple sensors communicate with a single fusion center via their respective direct links and relays. We propose schemes exploiting both quantize-and- forward (QF) and compressive sensing (CS) in relay networks, aiming to take full use of the diversity to recover the original sparse signals through the collection of a small number of samples. Such sub- sampling QF framework not only inherits the advantage of QF, but also enjoys the merits of reduced sampling rate by exploiting CS technique. The proposed two sub-sampling QF schemes place emphasis on: i) diversity gain in CS domain by employing different projection matrices in different sensors; ii) diversity gain in coding domain due to the correlations, respectively. We assess and compare the performance of the proposed schemes under AWGN channel. Simulation results demonstrate that the proposed schemes achieve excellent recovery performance with reduced communication overhead.

Recent work in the area of compressed sensing mainly focuses on the perfect recovery of the entire support for sparse signals. However, partial support recovery, where a part of the signal support is correctly recovered, may be adequate in many practical scenarios. In this study, in the high‐dimensional and noisy setting, the authors develop the probability of partial support recovery of the optimal maximum‐likelihood (ML) algorithm. When a large part of the support is available, the asymptotic mean‐square‐error (MSE) of the reconstructed signal is further developed. The simulation results characterise the asymptotic performance of the ML algorithm for partial support recovery, and show that there exists a signal‐to‐noise ratio (SNR) threshold, beyond which the increase of SNR cannot bring any obvious MSE gain.

In the multi-target localization scenario, adopting the compressive sensing technique can effectively reduce the acquisition costs by collecting only a small number of measurements to recover the target-position signal. This signal reveals the locations of the targets and is evidently sparse due to the spatial sparseness of point targets. However, the measurement noise may seriously degrade the localization performance. To improve the localization accuracy, this paper proposes a hierarchical multi-target localization approach using a cluster-based sensor network. Therein, several cluster heads collect and preprocess the measurements from their neighboring sensor nodes and then report these intra-cluster measurements to a fusion center which finally recovers the position signals. Solutions representing the measurements collected at all cluster heads are modeled to possess a useful mathematical property, namely the joint sparsity property. Accordingly, a row-based least absolute shrinkage and selection operator formulation is established to utilize this joint sparsity property. By doing so, the cooperation gains among all clusters are efficiently collected against the noise effect, through joint signal reconstruction. Simulation results show that the proposed cluster-based multi-target localization approach improves the localization accuracy over non-cluster approaches. Further, the simulation evaluation sheds light on the design guideline for the proposed approach implementation. That is, it can work well with a moderate number of clusters and a reasonable size of clusters.

Compressive sampling techniques can effectively reduce the acquisition costs of high-dimensional signals by utilizing the fact that typical signals of interest are often sparse in a certain domain. For compressive samplers, the number of samples Mrneeded to reconstruct a sparse signal is determined by the actual sparsity order Snzof the signal, which can be much smaller than the signal dimension N. However, Snzis often unknown or dynamically varying in practice, and the practical sampling rate has to be chosen conservatively according to an upper bound Smaxof the actual sparsity order in lieu of Snz, which can be unnecessarily high. To circumvent such wastage of the sampling resources, this paper introduces the concept of sparsity order estimation, which aims to accurately acquire Snzprior to sparse signal recovery, by using a very small number of samples Meless than Mr. A statistical learning methodology is used to quantify the gap between Mrand Mein a closed form via data fitting, which offers useful design guideline for compressive samplers. It is shown that Me≥ 1.2Snzlog(N/Snz+ 2) + 3 for a broad range of sampling matrices. Capitalizing on this gap, this paper also develops a two-step compressive spectrum sensing algorithm for wideband cognitive radios as an illustrative application. The first step quickly estimates the actual sparsity order of the wide spectrum of interest using a small number of samples, and the second step adjusts the total number of collected samples according to the estimated signal sparsity order. By doing so, the overall sampling cost can be minimized adaptively, without degrading the sensing performance.

In cognitive radio (CR) networks, multi-CR cooperation is required during spectrum sensing in order to cope with wireless fading effects and the hidden terminal problem. User cooperation offers not only channel diversity gain against fading, but also complexity gain in terms of reduced sampling costs per CR. The latter is particularly useful when the monitored spectrum has very wide bandwidth and yet individual CRs only have limited hardware capability. To jointly collect both diversity gain and complexity gain, this paper develops a novel cooperative spectrum sensing technique based on matrix rank minimization. Subject to sampling-rate limitations, CRs individually collect digital measurements from a segment of the wide spectrum via coordinated selective filtering, with optional compressive sampling to further reduce the sampling rates. The solutions representing the measurements of all users are modeled to possess a low-rank property, and the rank order is the same as the size of the nonzero support of the monitored wide spectrum. Accordingly, a nuclear norm minimization problem is formulated to jointly identify the nonzero support and hence the overall wideband spectrum occupancy. Both tradeoff evaluation and simulation results corroborate that the proposed cooperative sensing technique outperforms traditional averaging-based cooperative schemes given the same sampling costs, because the low-rank property enables efficient utilization and tradeoff of the user diversity in the absence of any channel knowledge.

In cognitive radio (CR) networks, multi-CR cooperation typically takes place during spectrum sensing, to cope with wire less fading effects and the hidden terminal problem. The user cooperation gain not only offers channel diversity against fading, but also allows for reduced sampling costs per CR, which is particularly relevant when the monitored spectrum has very wide bandwidth. To attain a desired tradeoff between channel diversity and sampling costs, this paper develops a new cooperative spectrum sensing technique based on matrix rank minimization. In the absence of channel knowledge, CRs individually collect digital measurements from a region of the wide spectrum via selective filtering, with optional compressive sampling to further reduce sampling rates. The solutions representing all the measurements are modeled to possess a low rank property, with the rank order being the same as the size of the nonzero support of the monitored wide spectrum. Accordingly, a nuclear norm minimization problem is formulated to jointly identify the nonzero support and hence the overall spectrum occupancy. Simulations show that the pro posed technique outperforms traditional averaging-based co operative schemes, given the same sampling costs.

For cognitive radios (CRs), compressive sampling (CS) techniques have been utilized for spectrum sensing in order to alleviate the high signal acquisition costs in the wideband regime. Given the desired sensing performance, the fundamental limit on the sampling rates is determined by the actual sparsity order Snzof the signal spectrum, which can be considerably lower than the Nyquist sampling rate. However, Snzis time-varying and hence unknown a priori for a dynamic CR network, and is typically available in the form of its statistical upper bound Smax. When the practical sampling rate is chosen according to Smaxin lieu of Snz, this rate is unnecessarily high for accurate spectrum sensing and hence wasteful of the sensing resources. To circumvent this problem, this paper develops a two-step compressed spectrum sensing (TS-CSS) scheme for efficient wideband sensing. The first step quickly estimates the actual sparsity order of the wide spectrum of interest using a small number of samples, and the second step adjusts the total number of samples collected according to the estimated signal sparsity order. By doing so, the overall sampling rate is minimized adaptively. The cornerstone of this work is the fact that the number of measurements required for estimating the signal sparsity order is (much) smaller than that for reconstructing the sparse signal itself. The gap between these two numbers is delineated in this paper in closed form, which offers valuable design guideline. Validated by simulations, the proposed TS-CSS scheme achieves the desired sensing performance at considerably reduced sensing costs, using a lowered average sampling rate compared with traditional one-step compressive sampling schemes.

A Virtual Polarization Detection (VPD) method based on the vector signal processing, is presented in this paper for the effective spectrum sensing of cognitive radios. The purpose of such VPD method is to exploit the orthogonal polarization component of primary signals besides the conjugate, in terms of vector information elements of signals. The spectrum sensing scenario of a single secondary user and multiple primary users is discussed, where the vector signals arrived at the secondary user are received by a pair of orthogonally polarized antennae. For the test of two-class problem (the primary user present class versus absent class), the secondary user optimizes the receiving polarization state to get the maximum primary signal to noise ratio by processing the received orthogonal polarization components. Specifically, it takes place in the processor of the secondary user virtually instead of antennae devices adaptation. The VPD method does not require any prior knowledge of the signal polarization states. The performance of our VPD method is compared with that of energy detection which uses scalar amplitude information only to sense the primary users. Simulation results show that the VPD method improves the spectrum sensing performance significantly.