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Spectrum sensing is a fundamental component in a cognitive radio network to utilize the frequency bands effectively. In this article a fast Riemannian distance-based K-medoids (FRDK)-based cooperative spectrum sensing (CSS) method is developed to identify the state of primary user (PU). In particular, two CSS scenarios are considered, one is secondary users (SUs) with a single antenna and the other is SUs with multiple antennas. In the multiantenna case, a Riemannian mean-based data fusion method is proposed to fuse sensing data from SUs with multiple antennas. To implement CSS, we propose a FRDK-based framework, where SUs collect sensing data, preprocess, and upload these data to an appointed fusion center (FC). Then, the FC transforms these data as samples on a manifold and uses the FRDK algorithm to train a classifier for identifying the state of PU. Furthermore, the convergence and the complexity analysis of training process are presented. Finally, the effectiveness of the proposed FRDK-based CSS method is verified under different conditions.

This paper concentrates on a globally sequential fusion state estimation problem for clustered wireless sensor networks (WSNs). Therein, frequent data communications in WSN will significantly increase energy consumption and communication burden, and it needs to be taken into account. To reduce unnecessary data transmissions and save energy, an event-triggered mechanism that decides whether the current measurement should be transmitted or not, therefore, is introduced. Then a novel variational Bayesian based event-triggered sequential measurement fusion (VB-ESMF) estimator is proposed to produce the local fused results of the clustered WSNs, where the variational Bayesian approach is used to infer the measurement noise covariance matrices of pseudo measurement noises. Therein, the local fused measurements of the clusters in the clustered WSNs are used sequentially by the remote fusion center, and thus a global fusion state estimation, which is globally optimal when all measurements are transmitted successfully, is computed. Additionally, certain boundedness and convergence conditions of the proposed estimator are derived, and an expected compromise between communication rate and estimation accuracy can be obtained by properly turning the trigger threshold. Finally, the effectiveness of both the VB-ESMF estimation and the globally sequential fusion state estimation is illustrated by simulation results.

This work conceives the robust linear transceivers for the estimation of an unknown vector parameter in a coherent multiple access channel (MAC)-based multiple-input multiple-output (MIMO) multi-sensor network under imperfect channel state information (CSI) at the fusion center (FC). Both the popular stochastic (S-) and norm ball CSI uncertainty (N-CSIU) models are considered for robust design. The proposed techniques are based on two design criterion, the first being, minimizing the mean squared error (MSE) of the estimate at the FC subject to total network power or individual sensor power constraints. Second, minimizing the total power consumption in the network while meeting a predefined level of MSE performance. Furthermore, the framework for precoder and combiner optimization is based on results from majorization theory, which leads to non-iterative closed-form solutions for the transceivers. While the most general scenario with correlated parameters and arbitrary observation SNR is considered to begin with, scenarios with uncorrelated parameters and high observation SNR are also considered as special cases, which makes the analysis comprehensive. Simulation results are presented to demonstrate the efficacy of the proposed schemes.

The paper considers distributed detection problem basis on using soft decision scheme both in the local sensors and in the fusion center (FC). The algorithm for making soft decisions when receiving data from local sensors in the fusion center and its performance characteristics, which are necessary for the formation decision fusion rule, are presented. The dependencies of the total error probability on the energy parameter taking into account signal-to-noise ratio at the level of local sensors and the channel’s signal-to-noise ratio are given. The gain of the fusion rule basis on the aggregation of soft decisions in the FC when receiving data about soft local decisions, in efficiency compared to hard fusion rule.

This article studies the performance evaluation of distributed linear regression Kalman filtering fusion for nonlinear systems. Sufficient conditions are established for the convergence of the centralized fusion (CF) under the assumption of bounded estimation error covariance, and a measure of performance is derived from the convergence conditions. By the performance analysis, it can be found that the CF has a better performance than the distributed fusion with feedback, especially at the beginning of the estimation. Moreover, the performance of the local estimator can be improved by receiving the fused estimate from the fusion center, which is different from the fusion estimation in linear systems. Finally, by simulations of a target tacking example, the comparisons of the centralized fusion and the distributed fusion with and without feedback are presented to show the accuracy of the performance analysis.

In this article, we address the problem of distributed detection of a noncooperative (unknown emitted signal) target with a wireless sensor network. When the target is present, sensors observe a (unknown) deterministic signal with attenuation depending on the unknown distance between the sensor and the target, multiplicative fading, and additive Gaussian noise. To model energy-constrained operations within Internet of Things, one-bit sensor measurement quantization is employed and two strategies for quantization are investigated. The fusion center receives sensor bits via noisy binary symmetric channels and provides a more accurate global inference. Such a model leads to a test with nuisances (i.e., the target position $\boldsymbol {x}_{T}$ ) observable only under $\mathcal {H}_{1}$ hypothesis. Davies’ framework is exploited herein to design the generalized forms of Rao and locally optimum detection (LOD) tests. For our generalized Rao and LOD approaches, a heuristic approach for threshold optimization is also proposed. The simulation results confirm the promising performance of our proposed approaches.

We consider the design of distributed detection algorithms for single-hop, single-channel wireless sensor networks in which sensor nodes send their local decisions to a fusion center (FC) by using a random access protocol. There is also limited time to collect local decisions before a final decision must be made. We thus propose and analyze a modified random access protocol in which the FC combines slotted ALOHA with a population-splitting algorithm called population-splitting-based random access (PSRA) and collision-aware distributed detection according to an estimate-then-fuse approach. Under the PSRA, only sensor nodes whose observations fall in a particular range of reliability will send their decisions in a specific frame by using slotted ALOHA. At the end of the collection time, the FC applies the collision-aware distributed detection to make a final decision. Here, the FC will first observe the state of each time slot—idle, successful, collision—in each frame, use this information to estimate the number of sensor nodes participating in each frame, and, then, compute a final decision using a population-based fusion rule. An approximation of the optimal transmission probability of the slotted ALOHA is determined to minimize the probability of error. Numerical results show that, unlike slotted-ALOHA-based data networks, the transmission probability maximizing the number of successful time slots does not optimize the performance of the proposed distributed detection. Instead, the proposed distributed detection performs best with a transmission probability that induces many collisions.

We consider a distributed detection problem where measurements at each sensor follow a general parametric distribution. The network does not have a central processing unit or fusion center (FC). Thus, each node takes some measurements, does some processing, exchanges messages with its neighbors and finally makes a decision (typically the same for all nodes) about the phenomenon of interest. The problem can be formulated as a composite hypothesis test with unknown parameters where, in general, a uniformly most powerful test does not exist. This leads naturally to the use of the Generalized Likelihood Ratio (GLR) test. As the measurements follow a general parametric distribution (which could model spatial dependence of the data), the implementation of fully-distributed detection procedures could be demanding in network resources. For this reason, we study the use of a simpler test (referred as L-MP) which uses the product of the marginals of the measurements taken at each node, where the unknown parameters are easily estimated with only local measurements. Although this simple proposal still requires network-wide cooperation between nodes, the number of communications is significantly reduced with respect to the GLR test, making it a suitable choice in severely resource-constrained sensor networks. This simpler test does not exploit the full parametric model of data, so, it becomes important to analyze its statistical properties and its potential performance loss. This is done through the analysis of the L-MP asymptotic distribution. Interestingly, despite the fact that the L-MP is simpler and more efficient to implement than the GLR test, we obtain some conditions under which the L-MP has superior asymptotic performance to the GLR test. Finally, we present numerical results for a fully-distributed spectrum sensing application for cognitive radios., 13 pages, 6 figures. Submitted to the IEEE Transactions on Signal and Information Processing over Networks

In this paper, we develop a new algorithm for centralized target detection in passive MIMO radar (PMR) using sparse recovery technique. PMRs use a network of receivers and illuminators of opportunity to detect and localize targets. We consider a widely separated PMR network assuming the availability of reference channels. We first transform the collected information of all receivers to a common space and combine them to attain a unified model. The problem of target detection in the extracted model is equal to a block sparse recovery problem. Since employing the generic sparse recovery tools are impractical due to the ultra-large dimension of the sensing matrix, we exploit the structure of the involving matrices and propose a very efficient distributed algorithm which extracts all scatterers, including targets and clutter simultaneously with a unified procedure. The proposed algorithm is highly efficient, and it does not require a high bandwidth link to transfer raw data from nodes to the fusion center. Moreover, the algorithm inherently benefits from parallel processing and distributes the extensive computations among receivers. Our simulation results demonstrate that the proposed algorithm outperforms the popular PMR detection algorithm, especially in the presence of interfering targets and any strong clutter residue.

Hidden Primary User problem caused by fading and shadowing severely affects the detection rate of the cognitive radio systems with a single spectrum sensor. Cooperative Spectrum Sensing has been introduced to tackle this problem by using the spatial diversity of spectrum sensors. It is shown that the use of soft decision algorithms in fusion center has a better performance than hard decision algorithms. The problem of soft decision based on sensor measurements perfectly matches the Machine Learning paradigm. In this brief, a novel fast soft decision algorithm is proposed based on Machine Learning theory for wideband Cooperative Spectrum Sensing, which finds a decision boundary to classify the Power Spectral Density (PSD) measurement vectors of sensors into the empty and occupied channel classes. The statistical characteristics of sensors PSD samples are employed to derive a fast solution, which outperforms the SVM-linear algorithm. By solving an optimization problem a Constant False Alarm Rate algorithm is introduced and then it is improved to the Adaptive False Alarm Rate algorithm. The proposed algorithm reduces the average training time to one tenth of the SVM-linear training time, while the detection probability is the same. The hardware implementation of the proposed algorithm is described in Verilog HDL and the corresponding simulation results are presented.

This paper is concerned with the Tobit Kalman fusion estimation problem for a class of multi-sensor systems subject to parametric uncertainties and measurement censoring. The parametric uncertainty is characterized by the multiplicative noise appearing in both state and observation equations, and the measurement censoring is governed by the Tobit observation model. The fusion estimation is implemented via two stages: at the first stage, each sensor sends its observations to the local estimator and, at the second stage, the local estimates are then transmitted to the fusion center so as to generate the fused estimate. The local estimator realizes a Tobit Kalman filtering algorithm which is devised in accordance with a modified regression model, whilst the fusion center carries out the fusion estimation by resorting to the federated fusion rule. Furthermore, the monotonicity of the fused error covariance with respect to the censoring threshold is discussed and, subsequently, the boundedness property is also examined where both lower and upper bounds are acquired for the fused error covariance. The validity of the fusion estimator is finally shown via two numerical examples.

This paper considers the problem of sequential binary hypothesis testing based on observations from a network of $m$ sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average sample number required to reach a certain level of error probability is selected as the performance metric of the system. We propose an asymptotically optimal voting algorithm for the sensor network with a fusion center and generalize it to fully-distributed networks, where the algorithm stays asymptotically optimal under the weak assumption that the sensor network is connected. Moreover, we prove that both of the proposed algorithms are asymptotically optimal in the presence of Byzantine sensors, in the sense that each of them forms a Nash equilibrium with the worst-case attack (flip-attack). Compared to existing distributed detection strategies, the proposed scheme has a low message complexity, which is independent of the error probability and the sample number, by taking advantage of the sparsity of votes. The results are corroborated by numerical simulations.

Due to the requirement of anti-interception and the limitation of processing capability of the fusion center, the subarray selection is very important for the distributed multiple-input multiple-output (MIMO) radar system, especially in the hostile environment. In such conditions, an efficient subarray selection strategy is proposed for MIMO radar performing tasks of target tracking and detection. The goal of the proposed strategy is to minimize the worst-case predicted posterior Cramer-Rao lower bound (PCRLB) while maximizing the detection probability for a certain region. It is shown that the subarray selection problem is NP-hard, and a modified particle swarm optimization (MPSO) algorithm is developed as the solution strategy. A large number of simulations verify that the MPSO can provide close performance to the exhaustive search (ES) algorithm. Furthermore, the MPSO has the advantages of simpler structure and lower computational complexity than the multi-start local search algorithm.

Instead of only considering the radar estimation error in the traditional radar system (TRS), for the integrated radar and communication system (IRCS), we investigate the Cramer-Rao bound (CRB) of the localization estimation, which is influenced by both radar estimation error and communication transmission error. The functions of radar and communication are operated simultaneously by embedding the communication symbols into the multicarrier radar waveforms. Firstly, we derive the CRB of time/direction of arrival (TOA/DOA) estimation. To minimize the estimation error, we maximize the signal-to-interference-plus-noise ratio (SINR) of radar by iteratively optimizing the radar transmit and receive beamformers (with the constraint of available transmit power). Then, the CRB of localization estimation is derived using hybrid TOA/DOA measurement. The local CRBs from different IRCSs are fused according to the linear fusion rule at the fusion center (FC). Finally, numerical results demonstrate that the additional estimation errors for the IRCS are mainly determined by the channel conditions of communication and available transmit power; the estimation accuracy for both IRCS and TRS can be improved through the iterative transmit and receive beamforming (ITRB) technique.

Over the past few years, dynamic spectrum access has been gaining an increasing attention as a solution to the spectrum scarcity problem. In this paper, a primary user detection technique based on Maximum A Posteriori estimation is proposed for dynamic spectrum access networks. In the proposed technique, a set of secondary users acting as sensing nodes send their individual decisions about the existence of the primary user to a central fusion center. The fusion center uses the received data to form a codeword then, applies the maximum a posteriori estimation rule to make a final decision regarding the presence of the primary user. The proposed technique takes into consideration the accuracy of the local decisions provided by the secondary users when making a final decision. In this paper, we analyze the performance of the proposed scheme and derive closed-form expressions for the upper bounds of the false alarm and misdetection probabilities. The results show that the proposed technique outperforms other combining techniques in terms of its ability to detect the primary user and, accordingly, minimizes the harmful interference to the licensed network. Moreover, the proposed technique achieves better performance at a lower number of reporting secondary users which compensates for the complexity of the maximum a posteriori estimation.

An optimal precoder design is conceived for the decentralized estimation of an unknown spatially as well as temporally correlated parameter vector in a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) based wireless sensor network (WSN). Furthermore,exploiting the temporal correlation present in the parameter vector, a rate-distortion theory based framework is developed for the optimal quantization of the sensor observations so that the resultant distortion is minimized for a given bitbudget. Subsequently, optimal precoders are also developed that minimize the sum-MSE (SMSE) for the scenario of transmitting quantized observations. In order to reduce the computational complexity of the decentralized framework, distributed precoder design algorithms are also developed which design precodersusing the consensus based alternating direction method of multipliers(ADMM), wherein each SN determines its precoderswithout any central coordination by the fusion center. Finally,new robust MIMO precoder designs are proposed for practicalscenarios operating in the face of channel state information (CSI)uncertainty. Our simulation results demonstrate the improvedperformance of the proposed schemes and corroborate ouranalytical formulations.

Distributed or decentralized estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years, and applications in array processing have been indicated in some detail. Inspired by these, this paper provides a detailed development of several distributed algorithms for array processing. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares-ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, and distributed implementation of the spatial smoothing method for coherent sources. A distributed implementation of a recently proposed beamspace method called the convolutional beamspace (CBS) is also proposed. The proposed algorithms are fully distributed – an average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a recently reported finite-time version of AC which converges to the exact solution in a finite number of iterations. Numerical examples are given throughout the paper to show the effectiveness of the proposed algorithms.

In multi-sensor tracking and fusion system, due to the different pre-processing time and sampling rate of sensors, as well as the inherent random communication delay of the channel, the measurement data of sensor may arrive at the fusion center in an unordered manner. The current out-of-order measurement filtering methods cannot fully meet the engineering requirements in terms of tracking accuracy and computational complexity. This paper proposes a centralized data fusion method based on lag compensation. This method can deal with one-step or even multi-step delay measurement data, and the compensation accuracy can be closed to the fusion accuracy under orderly measurement. At the same time, this method has the ability of selective fusion, which improves the positioning accuracy while relatively reducing the amount of calculation and storage. The simulation results verify the effectiveness of the algorithm.

We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary-input symmetric-output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions differing only in the Markov chain conditions imposed are characterized., Shorter version to appear in the IEEE International Symposium on Information Theory 2021

The problem of quickest change detection in anonymous heterogeneous sensor networks is studied. The sensors are clustered into $K$ groups, and different groups follow different data generating distributions. At some unknown time, an event occurs in the network and changes the data generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where at each time step, the fusion center receives unordered samples without knowing which sensor each sample comes from, and thus does not know its exact distribution. In [1], an optimal algorithm was provided, which however is not computational efficient for large networks. In this paper, a computationally efficient test is proposed and a novel theoretical characterization of its false alarm rate is further developed.

The problem of quickest dynamic anomaly detection in anonymous heterogeneous sensor networks is studied. The $n$ heterogeneous sensors can be divided into $K$ types with different data generating distributions. At some unknown time, an anomaly emerges in the network and changes the data generating distribution of the sensors. The goal is to detect the anomaly as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where the fusion center does not know which sensor that each sample comes from, and thus does not know its exact distribution. Firstly, the static setting is investigated where the sensor affected by the anomaly does not change with time. A generalized mixture CuSum algorithm is constructed and is further shown to be asymptotically optimal. The problem is then extended to a dynamic setting where the sensor affected by the anomaly changes with time. An asymptotically optimal weighted mixture CuSum algorithm is proposed. Numerical results are also provided to validate the theoretical results.

The advent of Internet of Things (IoT) has bring a new era in communication technology by expanding the current inter-networking services and enabling the machine-to-machine communication. IoT massive deployments will create the problem of optimal power allocation. The objective of the optimization problem is to obtain a feasible solution that minimizes the total power consumption of the WSN, when the error probability at the fusion center meets certain criteria. This work studies the optimization of a wireless sensor network (WNS) at higher dimensions by focusing to the power allocation of decentralized detection. More specifically, we apply and compare four algorithms designed to tackle Large scale global optimization (LGSO) problems. These are the memetic linear population size reduction and semi-parameter adaptation (MLSHADE-SPA), the contribution-based cooperative coevolution recursive differential grouping (CBCC-RDG3), the differential grouping with spectral clustering-differential evolution cooperative coevolution (DGSC-DECC), and the enhanced adaptive differential evolution (EADE). To the best of the authors knowledge, this is the first time that LGSO algorithms are applied to the optimal power allocation problem in IoT networks. We evaluate the algorithms performance in several different cases by applying them in cases with 300, 600 and 800 dimensions.

In this letter, a double threshold-based log-likelihood ratio (LLR) detector with a novel hard-soft combining rule (DT-LLR-HSC) is proposed for spectrum sensing in cooperative cognitive radio networks (CRNs) under the block Rayleigh fading scenario. A novel weighted hard-soft combining scheme is adopted at the fusion center to combine local binary/energy information resulting in global binary decision. A trust-based novel weight vector estimation considering both the sensing and reporting channel signal-to-noise ratio is also proposed. Further, the proposed DT-LLR-HSC scheme is adopted in full-duplex cooperative CRNs under Nakagami-m fading channel. The analytical expressions for the average probability of detection are derived and verified for both the half-duplex and full-duplex cases.

This paper is concerned with globally optimal sequential and distributed fusion estimation algorithms in the linear minimum variance (LMV) sense for multi-sensor systems with cross-correlated noises, where the measurement noises from different sensors are cross-correlated with each other at the same time step and correlated with the system noise at the previous time step. First, a globally optimal sequential fusion filter is proposed by considering the estimators for measurement noises. The equivalence on estimation accuracy of the proposed sequential fusion filter and centralized fusion filter is proven. It has reduced computational cost since it avoids the measurement augmentation. Then, a distributed fusion filter is also proposed by considering the prior fusion estimator and feedback from the fusion center. Under the condition that local gain matrices are full column rank, the proposed distributed fusion filter has the same estimation accuracy as the centralized fusion filter, that is, it also has global optimality. Their equivalence on estimation accuracy is proven. Stability and steady-state properties of the proposed algorithms are analyzed. A sufficient condition for the existence of steady-state filters is given. Finally, simulation results for a target tracking system show the effectiveness of the proposed algorithms.

In this paper, we study the problem of joint sparse support recovery with 1-b quantized compressive measurements in a distributed sensor network. Multiple nodes in the network are assumed to observe sparse signals having the same but unknown sparse support. Each node quantizes its measurement vector element-wise to 1 b. First, we consider that all the quantized measurements are available at a central fusion center. We derive performance bounds for sparsity pattern recovery using 1-bit quantized measurements from multiple sensors when the maximum likelihood decoder is employed. We further develop two computationally tractable algorithms for joint sparse support recovery in the centralized setting. One algorithm minimizes a cost function defined as the sum of the likelihood function and the $l_{1,\infty }$ quasi-norm, while the other algorithm extends the binary iterative hard thresholding algorithm to the multiple measurement vector case. Second, we consider a decentralized setting where each node transmits 1-b measurements to its one-hop neighbors. The basic idea behind the algorithms developed in the decentralized setting is to embed collaboration among nodes and fusion strategies. We show that even with noisy 1-b compressed measurements, joint support recovery can be carried out accurately in both centralized and decentralized settings. We further show that the performance of the proposed 1-bit compressive sensing-based algorithms is very close to that of their real-valued counterparts except when the signal-to-noise ratio is very small.

In this paper, localization using narrowband communication signals are considered in the presence of fading channels with time of arrival measurements. When narrowband signals are used for localization, due to existing hardware constraints, fading channels play a crucial role in localization accuracy. In a location estimation formulation, the Cramer-Rao lower bound for localization error is derived under different assumptions on fading coefficients. For the same level of localization accuracy, the loss in performance due to Rayleigh fading with known phase is shown to be about 5dB compared to the case with no fading. Unknown phase causes an additional 1dB loss. The maximum likelihood estimators are also derived. In an alternative distributed detection formulation, each anchor receives a noisy signal from a node with known location if the node is active. Each anchor makes a decision as to whether the node is active or not and transmits a bit to a fusion center once a decision is made. The fusion center combines all the decisions and uses a design parameter to make the final decision. We derive optimal thresholds and calculate the probabilities of false alarm and detection under different assumptions on the knowledge of channel information. Simulations corroborate our analytical results., Accepted in Physical Communications (PHYCOM)

In centralized cooperative spectrum sensing (CSS), cognitive radios (CRs) monitor the spectrum and send the related data to a fusion center (FC) via a control channel in order to more efficiently detect possible idle bands for opportunistic occupation. In centralized cooperative spectrum sensing (CSS), cognitive radios (CRs) monitor the spectrum and send the related data to a fusion center (FC) via a control channel in order to more efficiently detect possible idle bands for opportunistic occupation. In practice, such data must be quantized prior to transmission, which can lead to loss of the global spectrum sensing performance due to quantization errors. Additionally, wireless control channel impairments, such as the multipath fading, further contributes to performance degradation. In many researches, the control channel is considered error-free. Even when errors are considered, they usually affect the transmitted symbols independently, that is, the control channel is assumed to be memoryless. Error bursts come from the memory effect of the channel, and are typically found in wireless communications. In this paper we consider the effects of burst errors in the control channel as well as the problem of signal distortion caused by three methods of quantization in centralized CSS with sample fusion. The Gerschgorin Radii and Centers Ratio (GRCR) detector is used as the test statistic for spectrum sensing. Our findings show that: i) the GRCR is robust in the scenarios taken into consideration, ii) the uniform quantization may be preferred in some cases when the control channel is considered perfect, iii) the nonuniform quantization attains better performance under errors in the control channel, and iv) the effect of memory in the control channel may produce, in some situations, performance gains with respect to the memoryless channel, when both have the same average bit error rate.

We consider a distributed detection problem with statistically spatial dependent measurements in a sensor network, when there is not a fusion center. Thus, each node takes some measurements, does some processing, exchanges messages with its neighbors and finally makes a decision (typically the same for all nodes) about the phenomenon of interest. A cooperative algorithm is proposed for reducing the number of communications between sensors and thus make an efficient use of the energy budget of a wireless sensor network (WSN). The problem is formulated as a composite hypothesis test using a general probability density function with unknown parameters leading naturally to the use of the generalized likelihood ratio (GLR) test. As the sensors observe statistically spatial dependent samples, which makes difficult the implementation of fully distributed detection procedures, we propose a simpler algorithm for making a decision about the true hypothesis. We also compute its asymptotic distribution to characterize its performance. Interestingly, despite the fact that our proposal is more simple and efficient to implement than the GLR test, we find relevant scenarios for which it outperforms the latter, even in finite length regimes.

A scalable algorithm is derived for multilevel quantization of sensor observations in distributed sensor networks, which consist of a number of sensors transmitting a summary information of their observations to the fusion center for a final decision. The proposed algorithm is directly minimizing the overall error probability of the network without resorting to minimizing pseudo objective functions such as distances between probability distributions. The problem formulation makes it possible to consider globally optimum error minimization at the fusion center and a person-by-person optimum quantization at each sensor. The complexity of the algorithm is quasi-linear for i.i.d. sensors. Experimental results indicate that the proposed scheme is superior in comparison to the current state-of-the-art.

In autonomous driving systems, distributed sensor fusion is widely used where each sensor has its tracking system and only the local tracks (LT) are transmitted to the fusion center. We consider the fusion of LTs taking into account all the Fusion Center (FC) track-to-LT association hypotheses via probabilities in the proposed Hybrid Probabilistic Information Matrix Fusion (HPIMF) algorithm. In HPIMF, the track association and fusion are carried out with probabilistic weightings rather than using a single track association only. Different from track-to- track fusion (T2TF), which is one of the most commonly used approaches for distributed tracking systems, the associations considered in HPIMF are between the predicted FC state and the LTs from local sensors. At each time for an association event, up to one of the tracks within the track list of a local sensor can be associated with the FC state. In real world scenarios there can be large uncertainties and missed tracks due to sensor imperfections and sensor-target geometry. Consequently, the association might be unreliable and fusion based on only a single association hypothesis could fail. It is shown in the simulations of a realistic autonomous driving system that HPIMF can successfully track a target of interest and is superior to T2TF which relies on hard association decisions.

In this work, target localization is studied for cloud multiple-input multiple-output (MIMO) radar. Unlike previous work which quantizes local received signals, to reduce the communication burden, this paper proposes to quantize local time delays for cloud MIMO radar parameter estimation. At each local sensor, the time delay of the signal traveling from the transmitter and returning to the receiver is estimated and quantized prior to transmission to the fusion center. The target location is estimated using the quantized time delay estimates at the fusion center, and the corresponding Cramer-Rao bound (CRB) is derived. Compared with existing methods based on received signal quantization, the proposed time delay quantization-based method can provide enhanced performance.

The output of the network in a deep learning (DL) based single-user signal detector, which is a normalized 2 × 1 class score vector, needs to be transmitted to the fusion center (FC) by occupying a large amount of the communication channel (CCH) bandwidth in the cooperative spectrum sensing (CSS). Obviously, in cognitive radio for vehicle to everything (CR-V2X), it is particularly important to propose a method that makes full use of the bandwidth-constrained CCH to obtain the optimal detection performance. In this paper, we firstly propose a novel single-user spectrum sensing method based on modified-ResNeXt in CR-V2X. The simulation results show that our proposed method performs better than two advanced DL based spectrum sensing methods with shorter inference time. We then introduce a quantization-based cooperative spectrum sensing (QBCSS) algorithm based on DL in CR-V2X, and the impact of the number of reported bits on the sensing results is also discussed. Through the experimental results, we conclude that the QBCSS algorithm reaches the optimal detection performance when the number of bits for quantizing local sensing data is 4. Finally, according to the conclusion, a bandwidth-constrained QBCSS scheme based on DL is proposed to make full use of the CCH with limited capacity to achieve the optimal detection performance.

Aiming at the problem of time-delay in wireless sensor networks (WSNs), a multi-rate fusion method is proposed from the perspective of data fusion. The sensor uses different sampling and transmission rates for data collection and transmission. Firstly, in order to enhance the adaptability of cubature Kalman filter (CKF), the filtering performance of CKF is further improved. In this paper, the covariance matrix is modified online by constructing adaptive factors. The improved cubature Kalman filter (ICKF) is used to process these data collected by sensor nodes to generate local estimation (LE), and then the LE is formed into fusion estimation (FE) in the fusion center. The simulation results show that, compared with the traditional CKF and unscented Kalman filter (UKF), the ICKF algorithm has higher estimation performance and better stability.

International audience; In this work, we propose a novel framework for distributed detection by resorting to the Random Distortion Testing with linear measurements (RDTlm) approach. The goal is to collaboratively detect a signal, with unknown distribution embedded in noise, with the help of multiple sensors distributed spatially in the Region of Interest (RoI). The sensors observe the phenomenon and forward a compressed summary of the observations to a Fusion Center (FC). The FC then employs RDTlm to perform the hypothesis test. In contrast to classical likelihood ratio based approaches that cannot be employed in case of imprecise knowledge of the signal distributions, framing the problem within the RDTlm framework leads to performance guarantees, irrespective of the signal distributions under each hypothesis and without the need to estimate the unknown distributions. Moreover, we show the equivalence between the proposed distributed approach where a compressed summary is forwarded by the sensors and the centralized approach where the sensors forward raw observations to the FC.

Spectrum sensing (SS) has attracted much attention due to its important role in the improvement of spectrum efficiency. However, the limited sensing time leads to an insufficient sampling point due to the tradeoff between sensing time and communication time. Although the sensing performance of cooperative spectrum sensing (CSS) is greatly improved by mutual cooperation between cognitive nodes, it is at the expense of computational complexity. In this paper, efficient approximations of the N-out-of-K rule-based CSS scheme under heterogeneous cognitive radio networks are provided to obtain the closed-form expression of the sensing threshold at the fusion center (FC), where the false alarm probability and its corresponding detection probability are approximated by the Poisson distribution. The computational complexity required to obtain the optimal sensing threshold at the FC has greatly decreased and theoretical derivations state that the approximation error is negligible. The simulations validate the effectiveness of the proposed scheme.

In this paper, we address the problem of covert communication under the presence of multiple wardens with a finite blocklength. The system consists of Alice, who aims to covertly transmit to Bob with the help of a jammer. The system also consists of a Fusion Center (FC), which combines all the wardens’ information and decides on the presence or absence of Alice. Both Alice and jammer vary their signal power randomly to confuse the FC. In contrast, the FC randomly changes its threshold to confuse Alice. The main focus of the paper is to study the impact of employing multiple wardens on the trade-off between the probability of error at the FC and the outage probability at Bob. Hence, we formulate the probability of error and the outage probability under the assumption that the channels from Alice and jammer to Bob are subject to Rayleigh fading, while we assume that the channels from Alice and jammer to the wardens are not subject to fading. Then, we utilize a two-player zero-sum game approach to model the interaction between joint Alice and jammer as one player and the FC as the second player. We derive the pay-off function that can be efficiently computed using linear programming to find the optimal distributions of transmitting and jamming powers as well as thresholds used by the FC. The benefit of using a cooperative jammer is shown by means of analytical results and numerical simulations to neutralize the advantage of using multiple wardens at the FC.

The proposed cooperative spectrum sensing network gives potential attributes to improve the detection performance. This research paper mainly focuses on the identification of unknown signals in Weibull fading environment using an improved energy detector (IED). The proposed network consists of multiple cognitive radio (CR) nodes, at each CR node number of antennas are used and selection combining (SC) is used to select the maximum value of detection probability. Further, the activity of primary user (PU) is identified using fusion rules at fusion center (FC). Initially, closed-form of missed detection and false alarm probabilities are proficiently derived. Later on, energy efficiency and an average channel throughput analysis are evaluated using $k= 1 +n$ and $k=N- n$ rules at FC.

Cognitive radio networks (CRNs) uses Spectrum sensing(SS) for assessment the vacant spectrum in the licensed band .Cooperative spectrum sensing(CSS) is the best method for evaluation of white space when multiple secondary user work in the collaboration .All local node scan the licensed band give their decision to central fusion center. Central fusion center then aggregate the local nodes decision by soft fusion or hard fusion rules and give the final conclusion whether white space is available or not. Cooperative spectrum sensing enhances the spectrum detection efficiency by reducing the effect of fading and shadowing using spatial diversity and also reduced noise uncertainty problem. The simulation result in this article shows a relative comparison between various soft fusion and hard fusion rule. Soft fusion rule has high value of the detection efficiency in comparison of the hard fusion scheme at the cost of bandwidth.

Cooperative spectrum sensing (CSS) has been considered as an essential paradigm of cognitive radio (CR) to significantly improve spectrum utilization. However, due to the presence of Byzantine attack and the imperfect reporting channel, the sensing results may be falsified and distorted, and then are submitted to the fusion center (FC) to cooperate in CSS, resulting in the drastic degradation of the CSS performance. To mitigate the negative impact of Byzantine attack and the imperfect reporting channel, we propose a sequential single symbol differential voting (S3DV) rule, which exploits the single symbol differential method to solve the problem of the imperfect reporting channel and makes use of the data transmission monitoring process to defend against Byzantine attack. Comparing to the existing voting rules, simulation results show that the proposed S3DV can not only significantly reduces the report sample size, but also provide better performance in the front of Byzantine attack and the imperfect reporting channel.

The current issues in the wireless sensor networks (WSN) are to enhance the efficiency of sensor nodes and their strength to handle node failure. This paper introduced an energy enhancement algorithm for clustering based on the properties of the fuzzy c-means. A novel algorithm is proposed using a fuzzy membership function and the Euclidean distance known as Fuzzk. The membership value of each node is calculated by the certainty that the highest value is considered as high if maximum sensor nodes situated closer to the head of the cluster. The proposed algorithm performed better to select the fusion center or cluster head as a base station of the network, so that energy consumption can be reduced as compared to the existing algorithm. The simulation results show that the energy consumption is reduced in our proposed Fuzzk algorithm that the same as LEACH, DEEC, and K-MEANS.

This paper combines the distributed sensor fusion system with the signal detection under chaotic noise to realize the distributed sensor fusion detection from chaotic background. First, based on the short-term predictability of the chaotic signal and its sensitivity to small interference, the phase space reconstruction of the observation signal of each sensor is carried out. Second, the distributed sensor local linear autoregressive (DS-LLAR) model is constructed to obtain the one-step prediction error of each sensor. Then, we construct a Bayesian risk model and also obtain the corresponding conditional probability density function under each sensor’s hypothesis test which firstly needs to fit the distribution of prediction errors according to the parameter estimation. Finally, the fusion optimization algorithm is designed based on the Bayesian fusion criterion, and the optimal decision rule of each sensor and the optimal fusion rule of the fusion center are jointly solved to effectively detect the weak pulse signal in the observation signal. Simulation experiments show that the proposed method which used a distributed sensor combined with a local linear model can effectively detect weak pulse signals from chaotic background.

This paper tackles unknown signal detection in a distributed fashion via a Wireless Sensor Network (WSN) made of tiny and low-cost sensor devices. The sensors are assumed to measure an unknown deterministic parameter within unimodal and symmetric noise. Since usual Internet of Things (IoT) scenarios require energy-constrained operations, one-bit quantization of the raw measurement is locally performed at each sensor. A Fusion Center (FC) receives noisy quantized sensor observations through reporting parallel-access Rayleigh channels and makes a global decision. We propose the Rao test as a simpler alternative to the Generalized Likelihood Ratio Test (GLRT) for multisensor fusion. The intent of our work is performing fusion directly from the received signals, following a decode-and-fuse approach. Then, we study the design of the (channel-aware) quantizer of each sensor with the intent of maximizing the asymptotic detection probability. Finally, we compare the performance of the Rao test with that of the GLRT by simulations (related to a practical WSN scenario).

We consider decentralized detection (DD) of an uncooperative moving target via wireless sensor networks (WSNs), measured in zero-mean unimodal noise. To address energy and bandwidth limitations, the sensors use multi-level quantizers. The encoded bits are then reported to a fusion center (FC) via binary symmetric channels. Herein, we propose a generalized Rao (G-Rao) test as a simpler alternative to the generalized likelihood ratio test (GLRT). Then, at the FC, a truncated one-sided sequential (TOS) test rule is considered in addition to the fixed-sample-size (FSS) manner. Further, the asymptotic performance of a trajectory-clairvoyant (multi-bit) Rao test is leveraged to develop an offline and per-sensor quantizer design. Detection gain measures are also introduced to assess resolution improvements. Simulations show the appeal of G-Rao test with respect to the GLRT, and the gain in detection by using multiple bits for quantization, as well as the advantage of the sequential detection approach.

In this paper, we discussed the parametric optimization of improved sensing schemes in multi-antenna cognitive radio (CR) networks over an erroneous channel. The CR utilizes an improved energy detector (IED) by making the binary decision statistics of the absence or presence of a primary user. From primary users’ statistics, the improved energy detector measures power with respect to the threshold so as to make correct spectrum decisions. This decision is further transferred to the fusion center (FC) by the erroneous channel, which decides the complete decision of the existence of PU. For the detection of the spectrum hole and to obtain an optimized number of CRs, we minimize the total error rate (TER) in cooperative spectrum sensing. An optimized value of sensing threshold and arbitrary positive power (p) of each CR is also accessed by considering the TER. The numerical-based simulation results show the validation of correct sensing performance.

The distributed object decision (DOD) was applied to choose a single solution for problem among many complexes solutions. Most of DOD systems depend on traditional technique like small form factor optical (SFFO) method and scalable and oriented fast-based local features (SOFF) method. These two methods were statistically complex and depended to an initial value. In this paper proposed new optimal technical called gray wolf optimization (GWO) which is used to determine threshold of sensor decision rules from fusion center. The new algorithm gave better performance for fusion rule than numerical results. The results are providing to demonstrate of fusion system reduced of bayes risk by a high rate of 15%-20%. This algorithm also does not depend on the initial values and shows the degree of complexity is better than other algorithms.

Over-the-air computation (AirComp) is an emerging wireless technique with wide applications (e.g., in distributed edge learning), which can swiftly compute functions of distributed data from different wireless devices (WDs) by exploiting the superposition property of wireless channels. Different from prior works focusing on the AirComp over one single cell in a small area, this paper considers a new hierarchical architecture to enable AirComp in a large area, in which a set of intermediate relays are exploited to help the fusion center to aggregate data from massive WDs for functional computation. In particular, we present a two-phase amplify-and-forward (AF) relaying design for hierarchical AirComp. In the first phase, the WDs simultaneously send their data to the relays, while in the second phase, the relays amplify the received signals and concurrently forward them to the fusion center for aggregation. Under this setup, we minimize the computation distortion measured by the mean squared error (MSE), by jointly optimizing the transmit coefficients at the WDs and relays and the de-noising factor at the fusion center, subject to their individual transmit power constraints. For the highly non-convex MSE minimization problem, we develop an alternating-optimization-based algorithm to obtain a high-quality solution. The optimized solution shows that for each WD, the phase of its transmit coefficient is opposite to that of the composite channel from the WD itself to the relays to the fusion center, such that they can be aligned at the fusion center, and its transmit power follows a regularized composite-channel-inversion structure to strike a balance between minimizing the signal misalignment error and the noise-induced error. Numerical results show that our proposed design achieves a significant MSE performance gain over benchmark schemes with full-power transmission at the WDs and/or relays.

An efficient machine learning algorithm based on stochastic gradient is proposed and discussed for spatial tracking of correlated spatial signals from the sensor observations in wireless sensor field. The proposed algorithm can be used for environmental monitoring applications such as efficient temporal monitoring of temperature in hot island, or efficient monitoring of the distribution of pollutant gasses in wide areas for example terrain of large cities, etc. The proposed algorithm is computationally efficient and is low cost. In this paper the number of reporting sensors in tracking of signal is defined as cost. The spatial signal is compressed into a number of its isocontours at specific levels and the sensors whose sensor readings are in given margin of these contour levels, report their sensor readings to the fusion center (FC). The algorithm is done in two phases of spatial modeling and spatial tracking, where it uses the correlation between the spatial signal before and after variation of the spatial signal and updates the new set of contour levels for spatial tracking. The proposed machine learning algorithm finds the modeling parameters during the spatial modeling phase, and then updates them in spatial tracking phase. The performance analysis of the proposed algorithm shows that it successfully tracks the spatial variations of the signal at low cost with similar modeling performance to the spatial modeling.

The implementation of soft data combining methods for cooperative cognitive radio network (CCRN) in faded environment is proposed. Soft data combining functioning is performed by fusion center (FC) based on the energy samples obtained from several cognitive radios (CRs). Specifically, we investigate the interpretation of CCRN through different soft combining methods: Square law selection (SLS), maximal ratio combining (MRC), square law combining (SLC) and selection combining (SC) in noisy and Rayleigh faded environment. Towards that, we obtain analytical equations of probability of detection for several soft data combining methods over Rayleigh fading environment. The soft data fusion based CCRN behavior is shown relatively on behalf of various network specifications.

In this work, a cooptative spectrum sensing network (CSSN) for improved energy detection (IED) based CR nodes is proposed. All the CR nodes are equipped with number of antennas and perform themselves selection diversity (SC) techniques. Each CR node senses a PU through erroneous channels (sensing) and reports its sensing data (one-bit decision) to fusion center (FC) through erroneous channels. In FC, the global decision on the status of PU is made with the help of k-out-of-N fusion scheme. The expression for detection probability over noise plus Hoyt fading channels are derived and the mathematical framework for analysis of throughput of proposed network is developed. The simulation results is also presented to validate the analytically obtained performance characteristics. For several network parameters values, the investigation on comparison between IED and traditional energy detection method for different decision fusion rules is discussed. Further, performance curves are analytically illustrated for throughput over noise plus Hoyt fading channel. The impact of diversity technique and effect of fading severity parameters on the throughput is also investigated. The effect of channel error on total error performance for both proposed and conventional networks is shown. Finally, optimal network parameters values correspond to maximum throughput are also identified.

We consider decentralized detection (DD) of an uncooperative moving target via wireless sensor networks (WSNs), measured in zero-mean unimodal noise. To address energy and bandwidth limitations, the sensors use multi-level quantizers. The encoded bits are then reported to a fusion center (FC) via binary symmetric channels. Herein, we propose a generalized Rao (GRao) test as a simpler alternative to the generalized likelihood ratio test (GLRT). Further, the asymptotic performance of a trajectory-clairvoyant (multi-bit) Rao test is leveraged to develop an offline and per-sensor quantizer design. Simulations show the appeal of G-Rao test with respect to the GLRT, and the gain in detection by using multiple bits for quantization. Index Terms—Decentralized detection, Generalized Rao test, GLRT, multibit quantizer, wireless sensor networks.