We consider the problem of sparse signal reconstruction from noisy 1-bit compressed measurements using a statistically dependent signal, as an aid. We assume that this signal does not share joint sparse representation with the sparse signal and call it a heterogeneous side-information. We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip errors after quantization. We propose a generalized approximate message passing-based algorithm for signal reconstruction from noisy 1-bit compressed measurements which leverages the dependence between the signal and the heterogeneous side-information. We model the dependence between signal and heterogeneous side-information using copula functions and show, through numerical experiments, that the proposed algorithm yields a better reconstruction performance than 1-bit CS-based recovery algorithms that do not exploit the side-information.

Allowing humans to act as soft sensors is increasingly becoming an attractive solution to enhance decision making performance when the available physical (hard) sensors are limited. While the fusion problem with hard data has a rich history, fusion of hard and soft data requires further understanding due to human related factors associated with human sensor data. In this work, we investigate how the presence of human sensors can be modeled in the statistical signal processing framework and the factors that need to be taken into account when integrating soft human sensor data with hard data in a signal detection framework. We consider two cases. In the first case, both types of sensors are assumed to make threshold based individual decisions using identical observations. While physical sensors use a fixed threshold, the thresholds used by human sensors are assumed to be random variables. With a given distribution for the random thresholds used at the human sensors, by properly designing the thresholds at the physical sensors, an enhanced detection performance can be observed in the integrated system compared to performing fusion with only physical sensors. In the second case, we evaluate the fusion performance when human sensors possess some side information regarding the phenomenon in addition to the common observations available at the two types of sensors.

In this paper, we consider the problem of sparse signal detection with compressed measurements in a Bayesian framework. Multiple nodes in the network are assumed to observe sparse signals. Observations at each node are compressed via random projections and sent to a centralized fusion center. Motivated by the fact that reliable detection of the sparse signals does not require complete signal reconstruction, we propose two computationally efficient methods for constructing decision statistics for detection. First, using the Laplace prior directly to impose sparsity as widely considered in Bayesian Compressive Sensing (BCS), we develop an average likelihood ratio based detection method where the average is taken over the Laplace probability density function. Second, we exploit a three-stage hierarchical prior on the signal and construct decision statistics based on the noisy reconstruction (partial estimates) of the signals. Experimental results show that both average likelihood-based detection method and noisy-reconstruction based methods outperform most of the state-of-the-art algorithms.

We consider the problem of fusing probability scores from a set of classifiers to estimate a final fused probability score. Our interest is in scenarios where the classifiers are statistically dependent. To that end, we propose a new classifier fusion approach that is data driven and founded on the statistical theory of copulas. Numerical results with both simulated and real data show that our copula based classifier fusion approach produces better probability scores than individual classifiers and outperforms existing probability score fusion approaches.

In this letter, we investigate the problem of classification with high-dimensional data using low-dimensional random projections in the presence of inter- and intra-signal correlations. Each sensor is assumed to compress its high-dimensional (Gaussian) signal vector using random projections in a multisensor setting. In order to quantify the classification performance with compressed data, we consider the Bhattacharya distance as the performance metric. In the presence of intra-signal correlation at a given sensor, the degradation in the Bhattacharya distance with compressed data is shown to be nonlinear with the compression ratio in contrast to the case when there is no intra-signal correlation. In the presence of inter-signal correlation, the degradation in the Bhattacharya distance with compressed data depends on whether or not an identical projection matrix is used to compress data at multiple sensors.

Performing likelihood ratio based detection with high dimensional multimodal data is a challenging problem since the computation of the joint probability density functions (pdfs) in the presence of intermodal dependence is difficult. While some computationally expensive approaches have been proposed for dependent multimodal data fusion (e.g., based on copula theory), a commonly used tractable approach is to compute the joint pdf as the product of marginal pdfs ignoring dependence. However, this method leads to poor performance when the data is strongly dependent. In this paper, we consider the problem of detection when dependence among multimodal data is modeled in a compressed domain where compression is obtained using low dimensional random projections. We employ a Gaussian approximation while modeling inter-modal dependence in the compressed domain which is computationally more efficient. We show that, under certain conditions, detection with multimodal dependent data in the compressed domain with a small number of compressed measurements yields enhanced performance compared to detection with high dimensional data via either the product approach or other suboptimal fusion approaches proposed in the literature.

Automatic modulation classification (AMC) with multiple sensors is a challenging problem when the channel conditions are unknown at the receiver. In this paper, using the Markov chain Monte Carlo (MCMC) approach, we develop a novel algorithm for AMC when the amplitude and phase of the channel gains are unknown. Using sampling techniques, we marginalize over the unknown channel parameters that follow a certain probability distribution. This improves the estimate of the a posteriori distribution of the modulation formats, thereby improving the overall classification performance. Further, to overcome the problem of local extrema traps encountered in sampling algorithms, we introduce the idea of adding artificial noise beyond a certain threshold of signal-to-noise (SNR). This improves the performance of the sampling based AMC algorithm in the high SNR regime. Simulation results and comparisons are provided to show the efficiency of the proposed algorithm over the most related works in the literature.

Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing, it is often assumed that the signal of interest is sparse in an orthonormal basis. However, in many practical applications, this requirement may be too restrictive. A generalization of the standard sparsity assumption is that the signal lies in a union of subspaces. Recovery of such signals from a small number of samples has been studied recently in several works. Here, we consider the problem of only subspace recovery in which our goal is to identify the subspace (from the union) in which the signal lies using a small number of samples, in the presence of noise. More specifically, we derive performance bounds and conditions under which reliable subspace recovery is guaranteed using maximum likelihood (ML) estimation. We begin by treating general unions and then obtain the results for the special case in which the subspaces have structure leading to block sparsity. In our analysis, we treat both general sampling operators and random sampling matrices. With general unions, we show that under certain conditions, the number of measurements required for reliable subspace recovery in the presence of noise via ML is less than that implied using the restricted isometry property, which guarantees complete signal recovery. In the special case of block sparse signals, we quantify the gain achievable over standard sparsity in subspace recovery. Our results also strengthen existing results on sparse support recovery in the presence of noise under the standard sparsity model.

In this paper, we consider the problem of automatic modulation classification with multiple sensors in the presence of unknown time offset, phase offset and received signal amplitude. We develop a novel hybrid maximum likelihood (HML) classification scheme based on a generalized expectation maximization (GEM) algorithm. GEM is capable of finding ML estimates numerically that are extremely hard to obtain otherwise. Assuming a good initialization technique is available for GEM, we show that the classification performance (in terms of the probability of error) can be greatly improved with multiple sensors compared to that with a single sensor, especially when the signal-to-noise ratio (SNR) is low. We further demonstrate the superior performance of our approach when simulated annealing (SA) with uniform as well as nonuniform grids is employed for initialization of GEM in low SNR regions. The proposed GEM based approach employs only a small number of samples (in the order of hundreds) at a given sensor node to perform both time and phase synchronization, signal power estimation, followed by modulation classification. We provide simulation results to show the efficiency and effectiveness of the proposed algorithm.

To solve the problem of joint sparsity pattern recovery in a decentralized network, we propose an algorithm named decentralized and collaborative subspace pursuit (DCSP). The basic idea of DCSP is to embed collaboration among nodes and fusion strategy into each iteration of the standard subspace pursuit (SP) algorithm. In DCSP, each node collaborates with several of its neighbors by sharing high-dimensional coefficient estimates and communicates with other remote nodes by exchanging low-dimensional support set estimates. Experimental evaluations show that, compared with several existing algorithms for sparsity pattern recovery, DCSP produces satisfactory results in terms of accuracy of sparsity pattern recovery with much less communication cost.

In this paper, we consider the problem of sensor management for target tracking in a wireless sensor network (WSN). To determine the set of sensors that have the most information, we develop a probabilistic sensor management scheme based on the concepts developed in compressive sensing. In the proposed scheme, each senor node decides whether it should transmit its observation via multiple access channels to the fusion center with a certain probability. With this probabilistic transmission scheme, the observation vector received at the fusion center becomes a compressed version of the original observations. Our goal is to determine the optimal values of the probability using which each node should transmit so that the determinant of the Fisher information matrix (FIM) is maximized at any given time instant with a constraint on the available energy. Numerical examples are provided to show the performance of the proposed scheme.

This paper considers the problem of distributed compressive detection under a perfect secrecy constraint. More specifically, we consider the problem where the distributed inference network operates in the presence of an eavesdropper who wants to discover the state of the nature being monitored by the system. It is shown that perfect secrecy can be achieved by using cooperating trustworthy nodes that assist the Fusion Center (FC) by providing falsified data to the eavesdroppers. We also consider the problem of determining optimal system parameters which maximize the detection performance at the FC, while ensuring perfect secrecy at the eavesdropper.

In this letter, we investigate the asymptotic performance of categorical decision fusion in a human decision making framework. We assume that multiple human agents send categorized information to a moderator for final decision making. The local categorization is performed via a threshold based scheme where thresholds are assumed to be random variables. Considering the cases where the moderator has the knowledge of exact threshold values as well as when it has only probabilistic information of the individual thresholds, we analyze the asymptotic performance of likelihood ratio based decision fusion at the moderator in terms of the Chernoff information. Numerical results are presented for illustration.

In this paper, we address the problem of sparsity pattern recovery of a sparse signal with multiple measurement data in a distributed network. We consider that each node in the network makes measurements via random projections regarding the same sparse signal. We propose a distributed greedy algorithm based on Orthogonal Matching Pursuit (OMP) in which the locations of non zero coefficients of the sparse signal are estimated iteratively while performing fusion of estimates at distributed nodes. In the proposed distributed framework, each node has to perform less number of iterations of OMP compared to the sparsity index of the sparse signal. With each node having a very small number of compressive measurements, a significant performance gain in sparsity pattern detection is achieved via the proposed collaborative scheme compared to the case where each node estimates the sparsity pattern independently and then fusion is performed to get a global estimate. We further extend the algorithm to a binary hypothesis testing framework, where the algorithm first detects the presence of a sparse signal collaborating among nodes with a fewer number of iterations of OMP and then increases the number of iterations to estimate the sparsity pattern only if the signal is detected.

In cognitive radio (CR) networks, spectrum sensing has to be performed in a reliable manner in challenging environments that arise due to propagation channels which undergo multi-path fading and non-Gaussian noise at CRs. Most existing literature on spectrum sensing has focused on impairments introduced by additive white Gaussian noise (AWGN). However, this assumption fails to model the behavior of certain noise types in practice, such as impulsive noise. In this paper, the use of a non-parametric, easily implementable detection device, polarity-coincidence-array (PCA) detector, is proposed for weak primary signal detection with a cognitive radio equipped with multiple antennas. The detector performance in terms of the probabilities of detection and false alarm is derived when the communication channels between the primary user transmitter and the multiple antennas at the cognitive radio undergo Rayleigh fading. From the numerical results, it is observed that a significant performance enhancement is achieved by the PCA detector compared to that of the simple energy detector as the heaviness of the tail of the non-Gaussian noise increases.

One of the main requirements of cognitive radio (CR) systems is the ability to perform spectrum sensing in a reliable manner in challenging environments that arise due to propagation channels which undergo multipath fading and non-Gaussian noise. While most existing literature on spectrum sensing has focused on impairments introduced by additive white Gaussian noise (AWGN), this assumption fails to model the behavior of certain types of noise found in practice. In this paper, the use of a non-parametric and easily implementable detection device, namely the polarity-coincidence-array (PCA) detector, is proposed for the detection of weak primary signals with a cognitive radio equipped with multiple antennas. Its performance is evaluated in the presence of heavy-tailed noise. The detector performance in terms of the probabilities of detection and false alarm is derived when the communication channels between the primary user transmitter and the multiple antennas at the cognitive radio are AWGN as well as when they undergo Rayleigh fading. From the numerical results, it is observed that a significant performance enhancement is achieved by the PCA detector compared to that of the energy detector with AWGN as well as fading channels as the heaviness of the tail of the non-Gaussian noise increases.

In this paper, we propose a novel mobility protocol for mobile node navigation in a hybrid sensor network consisting of both static and mobile nodes to improve the dynamic coverage. Use of mobile nodes in sensor networks for coverage improvement is suggested in recent research. However, most of the existing literature on hybrid sensor networks considered the use of node mobility at the deployment stage in which nodes do not move after the initial deployment. In this paper, our focus is on efficiently managing the node mobility to provide dynamic coverage in hybrid sensor networks compensating the lack of coverage provided by static nodes. The key feature of the proposed mobility protocol is that, mobile nodes are directed to move to maximize the coverage-time of the uncovered area by static nodes. The proposed mobility protocol can be implemented distributively by collaborating among mobile and static nodes locally. The effectiveness of the proposed mobility protocol is shown in terms of the presence probability matrix and coverage-time.

In this paper, we propose a new mobility assisted tracking (MAT) algorithm for tracking a single target in a hybrid sensor network consisting of both static and mobile nodes. The network is assumed to be partitioned into clusters and cluster heads are formed from a set of high capacity static nodes. One cluster head is selected to perform the tracking task using particle filters at a given time based on the observations received from the nodes belonging to the corresponding cluster. We exploit the node mobility in the hybrid sensor network to dynamically maintain a certain coverage level at the predicted target location at each time. In the proposed MAT algorithm mobile nodes are directed to move towards the predicted target position at each time step if the predicted target position is not covered to the desired coverage level by static nodes. Simulation results show that with the proposed MAT algorithm, an improved performance closer to the PCRLB is achieved with a relatively small number of mobile nodes in the network compared to the scenario when all nodes are static. The proposed scheme is also robust against static node as well as cluster head failures.

We investigate the impact of mobile node density on several detection performance measures for stationary target detection by a hybrid sensor network consisting of both static and mobile nodes. Such hybrid sensor networks are becoming attractive with the recent advances in sensor nodes equipped with mobile platforms. However, adding a large number of mobile nodes to a sensor network for continuous coverage improvement might be expensive due to mobile node's higher energy consumptions compared to that with static nodes. Motivated by these, we investigate the trade-off between the density of mobile nodes and the network performance in a hybrid sensor network with respect to several performance measures of interest, when mobile nodes perform random mobility. We derive analytical (exact and/or approximate) formulae for detection probability, detection latency and mean first contact distance, by applying the theory of coverage processes and use them to evaluate the tradeoff between the fraction of mobile nodes and these performance measures. Analytical results presented in this paper give insights on how to select optimal network parameters in designing hybrid sensor networks to achieve desired performance requirements. Validity of the derived analytical results is verified via Monte-Carlo simulations.

This paper proposes a framework for distributed sequential parameter estimation in wireless sensor networks. In the proposed scheme, the estimator is updated sequentially at the current node with its new measurement and the noisy corrupted local estimator from the previous node. Since all nodes in the network may not carry useful information, methodologies to find the best set of nodes and the corresponding node ordering for the sequential estimation process are investigated. It is shown that the determining the optimal set of nodes that leads to the globally optimal performance is computationally complex when the network size is large. We develop two distributed greedy type node selection algorithms with reduced computational and communication complexities. In these algorithms, the next best node is selected at the current node such that it optimizes a certain reward function. It is shown that the performance of both proposed greed type schemes leads to exact, or close to exact, results to the optimal scheme computed via forward dynamic programming, under certain conditions. Moreover, contrast to existing methodologies, our work considers the node selection and inter-node communication noise jointly in the sequential estimation process.

Optimal power scheduling for distributed detection in a Gaussian sensor network is addressed for both independent and correlated observations. We assume amplify-and-forward local processing at each node. The wireless link between sensors and the fusion center is assumed to undergo fading and coefficients are assumed to be available at the transmitting sensors. The objective is to minimize the total network power to achieve a desired fusion error probability at the fusion center. For i.i.d. observations, the optimal power allocation is derived analytically in closed form. When observations are correlated, first, an easy to optimize upper bound is derived for sufficiently small correlations and the power allocation scheme is derived accordingly. Next, an evolutionary computation technique based on particle swarm optimization is developed to find the optimal power allocation for arbitrary correlations. The optimal power scheduling scheme suggests that the sensors with poor observation quality and bad channels should be inactive to save the total power expenditure of the system. It is shown that the probability of fusion error performance based on the optimal power allocation scheme outperforms the uniform power allocation scheme especially when either the number of sensors is large or the local observation quality is good.

We consider the problem of optimal power scheduling for decentralized detection of a deterministic signal in a wireless sensor network with correlated observations. Each distributed sensor node independently performs amplify-and-forward (AF) processing of its observation. The fading coefficients of wireless links from distributed sensors to the fusion center (FC) are assumed to be available at transmitting nodes. When sensor observations are correlated it is difficult to derive a closed form solution for optimal power values to achieve a required fusion error performance. In this work, we develop an evolutionary computation technique based on Particle Swarm Optimization (PSO) to obtain the optimal power allocation under a required fusion error probability threshold constraint. It is shown that the optimal power allocation scheme turns off the nodes with poor channels and provides significant system power savings compared to that of uniform power allocation scheme especially when either the number of sensors in the system is large or the local observation quality is good.

In this paper we consider the problem of optimal power allocation for fusion of a deterministic signal in an inhomogeneous wireless sensor network (WSN) with correlated observations. We assume that each distributed node performs analog-relay amplifier local processing on its observation and transmits locally processed data to the fusion center over a wireless channel. We also assume that the channel between the fusion center and sensors undergoes fading and the fading coefficients are assumed to be known to the transmitter. We derive exact fusion error probability and an easy to optimize upper bound for the fusion error probability that is valid for sufficiently small correlations. The transmit power is allocated to sensor nodes to keep the fusion error probability bound under a required threshold while minimizing the total power spent by the network. It is shown that the optimal scheme inactivates the sensor nodes with poor observation quality and low fading coefficients. For the remaining active sensors the transmit power is determined by the individual channel gains, local observation quality, required fusion error probability bound and the correlation coefficient. From numerical results we see that this optimal scheme has a significant gain over the uniform power allocation scheme when either local observations are good or the number of sensors is large and the correlation coefficient is sufficiently small. It is also shown that the optimal power allocation scheme can be implemented distributively with a minimal feedback from the fusion center.

We consider the problem of optimal power scheduling for the decentralized detection of a deterministic signal in an inhomogeneous wireless sensor network. The observation noise at local sensors is assumed to be independently and identically distributed (i.i.d.) and at the local sensors each node performs analog-relay amplifier processing for its observation independently. The communication between the local sensors and the fusion center is assumed to be through an inhomogeneous channel. The optimal power scheduling scheme suggests that the sensors with poor observation quality and channels should be inactive in order to save total power expenditure of the system. For the remaining active sensors the optimal transmit power is determined jointly by the individual channel gains, total number of active sensors, local observation signal to noise ratio (SNR) and the required probability of error at the fusion center. We show that the optimal scheme can provide significant system power savings compared to the uniform power allocation scheme when the number of sensors in the system is large.