Robust Detection of Random Events with Spatially Correlated Data in Wireless Sensor Networks via Distributed Compressive Sensing

In this paper, we exploit the theory of compressive sensing to perform detection of a random source in a dense sensor network. When the sensors are densely deployed, observations at adjacent sensors are highly correlated while those corresponding to distant sensors are less correlated. Thus, the covariance matrix of the concatenated observation vector of all the sensors at any given time can be sparse where the sparse structure depends on the network topology and the correlation model. Exploiting the sparsity structure of the covariance matrix, we develop a robust nonparametric detector to detect the presence of the random event using a compressed version of the data collected at the distributed nodes. We employ the multiple access channel (MAC) model with distributed random projections for sensors to transmit observations so that a compressed version of the observations is available at the fusion center. Detection is performed by constructing a decision statistic based on the covariance information of uncompressed data which is estimated using compressed data. The proposed approach does not require any knowledge of the noise parameter to set the threshold, and is also robust when the distributed random projection matrices become sparse

Distributed Detection of Sparse Stochastic Signals via Fusion of 1-bit Local Likelihood Ratios

In this letter, we consider the detection of sparse stochastic signals with sensor networks (SNs), where the fusion center (FC) collects 1-bit data from the local sensors and then performs global detection. For this problem, a newly developed 1-bit locally most powerful test (LMPT) detector requires 3.3Q sensors to asymptotically achieve the same detection performance as the centralized LMPT (cLMPT) detector with Q sensors. This 1-bit LMPT detector is based on 1-bit quantized observations without any additional processing at the local sensors. However, direct quantization of observations is not the most efficient processing strategy at the sensors since it incurs unnecessary information loss. In this letter, we propose an improved-1-bit LMPT (Im-1-bit LMPT) detector that fuses local 1-bit quantized likelihood ratios (LRs) instead of directly quantized local observations. In addition, we design the quantization thresholds at the local sensors to ensure asymptotically optimal detection performance of the proposed detector. It is shown theoretically and numerically that, with the designed quantization thresholds, the proposed Im-1-bit LMPT detector for the detection of sparse signals requires less number of sensor nodes to compensate for the performance loss caused by 1-bit quantization.Comment: 5 pages,2 figures, published in IEEE Signal Processing Letters (SPL

Sparse Signal Detection with Compressive Measurements via Partial Support Set Estimation

In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which share a common but unknown support. While in the traditional compressive sensing (CS) framework, the goal is to recover the complete sparse signal, in sparse signal detection, complete signal recovery may not be necessary to make a reliable detection decision. In particular, detection can be performed based on partially or inaccurately estimated signals which requires less computational burden than that is required for complete signal recovery. To that end, we investigate the problem of sparse signal detection based on partially estimated support set. First, we discuss how to determine the minimum fraction of the support set to be known so that a desired detection performance is achieved in a centralized setting. Second, we develop two distributed algorithms for sparse signal detection when the raw compressed observations are not available at the central fusion center. In these algorithms, the final decision statistic is computed based on locally estimated partial support sets via orthogonal matching pursuit (OMP) at individual nodes. The proposed distributed algorithms with less communication overhead are shown to provide comparable performance (sometimes better) to the centralized approach when the size of the estimated partial support set is very small

Application of Compressive Sensing Techniques in Distributed Sensor Networks: A Survey

In this survey paper, our goal is to discuss recent advances of compressive sensing (CS) based solutions in wireless sensor networks (WSNs) including the main ongoing/recent research efforts, challenges and research trends in this area. In WSNs, CS based techniques are well motivated by not only the sparsity prior observed in different forms but also by the requirement of efficient in-network processing in terms of transmit power and communication bandwidth even with nonsparse signals. In order to apply CS in a variety of WSN applications efficiently, there are several factors to be considered beyond the standard CS framework. We start the discussion with a brief introduction to the theory of CS and then describe the motivational factors behind the potential use of CS in WSN applications. Then, we identify three main areas along which the standard CS framework is extended so that CS can be efficiently applied to solve a variety of problems specific to WSNs. In particular, we emphasize on the significance of extending the CS framework to (i). take communication constraints into account while designing projection matrices and reconstruction algorithms for signal reconstruction in centralized as well in decentralized settings, (ii) solve a variety of inference problems such as detection, classification and parameter estimation, with compressed data without signal reconstruction and (iii) take practical communication aspects such as measurement quantization, physical layer secrecy constraints, and imperfect channel conditions into account. Finally, open research issues and challenges are discussed in order to provide perspectives for future research directions