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.

[1]  D. Warren,et al.  Optimum quantization for detector fusion: some proofs, examples, and pathology , 1999 .

[2]  Thomas C. M. Lee,et al.  Consistent Estimation for Partition-Wise Regression and Classification Models , 2016, IEEE Transactions on Signal Processing.

[3]  Alfred O. Hero,et al.  Event-Based Statistical Signal Processing , 2018, Event-Based Control and Signal Processing.

[4]  Gang Li,et al.  Two-Level Block Matching Pursuit for Polarimetric Through-Wall Radar Imaging , 2018, IEEE Transactions on Geoscience and Remote Sensing.

[5]  Pramod K. Varshney,et al.  Compressive Sensing-Based Detection With Multimodal Dependent Data , 2017, IEEE Transactions on Signal Processing.

[6]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[7]  Steven Hong Direct spectrum sensing from compressed measurements , 2010, 2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE.

[8]  Bernard Picinbono,et al.  Quantization and distributed detection , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[9]  Haopeng Zhang,et al.  Global convergence analysis of swarm optimization using paracontraction and semistability theory , 2016, 2016 American Control Conference (ACC).

[10]  Mehmet Necip Kurt,et al.  Multisensor Sequential Change Detection With Unknown Change Propagation Pattern , 2017, IEEE Transactions on Aerospace and Electronic Systems.

[11]  Gang Li,et al.  Distributed Detection of Weak Signals From One-Bit Measurements Under Observation Model Uncertainties , 2019, IEEE Signal Processing Letters.

[12]  Peter Willett,et al.  On the optimality of the likelihood-ratio test for local sensor decision rules in the presence of nonideal channels , 2005, IEEE Transactions on Information Theory.

[13]  Gang Li,et al.  Detection of Sparse Signals in Sensor Networks via Locally Most Powerful Tests , 2018, IEEE Signal Processing Letters.

[14]  Pramod K. Varshney,et al.  Compressive Sensing Based Signal Processing in Wireless Sensor Networks: A Survey , 2017 .

[15]  Massoud Babaie-Zadeh,et al.  Compressive detection of sparse signals in additive white Gaussian noise without signal reconstruction , 2017, Signal Process..

[16]  Danijela Cabric,et al.  Compressive Detection of Random Subspace Signals , 2015, IEEE Transactions on Signal Processing.

[17]  Gang Li,et al.  Detection of Sparse Stochastic Signals With Quantized Measurements in Sensor Networks , 2019, IEEE Transactions on Signal Processing.

[18]  Pramod K. Varshney,et al.  Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[19]  T. Apostol Mathematical Analysis , 1957 .

[20]  Symeon Chatzinotas,et al.  Compressive Sparsity Order Estimation for Wideband Cognitive Radio Receiver , 2014, IEEE Transactions on Signal Processing.

[21]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[22]  Ramanarayanan Viswanathan,et al.  Optimal distributed decision fusion , 1989 .

[23]  Pramod K. Varshney,et al.  Collaborative Compressive Detection With Physical Layer Secrecy Constraints , 2015, IEEE Transactions on Signal Processing.

[24]  Pramod K. Varshney,et al.  On Weak Signal Detection With Compressive Measurements , 2018, IEEE Signal Processing Letters.

[25]  Mehdi Korki,et al.  Double Detector for Sparse Signal Detection From One-Bit Compressed Sensing Measurements , 2016, IEEE Signal Processing Letters.

[26]  Zhiping Lin,et al.  Bayesian signal detection with compressed measurements , 2014, Inf. Sci..

[27]  Jun Fang,et al.  One-Bit Quantizer Design for Multisensor GLRT Fusion , 2013, IEEE Signal Processing Letters.

[28]  Pramod K. Varshney,et al.  Distributed Detection and Data Fusion , 1996 .

[29]  H. Vincent Poor,et al.  Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework , 2010, IEEE Transactions on Signal Processing.

[30]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[31]  Kenneth E. Barner,et al.  Design of IIR Multi-Notch Filters Based on Polynomially-Represented Squared Frequency Response , 2016, IEEE Transactions on Signal Processing.

[32]  Steven M. Kay,et al.  Optimal invariant detection of a sinusoid with unknown parameters , 2002, IEEE Trans. Signal Process..

[33]  Louis L. Scharf,et al.  Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors , 2012, IEEE Transactions on Information Theory.

[34]  Mehdi Korki,et al.  One-Bit Spectrum Sensing in Cognitive Radio Sensor Networks , 2019, Circuits Syst. Signal Process..

[35]  Douglas L. Jones,et al.  Decentralized Detection With Censoring Sensors , 2008, IEEE Transactions on Signal Processing.

[36]  Gang Li,et al.  On the detection of sparse signals with sensor networks based on subspace pursuit , 2014, 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[37]  Venugopal V. Veeravalli Decentralized quickest change detection , 2001, IEEE Trans. Inf. Theory.

[38]  Shiyuan Yang,et al.  Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm , 2007, Inf. Process. Lett..

[39]  John S. Baras,et al.  Adaptive Sampling for Linear State Estimation , 2009, SIAM J. Control. Optim..

[40]  Andreas M. Maras,et al.  Threshold parameter estimation in nonadditive non-Gaussian noise , 1997, IEEE Trans. Signal Process..

[41]  Guangming Shi,et al.  UWB Echo Signal Detection With Ultra-Low Rate Sampling Based on Compressed Sensing , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.