Quantizer Design for Distributed GLRT Detection of Weak Signal in Wireless Sensor Networks

Abstract

We consider the problem of distributed detection of a mean parameter corrupted by Gaussian noise in wireless sensor networks, where a large number of sensor nodes jointly detect the presence of a weak unknown signal. To circumvent power/bandwidth constraints, a multilevel quantizer is employed in each sensor to quantize the original observation. The quantized data are transmitted through binary symmetric channels to a fusion center where a generalized likelihood ratio test (GLRT) detector is employed to perform a global decision. The asymptotic performance analysis of the multibit GLRT detector is provided, showing that the detection probability is monotonically increasing with respect to the Fisher information (FI) of the unknown signal parameter. We propose a quantizer design approach by maximizing the FI with respect to the quantization thresholds. Since the FI is a nonlinear and nonconvex function of the quantization thresholds, we employ the particle swarm optimization algorithm for FI maximization. Numerical results demonstrate that with 2-or 3-bit quantization, the GLRT detector can provide detection performance very close to that of the unquantized GLRT detector, which uses the original observations without quantization.Index Terms-Wireless sensor networks, multilevel quantization, distributed detection, particle swarm optimization algorithm (PSOA).

Decision fusion for composite hypothesis testing in wireless sensor networks over a shared and noisy collision channel

“…Similarly, the test statisticsL (Á) in equations (30), (31), and (32) have the same asymptotic distributionL…”

“…Composite hypothesis testing problems have been extensively studied in distributed detection. [29][30][31][32][33][34] Fusion rules based on the GLRT, Rao test, and locally optimum-detection approaches under many scenarios have been derived and evaluated. However, all of them, here, are assumed that the local decisions are transmitted over PACs (parallel access channels).…”

“…The operations of the fusion rules in Proposition 2 can be explained as follows. For the GLRT fusion rule as shown in equation (30), the FC computes the maximum likelihood (ML) estimatesq mj1 , for 1 ł m ł M.…”

Aspect-Aware Target Detection and Localization by Wireless Sensor Networks

“…The optimal multi-bit (or multi-level) quantizer design has been widely studied where the main challenge is the high computational complexity as the design of a multi-level quantizer often involves a nonlinear, multi-dimensional search process [9]. Due to the lack of knowledge of the target parameters, it seems impossible to optimize the quantization strategy.…”

“…For decentralized target detection by a WSN, one of the key problems is how to quantize the sensor observations. Some one-bit quantization [7] and multi-level quantization schemes [8,9] have been studied for decentralized detection. However, these quantization schemes only work under the assumptions of Gaussian noise and a single unknown parameter.…”