Distributed Detection With Multiple Sensors: Part I—Fundamentals

In this paper, basic results on distributed detection are reviewed. In particular, we consider the parallel and the serial architectures in some detail and discuss the decision rules obtained from their optimization based on the Neyman–Pearson (NP) criterion and the Bayes formulation. For conditionally independent sensor observations, the optimality of the likelihood ratio test (LRT) at the sensors is established. General comments on several important issues are made including the computational complexity of obtaining the optimal solutions, the design of detection networks with more general topologies, and applications to different areas

Impact of Channel Errors on Decentralized Detection Performance of Wireless Sensor Networks: A Study of Binary Modulations, Rayleigh-Fading and Nonfading Channels, and Fusion-Combiners

We provide new results on the performance of wireless sensor networks in which a number of identical sensor nodes transmit their binary decisions, regarding a binary hypothesis, to a fusion center (FC) by means of a modulation scheme. Each link between a sensor and the fusion center is modeled independent and identically distributed (i.i.d.) either as slow Rayleigh-fading or as nonfading. The FC employs a counting rule (CR) or another combining scheme to make a final decision. Main results obtained are the following: 1) in slow fading, a) the correctness of using an average bit error rate of a link, averaged with respect to the fading distribution, for assessing the performance of a CR and b) with proper choice of threshold, ON/OFF keying (OOK), in addition to energy saving, exhibits asymptotic (large number of sensors) performance comparable to that of FSK; and 2) for a large number of sensors, a) for slow fading and a counting rule, given a minimum sensor-to-fusion link SNR, we determine a minimum sensor decision quality, in order to achieve zero asymptotic errors and b) for Rayleigh-fading and nonfading channels and PSK (FSK) modulation, using a large deviation theory, we derive asymptotic error exponents of counting rule, maximal ratio (square law), and equal gain combiners

Two Rank Order Tests for \u3cem\u3eM\u3c/em\u3e-ary Detection

We consider a general M-ary detection problem where, given M groups of L samples each, the problem is to identify which unique group of L samples have come from the signal hypothesis. The optimal likelihood ratio test is unrealizable, when the joint distribution of ML samples is not completely known. In this paper we consider two rank order types of tests termed as the modified rank test (MRT) and the modified rank test with row sort (MRTRS). We examine through simulation, the small sample probability of error performances of MRT and MRTRS for detecting a signal among contaminants. Numerically computable closed –form error expressions are derived for some special cases. Asymptotic (large sample) error rate of MRT is also derived. The results indicate that MRTRS provides improved performance over other previously known rank tests

Performance of XOR Rule for Decentralized Detection of Deterministic Signals in Bivariate Gaussian Noise

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient r approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by \sqrt 1-r , as r approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of 1/(1-r) , the Bayes error of XORAP decreases to zero much slower

Optimal and Suboptimal Distributed Decision Fusion

The problem of decision fusion in distributed sensor systems is considered. Distributed sensors pass their decisions about the same hypotheses to a fusion center that combines then into a final decision. Assuming that the sensor decisions are independent from each other conditioned on each hypothesis, we provide a general proof that the optimal decision scheme that maximizes the probability of detection for fixed probability of false alarm at the fusion, is the Neymann-Pearson test at the fusion and Likelihood-Ratio tests at the sensors. The optimal set of thresholds is given via a set of nonlinear, coupled equations that depend on the decision policy but not on the priors. The nonlinear threshold equations cannot be solved in general. We provide a suboptimal algorithm for solving for the sensor thresholds through a one dimensional minimization. The algorithm applies to arbitrary type of similar or disimilar sensors. Numerical results have shown that the algorithm yields solutions that are extremely close to the optimal solutions in all the tested cases, and it does not fail in singular cases