Channel-aware M-ary distributed detection: Optimal and suboptimal fusion rules

We consider fusion rules for M-ary distributed Bayesian hypothesis testing in wireless sensor networks, assuming that sensors´ observations are conditionally independent, conditioned on the hypothesis. Sensors make decisions and send the decisions over wireless channels to fusion venter (FC). The wireless channels are subject to noise and Rayleigh fading. We consider both simple and composite hypothesis testing, when the the sensing channel noise variance is unknown at the FC. For simple hypothesis, optimal Likelihood Ratio Test (LRT) fusion rule and for composite hypothesis, Generalized LRT, majority, and Maximum Ratio Combining (MRC) fusion rules are provided. Our results show that at high wireless channel signal-to-noise ratio (SNR), majority and optimal LRT rules have similar performance for binary hypothesis testing. Also, at low wireless channel SNR, as M increases, performance of MRC rule approaches that of the optimal LRT rule, while in some cases MRC rule outperforms GLRT rule.