In this paper, we consider the problem of decision fusion for noncoherent detection in a wireless sensor network. Novel to the current work is the integration of the hybrid multi-access channel (MAC) in the fusion rule design. We assume that sensors transmit their local binary decisions over a hybrid MAC which is a composite of conventional orthogonal and nonorthogonal MACs. Under Rayleigh fading scenario, we present a likelihood ratio (LR)-based fusion rule, which has been shown to be optimal through theoretical analysis and simulation. However, it requires a large amount of computation, which is not easily implemented in resource-constrained sensor networks. Therefore, three sub-optimal alternatives with low-complexity are proposed, namely the weighed energy detector (WED), the deflection-coefficient-maximization (DCM), and the two-step (TS) rules. We show that when the channel signal-to-noise ratio (SNR) is low, the LR-based fusion rule reduces to the WED rule; at high-channel SNR, it is equivalent to the TS rule; and at moderate-channel SNR, it can be approached closely by the DCM rule. Compared with the conventional orthogonal and nonorthogonal MACs, numerical results show that the hybrid MAC with the proposed fusion rules can improve the detection performance when the channel SNR is medium.
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