Abstract
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.
Highlights
We show that when the channel signal-to-noise ratio (SNR) is low, the likelihood ratio (LR)-based fusion rule reduces to the weighed energy detector (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
Each group makes a binary decision uek based on zk. This is equivalent to a distributed detection using the nonorthogonal multi-access channel (MAC), and the decision uek can be obtained through the maximum likelihood (ML) detector [39] as uek =1 p(zk | H1 ) ≷ p(zk | H0 )
We study the problem of decision fusion under the hybrid MAC scheme
Summary
Wireless sensor networks (WSNs) consist of a large number of geographically distributed sensors that have limited resources, such as energy, processing capabilities, and communication bandwidth [1]. Numerous researchers have focused on the problem of distributed detection (decision fusion) over orthogonal MACs [10,11,12,13,14,15,16,17,18,19,20,21] Another type of MACs from sensors to the FC is the nonorthogonal MAC [22]. Multiple sensors are allowed to communicate with an FC through the same channel Using this scheme, bandwidth requirement or detection delay can be significantly reduced. Using coherent detection and assuming channel gains are available, the hybrid MAC is shown to provide more performance choices than orthogonal and nonorthogonal MACs [38]. Notation—Lower-case bold letters denote vectors; E[·], Var[·], D [·], and (·) T are used to denote expectation, variance, deflection coefficient, and transpose, respectively; P(·), p(·) denote probability mass functions and probability density functions (pdf), in particular P( A| B ) and p( a|b ) represent the probability of event A conditioned on event B and the pdf of random variable a conditioned on random variable b, respectively
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