Nonorthogonal Transmission and Noncoherent Fusion of Censored Decisions

Abstract

In this paper, we consider the binary-distributed hypothesis testing problem, where a wireless sensor network (WSN) is used to determine the true state of nature. We propose a novel signaling scheme where signature vectors (SVs) are used to transmit censored sensor decisions to the fusion center (FC). In particular, the length of the SVs is chosen to be smaller than the number of sensors, resulting in nonorthogonal sensor channels and allowing a desirable tradeoff between bandwidth and power efficiency in WSNs. We consider deterministic SVs that are assumed to be known to the FC and random SVs that are unknown to the FC. For both cases, the optimum noncoherent fusion rules are derived, assuming independent Ricean fading sensor-FC channels. Since the complexity of these optimum fusion rules is prohibitively large, even for WSNs of moderate size, we also consider a low-complexity suboptimum energy-based fusion rule and show that it is equivalent to the optimum fusion rules under certain conditions. Furthermore, we calculate the system probabilities of detection and false alarm for the energy-based fusion rule for both deterministic and random SVs. Numerical and simulation results show that with the proposed nonorthogonal signaling scheme, significant improvements in bandwidth efficiency are possible at the expense of only a small loss in power efficiency.