Energy Efficient Signal Detection Using SPRT and Ordered Transmissions in Wireless Sensor Networks

Abstract

In a distributed detection system with multiple sensors, the ordered transmission scheme (OTS) proposed by Blum and Sadler requires a fewer number of transmissions in comparison with a fixed sample size test with the same probability of error performance. In this work, we propose an ordered transmission scheme using a truncated sequential probability ratio test (SPRT), termed as OSPRT. With a suitable choice of two design parameters, the probability of error of the OSPRT can be upper bounded by no more than a certain percentage above the probability of error of OTS, yet achieving significant savings in both the average number of samples needed to arrive at a decision, and the average energy in signal transmission. The superiority of ordered transmissions over unordered transmissions is quantified in terms of Kullback-Leibler information. Simulation analysis for the detection of a constant signal of moderate strength in Gaussian noise shows that the probability of error of OSPRT, which is substantially below the theoretical upper bound, is only negligibly larger than the OTS error. Analysis also shows that OSPRT is more energy efficient than the original OTS.