A Sufficient Condition for Optimality of Digital versus Analog Relaying in a Sensor Network

Abstract—This paper compares the efficacy of digital versus analog relaying in a sensor network when the ultimate goal is detection. A simplified scenario is considered in which a binary decision is to be made at a fusion center based on data it receives from a single sensor. The sensor computes a statistic corresponding to its observations and forwards it over a noisy channel to the fusion center. Two relay schemes: “estimate-and-forward” (analog relaying) and “detect-and-forward ” (digital relaying) are compared, in terms of the ultimate detection performance they support at the fusion center. With this performance criterion, the relative merit of the two schemes is shown to depend on the observation SNR at the sensor and the SNR of the communication link connecting the sensor and the fusion center. A sufficient condition, in terms of these SNRs, for the superiority of digital relaying over analog relaying is derived for this simple network model. Index Terms—Hypothesis-testing, signal-to-noise ratio, sensor networks, analog/digital relays. I