Selection Square Combining: A Fully-Distributed Radio Source Detector for Fast Fading Channels Based on Energy Measurements

In this article, we tackle the problem of fully-distributed detection of a radio source emitting a signal in a fast fading scenario. We consider that geographically distributed sensor nodes obtain energy measurements and compute cooperatively and in a distributed fashion a decision metric for detecting if the source is present or absent without the need of a central node. Since we assume that the sensing channels -from the source to the nodes- vary rapidly due to the nodes and/or the source mobility, we derive an algorithm based on the average probability density function (PDF) of the measurements with respect to the channel PDF. The derived model has some unknown parameters (like the source transmitted energy or the channel mean attenuation). Therefore, we follow the philosophy of the Generalized Likelihood Ratio Test (GLRT) theory and obtain two test statistics suitable for practical scenarios: i) the S-GLRT statistic, and ii) the selection square combining (SSC) statistic. We show that SSC is asymptotically equivalent to S-GLRT in the low signal-to-noise ratio regime, and compute its theoretical performance in that scenario. Finally, we compare the algorithms' performance in finite regimes through Monte Carlo simulations. We show that the two proposed algorithms offer similar performance, and are capable of exceeding that of other algorithms which are frequently used in fast fading scenarios.