Low-complexity one-dimensional edge detection in wireless sensor networks

In various wireless sensor network applications, it is of interest to monitor the perimeter of an area of interest. For example, one may need to check if there is a leakage of a dangerous substance. In this paper, we model this as a problem of one-dimensional edge detection, that is, detection of a spatially nonconstant one-dimensional phenomenon, observed by sensors which communicate to an access point (AP) through (possibly noisy) communication links. Two possible quantization strategies are considered at the sensors: (i) binary quantization and (ii) absence of quantization. We first derive the minimum mean square error (MMSE) detection algorithm at the AP. Then, we propose a simplified (suboptimum) detection algorithm, with reduced computational complexity. Noisy communication links are modeled either as (i) binary symmetric channels (BSCs) or (ii) channels with additive white Gaussian noise (AWGN).