Low-Complexity One-Dimensional Edge Detection in Wireless Sensor Networks

Marco Martalò,Gianluigi Ferrari

doi:10.1155/2010/751520

Marco Martalò, Gianluigi Ferrari

Open Access

https://doi.org/10.1155/2010/751520

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Abstract

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).

Highlights

Introduction and Related WorkSensor networks have been an active research field in the last years [1]
The Monte Carlo simulation results are obtained through the following steps: (1) the number of edges is randomly generated—the access point (AP) is assumed to know this number in the minimum mean square error (MMSE) case; (2) for a selected number of edges, their positions are randomly generated
After all edges’ positions are extracted, they are ordered.) ; (3) either the sensors’ decisions or the probability density function (PDF) of the observables, according to the chosen quantization strategy at the sensors, are transmitted to the AP; (4) a noisy version of the transmitted data is received at the AP; (5) the AP detects the edges’ positions through either MMSE or simplified detection algorithms; (6) the distance D is evaluated, on the basis of the detected sequence of edges’ positions; (7) steps (1) ÷ (6) are repeated for sufficiently large number of times in order to derive statistically meaningful results; 20 15 D 10

Summary

Introduction

Introduction and Related WorkSensor networks have been an active research field in the last years [1]. (In the remainder of this paper, by “sensor” we will denote the wireless transceiver which includes the sensing element It has (limited) processing capabilities and can communicate with the AP.) At a given time, it may happen that there is a leakage: some of the sensors (namely, sensors s2, s3, s5, and s6 in Figure 1(b)) detect the presence of the gas (namely, sensors s2, s3, s5, and s6) whereas the remaining sensors (namely, s1 and s4) do not. This problem reduces to a distributed detection problem of a spatially nonconstant binary phenomenon, as shown in Figure 1(c) and described in more detail later. Our goal is to show how lowcomplexity distributed detection can be successfully applied to solve a general one-dimensional edge detection problem

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