In wireless sensor networks, distributed consensus algorithms can be employed for distributed detection. Each sensor node can compute its log-likelihood ratio (LLR) from local observations for a target event and using an iterative distributed algorithm, the average of sensors’ LLRs can be available to all the sensor nodes. While the average of sensors’ LLRs allows each sensor node to make a final decision as a decision statistic for an overall detection problem with all sensors’ LLRs, it may be desirable if all sensors’ LLRs or local observations, which form a full information vector and denoted by x, could be available to each sensor for other purposes more than the detection of a target event. In this paper, we show that each sensor can have not only the average of local observations, but also full information vector, x, (or its estimate) using a well-known iterative distributed algorithm. We extend the proposed approach to estimate x when x is sparse based on the notion of compressed sensing.

I. INTRODUCTION

Wireless sensor networks (WSNs) have various applications including environmental monitoring and surveillance [1], [2]. In the context of distributed detection , the central unit is called a fusion center (FC) as all sensors’ local decisions regarding a target event are collected and combined for a final decision, in which each node only makes a local decision. The detection performance at the FC depends on the number of sensors if local decisions can be correctly received at the FC. However, if local decisions from sensors are not reliably received at the FC due to wireless channel impairments, the channel conditions also affect on the performance. In general, the signals from sensor nodes that are far away from the FC may not be reliably received at the FC , which is not desirable as sensor nodes could have limited power sources. In the centralized approach with a FC, when the final decision is required at sensor nodes for further processing, the FC can broadcast it to sensors. However, in this case, the sensors that are far away may not reliably receive this final decision.

Distributed consensus algorithms (DCAs) [3], [4] can be employed for WSNs to overcome these problems. As DCAs only require local communications between neighbor sensor nodes, the transmission power could be lower than that in the centralized approach with a FC for distributed detection. Through iterative information exchanges between neighbor sensor nodes, the consensus or averaging can be achieved at all the sensor nodes. Each sensor can have the average of all sensors’ log-likelihood ratios (LLRs) by an iterative distributed algorithm for distributed detection [3]. As each signal transmission for information exchange requires a certain amount of energy consumption, in general, iterative distributed algorithms of fast convergence rate are required [4], [5].

Suppose that Xl denotes the observation or local LLR at sensor 1. DCAs can provide each sensor with the average of XL’S. In some applications, however, sensor nodes may need to know more than the average of sensors’ LLRs or observations. In this case, DCAs could be modified. In this paper, we show that a well-known iterative distributed algorithm can be used to provide every sensors’ observations to all sensor nodes without any modification. In particular, if the sensors’ observations are sparse, compressed sensing based approaches [6], [7], [8] can be used to estimate spare sensors’ observations with an iterative distributed algorithm. As a result, each sensor node can have the average of sensors’ observations as well as an estimate of all sensors’ observations.