Distributed Optimal Quantization and Power Allocation for Sensor Detection via Consensus

Abstract

Abstract-We address the optimal transmit power allocation problem (from the sensor nodes (SNs) to the fusion center (FC)) for the decentralized detection of an unknown deterministic spatially uncorrelated signal which is being observed by a distributed wireless sensor network. We propose a novel fully distributed algorithm, in order to calculate the optimal transmit power allocation for each sensor node (SN) and the optimal number of quantization bits for the test statistic in order to match the channel capacity. The SNs send their quantized information over orthogonal uncorrelated channels to the FC which linearly combines them and makes a Þnal decision. What makes this scheme attractive is that the SNs share with their neighbours just their individual transmit powers at the current states. As a result, the SN processing complexity is further reduced.

Distributed detection in practical wireless sensor networks via a two-step consensus algorithm

“…Fig. 5 shows the behavior of the proposed distributed two-step algorithm compared to the quantized (2 bits) equal combining scheme in [3]. As expected, there is an optimum K 1 that maximizes P g d and after that P g d decreases.…”

“…The case where spatially distributed SNs report to the FC (i.e., the centralized approach) via dedicated parallel access channels (PAC) is investigated in [3,5]. Here, (equal) linear soft decision combining at the FC gives:…”

“…However, this will be counterbalanced by an 2 A connected network is any network where there is a path between every pair of SNs in the network. 3 We assume that SNs transmit their observations through a parallel access channel (PAC). This assumption is reasonable for a small-scale WSNs.…”

“…As k becomes large, it is clear that the second term of (24) grows and the performance of the distributed algorithm using quantized test statistics does not converge across the network to its counterpart of the centralized quantized detector [3] (i.e., lim (13) of [3], ∀i). Now, it is also clear that the value of k establish a tradeoff between the local SNs test statistic improvement and the quantization error degradation.…”

“…1) are tasked to decide on a global activity from locally collected measurements. Some strategies consider the centralized solution of a fusion center (FC) where the noisy observations from distributed SNs are collected and the FC is able to compute the test statistic in a single shot [1][2][3][4][5]. Recent publications [6,7] consider SN collaboration in the context of distributed estimation where after the exchange of information the SNs report to the FC.…”