# Fusion Rules for Distributed Detection in Clustered Wireless Sensor Networks with Imperfect Channels

## TL;DR

This paper develops a sub-optimal linear fusion rule for distributed detection in clustered wireless sensor networks with noisy channels, providing near-optimal performance and an efficient power allocation strategy.

## Contribution

It introduces a practical linear fusion rule with an approximate maximum likelihood implementation and an optimal power allocation method for clustered WSNs with imperfect channels.

## Key findings

- LFR achieves near-optimal detection performance.
- Proposed power allocation reduces power consumption significantly.
- Derived upper bounds for detection and false alarm probabilities.

## Abstract

In this paper we investigate fusion rules for distributed detection in large random clustered-wireless sensor networks (WSNs) with a three-tier hierarchy; the sensor nodes (SNs), the cluster heads (CHs) and the fusion center (FC). The CHs collect the SNs' local decisions and relay them to the FC that then fuses them to reach the ultimate decision. The SN-CH and the CH-FC channels suffer from additive white Gaussian noise (AWGN). In this context, we derive the optimal log-likelihood ratio (LLR) fusion rule, which turns out to be intractable. So, we develop a sub-optimal linear fusion rule (LFR) that weighs the cluster's data according to both its local detection performance and the quality of the communication channels. In order to implement it, we propose an approximate maximum likelihood based LFR (LFR-aML), which estimates the required parameters for the LFR. We also derive Gaussian-tail upper bounds for the detection and false alarms probabilities for the LFR. Furthermore, an optimal CH transmission power allocation strategy is developed by solving the Karush-Kuhn-Tucker (KKT) conditions for the related optimization problem. Extensive simulations show that the LFR attains a detection performance near to that of the optimal LLR and confirms the validity of the proposed upper bounds. Moreover, when compared to equal power allocation, simulations show that our proposed power allocation strategy achieves a significant power saving at the expense of a small reduction in the detection performance.