A Notion of Diversity Order in Distributed Radar Networks

Abstract

We introduce the notion of diversity order in distributed radar networks. Our long-term goal is to analyze the trade-off between distributed detection and centralized detection using co-located antennas. In contrast with the asymptotically high Signal-to-Noise Ratio (SNR) definition in wireless communications, we define the diversity order of a distributed radar network as the slope of the probability of detection (PD) versus SNR curve at PD= 0.5. In this paper we restrict our analysis to noise-limited systems. We evaluate the diversity order of fully distributed systems, and prove that for the OR rule, the gain in diversity is only logarithmic in the number of distributed sensors, denoted K. The AND rule does not lead to any gain in diversity order. We finally present some recent results, and provide preliminary analysis regarding the characterization of a Diversity-Multiplexing tradeoff in distributed radar detection.

Detection diversity of multiantenna spectrum sensors

“…2 that it increases at a rate no larger than √ M . It is conjectured that the diversity order of the OR detector is logarithmic in M , similarly to [4].…”

“…Let the minimum operational SNRζ * of the detector be defined bȳ P D (ζ * ) = 0.5. Following [4], the diversity order d is defined as…”

“…This calls for a different definition of the diversity order better suited to the detection problem. For example, Daher and Adve [4] define diversity order as the slope of the average probability of detection (P D ) curve with respect to the SNR atP D = 0.5. Using this, [4] analyzed the performance of distributed radar detectors with Swerling-II targets, in which each radar sensor is equipped with multiple antennas, the steering vectors are known and a single snapshot is used per sensor for detection.…”

“…For example, Daher and Adve [4] define diversity order as the slope of the average probability of detection (P D ) curve with respect to the SNR atP D = 0.5. Using this, [4] analyzed the performance of distributed radar detectors with Swerling-II targets, in which each radar sensor is equipped with multiple antennas, the steering vectors are known and a single snapshot is used per sensor for detection. When sensing on wireless channels, these assumptions have to be suitably modified: antennas are usually omnidirectional, and sensing times are longer in order to acquire several signal samples.…”

Collecting Detection Diversity and Complexity Gains in Cooperative Spectrum Sensing

“…To this end, we use another measure of diversity order proposed originally for distributed radar networks operating in low-SNR conditions. This measure is termed as detection diversity D and defined as the slope of the probability of detection P d versus SNR curve at P d = 0.5 [21], that is,…”