Heuristic Sensing Schemes for Four-Target Detection in Time-Constrained Vector Poisson and Gaussian Channels

TL;DR

This paper explores sensing schemes for detecting four targets in vector Poisson and Gaussian channels under limited sensing time, analyzing mutual information and detection probability to optimize resource allocation.

Contribution

It introduces an analysis of mutual information and detection probability optimization for sensing schemes in Poisson and Gaussian channels under time constraints.

Findings

Mutual information and Bayes risk are not always aligned.

Mutual information is concave with respect to sensing time under certain conditions.

Abstract

In this work, we investigate the different sensing schemes for the detection of four targets as observed through a vector Poisson and Gaussian channels when the sensing time resource is limited and the source signals can be observed through a variety of sum combinations during that fixed time. For this purpose, we can maximize the mutual information or the detection probability with respect to the time allocated to different sum combinations, for a given total fixed time. It is observed that for both Poisson and Gaussian channels; mutual information and Bayes risk with $0-1$ cost are not necessarily consistent with each other. Concavity of mutual information between input and output, for certain sensing schemes, in Poisson channel and Gaussian channel is shown to be concave w.r.t given times as linear time constraint is imposed. No optimal sensing scheme for any of the two channels is investigated in this work.