Sensing Method for Two-Target Detection in Time-Constrained Vector Gaussian Channel

TL;DR

This paper investigates optimal sensing strategies for detecting two targets in a vector Gaussian channel by maximizing mutual information and MAP detection under time constraints, revealing different optimal solutions for each metric.

Contribution

It introduces a novel analysis of optimal linear transformations for two-target detection in Gaussian channels, highlighting the differing solutions for mutual information and MAP criteria.

Findings

Different optimal solutions for mutual information and MAP detection.

Monte Carlo method effectively used for computational analysis.

Optimal scaling matrices depend on the detection metric chosen.

Abstract

This paper considers a vector Gaussian channel of fixed identity covariance matrix and binary input signalling as the mean of it. A linear transformation is performed on the vector input signal. The objective is to find the optimal scaling matrix, under the total time constraint, that would: i) maximize the mutual information between the input and output random vectors, ii) maximize the MAP detection. It was found that the two metrics lead to different optimal solutions for our experimental design problem. We have used the Monte Carlo method for our computational work.