Abstract
In this work we investigate the different sensing schemes for 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.
Highlights
In [1], [2] and [3] a two-target detection in vector Poisson and Gaussian channels is considered
We study the problem in higher dimensions, we are hampered by the limitations of the deterministic computational methods which fails to work efficiently, in terms of computational time, due to the curse of the dimensionality issue
This paper considers an experimental design problem of setting, sub-optimally, the time-proportions for identifying a four-long binary random vector that is passed through a vector Poisson and vector Gaussian channels, and based on the observation vector; classification of the input vector is performed and performance of any sensing scheme is compared
Summary
In [1], [2] and [3] a two-target detection in vector Poisson and Gaussian channels is considered. There are 15− conditional point processes (in total) that we have to deal with to extract the maximum possible information or perform the best input signal detection by setting the counting times from T1 to T15 in a fixed given time. To answer this we first fixed p, and we consider T as a free parameter and compute both the mutual information [11], [12] and Bayes probability of total correct detections [13], for a given set of parameters, and searched if there exist any instance for which one configuration is the best for some time and another configuration becomes the best and so on.
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