Date of Award
Open Access Dissertation
Doctor of Philosophy in Electrical Engineering (PhD)
Administrative Home Department
Department of Electrical and Computer Engineering
Daniel R. Fuhrmann
Committee Member 1
Timothy J. Schulz
Committee Member 2
Committee Member 3
Alexander E. Labovsky
In this dissertation we consider a sensor scheduling or resource management problem for a vector Poisson and Gaussian channels. The input is a binary random vector and the output is a set of conditionally independent Poisson or Gaussian random variables. The objective is to design a scaling matrix, which is a linear transformation whose purpose is to entangle the different inputs, under a total given energy/time constraint. The two metrics are adopted to quantify the performance of the designed scaling matrix: mutual information and Bayesian inference. In other words, it is an experimental design problem where the objective is to glean the information about the binary inputs and perform the classification of the input random vector in a fixed time-resource, that is transmitted through a vector Poisson and Gaussian channel, based on the output observations.
No optimal solution is claimed in this dissertation for the above problem for either of the Poisson or Gaussian channels; from either of the two perspectives: mutual information or Bayes detection. However, time-symmetry does exist in the said problem. It is further noted that the problem is concave in its domain (i.e. sensing times) from mutual information criterion; and this is based on the observations in the computational results. If this concavity does exist in the problem then together with the time-symmetry result; it can be deduced that the optimal solution has a symmetry too; and that would reduce the exponentially rising dimensionality of the search-space to the linear one (w.r.t dimension of the input random vector). However, concavity of the objective function in the Bayes framework does not exist.
Further, it is noted that the classification criterion in the above two channels; and mutual information criterion do not generally lead to the same solution when subjected to the same fixed time constraint and model parameters.
It is also noted that the combinatorial explosion is inevitable, that occurs while addressing the problem through computational means, even with exploiting the inherent time-symmetry and the concavity in the objective. This curse of the dimensionality is the main obstacle in exploring the problem for targets greater than four (i.e. for dimension of the input vector greater than 4).
Fahad, Muhammad, "Sensing Methods for Two-Target and Four-Target Detection in Time-Constrained Vector Poisson and Gaussian Channels", Open Access Dissertation, Michigan Technological University, 2021.