Detection with partial information for the Gaussian setup in the potential presence of a jammer

Abstract

We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. We study this setup in a binary detection theoretic context for the additive colored Gaussian noise channel in the potential presence of a jammer. In our proposed setup, the partial information available at the detector consists of dimensionality-reduced versions of the transmitter codewords, where the dimensionality reduction is achieved via a linear transform. In the first part of the thesis, we focus on the “no-jammer” case and accordingly find the MAP-optimal detection rule and the corresponding conditional probability of error (conditioned on the partial information the detector possesses). Then, we constructively quantify two optimal classes of linear transforms: For the first class, the cost function is the expected Chernoff bound on the conditional probability of error of the MAP-optimal detector; for the second class, the cost function is a certain upper bound on the failure probability, which is defined as the probability of the aforementioned conditional error probability being greater than a given constant. In the second part of the thesis, we study the case where an active jammer is present (subject to a peak power constraint) together with additive colored Gaussian noise. In this case, we first derive the conditional probability of error of a minimum Euclidean distance detector as a function of the receiver partial information and the jammer signal. Then, we quantify the worst-case jammer strategy, which maximizes the aforementioned conditional probability of error. As a result, we propose a criterion for choosing the dimensionality-reducing linear transforms in the sense of worst-case failure probability.