Abstract
The probability of detection is a key performance metric that assesses a receiver's ability to detect the presence of a signal. Receiver performance is evaluated by comparing empirical measurements against an exact or a bounded theoretical limit. If the detection statistic is based on multiple, independent measurements, it is relatively straight forward to formulate the joint probability density function (PDF) as a multi-variate Gaussian distribution (MVG). In this work, we consider the detection statistic that arises when combining correlated measurements from a two-dimensional array of sensors. The joint PDF does not readily fit into a multi-variate Gaussian model. We illustrate a method by which we can construct a block-diagonal covariance matrix that can be used to cast the joint PDF into the standard MVG form. This expression can then be evaluated numerically to compute a theoretical probability of detection. We validate the authenticity of the joint PDF using Monte-Carlo simulations. We quantify the impact of correlated measurements on the probability of detection.
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