Adaptive detection using randomly reduced dimension generalized likelihood ratio test

Abstract We address the problem of detecting a signal of interest in the presence of Gaussian noise with unknown statistics when the number of training samples available to learn the noise covariance matrix is less than the size of the observation space. Following an idea by Marzetta, a series of K random semi-unitary matrices are applied to the data to achieve dimensionality reduction. Then, the K corresponding generalized likelihood ratios are computed and their median value provides the final detector. We show that the semi-unitary matrices can be replaced by random Gaussian matrices without affecting the final test statistic. The new detector avoids eigenvalue decomposition and is easily amenable to parallel implementation. It is compared to conventional techniques based on diagonal loading of the sample covariance matrix or based on rank reduction through eigenvalue decomposition and is shown to perform well.