A Generalized Version of ACE and Performance Analysis

This paper considers the problem of detecting a signal that belongs to an unknown one dimensional subspace of \mathbb {C}^{N \times 1} in additive interference-plus-noise whose covariance matrix is unknown. The interference-plus-noise is assumed to be modeled as a complex multivariate zero-mean random vector whose covariance matrix {\bf R}, is estimated from signal-free training vectors. The hypothesis test, labeled the generalized Adaptive Coherence Estimator (GACE) involves two test vectors, both of which contain the unknown signal. The test statistic reduces to the ACE test statistic as the signal-to-interference-plus-noise ratio of any one of the test vectors increases without limit. In the limit of large number of training samples the GACE test statistic reduces to the magnitude square of the inner-product of a signal vector in additive statistically independent white noise vectors. Analytical expressions for the probability of false alarm and the probability of detection of the GACE test are derived and the test is shown to have the constant false alarm rate (CFAR) property. Sample results to illustrate the performance of the detector are provided and compared with the performance of the generalized likelihood ratio test (GLRT) for the specific problem, along with results on the sequential application of the GLRT and GACE.