Adaptive Detection of Second-Order Subspace Signals Using Rao and Durbin Tests

We consider adaptive detection of multidimensional second-order subspace signals in colored noise with a view to provide simpler alternatives to the generalized likelihood ratio test which requires alternate maximization over two sets of matrices. Since the main problem comes from maximum likelihood estimation of the unknown parameters under the alternative hypothesis we consider detection schemes that do not need it. Towards this end we derive closed-form expressions of Rao and Durbin tests for the problem at hand. These detectors are computationally simple and provide a constant false alarm rate. Through numerical simulations we illustrate the trade-off between computational complexity and detection performance.