Adaptive Detection of a Signal Whose Signature Belongs to a Cone

We address the problem of detecting a signal of interest, taking into account a possible mismatch between the actual steering vector and the presumed one. More precisely, we assume that the former belongs to a cone, whose axis is the presumed steering vector. We consider a partially homogeneous environment in which the covariance matrix of the vector under test has the same structure as that of the training samples, but possibly different level. The generalized likelihood ratio test (GLRT) is derived. It is shown that it involves solving a minimization problem with the constraint that the signal of interest lies inside a cone. A Lagrange multiplier technique is invoked to solve the aforementioned problem, resulting in a computationally efficient maximum likelihood estimator (MLE). Numerical simulations illustrate the performance and the robustness of this new detector, and compare it with the adaptive coherence estimator which assumes that the steering vector is known