Generalised parametric Rao test for multi-channel adaptive detection of range-spread targets

This study considers the problem of detecting a multi-channel signal of range-spread targets in a homogeneous environment, where the disturbances in both test signal and training signals share the same covariance matrix. To this end, a generalised parametric Rao (GP-Rao) test is developed by modelling the disturbance as a multi-channel auto-regressive process. The GP-Rao test uses less training data and is computationally more efficient, when compared with conventional covariance matrix-based solutions. The theoretical detection performance of the GP-Rao test is characterised in terms of the asymptotic distribution under both hypotheses. Numerical results indicate that the proposed GP-Rao test attains asymptotically the constant false alarm rate property. Numerical results show that the GP-Rao test achieves better detection performance and uses significantly less training signals than the covariance matrix-based approach.