Wald Test for Adaptive Array Detection with General Configuration

Assume that a modern radar system has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. We consider the target detection problem for such array radar systems in Gaussian disturbance with unknown covariance matrix. An adaptive detector is proposed according to the criterion of Wald test. The statistical properties of the proposed detector are provided in the mismatched case, where the nominal target steering vector may not be aligned with the true target steering vector. An analytical expression for the probability of false alarm is derived, which reveals that the proposed detector has a constant false alarm rate property with respect to the disturbance covariance matrix. Moreover, a closed-form expression for the detection probability is obtained in the mismatched case. Simulation results demonstrate that the proposed detector exhibits strong robustness against the target steering vector mismatch.