We consider a modern radar system which has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. A generalized likelihood ratio test (GLRT) was proposed in this context for target detection and direction of arrival estimation. However, the analytical performance of the GLRT has not been provided yet. In this paper, we derive finite-sum expressions for the probabilities of false alarm and detection. It is proven that the GLRT exhibits a constant false alarm rate against the overall interference disturbance covariance matrix. Numerical examples show that the detection performance of the GLRT may not necessarily improve when the number of sensors increases