Invariant tests for rapid-fluctuating radar signal detection with unknown arrival time

We study the rapid-fluctuating radar signal detection, where the arrival time of the received signal, i.e., the range cell index of the target, as well as the complex amplitude of the signal and the noise are unknown. We show that even in additive white Gaussian noise (AWGN) environment, uniformly most powerful invariant (UMPI) test does not exist. Instead, the UMPI detector in known SNR is used as an upper performance bound for performance evaluation of any invariant detector performance. In addition, we derive generalized likelihood ratio (GLR) detectors for this signal in AWGN with unknown noise variance and also in clutter with unknown covariance matrix. The GLR test statistic for AWGN represents the ratio of the maximum power over all cells to the total power. The GLRT for a clutter environment is also a power ratio which is the maximum over all range cells of the Euclidean norms of the spatially whitened observed sequence. Simulation results demonstrate that the performance of the proposed GLR test in AWGN is very close to the upper bound performance, i.e., to that of the UMPI test in known SNR.