Signal detection in partially known cyclostationary non-Gaussian noise

The detection of a signal embedded in cyclostationary white non-Gaussian noise with unknown (but nonrandom) periodic noise intensity level is considered. The generalized log-likelihood ratio test (GLLRT) is considered because of its asymptotic optimality properties. The performance of GLLRT is compared with that of the optimum and asymptotically optimum detectors (OD and AOD) whose synthesis is based on a complete characterization of the noise. A modified version of the asymptotically optimum detector which does not need the complete characterization of the noise is also considered. Provided that the exact waveform of the periodic noise intensity variations is known and a perfect synchronization of the detector to such variations is available, OD and AOD turn out to be those for stationary noise preceded by a time-varying invertible transformation. The performance of all detectors has been evaluated by computer simulations on the assumption of a generalized Gaussian noise. The results show that the performance loss of GLLRT with respect to the OD and AOD is significant only for a small sample size on the whole range of the values of the parameter governing the rate of the noise pdf decay