AbstractThe paper deals with the detection of a known signal embedded in cyclostationary white generalized Gaussian noise. Two cases are considered: the former assumes unknown (but nonrandom) the periodic noise intensity, the latter considers unknown also the noise‐shape parameter. Since for these detection problems non uniformly most powerful test exists, the generalized log‐likelihood ratio test (GLLRT) is considered because of its asymptotic optimality properties. The GLLRT‐based detectors for both cases are synthesized and their asymptotic (i.e., for large sample size) performances are analytically evaluated. Moreover, for finite sample size, the performances, carried out via computer Monte Carlo simulations, are compared with that of the optimum detector, whose synthesis is based on a complete noise characteriz