Regularization of Fourier Series with Approximate Coefficients for the Problem of Phase Probability Density Function Estimation

This paper considers the problem of phase probability distribution function estimation for phase-shift-keying signals. The modulating sequence and, accordingly, the symbol phases, as well as statistical characteristics of this sequence, are unknown. The Fourier coefficients are calculated on a limited sample for estimating the phase probability distribution function. In this case, the thus obtained Fourier coefficients are regularized. A multiparameter regularization method for increasing the estimation accuracy is considered. Numerical simulation results are presented.