Efficient calculation of the power spectral density of filtered and nonlinearly distorted digital signals

A closed form method is derived for the calculation of the power spectral density of linear filtered and nonlinearly distorted digital signals, applying to baseband signals as well as to linear modulated M-PSK (phase shift keying) and M-QAM (quadrature amplitude modulation) signals. A method of modeling the output of the transmitter as the output of a Markov chain, is modified in such a way as to avoid the use of large state transition matrices and M-step transition probability matrices. Large amounts of memory space in a digital computer can thus be saved, allowing the calculation of the power spectral density even for signals with large memory. A method for reducing the calculation complexity for M-PSK signals is also presented. The application of the derived formula is demonstrated for square-root-Nyquist filtered binary PSK and quadrature PSK signals, when distorted by a travelling wave tube