Spectral analysis of M-ary PSK modulation with smooth and monotonic phase variations

Computer simulation has shown that smooth and monotonic phase variations in constant envelope Af-ary PSK modulation offer a significant reduction in the mainlobe width of the trasmitted signal, as compared with alternative conventional PSK modulation schemes. In this paper it is shown that the above modulation scheme can be considered as a special case of CPFSK signals with constant modulation index equal to I/M. A closed-form expression for the power density spectrum is theoretically derived, and spectral comparisons to conventional PSK schemes with abrupt phase variations are performed, Theoretical results are verified using computer simulation, for M equal to 2, 4 and 8.