Spectra of PSK Signals with Overlapping Baseband Pulses

This paper derives a new power spectrum formula for constant-envelope PSK signals. The only signal constraints are that the baseband pulses be of finite duration and the pulse amplitudes be mutually independent. The computer program used to implement the formula is made highly efficient by the use of fast Fourier transform (FFT) algorithms. The key contribution of the new result is the high degree of baseband pulse overlap permitted before the computation cost becomes excessive. In some computation approaches, this cost grows as L
^N
, where
L
is the number of modulation levels and
N
is the number of data periods spanned by the pulse. In the approach developed here, the cost is independent of
L
and grows roughly linearly with
N
. The cost improvement, which is substantial for large
L
and
N
, is exploited here by using the new approach for a wide variety of baseband pulses. Results are given which demonstrate the potential value, in terms of narrower spectra and lower sidelobes, of using overlapping pulses.