The Spectrum of a TDM PPM Signal

The spectrum of a time-division-multiplexed (TDM) pulse-position-modulated (PPM) signal consists of three parts-the continuous part, which is simply the sum of the continuous parts of the spectra of the separate channels; lines on harmonics of the maximum overall pulse-repetition frequency (PRF), which are also independent of any permutation among the channels; and the lines on the other harmonics of the single-channel PRF. Simple expressions are found for all three parts under the assumption that
N - m - n
channels are empty,
n
are unmodulated, and the remaining
m
contain independent, identically uniformly distributed pulse positions. A complicated expression is found for the variances of the lines in the last part of the spectrum under a random choice of the modulated and unmodulated channels, and a simple approximation is presented for it.