Power-Bandwidth Performance of Smoothed Phase Modulation Codes

Constant envelope phase varying sinusoids of the form are studied, in which the phase function follows some coded pattern in response to data. Power and bandwidth performance are studied for such patterns. The patterns depend on a phase shaping function, a modulation index ( ), and a sequence of -ary underlying changes in phase which are chosen at random. A cutoff rate-like parameter R0is computed, which guarantees existence of codes at all rates bits/ -interval whose error performance varies as exp , where is the code word length in -intervals. Plots of R0are given as a function of interval energy , the shaping function and . Extensive spectral calculations give the spectra of these phased sinusoids, and their performance is plotted in the power-bandwidth plane. The results give strong evidence that phase codes can approximate any power-bandwidth combination consistent with Shannon\´s Gaussian channel capacity, and that linear channels are not required for narrow-band transmission.