Phase smoothing functions for continuous phase modulation

In this paper, the problem of signal design for continuous phase modulation is examined. Using the performance measures of effective bandwidth and minimum distance, “optimal” signal shapes are calculated for various receiver observation intervals for full and partial response signalling. For the partial response case, the optimization could only be done for receiver observation interval of one symbol due to the difficulty of the optimization. Therefore, a family of signals based on previously calculated optimal signals is introduced. The tradeoffs that result between bandwidth and bit error rate are then compared as a function of the receiver observation interval and as a function of the memory length of the signalling scheme. Then, the signals introduced in this paper are compared to well known signals in terms of their effective bandwidth-minimum distance tradeoffs, power spectra and percent-in-band-power. The signals obtained by the optimization process are found to have good spectral properties in relation to well known signals