Optimum bandwidth-distance performance in full response CPM systems

The problem of minimizing the effective bandwidth of a binary full-response continuous-phase-modulation (CPM) signal with respect to the shape of the frequency pulse for a prescribed value of the minimum Euclidean distance, which is directly related to the error probability for high signal-to noise ratio, is considered. An analytical procedure is presented that allows the determination of the optimum pulse shape together with its bandwidth and the minimum-distance characteristics. The solution contains an unknown parameter that is determined by numerical of a nonlinear equation. The results are compared to some standard pulses in terms of bandwidth, spectral density, minimum Euclidean distance, and error probability. Some gain in bandwidth is obtained for high values of minimum distance