Signal Design for Frequency-Phase Keying

A new digital modulation scheme, termed frequency-phase keying (FPK), that combines frequency-shift keying (FSK) and phase-shift keying (PSK), is presented. Optimized signal designs for $M$ -ary FPK that jointly select the phase and frequency of the modulating signal in order to minimize the union bound on the symbol error probability with maximum likelihood reception are obtained. Solutions for baseband communication in additive white Gaussian noise channels and for passband communication in Rayleigh fading with receive diversity are derived. In contrast to conventional FSK and PSK, and to existing hybrid FSK/PSK schemes, the designed FPK signal constellations have the desirable property that the maximum correlation coefficient between any two signals is negative. We demonstrate that the proposed FPK solutions yield improved error performance for both baseband and passband communication.