Coded nonuniform phase/frequency modulation.

Coded nonuniform phase/frequency modulation is proposed to achieve a performance gain over uniformly spaced signal-constellation-coded phase/frequency modulation. In particular, the joint design of m/(m+1) systematic convolutional encoders and nonuniform 2FSK/2 ^mPSK modulation signals are considered. The minimum free Euclidean distance of the trellis is calculated for several classes of codes, and the asymptotic performance gains due to coding and nonuniformity are evaluated. Numerical results on bit error probability are also presented for some codes to demonstrate the additional savings in required energy bit to noise ratio. It is shown that by designing the signal constellations to be nonuniform, performance gain can be obtained over the conventional coded uniform phase/frequency modulation in many instances.