Multiple-symbol trellis-coded modulation applied to noncoherent continuous-phase frequency shift keying

This paper considers a maximum-likelihood (ML) noncoherent detection scheme for multiple full response continuous-phase frequency shift keying (CPFSK) waveforms and introduces a trellis-coded modulation (TCM) scheme for this noncoherent modulation. By utilizing a Gaussian approximation for Rician random variables, we express the pairwise error probability as a function of the equivalent normalized squared distance (ENSD). ENSD plays the same role as normalized squared Euclidean distance when evaluating error probability performance for coherent detection. We derive an analytical approximation on the bit-error probability by employing ENSD for both the coded system and the uncoded system. For the uncoded system we show that the bit-error probability of noncoherent detection approaches that of coherent symbol-by-symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal-to-noise ratio (SNR), We determine specific optimal trellis encoders for binary and 4-ary CPFSK with modulation index 1/2 and 1/4, respectively, by application of Ungerboeck´s (1982) set partitioning approach