M-ary frequency shift keying (MFSK) is a power-efficient modulation method that is useful for low power and low data rate applications. The power efficiency of this modulation method increases as the signal alphabet increases at the expense of increased complexity and reduced bandwidth efficiency. We present an analysis of its uncoded and coded performance in Rician-fading channels using noncoherent demodulation with Reed-Solomon (RS) codes and hard decision decoding. Previous numerical difficulties encountered in determining the performance of large alphabet sizes are circumvented by the analysis presented, and the results obtained are used to quantify performance gains that can be realized by expanding the modulation's alphabet size. Optimum RS codes for hard decision decoding are determined using bit error probability as performance measure for a wide range of Rician channel parameters. The results of this paper should be useful as benchmarks of obtainable performance and as a reference for validating the results of simulation studies.

The performance of a hybrid modulation technique derived from binary frequency shift keying is presented. In the hybrid scheme, each frequency is allowed to be phase modulated with any of p discrete, equally spaced phase shifts. The spectral separation between frequencies is chosen to make the carriers orthogonal, thus generating a multidimensional modulation scheme. The performance of complete and expurgated phase codes is examined for the Gaussian and Rayleigh fading channels, and their spectral characteristics are determined.>

Steiner systems constitute an example of codes that achieve asymptotic error-free transmission for the Gaussian channel. In contrast to simplex and orthogonal codes which also have this property, these codes make more efficient use of the bandwidth by reducing the required dimensionality to generate the M signals. Tight upper bounds for the symbol error probability are derived for coherent and noncoherent detection that include previously reported results as special cases. The relative bandwidth efficiency with respect to orthogonal codes is presented, and a combined performance plot is given that allows a meaningful comparison between the different coding schemes considered.>