The performance of Rayleigh fast-fading channels with intersymbol interference: and additive Gaussian noise

Presented herein is an analysis of the effects of intersymbol interference on the performance of digital communication systems operating over channels corrupted by Rayleigh fast-fading and additive Gaussian noise. The results are applicable to systems employing coherent detection schemes. For mean signa1-to-noise ratios of 15 dB or less, and for typical pulse shapes with reasonably well synchronized sampling, intersymbol interference is shown to contribute no significant amount to the total probability of bit-error over the Rayleigh fast-fading channels. (The fraction of bit error rate due to intersymbol interference is less than 0.2 of the total bit-error probability for most cases) As the mean signal -to-noise ratio is increased to higher levels, the effects of intersymbol interference on the performance of the digital communication systems become more significant. For mean signa1-to-noise ratios of 25 dB or more, the incremental bit-error probability caused by intersymbol interference begins to play a dominant part of the total biterror probability over the bit-error rate due to additive noise alone. For mean signa1-to-noise ratios of 45 dB or more, the total bit-error probability is almost entirely due to intersymbol interference. An irreducible error rate is created thereafter due to the severity of intersymbol interference. Such results are different from those obtained in the absence of fading, in which case the bit-error probability at signa1-to-noise ratios in excess of 15 dB is almost entirely due to intersymbol interference. They also contrast sharply with those obtained in Rayleigh slow-fading channels where the incremental bit-error probability caused by intersymbol interference is seen to be limited to some small fractional part of the total bit-error probability as the mean signa1 -to-noise ratio is increased to higher levels.