Suppression of the irreducible errors in a frequency-selective fading channel by fractional-bit differential detection

The irreducible errors in digital mobile communications with high data rate in low-delay-spread channels are mainly caused by time dispersion (frequency selectivity) of the channel. The errors originate in the transition regions between adjacent symbols when deep fades occur. We show that fractional-bit differential detection with proper timing avoids these transition regions and decreases the irreducible errors. Assuming an MSK modulation format and slow Rayleigh fading, we derive a formula for calculation of the error probability in which we apply an “effective delay spread.“ A procedure to predict the effective delay spread is proposed. We verify the calculated error probability by a Monte Carlo software simulation for three different delay power profiles. The approach increases the tolerable delay spread in an unequalized receiver by a factor of 2 to 5 depending on the details of the delay power profile. Filtering the MSK signal tends to smear the transition region over the entire symbol duration, reducing the effectiveness of fractional-bit detection. This explains qualitatively the mismatch between theory and experiment in previously published results. We discuss the conditions of filtering and of finite signal-to-noise ratio (SNR) under which fractional-bit detection is effective. For instance, for a delay spread around one-tenth of the symbol length, improvement is gained if the SNR is above 15 dB