Matched filter for transmission over channels with ISI employing the distribution of interference

In this paper, we analyze the matched filter (MF) applied for transmission over channels with ISI (intersymbol interference) with the MF being matched to the convolution of the transmit pulse and the channel impulse response. When convolutional coding is applied, the distribution of occurring interference and noise is commonly assumed to be Gaussian for calculation of post-detection probabilities for a subsequent MAPSSE (maximum a-posteriori symbol-by-symbol estimation) decoder. Here, we analyze the MF when employing the actual probability density function of ISI and noise for calculation of post-detection probabilities. It turns out, that these values are much more reliable especially for high signal-to-noise ratios (SNR). Therefore, the bit error ratio after decoding can be reduced by the new scheme e.g. for the considered three tap multipath channel to 10^-5 and less for high SNR whereas it remains about 10^-2 for the common scheme exploiting the Gaussian assumption. The proposed scheme can also be employed to improve turbo equalization.