The Effect of Multipath Interference on the Performance of a Digital Matched Filter

We analyze the performance of a one-bit digital matched filter (DMF) responding to binary signaling through a noisy multipath channel. The output signal-to-noise ratio
(SNR_{o})
plays a key role in the analysis. The SNR
o
performance is fully studied for a two-path channel, both fading and non-fading. For the general
N
-path channel, results are obtained only for the fading case. All results are conditioned on the knowledge of the time delays of all paths, and are valid only for small input signal-to-noise ratio
(SNR_{i)
. Most of the results have been verified by computer simulations.