Estimation of Multi-Path Channels by Using the Annihilating Filter Method

Estimation of the channel distortion characteristics is of crucial importance for realizing a reliable communication. In order to estimate the channel, a received signal is sampled at some rate. The Nyquist rate is widely used notion to determine the sampling rate of the received signal. On the other hand, Vetterli introduced the concept of rate of innovation that is the degree of freedom of the signal space and proposed annihilating filter method, which solves a nonlinear simultaneous equation by means of finding roots of the characteristic polynomial of the equation. By using this technique, the number of samples can be reduced from the Nyquist rate. In this paper, we employ the annihilating filter method to perform the estimation of a multi-path channel. A spread spectrum signal with a wide bandwidth is transmitted, while the received signal is sampled at a very low sampling rate that is determined according to the rate of innovation.