Statistical Description of Wireless Multipath Channel

Abstract

In the following, we are going to describe the time variance of a multipath channel by statistical parameters. We assume a multipath channel with delay spread function $g_{c}(t,\tau )$ given in (7.3) and neglect the receiver noise in the following. For the receive signal (7.12), then holds with (7.13) and $u_{a}(t)=x(t)$.

$$\begin{aligned} q_{R}(t)=\sum _{\nu =1}^{N_{P}}x(t)\circledast \left[ \tilde{\alpha }_{\nu }(t)g_{I}\left( \tau -\tau _{\nu }(t)\right) \right] \circledast g_{R}(\tau ) \end{aligned}$$

As can be seen, even for a constant transmit signal $x(t)=const.$