1.3 Deterministic Description 7 1.3 DETERMINISTIC DESCRIPTION We next discuss some basic deterministic 1 characterizations of LTV channels. We consider a wire- less system operating at carrier frequency f c . We will generally describe this system in the equivalent complex baseband domain for simplicity (an exception being the wideband system considered in Section 1.3.2). The LTV channel will be viewed and denoted as a linear operator (Naylor & Sell, 1982) H that acts on the transmit signal s(t) and yields the receive signal r(t) = (Hs)(t). 1.3.1 Delay-Doppler Domain ­ Spreading Function As mentioned before, the physical effects underlying LTV channels are mainly multipath propagation and the Doppler effect. Hence, a physically meaningful and intuitive characterization of LTV channels is in terms of time delays and Doppler frequency shifts. Let us first assume an LTV channel H with P discrete propagation paths. The receive signal r(t) = (Hs)(t) is here given by P r(t) = p=1 h p s(t- p ) e j2 p t , (1.6)