(1.146) with d = L. The general exact expres- sion will be shown in (1.201). In many channels, such as the tropospheric scatter channel, it is more appropriate to view the received signal as consisting of a continuum of mul- tipath components. Such channels are usually characterized with channel output (see Proakis [33]), (1.188) where H(T;t) is a randomly time-varying filter. Associated with the randomly time-varying filter H(T;t) are two basic parameters; Tm denotes the total multipath delay spread of the channel and B denotes the Doppler spread of the channel. From these define Afc=Tm (1.189) as the "coherence bandwidth" and (1.190) as the "coherence time" of the channel. Roughly, if two CW signals of fre- quency separation greater than Afc were transmitted through the channel, then the output signals at the two carrier frequencies would have indepen- dent channel disturbances (phase and envelope). Similarly, when a single CW signal is transmitted through the channel, its output sampled at time sepa- rations greater than Atc would have independent channel disturbances at the sample times. Slow Fading Multipath Channels For the uncoded DS/BPSK signal one data bit is transmitted every Tb sec- onds. Assume (1.191) SO that intersymbol interference between data bits can be ignored. Also assume the channel is slowly varying SO that (1.192) Thus the channel disturbance is almost constant during a data bit time . Finally, since our signal is a wideband signal of bandwidth Wss assume (1.193) This model assumes many independent scatters are causing the continuum of multipath components. Thus the resulting channel output signal term is the sum of many independent scatters which justifies assuming it is a Gaussian random process. At any time it has a Rayleigh envelope probability distribution and an independent phase uniformly distributed over [0, 2]. Skywave propagation where an HF signal is reflected off the ionosphere is an example whre this model applies. If, however, there also exists a strong unfaded signal componen