e A(T) versus delay T where the term delay refers to the excess delay. It represents the signal's propagation delay that exceeds the delay of the first signal component arrival at the receiver. For a typical wireless communication Dual functions Vc V max Vc + V Tm Maximum excess delay Spectral broadening Multipath intensity profile Doppler power spectrum Fourier Fourier transforms transforms Dual functions Spaced-frequency correlation function Spaced-time correlation function Coherence bandwidth Coherence time Figure 3.3 Illustration of the duality principle in time and frequency domains [33]. 294 Chapter 3 channel, the received signal usually consists of several discrete multipath components. The received signals are composed of a continuum of multipath components in some channels such as the tropospheric channel. In order to perform measurements of the multipath- intensity profile, a wideband signal, that is, a unit impulse or Dirac delta function, is used. For a single transmitted impulse, the time Tm between the first and last received component is defined as the maximum excess delay during which the multipath signal power typically falls to some level 10-20 dB below that of the strongest component. Note that for an ideal system with zero excess delay, the function A(T) would consist of an ideal impulse with weight equal to the total average received signal power. In the literature, the Fourier trans- form of A(T) is referred to as spaced-frequency correlation function P(v). The spaced- frequency correlation function P(v) represents the channel's response to a pair of sinusoidal signals separated in frequency by V. The coherence bandwidth Afc is a measure of the fre- quency range over which spectral components have a strong likelihood of amplitude corre- lation. In other words, a signal's spectral components over this range are affected by the channel in a similar manner. Note that fo and Tm are inversely proportional (Afc 1 1/Tm). The maximum excess delay Tm is not the best indicator of how a given wireless 