unction, which is the autocorrelation function of the channel's response to a sinusoid. This function specifies the extent to which there is correlation between the channel's response to a sinusoid sent at time t1 and the response to a similar sinusoid sent at time t2, where At = t2 - t1. The coher- ence time is a measure of the expected time duration over which the channel's response is essentially invariant. To estimate P(t), a sinusoidal signal is transmitted through the chan- nel and the autocorrelation function of the channel output is calculated. The function P(t) and the coherence time T provide information about the rate of fading channel variation. Note that for an ideal time-invariant channel, the channel's response would be highly cor- related for all values of At and P(t) would be a constant function. If one ideally assumes uniformly distributed scattering around a mobile station with linearly polarized antennas, the Doppler power spectrum (i.e., the inverse Fourier transform of spaced-time correlation function A(v)) has a U-shaped distribution as shown in Fig. 3.3. In a time-varying fading channel, the channel response to a pure sinusoidal tone spreads over a finite frequency range Vc - Vmax + Vmax, where Vc and Vmax denote the frequency of the sinusoidal tone and the maximum Doppler spread, respectively. The RMS bandwidth of A(v) is referred to as Doppler spread and is denoted by VRMS that can be estimated as follows: VRMS = The coherence time is typically defined as the time lag for which the signal autocorrelation coefficient reduces to 0.7. The coherence time is inversely proportional to Doppler spread Tc 2 VRMS. A common approximation for the value of coherence time as a function of Doppler spread is T = 0.423/VRMS. It can be observed that the functions on the right side of Fig. 3.3 are dual of the functions on the left side (duality principle). 3.1.1.4 Angular Spread The angle spread refers to the spread in AoA of the multipath components at the receiver antenna array. At the transmitter, on th