 distri- bution, as shown in Figure 9-3. In a time-varying fading channel, the channel response to a pure sinusoidal tone spreads over a finite frequency range of Vc - Vmax V < Vc + 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: (9-7) where (9-8) CHAPTER 9 The IEEE 802. 16m Physical Layer (Part I) 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 T 11 1/V RMS. A common approximation for the value of coherence time as a function of Doppler spread is Tc = 0.423/ VRMS. It can be observed that the functions on the right side of Figure 9-3 are the dual of the functions on the left side (duality principle). The angle spread refers to the spread in angle of arrival (AoA) of the multipath components at the receiver antenna array. At the transmitter, on the other hand, the angle spread refers to the spread in the angle of departure (AoD) of the multipath components that leave the transmit antennas. If the angle spectrum function (A) denotes the average power as a function of AoA, then the RMS angle spread can be estimated as: (9-9) where (9-10) The angle spread causes space selective fading, which manifests itself as a variation of signal amplitude according to the location of the antennas. The space selective fading is characterized by the coherence distance Dc, which is the spatial separation at which the autocorrelation coefficient of the spatial fading reduces to 0.7. The coherence distance is inversely proportional to the angle spread Dc 1/ORMS. In Figure 9-3, a duality between multipath intensity function A(T) and Doppler power spectrum A(v) is identified. It means that the two functions exhibit similar behavior across time domain and frequency domains. As the A(T) function identifies expected power of th