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The second de nition is the coherence bandwidth, Bc , which describes a bandwidth over which the frequency correlation function is above 0.5 or 50%, or: Bc % 0:2s 1 t 1:35
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There is not any single exact relationship between coherence bandwidth and rms delay spread, and equations (1.34) and (1.35) are only approximate equations [1 6,7 10]. Doppler Spread and Coherence Time. To obtain information about the time varying nature of the channel caused by movements, from either the transmitter/ receiver or scatterers located around them, new parameters, such as the Doppler spread and the coherence time, are usually introduced to describe the time variation phenomena of the channel in a small-scale region. The Doppler spread BD is de ned as a range of frequencies over which the received Doppler spectrum is essentially nonzero. It shows the spectral spreading caused by the time rate of change of the mobile radio channel due to the relative motions of vehicles (and scatterers around them) with respect to the base station. According to [1 4,7 10], the Doppler spread BD depends on the Doppler shift fD and on the angle a between the direction of motion of any vehicle and the direction of arrival of the re ected and/or scattered waves (see Fig. 1.3). If we deal with the complex baseband signal presentation, then we can introduce the following criterion: If the baseband signal bandwidth is greater than the Doppler spread BD , the effects of Doppler shift are negligible at the receiver. Coherence time Tc is the time domain dual of Doppler spread, and it is used to characterize the time varying nature of the frequency dispersiveness of the channel in time coordinates. The relationship between these two-channel characteristics is: Tc % 1 l fm v 1:36
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We can also de ne the coherence time according to [1 4,7 10] as the time duration over which two multipath components of receiving signal have a strong potential for amplitude correlation. One can also de ne the coherence time as the time over which the correlation function of two various signals in the time domain is above 0.5 (or 50%). Then according to [7,10] we get Tc % 9 9l l 0:18 16pfm 16pv v 1:37
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This de nition is approximate and can be improved for modern digital communication channels by combining Equations (1.36) and (1.37) as the geometric mean between the two, this yields Tc % 0:423 l 0:423 fm v 1:38
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FIGURE 1.7. Comparison between signal and channel parameters.
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The de nition of coherence time implies that two signals arriving at the receiver with a time separation greater than Tc are affected differently by the channel. 1.4.5. Types of Fading in Multipath Communication Channels Let us now summarize the effects of fading, which may occur in static or dynamic multipath communication channels. Static Channel. In this case multipath fading is purely spatial and leads to constructive or destructive interference at various points in space, at any given instant in time, depending on the relative phases of the arriving signals. Furthermore, fading in the frequency domain does not change because the two antennas are stationary. The signal parameters, such as the signal bandwidth, Bs, the time of duration, Ts, with respect to the coherent time, Bc, and the coherent bandwidth, Tc, of the channel are shown in Figure 1.7. There are two types of fading that occur in the static channels: A. Flat slow fading (FSF) (see Fig. 1.8), where the following relations between signal parameters of the signal and a channel are valid [7 10]: Tc ) Ts ; 0 BD ( Bs ; st ( Ts ; Bc $ 0:02 ) Bs st 1:39
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Here all harmonics of the total signal are coherent. B. Flat fast fading (FFF) (see Fig. 1.9), where the following relations between the parameters of a channel and the signal are valid [7 10]: Tc ) Ts ; 0 BD ( Bs ; st 4Ts ; Bc ( B s 1:40
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