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In wireless communications, signal fading is caused by multi-path effect. Multi-path effect means that a signal transmitted from a transmitter may have multiple copies traversing different paths to reach a receiver. Thus, at the receiver, the received signal should be the sum of all these multi-path signals. Because the paths traversed by these signals are different; some are longer and some are shorter. The one at the direction of light of signal (LOS) should be the shortest. These signals interact with each other. If signals are in phase, they would intensify the resultant signal; otherwise, the resultant signal is weakened due to out of phase. This phenomenon is called channel fading. In general, there are two criteria to measure channel fading, including (1) Doppler spread, and (2) delay spread.
Doppler spread
Due to Doppler effect, if a transmitter is moving away from a receiver, the frequency of the received signal is lower than the one sent out from the transmitter; otherwise, the frequency is increased. In wireless communications, there are many factors that can cause relative movement between a transmitter and a receiver. It can be the movement of a mobile such as a cell phone; it can be the movement of some background objectives, which causes the change of path length between the transmitter and the receiver. The lengths of signal path are often different, which correspond to different movement speeds of transmitter signals, and in turn different frequency shifts on the signal paths. As a result, a frequency spread is caused in the signal spectrum.
Corresponding to Doppler spectrum spread, there is a concept called coherence time, which is related to the reciprocal of the maximum Doppler shit. Coherence time is used to measure a time interval, in which a smaller amount of fading is occurred. Specifically, if the baseband signal varies faster than the coherence time, the distortion from Doppler spread fading is negligible. Such a situation is called slow fading. Otherwise, if the baseband signal varies more slowly than the coherence time, the distortion from Doppler spread fading may be significant. This situation is called fast fading.
Delay spread
The different signal paths between a transmitter and a receiver correspond to different transmission times. For an identical signal pulse from the transmitter, multiple copies of signals are received at the receiver at different moments. The signals on shorter paths reach the receiver earlier than those on longer paths. The direct effect of these unsimultaneous arrivals of signal causes the spread of the original signal in time domain. This spread is called delay spread. The delay spread puts a constraint on the maximum transmission capacity on the wireless channel. Specifically, if the period of baseband data pulse is larger than that of delay spread, inter-symbol interference (ISI) will be generated at the receiver. That is, the data signals on two neighbouring pulse periods are received at the same time, which causes the receiver not to be able to distinguish them. Corresponding to the concept of delay spread, there is a term called coherence bandwidth used to measure the up-limit bandwidth that can be transmitted for a channel to be free of ISI. Coherence bandwidth is defined as 10% of the reciprocal of root mean square (rms) delay delay spread. If the bandwidth of a transmitter signal is less than the channel coherence bandwidth, the channel shows flat fading to be free of ISI. Otherwise, the channel shows frequency selective fading, and may surfer from ISI.
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