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If the delay spread D over a particular cellular communication path in an urban environment is 1.9 μs, then using equation above, the coherence bandwidth is approximately 0.53 MHz, which results in frequency selective fading over the IS-95 bandwidth.
The correspondence with the frequency domain is the notion of coherence bandwidth (CB), which is the bandwidth over which the channel can be assumed flat (i.e. channel that passes all spectral components with approximately equal gain and linear phase.). Coherence bandwidth is related to the inverse of the delay spread. The shorter the delay ...
Coherence time is actually a statistical measure of the time duration over which the channel impulse response is essentially invariant, and quantifies the similarity of the channel response at different times. In other words, coherence time is the time duration over which two received signals have a strong potential for amplitude correlation.
Small delay differences, or delay spread, smear adjacent modulation symbols together and cause unwanted intersymbol interference. Delay spread is inversely proportional to its frequency-domain counterpart, coherence bandwidth. This is the frequency range over which the channel gain is relatively constant.
The coherence time of the channel is related to a quantity known as the Doppler spread of the channel. When a user (or reflectors in its environment) is moving, the user's velocity causes a shift in the frequency of the signal transmitted along each signal path.
The so-called coherence bandwidth is thus defined as B C ≈ 1 T M {\displaystyle B_{C}\approx {\frac {1}{T_{M}}}} For example, with a multipath time of 3 μs (corresponding to a 1 km of added on-air travel for the last received impulse), there is a coherence bandwidth of about 330 kHz.
The resulting visibility of the interference pattern (e.g. see Figure 4) gives the temporal coherence at delay . Since for most natural light sources, the coherence time is much shorter than the time resolution of any detector, the detector itself does the time averaging. Consider the example shown in Figure 3.
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.