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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.
If the symbol duration is long enough compared to the delay spread (typically 10 times as big would be good enough), one can expect an equivalent ISI-free channel. 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 ...
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.
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 coherence of a linear system therefore represents the fractional part of the output signal power that is produced by the input at that frequency. We can also view the quantity 1 − C x y {\displaystyle 1-C_{xy}} as an estimate of the fractional power of the output that is not contributed by the input at a particular frequency.
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.
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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.