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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.
Coherence bandwidth is a statistical measurement of the range of frequencies over which the channel can be considered "flat", [1]: 7 or in other words the approximate maximum bandwidth or frequency interval over which two frequencies of a signal are likely to experience comparable or correlated amplitude fading.
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 ...
The most challenging case is when the delay and Doppler spreads are both large, i.e., the coherence bandwidth and coherence time are both small. This is more common on auroral and EME channels than on HF, but it can occur. A short coherence time limits the symbol time, or more precisely, the maximum coherent detection interval at the receiver.
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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It is easily measured empirically and can be used to extract certain channels' parameters such as the delay spread. For Small Scale channel modeling, the power delay profile of the channel is found by taking the spatial average of the channel's baseband impulse response i.e. | (,) | over a local area. [1]