To compare the different multipath channels and to quantify them, we define some parameters. They all can be determined from the power delay profile. These parameters can be broadly divided in to two types.

Time Dispersion Parameters

These parameters include the mean excess delay,rms delay spread and excess delay spread. The mean excess delay is the first moment of the power delay profile and is defined as

$\overline{\tau}=\frac{\sum_{k} a_{k}^{2} \tau_{k}}{\sum_{k} a_{k}^{2}}=\frac{\sum_{k} P\left(\tau_{k}\right) \tau_{k}}{\sum_{k} P\left(\tau_{k}\right)}$

The rms delay spread is the square root of the second central moment of the power delay profile and is defined to be

$\sigma_{\tau}=\sqrt{\tau^{2}-(\overline{\tau})^{2}}$

Where,

$\overline{\tau^{2}}=\frac{\sum_{k} a_{k}^{2} \tau_{k}^{2}}{\sum_{k} a_{k}^{2}}=\frac{\sum_{k} P\left(\tau_{k}\right) \tau_{k}^{2}}{\sum_{k} P\left(\tau_{k}\right)}$

Coherence Bandwidth

While the delay spread is a natural phenomenon caused by reflected and scattered propagation paths in the radio channel, the coherence bandwidth, $B_{c},$ is a defined relation derived from the rms delay spread.

Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered "flat" (i.e., a channel which passes all spectral components with approximately equal gain and linear phase).

In other words, coherence bandwidth is the range of frequencies over which two frequency components have a strong potential for amplitude correlation.

Two sinusoids with frequency separation greater than $B_{c}$ are affected quite differently by the channel. If the coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above $0.9,$ then the coherence bandwidth is approximately

$$B_{c} \approx \frac{1}{50 \sigma_{\tau}}$$

If the definition is relaxed so that the frequency correlation function is above $0.5,$ then the coherence bandwidth is approximately

$$B_{c} \approx \frac{1}{5 \sigma_{\tau}}$$

It is important to note that an exact relationship between coherence bandwidth and rms delay spread is a function of specific channel impulse responses and applied signals, and both equations are "ball park estimates."