Delay spread

In telecommunications, the delay spread is a measure of the multipath richness of a communications channel. In general, it can be interpreted as the difference between the time of arrival of the earliest significant multipath component (typically the line-of-sight component) and the time of arrival of the latest multipath component. The delay spread is mostly used in the characterization of wireless channels, but it also applies to any other multipath channel (e.g. multipath in optical fibers).

Delay spread can be quantified through different metrics, although the most common one is the root mean square (rms) delay spread, which is defined as follows: According to Goldsmith , let $A_{c}(\tau )$ be the power delay profile of a channel. Then, the mean delay of the channel is

${\overline {\tau }}={\frac {\int _{0}^{\infty }\tau A_{c}(\tau )d\tau }{\int _{0}^{\infty }A_{c}(\tau )d\tau }}$

Thus, the rms delay spread is

$\tau _{\text{rms}}={\sqrt {\frac {\int _{0}^{\infty }(\tau -{\overline {\tau }})^{2}A_{c}(\tau )d\tau }{\int _{0}^{\infty }A_{c}(\tau )d\tau }}}$

Bibliography

• Saunders, Antennas and propagation for Wireless communication systems, 2nd ed, pp246-250, 2007

External links

• Delay spread in wireless communications