In communications system

Communications system

In telecommunication, a communications system is a collection of individual communications networks, transmission systems, relay stations, tributary stations, and data terminal equipment usually capable of interconnection and interoperation to form an integrated whole...

s, a communication channel may change with time. Coherence time is the time duration over which the channel impulse response is considered to be not varying. Such channel variation is much more significant in wireless

Wireless

Wireless telecommunications is the transfer of information between two or more points that are not physically connected. Distances can be short, such as a few meters for television remote control, or as far as thousands or even millions of kilometers for deep-space radio communications...

 communications systems, due to Doppler effect

Doppler effect

The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

s.

Simple model

In a simple model, a signal transmitted at time will be received as
where is the channel impulse response (CIR) at time . A signal transmitted at time will be received as
Now, if is relatively small, the channel may be considered constant within the interval to .

Coherence time () will therefore be given by

Relation with Doppler frequency

Using Clarke's model, from the maximum Doppler frequency we can obtain 50% coherence time
Usually, we use the following relation