Coherence time (communications systems)

In communications systems, 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 communications systems, due to Doppler effects.

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 ^[1][2]

Usually, we use the following relation^[2]

References

1. P. Mohana Shankar, Introduction to Wireless Systems, John Wiley & Sons, 2002
2. T.S. Rappaport, Wireless Communications, Prentice Hall, 2002