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.

In a simple model, a signal ${\displaystyle x(t)}$ transmitted at time ${\displaystyle t_{1}}$ will be received as

where ${\displaystyle h_{t_{1}}(t)}$ is the channel impulse response (CIR) at time ${\displaystyle t_{1}}$. A signal transmitted at time ${\displaystyle t_{2}}$ will be received as

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