Question

Write notes on Doppler spread and coherence time

Answer 1

Doppler Spread and Coherence Time
Delay spread and coherence bandwidth are parameters which describe the time dispersive nature

of the channel in a local area. However, they do not offer information about the time varying

nature of the channel caused by either relative motion between the mobile and base station, or by

movement of objects in the channel. Doppler spread and coherence time are parameters which

describe the time varying nature of the channel in a small-scale region.

Doppler spread BD is a measure of the spectral broadening caused by the time rate of

change of the mobile radio channel and is defined as the range of frequencies over which the

received Doppler spectrum is essentially non-zero. When a pure sinusoidal tone of frequency

fc is transmitted, the received signal spectrum, called the Doppler spectrum, will have components

in the range fc – fd to fc + fd ,where fd is the Doppler shift. The amount of spectral broadening

depends on fd which is a function of the relative velocity of the mobile, and the angle θ

between the direction of motion of the mobile and direction of arrival of the scattered waves. If

the baseband signal bandwidth is much greater than BD the effects of Doppler spread are negligible

at the receiver. This is a slow fading channel.

Coherence time Tc is the time domain dual of Doppler spread and is used to characterize

the time varying nature of the frequency dispersiveness of the channel in the time domain. The

Doppler spread and coherence time are inversely proportional to one another. That is,



Coherence time is actually a statistical measure of the time duration over which the channel

impulse response is essentially invariant, and quantifies the similarity of the channel

response at different times. In other words, coherence time is the time duration over which two

received signals have a strong potential for amplitude correlation. If the reciprocal bandwidth of

the baseband signal is greater than the coherence time of the channel, then the channel will

change during the transmission of the baseband message, thus causing distortion at the receiver.

If the coherence time is defined as the time over which the time correlation function is above 0.5,

then the coherence time is approximately [Ste94]



where fm is the maximum Doppler shift given by fm = v ⁄ λ . In practice, (5.40.a) suggests a

time duration during which a Rayleigh fading signal may fluctuate wildly, and (5.40.b) is often

too restrictive. A popular rule of thumb for modern digital communications is to define the

coherence time as the geometric mean of Equations (5.40.a) and (5.40.b). That is,



The definition of coherence time implies that two signals arriving with a time separation

greater than TC are affected differently by the channel. For example, for a vehicle traveling

60 mph using a 900 MHz carrier, a conservative value TC of can be shown to be 2.22 ms from

Equation (5.40.b). If a digital transmission system is used, then as long as the symbol rate is

greater than 1 ⁄ TC = 454, the channel will not cause distortion due to motion (however,

distortion could result from multipath time delay spread, depending on the channel impulse

response). Using the practical formula of (5.40.c), TC = 6.77 ms and the symbol rate must

exceed 150 bits/s in order to avoid distortion due to frequency dispersion.

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