Doppler Spread and Coherence Time

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5.4.3 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 B_D 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

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

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

depends on f_d 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 B_D the effects of Doppler spread are negligible

at the receiver. This is a slow fading channel.

Coherence time T_c 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 f_m 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 T_C are affected differently by the channel. For example, for a vehicle traveling

60 mph using a 900 MHz carrier, a conservative value T_C 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 ⁄ T_C = 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), T_C = 6.77 ms and the symbol rate must

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

Example 5.6

Determine the proper spatial sampling interval required to make smallscale

propagation measurements which assume that consecutive samples

are highly correlated in time. How many samples will be required over 10 m

travel distance if f_c = 1900 MHz and v = 50 m/s. How long would it take to

make these measurements, assuming they could be made in real time from

a moving vehicle? What is the Doppler spread B_D for the channel?

Solution

For correlation, ensure that the time between samples is equal to T_C /2 and

use the smallest value of T_C for conservative design.

Using Equation (5.40.b)

Taking time samples at less than half T_C, at 282.5 μs corresponds to a

spatial sampling interval of

Therefore, the number of samples required over a 10 m travel distance is

The time taken to make this measurement is equal to

The Doppler spread is

Relevant NI products

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