Coherence Bandwidth

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5.4.2 Coherence Bandwidth

While the delay spread is a natural phenomenon caused by reflected and scattered propagation paths

in the radio channel, the coherence bandwidth, B_c, is a defined relation derived from the rms delay

spread. Coherence bandwidth is a statistical measure of the range of frequencies over which the

channel can be considered “flat” (i.e., a channel which passes all spectral components with

approximately equal gain and linear phase). In other words, coherence bandwidth is the range of

frequencies over which two frequency components have a strong potential for amplitude

correlation. Two sinusoids with frequency separation greater than B_c are affected quite differently

by the channel. If the coherence bandwidth is defined as the bandwidth over which the frequency

correlation function is above 0.9, then the coherence bandwidth is approximately [Lee89b]

If the definition is relaxed so that the frequency correlation function is above 0.5, then the coherence

bandwidth is approximately

It is important to note that an exact relationship between coherence bandwidth and rms delay

spread is a funtion of specific channel impulse responses and applied signals, and Equations (5.38)

and (5.39) are “ball park estimates.” In general, spectral analysis techniques and simulation are

required to determine the exact impact that time varying multipath has on a particular transmitted

signal [Chu87], [Fun93], [Ste94]. For this reason, accurate multipath channel models must be used

in the design of specific modems for wireless applications [Rap91a], [Woe94].

Example 5.5

Calculate the mean excess delay, rms delay spread, and the maximum

excess delay (10 dB) for the multipath profile given in the figure below.

Estimate the 50% coherence bandwidth of the channel. Would this channel

be suitable for AMPS or GSM service without the use of an equalizer?

Solution

Using the definition of maximum excess delay (10 dB), it can be seen that

τ₁₀ dB is 5 μs. The rms delay spread for the given multipath profile can be

obtained using Equations (5.35)–(5.37). The delays of each profile are measured

relative to the first detectable signal. The mean excess delay for the

given profile is

The second moment for the given power delay profile can be calculated as

Therefore the rms delay spread is

The coherence bandwidth is found from Equation (5.39) to be

Since B_c is greater than 30 kHz, AMPS will work without an equalizer. However,

GSM requires 200 kHz bandwidth which exceeds B_c, thus an equalizer

would be needed for this channel.

Relevant NI products

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