Parameters of Mobile Multipath Channels

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5.4 Parameters of Mobile Multipath Channels

Many multipath channel parameters are derived from the power delay profile, given

by Equation (5.18). Power delay profiles are measured using the techniques discussed

in Section 5.4 and are generally represented as plots of relative received power as

a function of excess delay with respect to a fixed time delay reference. Power delay

profiles are found by averaging instantaneous power delay profile measurements over

a local area in order to determine an average small-scale power delay profile.

Depending on the time resolution of the probing pulse and the type of multipath channels

studied, researchers often choose to sample at spatial separations of a quarter of a

wavelength and over receiver movements no greater than 6 m in outdoor channels

and no greater than 2 m in indoor channels in the 450 MHz–6 GHz range. This small-scale

sampling avoids large-scale averaging bias in the resulting small-scale statistics.

Figure 5.9 shows typical power delay profile plots from outdoor and indoor channels,

determined from a large number of closely sampled instantaneous profiles.

[+] Enlarge Image

Figure 5.9 Measured multipath power delay profiles: a) From a 900 MHz cellular

system in San Francisco [from [Rap90] © IEEE]; b) inside a grocery store at

4 GHz [from [Haw91] © IEEE].

5.4.1 Time Dispersion Parameters

In order to compare different multipath channels and to develop some general design

guidelines for wireless systems, parameters which grossly quantify the multipath channel

are used. The meanexcess delay, rms delay spread, and excess delay spread (X dB) are

multipath channel parameters that can be determined from a power delay profile.

The time dispersive properties of wide band multipath channels are most commonly

quantified by their mean excess delay  and rms delay spread  The mean excess

delay is the first moment of the power delay profile and is defined to be

The rms delay spread is the square root of the second central moment of the

power delay profile and is defined to be

where

These delays are measured relative to the first detectable signal arriving at the

receiver at . Equations (5.35)–(5.37) do not rely on the absolute power level

of , but only the relative amplitudes of the multipath components within . Typical

values of rms delay spread are on the order of microseconds in outdoor mobile

radio channels and on the order of nanoseconds in indoor radio channels.

Table 5.1 shows the typical measured values of rms delay spread.

It is important to note that the rms delay spread and mean excess delay are

defined from a single power delay profile which is the temporal or spatial

average of consecutive impulse response measurements collected and averaged

over a local area. Typically, many measurements are made at many local areas in

order to determine a statistical range of multipath channel parameters for a mobile

communication system over a large-scale area [Rap90].

The maximum excess delay (X dB) of the power delay profile is defined to be the

time delay during which multipath energy falls to X dB below the maximum.

In other words, the maximum excess delay is defined as , where  is the

first arriving signal and is the maximum delay at which a multipath component is

within X dB of the strongest arriving multipath signal (which does not necessarily

arrive at  ). Figure 5.10 illustrates the computation of the maximum excess delay for

multipath components within 10 dB of the maximum. The maximum excess delay

(X dB) defines the temporal extent of the multipath that is above a particular threshold.

The value of  is sometimes called the excess delay spread of a power delay profile,

but in all cases must be specified with a threshold that relates the multipath noise floor

to the maximum received multipath component.

[+] Enlarge Image

Figure 5.10 Example of an indoor power delay profile; rms delay spread, mean excess delay,

maximum excess delay (10 dB), and threshold level are shown.

 

In practice, values  for and  depend on the choice of noise threshold used to process

P(τ). The noise threshold is used to differentiate between received multipath components

and thermal noise. If the noise threshold is set too low, then noise will be processed as multipath,

thus giving rise to values of  and  that are artificially high.

It should be noted that the power delay profile and the magnitude frequency response (the

spectral response) of a mobile radio channel are related through the Fourier transform.

It is therefore possible to obtain an equivalent description of the channel in the frequency

domain using its frequency response characteristics. Analogous to the delay spread

parameters in the time domain,coherence bandwidth is used to characterize the channel in

the frequency domain. The rms delay spread and coherence bandwidth are inversely

proportional to one another, although their exact relationship is a function of the exact

multipath structure.

Example 5.4

Compute the RMS delay spread for the following power delay profile:

(b) If BPSK modulation is used, what is the maximum bit rate that can

be sent through the channel without needing an equalizer?

Relevant NI products

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