When a signal is transmitted, this signal can suffer a distortion caused by reflections and scattered propagation paths in the radio channel, and these phenomenons cause that an identical signal arrives at different times at its destination. These different times are due that to the signal arrives via multiple paths and in different incident angles. The time difference between the arrival moment of the first multipath component and the last one is called delay spread.

In order to compare different multipath channels and to develop some general design guidelines for wireless systems, some parameters are used to quantify the multipath channel. Some of these multipath parameters are the mean excess delay, rms delay spread, and maximum excess delay, and can be determined from a power delay profile. However, the mean excess delay and the rms delay spread are frequently used to quantify the time dispersive properties of wide band multipath channels.

**Mean Excess Delay**

The Mean Excess Delay is the first moment of the power delay profile (PDP) and is defined by

**RMS Delay Spread**

The root-mean-square (RMS) delay spread is probably the most important single measure for the delay time extent of a multipath radio channel. This parameter calculates the standard deviation value of the delay of reflections, weighted proportional to the energy in the reflected waves. This parameter can be considered like the square root of the second central moment of the power delay profile and is defined by

We must take into consideration that these delay are measured relative to the first detectable signal arriving at the receiver at = 0, and their equations do not rely on the absolute power level of P(),but only the relative amplitudes of the multipath components within P().

**Maximum Excess Delay (X dB)**

The maximum excess delay (X dB) of the power delay profile is defined as the time delay value after which the multipath energy falls to X dB below the maximum multipath energy (not necesarily belonging to the first arriving component). It is also called excess delay spread, but in all cases must be specified with a threshold that relates the multipath noise floor to the maximum received multipath component.

The values of these time dispersion parameters also depend on the noise threshold used to process P(), and if this noise is set too low, then the noise will be processed as multipath and thus causing the parameters to be higher.

**Environment**

**Coherence Bandwidth**

Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered “flat”.

If we define Coherence Bandwidth (BC) as the range of frequencies over which the frequency correlation is above 0.9, then

If we define Coherence Bandwidth as the range of frequencies over which the frequency correlation is above 0.5, then

The coherence bandwidth of the channel gives a good indication about the frequency variations of the channel in relation to the bandwidth of the transmitted signal. We can have two different cases, depending on this bandwidth. If a signal with a bandwidth larger than Bc is transmitted through the channel, it will be subject to frequency selective distortion. The channel will be, in this case, referred to as a frequency selective fading channel. However, if the signal transmitted has a bandwidth considerably less than Bc, it will experience amplitude attenuation only with no distortion since the channel characteristics will be the same all over the spectrum of the signal. In this case the channel is referred to as a frequency non-selective (flat) fading channel.

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