Parameters of Multipath channelsParameters of Multipath channels

M.Vignesh pandiM.Vignesh pandi A.VijayasekharA.Vijayasekhar

Coherence BandwidthCoherence Bandwidth

It is a measure of range frequencies over which the channel is It is a measure of range frequencies over which the channel is considered flat.considered flat.

Otherwise it is range frequencies over which two frequency Otherwise it is range frequencies over which two frequency component have a strong potential for amplitude correlation.component have a strong potential for amplitude correlation.

• It is used to characterize the channel in the frequency domain

• It is inversely proportional to the rms delay spread Bc=1/σ ז

•Two sinusoidal with frequency separation greater than Bc are affected quite differently by the channel.

• If the frequency correlation function is above 0.9, than the correlation bandwidth is

Bc=1/50 σ ז•If the frequency correlation function is above 0.5 than the coherence bandwidth is approximately

Bc=1/5 σ ז

Doppler spread and coherence time are parameters are Doppler spread and coherence time are parameters are describes the time varying nature of the channel in a small- describes the time varying nature of the channel in a small- scale region.scale region.

It is defined as the range of frequency over which the received It is defined as the range of frequency over which the received Doppler spectrum is essentially non-zeroDoppler spectrum is essentially non-zero

Doppler spread and Doppler frequency:Doppler spread and Doppler frequency:

Doppler spread BDoppler spread Bdd is defined as the range of frequencies over is defined as the range of frequencies over

which the received Doppler spectrum is essentially non-zero.which the received Doppler spectrum is essentially non-zero.

Doppler spread and coherence timeDoppler spread and coherence time

The maximum Doppler frequency fThe maximum Doppler frequency fd d is give byis give by

ffdd=v/=v/λλλλ =c/f =c/fffdd=v/=v/λλ==v/(c/f)v/(c/f)

ffdd=vf/c=vf/cWhere Where

C-velocity of lightC-velocity of lightV-speed of the mobile, including the speed of the mobileV-speed of the mobile, including the speed of the mobile

environment in m/senvironment in m/s λλ - wavelength of the radio signal in meters and - wavelength of the radio signal in meters andF- radio frequencyF- radio frequency

When a pure sinusoidal tone of frequency fc is transmitted the received When a pure sinusoidal tone of frequency fc is transmitted the received signal spectrum, will have components in the range fc-fd to fc+fdsignal spectrum, will have components in the range fc-fd to fc+fd

where fd is the Doppler shift. where fd is the Doppler shift.

Coherence Time (TCoherence Time (Tcc)) Coherence time is the time duration over which two Coherence time is the time duration over which two

received signal have a strong potential for amplitude received signal have a strong potential for amplitude correlationcorrelation

Distortion is occurred at the receiver, if the reciprocal Distortion is occurred at the receiver, if the reciprocal bandwidth of signal is greater than the coherence time bandwidth of signal is greater than the coherence time for the channelfor the channel

The Doppler spread & coherence time are inversely The Doppler spread & coherence time are inversely proportional to each otherproportional to each other

TTcc≈1/f≈1/fmm

If the time correlation function is above 0.5 than the If the time correlation function is above 0.5 than the coherence time is given ascoherence time is given as

TTcc ≈9/(16≈9/(16ππffmm))

wherewhere

ffmm=maximum Doppler shift=maximum Doppler shift

ffmm=v/=v/λλ If the digital transmission system is used,than the If the digital transmission system is used,than the

coherence time as geometric mean of above two coherence time as geometric mean of above two equation equation

TTcc=√(9/(16=√(9/(16ππffmm22))))

THE ENDTHE END