Wireless Ch

8/10/2019 Wireless Ch

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Fahreddin Sadkolu 1

Propogation Path Loss. FadingL2- Topics

Multipath characteristics of radio waves Long and short-term fading Rayleigh and Rician fadings

Long Term Fading Okumara Hata model for median loss Delay spread. Intersymbol interferences

Coherence Bandwidth Doppler spread


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Fahreddin Sadkolu 2

Multipath characteristics of radiowaves

Multipath occurs when radio waves arrive at a mobile receiver fromdifferent direction with different magnitude and time delays. As mobileterminal moves from one location to another the phase relationshipbetween the various incomming waves also change. Thus there aresubstantial amplitude and phase fluctations. This is known as fading.


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Fahreddin Sadkolu 3

Fast fading- rapid fluctations of amplitude when mobile terminal movesshort distance. FF is due to reflection of local objects and motionof user from this objects.

Slow fading arises when there are large reflected and difracted objects alongthe transmission path. The motion of the terminal to these distantobjects is small and corresponding propogation change slowly.

Short term fading r(t)

Long termFading m(t)

Power

Time

Existing the motion yields a Doppler shift of the frequency

in the received signal

Reseived signal s(t)=m(t).r(t)


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Fahreddin Sadkolu 4

Long and short-term fadingfast fading (Short term fading): rapid fluctuation is observed over distances

of about /2 . For VHF and UHF, a vehicle traveling at 30mph can pass through several fast fades in a second.

slow fading (Long-term) : path loss variation caused by changes in lands cape, i.e., building . variation.

In City

Out of City


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Fahreddin Sadkolu 5

Short term fadingProbability density function of short term fading is given by Rayleigh distributions.

02 )/2Pr(

0

ePrp(r)

2P0=22 is mean square power of the component subjected to STF; r 2 is instantenous power

02 /2PR e1P(R)R)P(r

r mean =1.25 ; Mean square 2P 0 = 2 2; Variance r 2=0.429 2; Median value r m=1.177


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Fahreddin Sadkolu 6

Level crossing rate and Average fade durationLCR N(R ), at the specified signal level R is defined as average number of times per second that thesignal envelope crocess the level in positive going directions (r>0).

v

2N(R)

Average fade duration:

Or N(R) =n 0n R

rmsR

R

2

R ; R rms- rms amplitude of the fading envelope; V-speed; -carrier wavelength

2R en

- is called normalized level-crossing rate. / f ;f 2n mm0

2

n1e

(R) 0

2


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Fahreddin Sadkolu 7

Rician FadingWhen there is dominanr signal component (ex. LOS), the SCF envelope distribution is Rician

distribution:

0r and0Afor ];[Ar/ .Ier

p(r) 20]

2

Ar [

2

2

22

Rician factor[dB]

2

A10logK 2

2

as A 0 Rician distribution degenerates to Rayleigh distribution

Long Term Fading

Probability density function is given by log-Normal distribution

])/2 m(Logme[2m

1p(m) 2m0m

m 0 is the mean of log m.


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Fahreddin Sadkolu 8

Ricean and Rayleigh fading distributions

Rayleigh fading

Rician fading


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Fahreddin Sadkolu 9

Delay spread. Coherence Bandwidth. Doppler Shift

Intersymbol interference (ISI) occurs if the delay spread of the channelexceeds the symbol time (or the sampling interval)

Cancellation of ISI is done via an equalizer at the receiver

1. Delay spread

BS

MUDirect

Reflected


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Fahreddin Sadkolu 10

d

Environment Delay spread ( s)

Open area


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Coherence BandwidthThe coherence B c is the bandwidth for which either amplitudes or phases of two receiversignals have a high degree of similarity. Bc is a statistical measure of range of frequencies

over which yhe channel passes all spectral components with approximately equal gain andlinear phase.

max

1

d c B

More useful measurement is often expressed in terms of rms delay spread drms . Two fading signal with frequencies f 1 and f 2, where f= | f 1-f 2 |, ifcorrelation function nbetween two faded signal R( f)=0.5, then

drmsc B f 2

1

More popular approximation isdrms

c B f 51

Bc1/Ts=Bw corresponds to flat fading (all freq. components are affected by channel a similarmanner) channel channel

For GSM Bw =200 kHz , an urban environment drms =2 s .and from (3) Bc=100 kHz


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Doppler spreadDoppler shift. If receiver is moving toward the source, then zero crossing ofthe signal appear faster, and receiver frequency becomes higher. The oppositeeffect occurs if the receiver moving away from the source.The resulting changeKnown as the Doppler shift.

f 0- carrier transmitted frequency; v-speed of moving; - angle betweenterminal motion and signal radiation directions.

Dopler spread. Dopler shift of each arriving path is generally different.Dopler spread is estimated by coherence time T 0=1/fd .

A popular rule to define T 0

d20 f

0.423f 16

9T d

Fast fading channel : BwT 0

Slow fading channel : Bw>f d or T s


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Emprical models1. Hata Okumara Model

1. Urban areaL 50= 69.55+26.16log f c-13.82log h b-a(hm)+(44.9-6.55log h b)log R L 50 median path loss with dB; fc=100-1500 MHz-frequency range;h b=30-200m-BS antenna height; R=1-20km distance from BSCorrection factor for mobile antenna height - a(hm)

For asmall or medium-sized city:a(hm)=(1.1fc-0.7)h m-(1.56 log fc-0.8) dB; h m =1-10 m-mobil e antenna height

2. Suburban areaL 50= L 50(urban)-2[log (fc/28) 2-5.4] dB

2. Open areaL 50= L 50(urban)-4.78log (fc)2+18.33log fc-40.94] dB


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Capacity of Communication Channel

Bw R

N E B

B N S BC bw

ww

02

02 1log1log

C-channel capacity (bits/s); Bw-one-way transmission bandwidth(Hz); Eb-energy per bit;R-inforemation rate (bits/s); S=E

bR-signal power; N

0 noise power spectral dencity.

An ideal systems R=C, and

w

b

b

BC

N E

BwC

N E

BwC

;12

1log

0

02

1/16 1/8 1/4 1/2

1 2 3 4-1.6

E b/N0(dB)

R/Bw

R/Bw>1Banwidth limited

R/Bw

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