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A! 3/17Received power

Received power at receiver base-band input

/Rx Tx Tx Rx Rx Txpath

P P G G L L L

o Trasmitted/receiver power:/Rx Tx

P

o Path loss:path

L

Frequency dependence will be returned to

o Transmit/receive antenna gains:/

/2

4Rx Tx

Rx TxA

G

Wavelength:

Effective antenna aperture (size):/Rx Tx

A

Antenna directivity proportional to aperture size/

2

Measured over an isotropic antenna radiating to 4 solid angle

Isotropic radiator has G=1 (0 dBi)

Typical value for omni antenna BS: G=13 dBi, for MS: G=2dBi

BS gain from concentrating radiation in horizontal plane

o Receiver/Transmitter losses (cable /connector losses etc), :/Rx Tx

L

A! 4/17Noise power

Thermal noise level /0

W HzT B

N k T

o Bolzmans constant: /231.3807 10 J KBk

o Noise temperature:0

T

o At 20P

PC,0

293KT and 21 / 174 /4.0410T

W Hz dBm HzN

Noise power spectral density0 0 FB

N k T N

o White noise power spectral density at base band

o Receiver noise figureF

N

Additional signal degradation in analog parts of receiver,

typically 5-9 dB

Received noise power:0 0

N N B

o noise floor

o Noise bandwidth:0

B


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A! 5/17

Signal-to-noise Power Ratio

Signal-to-noise power ratio

o Ratio of power per modulated symbol and noise

o Assume: Noise bandwidth = Modulated symbol rate:S

R

o Energy per symbol ES= PRx/RS

A! 6/17Receiver Sensitivity

=

The smaller the sensitivity, the better the receiver

Noise power on modulated symbol bandwidth 0 SN R affects sensitivityo E.g. if

SR =12 kbps,

0 SN R = -131 dBm + noise figure

o E.g. ifS

R =384 kbps,0 S

N R = -118 dBm + noise figure

Required minimum SNR for reliable reception:0 min

/S

E N

o The connection to baseband (BB) processing

o Depends on the modulation & coding scheme & BB receiver details

o Note: if performance of modulation is characterized in terms of0

/b

E N ,

energy per bit is 2/logSbE E MwhereMis the number of constellation

points and 2logMis the number of bits per symbol

Rx sensitivity is a measurable quantity Testing & standardization


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A! 7/17Fading and Interference Margins

Various statistical system impairments may be taken into account in

the link budget by using margins.

o Alternatively, statistical impairments can be taken into account

directly in the sensitivity when defining 0 min/SE N

o Or, packet radios are constructed to exploit the impairments

throughput analysis instead of link budgeting

Fast Fading Margin (FFM)

o Increase in average received power required to guarantee service

availability with given probability, taking fast fading into account

o Fast fading distribution assumed known, e.g. Rayleigh

distribution

Shadow Fading Margin (SFM)

o As above

Interference Margin (IM)

o Increase in the received power required to guarantee service

availability taking a specified interference scenario into account

A! 8/17Link Budget

Link budget = minimum received power required allowing reliable service

Linear scale: / / /Rx Rx

S P FFM SFM IM

dB-scale:Rx Rx

S P FFM SFM IM


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A! 9/17

Channel Model

- propagation effects created by the physical medium

A! 10/17Large and Small scale effects of Channel

Large scale effects:

1. Average path loss as function of

distance

2. Shadow fading due to largeobstacles (slow fading)

Small scale effects:

3. (Fast) fading & Multipath effects

lg r

pathloss(dB)


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A! 10/17Path loss as function of distance

The instantaneous path loss in dB-domain is path sf ffL L L L

Lis the distance-dependent average path loss in dB

sfL is the additional slow fade loss caused by large nearby obstacles,

changes over distances of tens of meters

ffL is the additional loss caused by multipath propagation interference (fast fading)

changes over distances of half a wavelength

sfL and ffL are modelled as random variables.

In link budget calculations slow & fast fading are taken into account

by defining a slow fade margin (SFM), e.g. giving a certain degree of coverage at cell

border or in the entire cell, and

by defining a fast fade margin (FFM) or including the effects of multipath fading

into the receiver sensitivity

or by calculating a receiver sensitivity for a specific channel with a specific receiver

(Es/N0 target)

A! 11/17Free Space Average Path Loss

average path loss in free space:

24

pathL r

o distance between Tx and Rx: r

o frequency (wave-length: )

the higher frequency, the larger path loss

this is not a law of nature, but a consequence of the definition of

antenna gains

path loss with Rx antenna gain:2

/4

RxA

G LRx path r

o no dependence of frequency

o fraction of the whole space solid angle seen by the antenna aperture

In other propagation environments (non-free space), similar path loss

models are used

o Path loss exponent changed from 2 , =1, 6

o Fitting to measurement results.

o if


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A! 12/17Average path loss as function of distance between

transmitter and receiver

single-slope model is often used

10 lgo oL L r r (dB)

oL is the average path loss at the reference distancer BoB, (e.g. 1 km, 1m etc.)

10 lg(4 / ) 10 lg(4 / )o o o oL r r f c

where the speed of light isc=3*10P8

Pm/s and of is the carrier frequency

is the path loss exponent, which depends on:

antenna heights

frequency

propagation environment

Example: Free space propagation at 2 GHz: = 2

92.45 20 lg(2) 98.47oL if ris given in km (i.e.r BoB= 1 km)

A! 13/17

Shadow Fading


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A! 14/17

Shadow (Slow) Fading

models large scale deviations from the average path loss

buildings, trees, etcmodelled statistically by a log-normal random variable

2

2

( )

21( )

2

i

L

L L

L

p L e

oL is the attenuation in dB (this makes it log-normal)

oLi is the average distance-dependent path loss

o Lis the standard deviation of the shadow fading, typically 6-8 dB

Shadow fading correlation:

o The shadow fading of paths to/from different base stations may be

correlated

Often shadow fading correlation 0.5 is assumed between base

stations

o The shadow fading at different MS locations are correlated

Often a correlation distance of 50 m is assumed for MS locations

A! 15/17Shadow Fading Margin

In link budget calculations, shadow fading may be taken into account

through a shadow fading margin

By adding a margin SFM Lin the link budget, you can guarantee the

availabilityof the link budgeted service with probability P

o Outage probability due to shadow fading would be 1 PProbability that path loss L [dB] is larger than average path loss 1L + L is

1

2 212

1 1

exp exp22

2 2

L

L

LL

LL L

L L x

LP L L L P L L L dL dx Q

L L90%50%

L

90%

=150.0 dB

SFM

= Lpath


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A! 16/17Fast Fading, Recapitulation

Fast fading channel channel coefficients ( )nh t are modelled as random

variables

Most commonly ( )nh t modeled by zero mean complex Gaussiandistribution

2

1( )

h

Pp h eP

o The average power channel power is P

Whenhis complex Gaussian, amplitude is Rayleigh distributed

Channel power 2 2| |P h a has exponential distribution

1( )

P

Pp P eP

link budget formula.pdf

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