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Politecnico di MilanoFacoltà di Ingegneria dell’Informazione

MRN-1 – Cell dimensioning

Mobile Radio NetworksProf. Antonio Capone

Cell radius

o How can we calculate the coverage radius of a radio base station?

o It should be quite easy, given:n PT = transmitted power (dBm)n Pth = receiver threshold (dBm) – receiver sensibilityn LP=PT - Pth maximum path loss

o We calculate the radius from the formula of LP as a function of the distance:n Propagation factor h:

n or using Okumura-Hata model

÷÷ø

öççè

æ×=

010log10)(dddLP h

A. Capone: Mobile Radio Networks 2

Exampleo Given:

n Received power at 10 m = 100 mWn Receiver threshold: Pth= -50 dBmn h = 3.7

o We get:

mR

RR

PdRdPRP

mPdP

thdBmRdBmR

dBmRdBmR

7801010

3770

10log50

10log3720

log10)()(

20)100(log10)10()(

3770

1010

010][0][

10][][0

=×=®

=÷øö

çèæ®-=÷

øö

çèæ-

=÷÷ø

öççè

æ-=

===

h

The outage probability at cell edge is however in this case 50%! Why?


Fading margin

o The example does not consider the shadowing that causes deviations from the value estimated by propagation models based on distance

o It is possible to consider shadowing reducing the cell radius for taking a safety margin on the variations of received power

o Fading marginn M = power at cell edge (dBm) –

receiver threshold (dBm)

Average path loss M

Pdf of path loss

LP=PT - Pth

LP=PT - Pth - M


Example (continuation)o Given:

n Received power at 10 m = 100 mWn Receiver threshold: Pth= -50 dBmn h = 3.7n Log-normal shadowing with sdB=4dBn Fading margin M=6 dB

o We get:

mRR

MPdRdPRP thdBmRdBmR

537101065010

log3720

log10)()(

3764

10

010][0][

=×=®+-=÷øö

çèæ-

+=÷÷ø

öççè

æ-= h


Outage probabilityo Since shadowing has a log-normal distribution which in

dB is Gaussian, we have:

fPdB (r ) (x) = 12π ⋅σ dB

e− x−PdB (r )( )2 /2σ dB2

PdB (r) = power at distance r, PdB (r) = ave. value

Outage is experienced when power < Pth (dB):

÷÷ø

öççè

æ -== ò

¥- dB

thdBP

rPoutPrPerfcdxxfr

th

dB s2)(

21)()(Pr )(


Outage probabilityo Re-writing power as a function of its value at cell edge (R)

we get:

PdB (r) = PdB (R)−10η log10rR

o And then:

÷÷ø

öççè

æ -=

=÷÷ø

öççè

æ --=

dB

dB

thdBout

RrMerfc

RrPRPerfcr

sh

sh

2/log10

21

2/log10)(

21)(Pr

10

10

÷÷ø

öççè

æ=

dBout

MerfcRs22

1)(Pr

o Obviously at cell edge:


Example (continuation)

o Then: Prout(R)=6.68%

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

400 500 600 700

r

Out

age

prob

abili

ty

■ PdB(10 m)= 20 dBm■ Pth= -50 dBm■ h = 3.7■ sdB=4dB■ M=6 dB■ R=537 m

Remind that: ϕ(x) = 12

1+ erf x2

!

"#

$

%&

'

()

*

+,, where ϕ(x) is the CDF of the normal distribution

and then: erfc(x) = 2 1−ϕ x 2( )'(

*+


Outage areao To calculate the outage area in a circular area

of radius R we just need to integrate:

ò

ò

ò

ò

÷ø

öçè

æ -=

=÷÷ø

öççè

æ -=

=÷÷ø

öççè

æ -=

==

1

0

1

0

10

0

10

02

2ln)ln(

2log10

2/log10

2)(Pr1)(Pr

dxxmerfcx

dxxMerfcx

RdrRrMerfc

Rr

drrrR

R

dB

R

dB

R

outAout

sh

sh

sh

pp

[ ][ ]ï

ïî

ïïí

ì

==

=

mWPmWRPm

th

M

dB

)(10

10

10ln

10/

ss


Outage area

o Let us define:

( )

( ) ( )

( ) ( )212

1

)(22

)2(

)(22

1

0 21

2212

1

12212

1

12

21

21

21

21

ln)(Pr

QQerfceQerfc

erfceQerfce

derfceQ

dxQxQerfcxR

QQQ

Q

QQQQQ

Q

QQ

Aout

+-=

=úûù

êëé ---=

==

=÷÷ø

öççè

æ-=

-

¥-+

¥+-ò

ò

qq

qq

q

q

hs

s2

2)ln(

21 == QmQ

changing variable θ =Q1 −ln(x)Q2


Outage area

■ It represents the fraction of area “not covered”

■ h = 4■ Example.

■ s=6■ Target 1%è M=10


Outage at cell edge

■ h = 4■ Es.

■ s=6■ Target 1%è M=14


Computing cell radiuso Step 1

n From target outage probabilityn At cell edgen Or on the whole area

n And from values of sn We compute margin M

o Step 2n From receiver threshold Pth , propagation factor hn and transmitted power (or the power at a reference

distance)n We calculate radius R


Computing cell radius

kmRR

MPdRdPRP thdBmRdBmR

217.4101001070100

log405

log10)()(

4065

10

010][0][

=×=®+-=÷øö

çèæ-

+=÷÷ø

öççè

æ-= h

o Examplen s = 6 dBn h = 4n Prout(R) £ 0.01Þ M = 10n PR(100 m) = 5 dBmn Pth= -70 dBm


Fast and slow fading

Pth Pth+M1 Pth+M1+M2

1-2%

1-2%

M1 = slow fading margin

M2 = fast fading margin


Transmission over radio channel



■ WARNING: very brief discussion

See Wireless Communication course

See alsoH. Walke: “Mobile Radio Networks”, chapter 2. Section 7


Transmission over radio channelo When signal-to-noise ratio (SNR) is small it is possible to

improve the Bit Error Rate (BER) using forward error correction (FEC) codes

BPSKNo coding

10-1

10-6

Bit ErrorRate

Eb/No (dB)11 dB4 dB



o Correction codes allow to correct wrong bits adding redundant bits in the transmitted flow

o If out of n bits transmitted k are of information and (n-k) are redundancy, we define code rate the ratio k/n



o FEC codes improve BER performance

Rate 1/2

Uncoded BPSK

10-1

10-6

Bit ErrorRate

Eb/No (dB)

11 dB4 dB

Rate 3/4



o Code types:n Block codes

o Hammingo BCHo Reed-Solomon

n Continuous codeso Convolutionalo Turbo



o Codes can be also used for revealing errors without being able to correct them

o When for instance we detect errors in a segment of coded voice it is possible to delete the segment and interpolate voice signal using correct samples

o When the type of service and the system allow (usually for data services) it is also possible to using retransmission techniques (ARQ –Automatic repeat ReQuest)



o In cellular systems the presence of high interference and high signal power fluctuations due to propagation pushed for the use of FEC codes with relatively small rates

o The use of FEC codes allows to reduce the minimum value of Signal-to-Noise and Interference Ration SIRmin tolerated by transmissions

o But at the cost of additional redundancy in the bit flow (the use of a ½ rate code halves the available capacity)

o Information theory demonstrates that channel capacity can be reached only using codes, however mobile radio channel is time varying and general conclusions cannot be easily drawn


Transmission over radio channelo Coding performance actually depends on the error statisticso Ideal BER curves of FEC codes assume white Gaussian

noise with independent errors (memoryless channel)o The radio channel in cellular systems tends to generate

correlated errors (memory channel) due to time varying characteristics of the channel and fluctuations of signal and interferences

Received power

t

Many errors

Few errors


Transmission over radio channelo The efficiency of most codes quickly decreases with

correlated errorso Therefore some mechanisms for shuffling transmitted bits

after coding are often used (bit interleaving)

Time

Am

plitu

de

Original Data Samples1 2 3 4 5 6 7 8 9

Interleaving Matrix

1 2 34 5 67 8 9

Transmitter

Interleaved Data Samples1 4 7 2 5 8 3 6 9

RF Transmission Path

Interleaved Data Samples1 4 7 2 5 8 3 6 9

Errors Clustered

De-Interleaving

Matrix

1 2 34 5 67 8 9

De-Interleaved Data Samples

1 2 3 4 5 6 7 8 9

Receiver

Errors DistributedA. Capone: Mobile Radio Networks 25

Delay spreado Propagation over multiple paths can cause also other more

complex problems in case of digital transmissiono Different delays of signal replicas reaching the receiver

(delay spread) enlarge in time the impulse response of the channel and can generate inter-symbol interference (ISI)


Delay spread

o The impact of the delay spread can be evaluated calculating its root mean square value (RMS Delay Spread):

( ) 2

1

2

1

1d

n

iiin

ii

RMS PP

ttt åå =

=

-=

( )

å

å

=

== n

ii

n

iii

d

P

P

1

1t

t

with■ tRMS RMS delay spread■ ti ritardo del path i■ Pi potenza ricevuta path i■ n numero di path


Delay spreado The inverse of the delay spread provides the coherence

bandwidtho If the coherence bandwidth is much larger than the signal

bandwidth than the delay spread has no impact on the reception

o If the coherence bandwidth is comparable or smaller than that of the signal, delay spread generates inter-symbol interference with degradation of reception

o In this case to overcome the frequency distortion of the channel we need to equalize it with a proper filter at reception

o Equalization techniques are usually based on channel estimation on known symbol sequences (see GSM), but can also be blind

o Other approaches are based on multi-carrier transmission


Voice coding


Voice coding: Time/Frequency characteristics

vocalized

Banda

See audio and video signal processing course


Voice coding: Codecs

o Waveform codecs

o Source codecs (vocoders)

o Hybrid codecs

Analog-to-digital converters for voice


Voice coding: Waveform codecs

o No ‘a priori’ information on the generated signal

o Required information: n Signal bandwidth B (classic telephony < 4 KHz)n Maximum quantization noise tolerable

samplerA to Db bits

Per sample

00100001

High quality, low complexity, low delay (one sample) Robustness to errors and background noise


Voice coding: Pulse Code Modulation (PCM)

o standardized by ITU in 1960: G.711

o B=4 kHz, sampling frequency Bc=8 kHz, 8 bit/sample, 64 kb/s

o Two different quantization rules (logarithmic) n America (µ-law) n Europe (A-law) n With standard conversion rules


Voice coding: Differential PCM (DPCM)

o Voice samples are correlated

o It is possible using prediction methods to estimate successive sample known previous ones

o And transmitting only the difference between predicted value and the real one

o Due to correlation the variance of the difference is smaller and require fewer bits for coding

predictor

+sampler +-

quant.


Voice coding: Adaptive DPCM (ADPCM)

o Performance improves if predictor and quantization are adaptive

o Standardized in 1980 by ITU ADPCM at 32 kbit/s: G.721

o Later versions of ADPCM at 40, 32, 24, 16 kbit/s: G.726 e G.727

Adaptive predictor

+sampler +- Adaptive

Quantiz.

Low quality


Voice coding: Sub Band Coding (SBC)

o Voice signal divided into sub-bands with filterso Signal of each sub-band is coded with techniques like

ADPCMo The advantage is that it is possible to use less bits for

the bands in witch human ear is less sensitive (more quantization noise is tolerable)

o Good quality:16-32 kbit/s higher complexity and delay

filtri codec

Es. G.722audio 7 kHz48,56, 64 kb/s


Voice coding: Source codecs (vocoders)

o Based on human voice generation models

o Models allows to remove redundancy up to the basic information necessary for reproducing voice

o High complexityo Delay quite higho Sensitive to errors, background noise

and non-human sounds


Voice coding: Model of human voice (phoneme)

o Reverberant filter with discrete parameterso Input signal (impulse sequence or white noise) o Parameters of the filter varying periodically (10-

20 ms)

pitch

Filter parameters Cn


Voice coding: Linear vocoder (LPC)

Linear vocoders use the discrete parameters model with linear filterAt regular intervals (10-20 ms) model parameters are estimated and

transmittedn filter coefficients ai , n voiced/unvoiced flag, variance, pitch

å=

-=p

ii insans

1)(')(ˆ

A(z)

Sgain

Sintetic voiceEccitazione(20 ms)

Parameters estimation is based on error variance)()(ˆ)( nsnsne -=


Voice coding: Linear Vocoder (LPC)

o Decoder uses received parameters for synthetizing a filter and reproducing voice

o High delay: segmentation, analysis, synthesis

o Quality: intelligible but not ‘natural’ (model limitations + problems with background noise)

o Low bit rate: < 2.4 kbit/s


Voice coding: Input signals

o Classical input LPC with two states (es. LPC-10)o gain, pitch, flag voice/unvoiced

o Mixed inputo Both periodic input and pseudo random used simultaneously o 2 synthesis filters (low freq. » periodic input, high freq. »

pseudo random input)

o Residual inputo Ideal input signal: e(n)o Low bit rate coding of e(n)o It is no longer a real vocoder … towards hybrid codecs


Voice coding: Hybrid codecs

o Hybrid codecs fill the gap between vocoders and waveform codecs

o More popular use the same approach of linear vocoder (LPC), but they optimize some parameters like the input signal (using the error signal)



o Multipulse-Excited Linear Prediction (MPLP), 1982

n Non uniform pulses with different amplitudes

n Position and amplitude of each pulse are determined based on an iterative procedure that minimizes error function

n ex. MPLP 9.6 kbit/s of BT for Skyphone service

o Regular Pulse Excitation (RPE)

n Regular pulse sequencen parameters: position of first pulse and periodn ex. LPT-RPE GSM 13 kbit/s



o Code Excited Linear Prediction (CELP)

n The input sequence is selected from a set of precoded sequences (code-book)

n Sequences in the code-book are instances of Gaussian processes

n Main problem: long delay due to the search procedure of the optimal sequence in the code book

n Algorithm semplification with efficient search methods and code-book modifications

G.728 low delay CELP codec 16 kbit/sG.729 CS-ACELP codec 8 kbit/sG.723.1 ACELP 5.3 kbit/s


Voice coding: summary

G.711 PCM

G.726 ADPCM

G.728 LD-CELP

G.729 CS-ACELP

G.723.1 MP-MLQ

G.723.1 ACELP

64

32

16

8

6.3

5.3

0.125

1

0.625

10

30

30

Codec Bit rate(kbit/s)

Framesize (ms)

0

0

0

5

7.5

5

Lookahead (ms)

1972

1990

1992-94

1995

1995

1996

Year

RPE-LTP (GSM) 13 20 01987

G.722 Subband ADPCM 48-64 0.125 1.51988


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