05 Propagation and Coding

Copyright 2000-2006 Networking Laboratory

Mobile Radio Propagation/Mobile Radio Propagation/Channel CodingChannel Coding

Mobile Computing

Fall 2006 Course, Sungkyunkwan University

Hyunseung [email protected]

mailto:[email protected]

Networking Laboratory 2/46Mobile Computing

Mobile Radio PropagationMobile Radio Propagation


ContentsContentsTypes of WavesRadio Frequency BandsPropagation MechanismsRadio Propagation EffectsFree-Space PropagationLand PropagationPath LossFading: Slow Fading / Fast FadingDoppler Shift Delay SpreadCo-Channel Interference


Types of WavesTypes of Waves

TransmitterEarth

Ground waveSpace wave

Sky wave

Receiver

Troposphere

(0~12 km)

Stratosphere

(12~50 km)

Mesosphere

(50~80 km)

Ionosphere

(80~720 km)


Radio Frequency Bands

Classification Band Initials Frequency Range Characteristics

Extremely low ELF < 300 Hz

Infra low ILF 300 Hz ~ 3 kHz

Very low VLF 3 kHz ~ 30 kHz

Low LF 30 kHz ~ 300 kHz

Medium MF 300 kHz ~ 3 MHz

High HF 3 MHz ~ 30 MHz Sky wave

Very high VHF 30 MHz ~ 300 MHz

Ultra high UHF 300 MHz ~ 3 GHz

Super high SHF 3 GHz ~ 30 GHz

Extremely high EHF 30 GHz ~ 300 GHz

Tremendously high THF 300 GHz ~ 3000 GHz

Satellite wave

Space wave

Surface/groundwave


Propagation Mechanisms

ReflectionPropagation wave impinges on an object which is large as compared to wavelength

e.g., the surface of the Earth, buildings, walls, etc.

DiffractionRadio path between transmitter and receiver obstructed by surface with sharp irregular edgesWaves bend around the obstacle, even when LOS (line of sight) does not exist

ScatteringObjects smaller than the wavelength of thepropagation wave

e.g., foliage, street signs, lamp posts


Radio Propagation EffectsRadio Propagation Effects


FreeFree--space Propagationspace Propagation

The received signal power at distance d:

where Pt is transmitting power, Ae is effective area, and Gt is the transmitting antenna gain. Assuming that the radiated power is uniformly distributed over the surface of the sphere.

24 dPGAP tte

r π=


Antenna GainAntenna GainFor a circular reflector antenna

Example:Antenna with diameter = 2 m, frequency = 6 GHz, wavelength = 0.05 mG = 39.4 dBFrequency = 14 GHz, same diameter, wavelength = 0.021 mG = 46.9 dB

* Higher the frequency, higher the gain for the same size antenna

light) of speed is(,)thus, 2 cfcf/cη(πDG λ==

0.55) typicallyheating, ohmic losses, aperture, antenna over theon distributi field electric on the (depends efficiencynet =η

2η(πD/λ)G =

diameter=D


Land PropagationLand Propagation

The received signal power:

Where Gr is the receiver antenna gain,L is the propagation loss in the channel, i.e.,

LPGGP trt

r =

FSP LLLL =Fast fadingSlow fadingPath loss


Path Loss (FreePath Loss (Free--space)space)

Definition of path loss LP:

Path Loss in Free-space:

where fc is the carrier frequency.

This shows greater the fc, more is the loss.

,r

tP P

PL =

),(log20)(log2045.32)( 1010 kmdMHzfdBL cPF ++=


Path Loss (Land Propagation)Path Loss (Land Propagation)

Simplest Formula:

whereA and α: propagation constantsd : distance between transmitter and receiverα : value of 3 ~ 4 in typical urban area

α−= dLp A


Example of Path Loss (FreeExample of Path Loss (Free--space)space)


FadingFading

Distance

Signal Strength

(dB)

Fast Fading(Short-term fading)

Slow Fading(Long-term fading)


Slow FadingSlow Fading

Log-normal distribution:The pdf of the received signal level is given in decibels by

where M is the true received signal level m in decibels, i.e., 10log10m,M is the area average signal level, i.e., the mean of M,σ is the standard deviation in decibels.

,21)( 2

2

2)(

σ

σπ

MM

eMp−

−=

The pdf of the received signal level

The long-term variation in the mean level is known as slow fading (shadowing or log-normal fading). This fading caused by shadowing.


Fast FadingFast FadingThe signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles.

When MS far from BS, the envelope distribution of received signal is Rayleighdistribution. The pdf is

where σ is the standard deviation.Middle value rm of envelope signal within sample range to be satisfied by

We have rm = 1.777...

0,)( 2

2

22 >=

−rerrp

rσ

σ

.5.0)( =≤ mrrPThe pdf of the envelope variation


Fast Fading (Continued)Fast Fading (Continued)

When MS far from BS, the envelope distribution of received signal is Rician distribution. The pdf is

whereσ is the standard deviation,I0(x) is the zero-order Bessel

function of the first kind.

0,)( 02

22

22

≥⎟⎠⎞

⎜⎝⎛=

+−

rrIerrpr

σα

σσα

The pdf of the envelope variation


Characteristics of Instantaneous Characteristics of Instantaneous AmplitudeAmplitude

Level Crossing Rate:Average number of times per second that the signal envelope crosses the level in positive going direction.

Fading Rate:Number of times signal envelope crosses middle value in positivegoing direction per unit time.

Depth of Fading:Ratio of mean square value and minimum value of fading signal.

Fading Duration:Time for which signal is below given threshold.


Doppler ShiftDoppler ShiftDoppler Effect: When a wave source and a receiver are moving towards each other, the frequency of the received signal will not be the same as the source.

When they are moving toward each other, the frequency of the received signal is higher than the source.When they are opposing each other, the frequency decreases.

Thus, the frequency of the received signal isfR = fC - fD

where fC is the frequency of source carrier,fD is the Doppler frequency.

Doppler Shift in frequency:

where v is the moving speed, λ is the wavelength of carrier.

θλ

cosvfD = θ


Delay SpreadDelay Spread

Each path has different path length, so the time of arrival for each path is different.This effect which spreads out the signal is called “Delay Spread”.

When a signal propagates from a transmitter to a receiver, signal suffers one or more reflections.This forces signal to follow different paths.

Delay Spread


Coherence BandwidthCoherence Bandwidth

Coherence bandwidth Bc:Represents correlation between 2 fading signal envelopes at frequencies f1 and f2.Is a function of delay spread.Two frequencies that are larger than coherence bandwidth fade independently.Concept useful in diversity reception

Multiple copies of same message are sent using different frequencies.


CochannelCochannel InterferenceInterference

Cells having the same frequency interfere with each other.rd is the desired signalru is the interfering undesired signalβ is the protection ratio, such thatrd ≤ βru (so that the signals interfere the least)If P is the probability that rd ≤ βru

Cochannel probability Pco = P


Channel CodingChannel Coding


ContentsContents

FEC (Forward Error Correction)Block CodesCRC (Cyclic Redundancy Check)Convolutional CodesInterleavingInformation Capacity TheoremTurbo CodesARQ (Automatic Repeat Request)

Stop-and-wait ARQGo-back-N ARQSelective-repeat ARQ


Forward Error Correction (FEC)Forward Error Correction (FEC)

The key idea of FEC is to transmit enough redundant data to allow receiver to recover from errors all by itself. No sender retransmission required.The major categories of FEC codes are

Block codes,Cyclic codes,Reed-Solomon codes (Not covered here),Convolutional codes, andTurbo codes, etc.


Block CodesBlock Codes

Information is divided into blocks of length kr parity bits or check bits are added to each block(total length n = k + r).Code rate R = k/nDecoder looks for codeword closest to received vector (code vector + error vector)Tradeoffs between

EfficiencyReliabilityEncoding/Decoding complexity


Block Codes: Linear Block CodesBlock Codes: Linear Block Codes

Linear Block CodeThe block length c(x) or C of the Linear Block Code is

c(x) = m(x) g(x) or C = m Gwhere m(x) or m is the information codeword block length, g(x) is the generator polynomial, G is the generator matrix.

G = [Ik | p]k*n ,where pi = Remainder of [xn-k+i-1/g(x)] for i=1, 2, .., k, and Ik is unit matrix of size k.The parity check matrix

H = [pT | I ], where pT is the transpose of the matrix p.


Block Codes: Linear Block CodesBlock Codes: Linear Block Codes

MessageVector

m

Generatormatrix

G

Codevector

C

Codevector

C

Parity check matrix

HT

Nullvector

0

Operations of the generator matrix and the parity check matrix

The parity check matrix H is used to detect errors in the received code by using the fact that c * HT = 0 (null vector)

Let x = c ⊕ e be the received message where c is the correct code and e is the error

Compute S = x * HT = ( c ⊕ e ) * HT = c HT ⊕ e HT = e HT

If S is 0 then message is correct else there are errors in it, from common known error patterns the correct message can be decoded.


Block Codes: ExampleBlock Codes: ExampleExample: Find linear block code encoder G if code generator polynomial g(x)=1+x+x3 for a (7, 4) code. We have n = the total number of bits = 7, k = the number of information bits = 4, and r = the number of parity bits = n - k = 3.

where[ ] ,

1...00...0.........

0...100...01

| 2

1

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

==

k

k

p

pp

PIGΘki

xgxofmainderip

ikn

...,,2,1,)(

Re1

=⎥⎦

⎤⎢⎣

⎡=

−+−

[ ]

[ ]

[ ]

[ ]⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

⎬

⎫

→+=⎥⎦

⎤⎢⎣

⎡++

=

→++=⎥⎦

⎤⎢⎣

⎡++

=

→+=⎥⎦

⎤⎢⎣

⎡++

=

→+=⎥⎦

⎤⎢⎣

⎡++

=

1010001111001010001001101000

10111

Re

11111

Re

0111

Re

11011

Re

23

64

23

53

23

42

3

31

G

xxx

xp

xxxx

xp

xxxx

xp

xxx

xp


Cyclic CodesCyclic CodesIt is a block code which uses a shift register to perform encoding and decoding.The code word with n bits is expressed as

c(x)=c1xn-1 +c2xn-2+…+cn

where each ci is either a 1 or 0.c(x) = m(x) xn-k + cp(x)

where cp(x) = remainder from dividing m(x) xn-k by generator g(x) if the received signal is c(x) + e(x) where e(x) is the error.To check if received signal is error free, the remainder from dividing c(x) + e(x) by g(x) is obtained (syndrome). If it is 0 then the received signal is considered error free, else error pattern is detected from known error syndromes.


Cyclic Redundancy Check (CRC)Cyclic Redundancy Check (CRC)Using parity, some errors are masked – careful choice of bit combinations can lead to better detection.Binary (n, k) CRC codes can detect the following error patterns1. All error bursts of length n-k or less.2. All combinations of minimum Hamming distance dmin-1 or fewer errors.3. All error patters with an odd number of errors if the generator polynomial

g(x) has an even number of nonzero coefficients.Common CRC Codes

Code Generator Polynomial g(x)

Parity check bits

CRC-12 1+x+x2+x3+x11+x12 12

CRC-16 1+x2+x15+x16 16

CRC-CCITT 1+x5+x15+x16 16


ConvolutionalConvolutional CodesCodes

For real time error correction; used in GSM and IS-95;Encoding of information stream rather than information blocks used in previous methodsValue of certain information symbol also affects the encoding of next M information symbols, i.e., memory MEasy implementation using shift register

Assuming k inputs and n outputs

Decoding is mostly performed by the Viterbi Algorithm (not covered in this course)


ConvolutionalConvolutional Codes: Codes: (n=2, k=1, M=2) Encoder(n=2, k=1, M=2) Encoder

Input: 1 1 1 0 0 0 …Output: 11 01 10 01 11 00 …

Input: 1 0 1 0 0 0 …Output: 11 10 00 10 11 00 …


State Transition DiagramState Transition Diagram

11

00

0110

10/1

01/1

11/0

01/0

00/1

10/0

11/1

00/0


Tree DiagramTree Diagram


Trellis DiagramTrellis Diagram


InterleavingInterleaving


Why Interleaving? (Example)Why Interleaving? (Example)


Information Capacity TheoremInformation Capacity Theorem(Shannon Limit)(Shannon Limit)

The information capacity (or channel capacity) C of a continuous channel with bandwidth B Hertz can be perturbed by additive Gaussian white noise of power spectral density N0/2 (Watts/Hertz), provided bandwidth Bsatisfies

where P is the average transmitted power P = EbRb (for an ideal system, Rb = C). (watts/bit*bit/sec = watts/sec)- Eb is the transmitted energy per bit;- Rb is transmission rate.

sec/1log0

2 bitBN

PBC ⎟⎟⎠

⎞⎜⎜⎝

⎛+=


Shannon LimitShannon LimitRb/B

Eb/N0 dB

=


Turbo CodesTurbo CodesA brief historic of turbo codes :The turbo code concept was first introduced by C. Berrou in ICC 1993. Today, Turbo Codes are considered as the most efficient coding scheme for FEC.Scheme with known components (simple convolutional or block codes, interleaver, soft-decision decoder, etc.)Performance close to the Shannon Limit (Eb/N0 = -1.6 db if Rb→ 0) at modest complexity!Turbo codes have been proposed for low-power applications such as deep-space and satellite communications, as well as for interference limited applications such as third generation cellular, personalcommunication services, ad hoc and sensor networks.


Turbo Codes: Encoder & DecoderTurbo Codes: Encoder & DecoderEncoder

Decoder


Automatic Repeat Request (ARQ)Automatic Repeat Request (ARQ)

Receive


StopStop--AndAnd--Wait ARQ (SAW ARQ)Wait ARQ (SAW ARQ)

Throughput:S = (1/T) * (k/n) = [(1- Pb)n / (1 + D * Rb/ n) ] * (k/n)

where T is the average transmission time in terms of a block durationT = (n /Rb + D) * PACK + 2 * (n /Rb + D) * PACK * (1- PACK)

+ 3 * (n /Rb + D) * PACK * (1- PACK)2 + …..= (1 + D * Rb/ n) / (1- Pb)n

where n = number of bits in a block, k = number of information bits in a block, D = round trip delay, Rb = bit rate, Pb = BER of the channel, and PACK = (1- Pb)n


GoGo--BackBack--N ARQ (GBN ARQ)N ARQ (GBN ARQ)

ThroughputS = (1/T) * (k/n) = [(1- Pb)n / ((1- Pb)n + N * (1-(1- Pb)n) )]* (k/n)whereT = 1 * PACK + (N+1) * PACK * (1- PACK) +2 * (N+1) * PACK * (1- PACK)2 + ….

= 1 + (N * [1 - (1- Pb)n])/(1- Pb)n


SelectiveSelective--Repeat ARQ (SR ARQ)Repeat ARQ (SR ARQ)

ThroughputS = (1/T) * (k/n) = (1- Pb)n * (k/n)

whereT = 1 * PACK + 2 * PACK * (1- PACK ) + 3 * PACK * (1- PACK )2 + ….

= 1/(1- Pb)n

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05 Propagation and Coding