11

Techniques to control noise and fadingTechniques to control noise and fadingTechniques to control noise and fadingTechniques to control noise and fading NoiseNoise and and fadingfading are the primary sources of are the primary sources of

distortion in communication channelsdistortion in communication channels Techniques to reduce noise and fading are Techniques to reduce noise and fading are

usually implemented at the receiverusually implemented at the receiver The most common mechanism is to have a The most common mechanism is to have a

receiver filter that can cancel the effects of receiver filter that can cancel the effects of noise and fading, at least partiallynoise and fading, at least partially

Digital technology has made it possible to Digital technology has made it possible to have have adaptive filtersadaptive filters

NoiseNoise and and fadingfading are the primary sources of are the primary sources of distortion in communication channelsdistortion in communication channels

Techniques to reduce noise and fading are Techniques to reduce noise and fading are usually implemented at the receiverusually implemented at the receiver

The most common mechanism is to have a The most common mechanism is to have a receiver filter that can cancel the effects of receiver filter that can cancel the effects of noise and fading, at least partiallynoise and fading, at least partially

Digital technology has made it possible to Digital technology has made it possible to have have adaptive filtersadaptive filters

22

Principle of EqualizationPrinciple of EqualizationPrinciple of EqualizationPrinciple of Equalization Equalization is the process of compensation Equalization is the process of compensation

at the receiver, to reduce noise effectsat the receiver, to reduce noise effects The channel is treated as a filter with transfer The channel is treated as a filter with transfer

functionfunction Equalization is the process of creating a filter Equalization is the process of creating a filter

with an inverse transfer function of the with an inverse transfer function of the channelchannel

Since the channel is a varying filter, equalizer Since the channel is a varying filter, equalizer filter also has to change accordingly, hence filter also has to change accordingly, hence the term the term adaptiveadaptive..

Equalization is the process of compensation Equalization is the process of compensation at the receiver, to reduce noise effectsat the receiver, to reduce noise effects

The channel is treated as a filter with transfer The channel is treated as a filter with transfer functionfunction

Equalization is the process of creating a filter Equalization is the process of creating a filter with an inverse transfer function of the with an inverse transfer function of the channelchannel

Since the channel is a varying filter, equalizer Since the channel is a varying filter, equalizer filter also has to change accordingly, hence filter also has to change accordingly, hence the term the term adaptiveadaptive..

33

Equalization Model-Signal detectionEqualization Model-Signal detectionEqualization Model-Signal detectionEqualization Model-Signal detection

TransmitterTransmitter Receiver Receiver Front EndFront End

ChannelChannel

IF StageIF Stage

DetectorDetector

CarrierCarrier

Message signal x(t)Message signal x(t)

Detected signal y(t)Detected signal y(t)

44

Equalization model-CorrectionEqualization model-CorrectionEqualization model-CorrectionEqualization model-Correction

d(t)d(t)

+EqualizerEqualizerDecision Decision MakerMaker

ReconstructedReconstructedSignalSignal

eqh (t)

y(t)

Equivalent Equivalent NoiseNoise

nb(t)

55

Equalizer System EquationsEqualizer System Equations

Detected signalDetected signal

Time domain:Time domain: y(t) = x(t) * f(t) + ny(t) = x(t) * f(t) + nbb(t)(t)

Frequency domain: Frequency domain: Y(f) = X(f) F(f) + NY(f) = X(f) F(f) + Nbb(f)(f)

Output of the Equalizer Output of the Equalizer

^̂ d(t) = y(t) * hd(t) = y(t) * heqeq(t) (t)

Equalizer System EquationsEqualizer System Equations

Detected signalDetected signal

Time domain:Time domain: y(t) = x(t) * f(t) + ny(t) = x(t) * f(t) + nbb(t)(t)

Frequency domain: Frequency domain: Y(f) = X(f) F(f) + NY(f) = X(f) F(f) + Nbb(f)(f)

Output of the Equalizer Output of the Equalizer

^̂ d(t) = y(t) * hd(t) = y(t) * heqeq(t) (t)

66

Equalizer System EquationsEqualizer System Equations

Desired outputDesired output

^̂ D(f) = Y(f) HD(f) = Y(f) Heqeq(f) = X(f)(f) = X(f)

=> H => Heqeq(f) X(f) F(f) = X(f)(f) X(f) F(f) = X(f)

=> H=> Heqeq(f) F(f) = 1(f) F(f) = 1

H Heqeq(f) = 1/ F(f) => (f) = 1/ F(f) => Inverse filterInverse filter

Equalizer System EquationsEqualizer System Equations

Desired outputDesired output

^̂ D(f) = Y(f) HD(f) = Y(f) Heqeq(f) = X(f)(f) = X(f)

=> H => Heqeq(f) X(f) F(f) = X(f)(f) X(f) F(f) = X(f)

=> H=> Heqeq(f) F(f) = 1(f) F(f) = 1

H Heqeq(f) = 1/ F(f) => (f) = 1/ F(f) => Inverse filterInverse filter

77

System EquationsSystem EquationsSystem EquationsSystem Equations

ErrorError

MSE Error =MSE Error =

Aim of equalizerAim of equalizer: To minimize MSE error: To minimize MSE error

ErrorError

MSE Error =MSE Error =

Aim of equalizerAim of equalizer: To minimize MSE error: To minimize MSE error

e(t) d(t) d(t)

2E[| e(t) | ]

88

Equalizer Operating Modes Equalizer Operating Modes Equalizer Operating Modes Equalizer Operating Modes

TrainingTraining TrackingTracking

TrainingTraining TrackingTracking

99

Training and Tracking functionsTraining and Tracking functionsTraining and Tracking functionsTraining and Tracking functions

Training sequence is a known fixed bit pattern Training sequence is a known fixed bit pattern sent by the transmittersent by the transmitter

The user data is sent immediately after the The user data is sent immediately after the training sequence training sequence

The equalizer uses training sequence to adjust The equalizer uses training sequence to adjust its frequency response Hits frequency response Heqeq (f) and is optimally (f) and is optimally ready for data sequenceready for data sequence

Adjustment goes on dynamically, hence it is Adjustment goes on dynamically, hence it is adaptive equalizeradaptive equalizer

Training sequence is a known fixed bit pattern Training sequence is a known fixed bit pattern sent by the transmittersent by the transmitter

The user data is sent immediately after the The user data is sent immediately after the training sequence training sequence

The equalizer uses training sequence to adjust The equalizer uses training sequence to adjust its frequency response Hits frequency response Heqeq (f) and is optimally (f) and is optimally ready for data sequenceready for data sequence

Adjustment goes on dynamically, hence it is Adjustment goes on dynamically, hence it is adaptive equalizeradaptive equalizer

1010

Block Diagram of Digital EqualizerBlock Diagram of Digital EqualizerBlock Diagram of Digital EqualizerBlock Diagram of Digital Equalizer

y(k) y(k 1) y(k 2)

Z-1 Z-1 Z-1

∑

y(k N)

d(k)

d(k)

e(k)

w0k w1kw2k wNk

Adaptive Algorithm ∑+

-

1111

Digital Equalizer equationsDigital Equalizer equationsDigital Equalizer equationsDigital Equalizer equations• Digital systems use time sampling: Digital systems use time sampling:

t = k Tt = k T T is the sampling intervalT is the sampling interval

•Equalizer output:Equalizer output:

• Digital systems use time sampling: Digital systems use time sampling: t = k Tt = k T

T is the sampling intervalT is the sampling interval

•Equalizer output:Equalizer output:

eqd(k) y(k) * h (k)

N

nkn 0

W y(k n)

ok 1k NkW y(k) W y(k 1)...W y(k N)

1212

Error minimizationError minimizationError minimizationError minimization The adaptive algorithm minimizes errorThe adaptive algorithm minimizes error

The adaptive algorithm minimizes errorThe adaptive algorithm minimizes error

e(k) d(k) d(k)

nk 1 nk k 1 nW W Ke * y

• The updating is continued until convergence

• The error signal updates the equalizer weights

1313

Diversity techniquesDiversity techniquesDiversity techniquesDiversity techniques

Diversity is a powerful communications Diversity is a powerful communications technique for minimizing fading effectstechnique for minimizing fading effects

It provides wireless link improvement at It provides wireless link improvement at relatively low costrelatively low cost

Unlike equalization, diversity requires no Unlike equalization, diversity requires no training overheadtraining overhead

Practical version is the popular Rake receiverPractical version is the popular Rake receiver

Diversity is a powerful communications Diversity is a powerful communications technique for minimizing fading effectstechnique for minimizing fading effects

It provides wireless link improvement at It provides wireless link improvement at relatively low costrelatively low cost

Unlike equalization, diversity requires no Unlike equalization, diversity requires no training overheadtraining overhead

Practical version is the popular Rake receiverPractical version is the popular Rake receiver

1414

Fading effectsFading effectsFading effectsFading effects Small Scale fading causes rapid amplitude Small Scale fading causes rapid amplitude

fluctuations in received wireless signalfluctuations in received wireless signal Fading results in signal loss and distortionFading results in signal loss and distortion

Small Scale fading causes rapid amplitude Small Scale fading causes rapid amplitude fluctuations in received wireless signalfluctuations in received wireless signal

Fading results in signal loss and distortionFading results in signal loss and distortion

1515

Principle of diversityPrinciple of diversityPrinciple of diversityPrinciple of diversity

If we space 2 antennas at 0.5 m, one may If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong receive a null while the other receives a strong signalsignal

By selecting the best signal at all times, a By selecting the best signal at all times, a receiver can mitigate or reduce small-scale receiver can mitigate or reduce small-scale fading. This concept is fading. This concept is Space diversity Space diversity or or Antenna DiversityAntenna Diversity

If we space 2 antennas at 0.5 m, one may If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong receive a null while the other receives a strong signalsignal

By selecting the best signal at all times, a By selecting the best signal at all times, a receiver can mitigate or reduce small-scale receiver can mitigate or reduce small-scale fading. This concept is fading. This concept is Space diversity Space diversity or or Antenna DiversityAntenna Diversity

1616

Space DiversitySpace DiversitySpace DiversitySpace Diversity Concept of using Concept of using moremore than one antenna than one antenna

(or branch )for reception(or branch )for reception

ParametersParameterso ii = instantaneous SNR = instantaneous SNRo = Average SNR= Average SNRo = Threshold SNR= Threshold SNR

Concept of using Concept of using moremore than one antenna than one antenna (or branch )for reception(or branch )for reception

ParametersParameterso ii = instantaneous SNR = instantaneous SNRo = Average SNR= Average SNRo = Threshold SNR= Threshold SNR

1717

SNR Improvement Using DiversitySNR Improvement Using Diversity SNR Improvement Using DiversitySNR Improvement Using Diversity

M diversity branchesM diversity branches

Probability [Probability [ii > > ] ]

Average SNR improvementAverage SNR improvement

M diversity branchesM diversity branches

Probability [Probability [ii > > ] ]

Average SNR improvementAverage SNR improvement

/ M1 (1 e )

M

k 1

/ 1/ k

1818

ExampleExample : :

Assume that 5 antennas are used to provide Assume that 5 antennas are used to provide space diversity. If average SNR is 20 dB, space diversity. If average SNR is 20 dB, determine the probability that the instantaneous determine the probability that the instantaneous SNR will be SNR will be 10 dB. Compare this with the case 10 dB. Compare this with the case of a single receiver.of a single receiver.

ExampleExample : :

Assume that 5 antennas are used to provide Assume that 5 antennas are used to provide space diversity. If average SNR is 20 dB, space diversity. If average SNR is 20 dB, determine the probability that the instantaneous determine the probability that the instantaneous SNR will be SNR will be 10 dB. Compare this with the case 10 dB. Compare this with the case of a single receiver.of a single receiver.

1919

SolutionSolution : : = 20 dB => 100 = 20 dB => 100

Threshold Threshold = 10 dB = 10 = 10 dB = 10

SolutionSolution : : = 20 dB => 100 = 20 dB => 100

Threshold Threshold = 10 dB = 10 = 10 dB = 10Prob Prob [[ii > >] = 1 – (1 – e ] = 1 – (1 – e – – / / ))MM

For M = 5 branches, For M = 5 branches,

Prob Prob = 1 – (1 – e = 1 – (1 – e – – 0.10.1 ))5 5 = 0.9999= 0.9999

For M = 1 branch (No Diversity), For M = 1 branch (No Diversity),

Prob Prob = 1 – (1 – e = 1 – (1 – e – – 0.10.1 )) = 0.905 = 0.905

Prob Prob [[ii > >] = 1 – (1 – e ] = 1 – (1 – e – – / / ))MM

For M = 5 branches, For M = 5 branches,

Prob Prob = 1 – (1 – e = 1 – (1 – e – – 0.10.1 ))5 5 = 0.9999= 0.9999

For M = 1 branch (No Diversity), For M = 1 branch (No Diversity),

Prob Prob = 1 – (1 – e = 1 – (1 – e – – 0.10.1 )) = 0.905 = 0.905

2020

Maximal Ratio Combining (MRC)Maximal Ratio Combining (MRC)Maximal Ratio Combining (MRC)Maximal Ratio Combining (MRC) MRC uses each of the M branches in co-MRC uses each of the M branches in co-

phased and weighted manner such that phased and weighted manner such that highest achievable SNR is availablehighest achievable SNR is available

If each branch has gain GIf each branch has gain G ii, ,

rrMM = total signal envelope = total signal envelope

= =

MRC uses each of the M branches in co-MRC uses each of the M branches in co-phased and weighted manner such that phased and weighted manner such that highest achievable SNR is availablehighest achievable SNR is available

If each branch has gain GIf each branch has gain G ii, ,

rrMM = total signal envelope = total signal envelope

= = M

i ii 1

G r

2121

SNR Improvement with MRCSNR Improvement with MRCSNR Improvement with MRCSNR Improvement with MRC

MAverage SNR M

k 1M

/M

k 1

( / )Pr obability ( ) e

(k 1)!

2222

ExampleExample : Repeat earlier problem for MRC case : Repeat earlier problem for MRC case ExampleExample : Repeat earlier problem for MRC case : Repeat earlier problem for MRC case

k 1M

/M

k 1

( / )Pr obability ( ) e

(k 1)!

= 10, = 100, M = 5

k 150.1

Mk 1

(0.5)Pr obability ( 10) e

(k 1)!= e - 0.1 [ 1 + 0.1 / 1 + 0.12 / 2 ! + 0.13 / 3 ! + 0.14 / 4 ! ]e-0.1

= 0.9999998

2323

Types of diversity Types of diversity Types of diversity Types of diversity Space Diversity Space Diversity

o Either at the mobile or base stationEither at the mobile or base station Polarization DiversityPolarization Diversity

o Orthogonal Polarization to exploit diversityOrthogonal Polarization to exploit diversity Frequency Diversity Frequency Diversity

o More than one carrier frequency is usedMore than one carrier frequency is used Time Diversity : Time Diversity :

o Information is sent at time spacings Information is sent at time spacings

Space Diversity Space Diversity o Either at the mobile or base stationEither at the mobile or base station

Polarization DiversityPolarization Diversityo Orthogonal Polarization to exploit diversityOrthogonal Polarization to exploit diversity

Frequency Diversity Frequency Diversity o More than one carrier frequency is usedMore than one carrier frequency is used

Time Diversity : Time Diversity : o Information is sent at time spacings Information is sent at time spacings

2424

Practical diversity – Rake receiverPractical diversity – Rake receiverPractical diversity – Rake receiverPractical diversity – Rake receiver

CDMA system uses RAKE Receiver to CDMA system uses RAKE Receiver to improve the signal to noise ratio at the improve the signal to noise ratio at the receiverreceiver

Generally CDMA systems do not require Generally CDMA systems do not require equalization due to multi-path resolution.equalization due to multi-path resolution.

CDMA system uses RAKE Receiver to CDMA system uses RAKE Receiver to improve the signal to noise ratio at the improve the signal to noise ratio at the receiverreceiver

Generally CDMA systems do not require Generally CDMA systems do not require equalization due to multi-path resolution.equalization due to multi-path resolution.

2525

Block Diagram Of Rake ReceiverBlock Diagram Of Rake ReceiverBlock Diagram Of Rake ReceiverBlock Diagram Of Rake Receiver

αα11

M1 M2 M3M1 M2 M3 αα22

r(t)r(t) ααMM Z’ Z’ Z Z

αα11

M1 M2 M3M1 M2 M3 αα22

r(t)r(t) ααMM Z’ Z’ Z Z

Correlator 1

Correlator 2

Correlator M

Σ ()dt

><

m’(t)

2626

Principle Of Operation Principle Of Operation Principle Of Operation Principle Of Operation M correlators – correlator i is synchronized to M correlators – correlator i is synchronized to

strongest multi-path Mstrongest multi-path M ii

The weights The weights 11 , , 22 ,……, ,……,MM are based on are based on SNR from each correlator outputSNR from each correlator output

Demodulation and bit decisions are then based Demodulation and bit decisions are then based on the weighted outputs of M correlatorson the weighted outputs of M correlators

M correlators – correlator i is synchronized to M correlators – correlator i is synchronized to strongest multi-path Mstrongest multi-path M ii

The weights The weights 11 , , 22 ,……, ,……,MM are based on are based on SNR from each correlator outputSNR from each correlator output

Demodulation and bit decisions are then based Demodulation and bit decisions are then based on the weighted outputs of M correlatorson the weighted outputs of M correlators