I t b l I t fIntersymbol Interference

• Any signal can be decomposed as the sum of orthogonalwaveforms (basis functions)

x t x tii

i( ) ( )

Si l i d id l h l h t t( ) ( )

i jt t dt ( ) ( ) 0 for i jand

Modulation : mapping constellation symbols to waveformsix• Signal transmitted over non-ideal channel h t t( ) ( )

r t x t h t x h t t x h tii

i ii

i( ) ( ) * ( ) ( ( ) * ( )) ( ) i i

S i t itt d b l i t f ith h th

In general, are not orthogonalh ti ( )

Successive transmitted symbols interfere with each other

Transmit Filter (Modulation Basis Function)

• Most common choice for basis function )()( iTtti

where T is symbol period• Analog transmitted waveform is Analog transmitted waveform is

generated by modulating the transmit filter by the symbols ix)(t y y

Throughput this course, unless otherwise stated, transmit filter is

i

,lumped with channel filter and receiver front-end continuous

2matched filter into one filter )(th

Scatter Diagram

3

Time-Domain View

For LTI channel, received noisy & match-filtered analog signal n(t) t kT t 0

r t x h t jT n tjj

( ) ( ) ( )

l d i kT

h(t)r(t)

x j

rk

Note that matched filter

)())(()()( 0000 kTtnTjkthxTthxkTtrrkj

jk

def

k

Sampled at time t kT t 0 ( is sampling offset)t0 is absorbed in h (t)

Desired ISI Noise

0 is decision delay

Signalpre-cursor

ISIpost-cursor

ISI

Cursor ( j = k- )

4

(j > k- ) (j < k- )

Frequency-Domain Viewq y

Id l (M l ISI f ) Ch l• Ideal (Memory-less or ISI-free) Channel• Constant Magnitude Response

Li Ph Rh t K t t( ) ( ) 0

H f K j ft( ) 2 0• Linear Phase Response• T-spaced sampling replicated spectrum at

i t lti l f ( di f )2

H f Ke j ft( ) 2 0

integer multiples of (radian frequency)• Nyquist’s Criterion for No ISI

2T

H w n( ) 2

Constant

5

H wTn

( ) Constant

Nyquist Pulsesyq

• Satisfy Nyquist’s condition for no ISIy yq• Impulse response is zero for all sampling instants except desired one, hence,

kkh

• h(t) = sinc (t/T) is only Nyquist pulse w/ minimum bandwidth equal to (sensitive to timing errors and difficult to realize in practice)

T

difficult to realize in practice)• Most popular choices in practice are raised-cosine and square-root raised cosine pulses with 15-35% excess BW, q p ,implemented as FIR digital filters (for 30% excess factor, 37 filter taps needed and the first sidelobe is 40 dB down)

6

Raised-Cosine Filter

h ttT

tT

tT

( ) ( )c o s ( )

( )

s in c

1

2 2

H w( )

T | | ( )wT

1

H w( )

T T1( i ( (| | )))

0 T

w( ) | |1

wT2

12

( sin( (| | )))

T

wT

( ) | | ( )1 1

7

Causes of ISICauses of ISI

R i Filt i ( t f b d i • Receive Filtering (out-of-band noise rejection, desired channel selection)T it l h i ( t d id• Transmit pulse shaping (e.g. to reduce side-lobes, narrow main-lobe)M l i h i h l f • Multipath propagation - channel frequency selectivity

• Higher transmission rates (using wider transmission bandwidth)

8

Transmitted WaveformTransmitted Waveform

Received Waveform

9

ISI Distortion Criteria

Peak Distortion Criterion |||||| kkjk hxxhDPeak Distortion Criterion |||||| max

k

kk

kjkp hxxhD

• Represents worst-case distance loss between signal pointsW ISI ( i i ) i f ll• Worst-case ISI (rare in practice)- input pattern of all

Mean Sq are Distortion ])E[(|| 22 hhSD

maxx

Mean Square Distortion ])E[(|| 2

ik

2

ikik

kxms hxhSD

• Assumes zero-mean I.I.D. input sequence• is added to noise ariance in probabilit of errorD• is added to noise variance in probability of errorQ-function calculations (only accurate if ISI is Gaussian)

Dms

10

Graphical Display of ISIGraphical Display of ISI

• Channel Impulse Response• Channel Impulse ResponseSingle impulse for ideal channel. ISI results in scaled & delayed impulses.Ch l F R• Channel Frequency ResponseFlat magnitude response and linear phase response for ideal channel. Nulls indicate severe ISI

• Eye DiagramsGenerated using oscilloscope to observe received signal when symbol timing is used as a trigger

• Scatter DiagramFor ideal channels looks like input signal constellation

Eye Diagrams

BPSK Constellation 4-PAM Constellation

R i d f i d d f ld d d i f 2 b l i d

12

Received waveforms superimposed and folded over duration of 2 symbol periods

Simple Example

2-Tap ISI Channel y x x nk k k k 1p

xk yknkk xk

^

1 3-1 -3 0 -3 0.35 -5.65 -31 -1 0.05 -3.95 -32 3 -0 1 1 9 1

-3 -1 1 3

4-PAM2 3 -0.1 1.9 13 1 0.25 4.25 3

Symbol-by-symbol detection is sub-optimum in presence of ISI because it does not exploit channel memory

13

ISI Channel Model

• Received analog signal is passed through an analog matched filter g g p g gand sampled at the symbol rate• T-spaced samples at matched filter output are sufficient statistics (i e no loss of information as far as data detection isstatistics (i.e. no loss of information as far as data detection is concerned) for representing the ISI channel (Forney ‘72)

Without loss of generality the combined effects of transmit filterWithout loss of generality, the combined effects of transmit filter, channel, and receive filter are modeled as FIR filter w/ memory

y h x nk m

mk m k

0

14

15

Examples of ISI ChannelsExamples of ISI Channels

Wi l T i i Ch l• Wireless Transmission Channels• Digital Cellular Radio (2G,3G,4G)

Di it l Vid B d t (DVB T DVB H)• Digital Video Broadcast (DVB-T, DVB-H)• Local Area Network (IEEE802.11x)

• Wireline Transmission ChannelsT i t d P i C Li (XDSL)• Twisted-Pair Copper Lines (XDSL)

• Coaxial Cable (DOCSIS)P Li C i ti (PLC)• Power Line Communications (PLC)

Mobile Digital Cellular Radio• Frequency band : around 1-2 GHz• Coverage area divided into cells ( h ith it b t ti )(each with its own base station)• 2G Standards : IS-136, GSM, IS-95, EDGE,..• 3G standards : CDMA based f2f6

f7

3G standards : CDMA based• 4G standards : OFDM based (LTE)

Impairments :

f1f3

f4f5

f2 f6

p• Path loss (proportional to )• Resolvable multipath reflections (in-band nulls), frequency –selective channel

Si l f di f t ll l f di d t lti th d l l l

55.2: R

• Signal fading : fast small-scale fading due to multipath , and slow large-scale fading (shadowing) due to obstacles in direct path• Doppler shift (mobility ), time-selective channelf v

d • Co-channel interference (a.k.a. inter-cell interference) frequency re-use factor)• Thermal Noise (modeled as additive white Gaussian noise (AWGN))

Wireless Channels : ChallengesWireless Channels : Challenges

Remote DominantReflector

Local Scatterersto Base

Co-Channel Mobile

Local Scatterersto Mobile

Base Station

Local ScatteringMultipath PropagationM bil M ti

FadingIntersymbol InterferenceTi V i Ch l

18Remote Dominant Reflector

Local Scatterersto Base

Mobile MotionCellular Spectrum Reuse

Time Varying ChannelCo-channel Interference

Signal Level in Wireless Channels

Mean Path Loss

Short Term Fading

(dB)

Sig

nal L

evel

(

Long Term Fading

Distance (dB)

•• Slow fadingSlow fading (shadowing) caused by large obstructions between transmitter and receiver

•• Fast fadingFast fading is due to reflection and scattering of the signal by objects near transmitter

19•• Path lossPath loss proportional to 1/r <5

Signal FadingSignal Fading

L t ( l ) f di ( k • Long-term (slow) fading (a.k.a. shadowing) occurs over long distances and is log normal distributed (i e and is log-normal distributed (i.e. Gaussian in dB) about the mean path loss (which is inversely proportional to loss (which is inversely proportional to nth power of propagation distance where 2.5<n<5where 2.5<n<5

• Short-term (fast) fading is Rayleigh-distributed relative to local mean P

20

distributed relative to local mean P)(

1]Pr[ PP

received ePP

Cell Planning

• Typical reuse factors are K= 4,7, and 12Typical reuse factors are K 4,7, and 12

• Tradeoffs : for small cells, transmitted signals Tradeoffs : for small cells, transmitted signals encounter smaller propagation loss which translates into transmit power savings. Also,

ll ll ll f f smaller cells allow for more frequency re-use which translates into capacity increase (assuming effective interference cancellation). (assuming effective interference cancellation). However, more base stations are needed (infrastructure cost)

21

Multipath Propagationp p g

Multipath Delay Spread of Channel

Range of time delays over which an impulse transmitted at time 0is received with non-zero energy (also called memory of channel)

Coherence Bandwidth of ChannelFrequency range over which two transmitted sinusoids are affected the same (in magnitude & phase) by the channel

Delay Spread = 1 / Coherence Bandwidth

Frequency non-selective channel (memoryless, ISI-free, non-dispersive)eque cy o se ec ve c a e ( e o y ess, S ee, o d spe s ve)

Signal Bandwidth << Coherence Bandwidth

Symbol period >> Delay Spread

(negligible delay spreadnarrow-band signaling)

22

Symbol period >> Delay Spread

Typical NumbersI d i t ( bi l ffi ) • Indoor environment (e.g. cubicle offices)

MHzBc 10sec-nano100

• Outdoor environment (e.g. urban cellular)

kHzBc 200sec-micro 5

23

Multipath PropagationMultipath PropagationDoppler Spread of Channel

Range of frequencies over which a tone transmitted at time 0is received with non-zero energy

Coherence Time of ChannelTime range over which two transmitted impulses are affected the same (in magnitude & phase) by the channel

Doppler Frequency = 1 / Coherence Time

Condition for Slowly Time Varying ChannelCo d o o S ow y e Va y g C a e

Transmission Block Duration << Coherence Time

1/(Block Length * Symbol period) >> Doppler Frequency

24

1/(Block Length * Symbol period) >> Doppler Frequency

sd

s NTvvf

NT

1

Example

101.03 dc fmGHzf

• Pedestrian Speed :

sec3330sec/3 mTHzfm cd

• Highway Speed :

sec33.333sec/3.33/120 mTHzfmhrKm cd

Guidelines for choosing block length : Doppler complexity memory overhead

25

Guidelines for choosing block length : Doppler, complexity, memory, overhead

Narrowband vs. Wideband

If a signal u(t) propagates distance “d” • If a signal u(t) propagates distance “d” experiencing attenuation of “A”, then the passband received signal is given by p g g y

tfjetuAty c )(2 })(.{)(

djtfj

ddeetuA

y

c

2

2 })(.{

})({)(

ccd

cdff

theoffunction transfer theTherefore,

where

26djfj eAe

22 is channel baseband equivalent

,

Narrowband vs. Wideband

In narrowband transmission, channel appears to have

A e e A e ej f j d j f j d22

22

11

22

, ppconstant gain & delay for all frequencies

2-path model Using superpositionA e e A e e1 2

A e e A

Ae ej f j d j f j d

12

22

1

22

11 1

( )

2-path model Using superposition

1

d wavelength delay spread path length diff.

Condition for Narrow-band transmission Only frequency-dependent

| |maxf 1y q y p

term in channel magnituderesponse iswhere is complex const.

fje 21Non-resolvable

multipath max

1|| maxftransmission BW coherence BW

ExampleExample

101

2−path channel, 1 microsec delay spread10

52−path channel, 1 microsec delay spread

10

10−5

100

10

gn

itu

de

Re

sp

on

se

10−20

10−15

10−10

ag

nitu

de

Re

sp

on

se

Ma

gn

10−30

10−25

10−20

Ma

g

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000010

0

Frequency (Hz)

0 1 2 3 4 5 6 7 8 9 10

x 106

10−35

Frequency (Hz)

H f e j f( ) 1 2 sec1

)(cos4|)(| 22 ffH Coherence BW = 1MHz

Indoor/Outdoor Wireless StandardsIndoor/Outdoor Wireless StandardsIndoor/Outdoor Wireless StandardsIndoor/Outdoor Wireless StandardsWWAN/WMAN/WRAN (few Km)

2.5/3G/4G(GPRS/WCDMA/LTE/DVB-H)Channel is time

and frequency

WLAN (100M)

and frequency selective, wider

coverage

Long delay spreads(10 micro)

Large # users

WLAN (100M)

Medium delay spreads

(1 micro)

Medium # users

802.11a/b/g/n/ad

802 11

WPAN (10M)Bluetooth, Zigbee

(1 micro)

Short delay802.11

Low mobilityShorter Coverage

Short delay spreads

(0.05-0.1 micro)

RangeSmall # users

29A single technology may not be ‘optimal’ for all spheres A single technology may not be ‘optimal’ for all spheres

source : Intelsource : Intel

10m 100m 1km+Range

Wireless Comm. ChallengesWireless Comm. Challenges

• Reliability impaired by fading frequency • Reliability impaired by fading, frequency selectivity, noise, interference (co-channel, adjacent channel), mobility (Doppler)adjacent channel), mobility (Doppler)

• Shared medium : interference management (TDMA/FDMA/CDMA/SDMA)(TDMA/FDMA/CDMA/SDMA)

• Scarcity & Cost of suitable RF spectrum(licensed vs unlicensed transmissions)(licensed vs. unlicensed transmissions)

• Low power/form factor terminal constraints (battery lifetime high circuit integration)

30

(battery lifetime, high circuit integration)

Design Tradeoffs

I l i C l iImplementation Complexity

31

Rate Reliability

Copper Twisted-Pair Channel(a k a Telephone lines)(a.k.a. Telephone lines)

• Used for connecting phone equipment to central office

RX

Subscriber Central Officebridged tap• Channel Model

| ( )|H f e f2 TXRX

RX

TX

RX

FEXT

| ( )|H f e• Impairments

ISI NEXTTXRX

RX

TX

- ISI- Crosstalk (NEXT + FEXT)- In-band nulls (bridged taps, gauge changes)

Th l i ( l i )- Thermal noise (electronics)-Impulse noise (switching)- External Radio Frequency Interference (RFI)q y ( )- Loading Coils : low-pass filters which limit broadband transmission and must be removed for DSL service

Unshielded Twisted Pair (UTP) Channel

• Attenuation increases exponentially w/ frequency and length of loop

• Different frequency components of signal attenuated differently (dispersion)

• Connecting several UTP’s w/o proper termination results in frequency nulls

• A.G. Bell patented twisting and differential signaling on telephone lines to reduce electromagnetic radiation and

33

cancel external common-mode noise

Asymmetric Digital Subscriber Lines (ADSL)

I t t

digitaldigital

Splitter

analoganalog

Splitter

GGAATTEE

Mux

or

D

ADSL

modem

.

ADSL

modem

InternetServiceProvider

Voice

Service analoganalog 00--4 miles4 miles

WWAAYYSS

DSLAM

DemuxADSL

modem

.ADSL

Telephone company officeTelephone company office

Provider

POTSdigitaldigital customer premisescustomer premises

• Upstream : 26 kHz to 137 kHz, rates up to 1.4 Mbps• Downstream : 138 kHz to 2 2 MHz rates up to 24 Mbps

34

• Downstream : 138 kHz to 2.2 MHz, rates up to 24 Mbps

Other Noises

• Radio Noise, AM, HAM• narrowband• narrowband• must reject HAM by 70-90 dB (VDSL) and 70 90 dB (VDSL) and AM by 20-40 dB (ADSL)

• Impulse Noise• 10’s millivolts strength• 100’s microseconds duration

35

Very High Speed DSL (VDSL)

To 100 MbpsTo 100 Mbps

Sp

ONU

fiberSpli

VDSL

.1- 2 km

plit

VDSL

t

POTS

Hybrid Fiber/copper y ppDownstream bandwidth up to 30 MHz

Rates : 100 Mbps at 0.5 km and 50 Mbps at 1 kmExample : AT&T U-verse System

36

Example : AT&T U verse System

VDSL Loops

loops with bridge tapsloops with bridge tapsShorter loops Shorter loops

37

Crosstalk in Digital Subscriber Lines (VDSL)

FDD is used in VDSL to eliminate NEXT

2/3f 22 |)(| fHlfFDD is used in VDSL to eliminate NEXT

Next-generation VDSL modems

d d FEXTuse advanced FEXT

Cancellation Algorithms

g.Vector standard A d i 2010

38

Approved in 2010