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