DSSS, ISI Equalization and OFDM

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DSSS, ISI Equalization and OFDM

• Y. Richard Yang
• 01/22/2009

2
Outline

• Admin. and recap
• Direct sequence spread spectrum
• Delay spread and ISI equalization
• OFDM

3
Admin.

• Homework 1 is linked on the schedule page
• Please start to think about project

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Recap Main Story of Flat Fading

• Communication over a wireless channel has poor
  performance due to significant probability that
  channel is in a deep fade, or has interference
• Reliability is increased by using diversity
  more resolvable signal paths that fade
  independently
• time diversity send same info (or coded version)
  at different times
• space diversity send/receive same info at
  different locations
• frequency diversity send info at different
  frequency
• frequency hopping direct sequence

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Direct Sequence Spread Spectrum (DSSS)

• One symbol is spread to multiple chips
• the number of chips is called the expansion
  factor
• examples
• IS-95 CDMA 1.25 Mcps 4,800 sps
• how many chips per symbol?
• 802.11 11 Mcps 1 Msps
• how may chips per symbol?
• The increased rate provides frequency diversity
  (explores frequency in parallel)

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Effects of Spreading and Interference
dP/df
sender
f
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DSSS Encoding/Decoding An Operating View
spread spectrum signal
transmit signal
user data
X
modulator
chipping sequence
radio carrier
transmitter
correlator
sampled sums
products
received signal
data
demodulator
X
low pass
decision
radio carrier
chipping sequence
receiver
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DSSS Encoding
chip

• Data 1 -1
  

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DSSS Encoding
tb
user data d(t)
1
-1
X
tc
chipping sequence c(t)
-1
1
1
-1
1
-1
1
-1
1
-1
-1
1
1
1

resulting signal
-1
1
1
-1
-1
1
-1
1
1
-1
1
-1
-1
1
tb bit period tc chip period
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DSSS Decoding
chip

• Data 1 -1

Trans chips
decoded chips
Chipseq
innerproduct
6
-6
decision
1
-1
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DSSS Decodingwith noise
chip

• Data 1 -1

Trans chips
decoded chips
1
-1
1
1
-1
-1
-1
1
1
-1
-1
-1
Chipseq
innerproduct
4
-2
-1
decision
1
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DSSS Decoding (BPSK) Another View
bit time
take N samples ofa bit time sum 0 for i 0
sum yi ci si if sum gt 0
return 1 else return -1
y received signal
c chipping seq.
s modulating sinoid
compute correlationfor each bit time
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Outline

• Admin. and recap
• Direct sequence spread spectrum
• operating view
• why does DSSS work?

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Assume no DSSS

• Consider narrowband interference
• Consider BPSK with carrier frequency fc
• A worst-case scenario
• data to be sent x(t) 1
• channel fades completely at fc (or a jam signal
  at fc)
• then no data can be recovered

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Why Does DSSS WorkA Decoding Perspective

• Assume BPSK modulation using carrier frequency f
  
• A amplitude of signal
• f carrier frequency
• x(t) data 1, -1
• c(t) chipping 1, -1

y(t) A x(t)c(t) sin(2? ft)
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Add Noise/Jamming/Channel Loss

• Assume noise at carrier frequency f
• Received signal y(t) w(t)

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DSSS/BPSK Decoding
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Why Does DSSS WorkA Spectrum Perspective
dP/df
sender
i)
f
receiver
dP/df
dP/df
dP/df
iii)
iv)
v)
f
f
f
i) ? ii) multiply data x(t) by chipping
sequence c(t) spreads the spectrum ii) ? iii)
received signal x(t) c(t) w(t), where w(t) is
noise iii) ? iv) (x(t) c(t) w(t)) c(t) x(t)
w(t) c(t) iv) ? v) low pass filtering
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Outline

• Admin. and recap
• Direct sequence spread spectrum
• Delay spread and ISI equalization
• OFDM

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Recall Representation of Wireless Channels

• So far we considered inter-symbol interference
  small
• (also called flat fading channel)
• In the general case, received signal at time m is
  ym, hlm is the strength of the l-th tap, wm
  is the background noise

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ISI Effects
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ISI Problem Formulation

• The problem given received ym, m 1, , L2,
  where L is frame size and assume 3 delay taps (it
  is easy to generalize to D taps) y1 x1
  h0 w1 y2 x2h0 x1 h1 w2
  y3 x3h0 x2h1 x3 h2 w3 y4
  x4h0 x3h1 x2 h2 w4 y5
  x5h0 x4h1 x3 h2 w5 yL
  xLh0 xL-1h1 xL-2h2 wL yL1
  xLh1 xL-1h2 wL1 yL2 xLh2
  wL2
• determine x1, x2, xL

http//en.wikipedia.org/wiki/Andrew_Viterbi
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ISI Equalization Given y, what is x?
y1 x1 h0 w1 y2 x2h0
x1 h1 w2 y3 x3h0 x2h1 x3
h2 w3 y4 x4h0 x3h1 x2 h2
w4 y5 x5h0 x4h1 x3 h2 w5
yL xLh0 xL-1h1 xL-2h2
wL yL1 xLh1 xL-1h2 wL1
yL2 xLh2 wL2
y
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Solution Technique

• Maximum likelihood detection
• if the transmitted sequence is x1, , xL,
  then there is a likelihood we observe y1, y2,
  , yL2
• we choose the x sequence such that the likelihood
  of observing y is the largest

y1 x1 h0 w1 y2 x2h0
x1 h1 w2 y3 x3h0 x2h1 x3
h2 w3 y4 x4h0 x3h1 x2 h2
w4 y5 x5h0 x4h1 x3 h2 w5
yL xLh0 xL-1h1 xL-2h2
wL yL1 xLh1 xL-1h2 wL1
yL2 xLh2 wL2
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Likelihood

• For given sequence x1, x2, , xL
• Assume white noise, i.e, prob. w z is
• What is the likelihood (prob.) of observing y1?
• it is the prob. of noise being w1 y1
  x1 h0

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Likelihood

• The likelihood of observing y2
• it is the prob. of noise being w2 y2
  x2h0 x1h1, which is
• The overall likelihood of observing the whole y
  sequence (y1, , yL2) is the product of the
  preceding probabilities

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One Technique Enumeration

• foreach sequence (x1, , xL)
• compute the likelihood of observing the y
  sequence
• pick the x sequence with the highest likelihood

Question what is the computational complexity?
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Viterbi Algorithm

• Objective avoid the enumeration of the x
  sequences
• Key observation the memory (state) of the
  wireless channel is only 3 (or generally D for D
  taps)
• Let s0, s1, be the states of the channel as
  symbols are transmitted
• s0 initial state---empty
• s1 x1 is transmitted, two possibilities 0,
  or 1
• s2 x2 is transmitted, four possibilities
  00, 01, 10, 11
• s3 x3 is transmitted, eight possibilities
  000, 001, , 111
• s4 x4 is transmitted, eight possibilities
  000, 001, , 111
• We can construct a state transition diagram
• If we know the x sequence we can construct s, and
  vice versa

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observe y4
observe y1
observe y2
observe y3
s2
s0
s1
s3
s4
x10
x20
x30
0
00
000
000
x31
001
001
x11
x21
x30
01
010
010
x31
011
011
x20
x30
1
10
100
100
x31
x21
101
101
x30
11
110
110
x31
111
111
prob. of observing y1w1 y1-x1h0
prob. of observing y2w2 y2-x1h0-x2h1
prob. of observing y4w4
y4-x4h0-x3h1-x2h2
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Viterbi Algorithm

• Each path on the state-transition diagram
  corresponds to a x sequence
• each edge has a probability
• the product of the probabilities on the edges of
  a path corresponds to the likelihood that we
  observe y if x is the sequence sent
• Then the problem becomes identifying the path
  with the largest product of probabilities

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Viterbi Algorithm Largest Product to Shortest
Path

• If we take -log of the probability of each edge,
  the problem becomes identifying the shortest path
  problem!

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Viterbi Algorithm Summary

• Invented in 1967
• Utilized in CDMA, GSM, 802.11, Dial-up modem, and
  deep space communications
• Also commonly used in
• speech recognition,
• computational linguistics, and
• bioinformatics

Original paper Andrew J. Viterbi. Error bounds
for convolutional codes and an asymptotically
optimum decoding algorithm, April
1967http//ieeexplore.ieee.org/search/wrapper.jsp
?arnumber1054010
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Outline

• Admin. and recap
• Direct sequence spread spectrum
• Delay spread and ISI equalization
• OFDM

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Orthogonal Frequency Division Multiplexing
Motivation

• Viterbi algorithm handles ISI
• Problem?
• Its complexity grows exponentially with D, where
  D is the number of multipaths taps relative to
  the symbol time
• If we have a high symbol rate, then D can be
  large, andwe need complex receivers

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Multiple Carrier Modulation

• Uses multiple carriers modulation (MCM)
• each subcarrier uses a low symbol rate
• reduce symbol rate and reduce ISI
• for N parallel subcarriers, the symbol time can
  be N times longer
• spread symbols across multiple subcarriers
• also gains frequency diversity

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Multiple Carrier Modulation
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Multiple Carrier Modulation (MCM) Problem

• Traditional approach of using multiple
  subcarriers uses guard band to avoid interference
  among subcarriers
• Guardband wastes spectrum

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Orthogonal Frequency Division Multiplexing Key
Idea

• Avoid subcarrier interference by using orthogonal
  subcarriers

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OFDM Orthogonal Subcarriers

• Frequencies chosen so that an integral number of
  cycles in a symbol period

They do not need to have the same phase, so long
integral number of cycles in symbol time T !
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OFDM Modulation
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OFDM Orthogonal Subcarriers

• Frequencies chosen so that an integral number of
  cycles in a symbol period

They do not need to have the same phase, so long
integral number of cycles in symbol time T !
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Orthogonal Frequency Division Multiplexing

• OFDM allows overlapping subcarriers frequencies

http//www1.linksys.com/products/images/ofdm.gif
802.11a
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OFDM Implementation

• Take N symbols and place one symbol on each
  subcarrier (freq.)
• Q any problem with the straightforward
  implementation strategy?

freq0
freqN-1
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OFDM Key Idea 2

• Straightforward implementation can be expensive
  if we use one oscillator for each subcarrier
• Consider data as coefficients in the frequency
  domain, use inverse Fourier transform to generate
  time-domain sequence

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OFDM Implementation FFT
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OFDM Implementation

• Parallel data streams are used as inputs to an
  IFFT
• IFFT does multiplexing and modulation in one step
  !

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OFDM Implementation

• OFDM also uses cyclic prefix to avoid
  intercarrier and intersymbol interference caused
  by multipath delays
• For details see Chap. 13.1.4 of

http//proquest.safaribooksonline.com/0596100523?t
ocviewtrue
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Outline

• Admin. and recap
• Direct sequence spread spectrum
• Delay spread and ISI equalization
• OFDM
• Delay spread as diversity

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Reducing to Transmit Diversity

• Delay spread is really a type of transmit
  diversity

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Multipath Diversity Rake Receiver

• Instead of considering delay spread as an issue,
  use multipath signals to recover the original
  signal
• Used in IS-95 CDMA, 3G CDMA, and 802.11
• Invented by Price and Green in 1958
• R. Price and P. E. Green, "A communication
  technique for multipath channels," Proc. of the
  IRE, pp. 555--570, 1958

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Multipath Diversity Rake Receiver
LOS pulse
multipath pulses

• Use several "sub-receivers" each delayed slightly
  to tune in to the individual multipath components
• Each component is decoded independently, but at a
  later stage combined
• this could very well result in higher SNR in a
  multipath environment than in a "clean"
  environment

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Rake Receiver Blocks
Correlator
Combiner
Finger 1
Finger 2
Finger 3
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Rake Receiver Matched Filter

• Impulse response measurement
• Tracks and monitors peaks with a measurement rate
  depending on speeds of mobile station and on
  propagation environment
• Allocate fingers largest peaks to RAKE fingers

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Rake Receiver Combiner

• The weighting coefficients are based on the
  power or the SNR from each correlator output
• If the power or SNR is small out of a particular
  finger, it will be assigned a smaller weight

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Comparison PAH95
MCM is OFDM