Spread Spectrum Modulation

One day Tutorial

CDMA FOR WIRELESS COMMUNICATIONS

by Dr. Rodger Ziemer, Fellow IEEE

Organised by

Communications Society Chapter

IEEE Bombay Section, IndiaMay 28, 2002

Spread Spectrum Modulation

Lecture 2

Rodger E. Ziemer

May - June, 2002

COMSOC, IEEE Bombay Section

Copyright May 2002; R. E. Ziemer

3

Types of Spread Spectrum Modulation

DSSS BPSK QPSK balanced QPSK dual channel

Frequency-Hop Spread Spectrum (FHSS) Noncoherent slow Noncoherent fast

Hybrid



4

BPSK Direct Sequence Modulation

Datamodulatord(t)

Carrier c(t)BPF Data

demodulator

cc t T

0ˆ2 cosd c d dP c t T c t T t t T

ˆNote: if , then

ˆ 1

d d

d c

T T

c t T c t T



5

BPSK/BPSK Spread Spectrum Performance in AWGN

Data modulator is BPSK (Eb = bit energy; N0 = AWGN PSD)

Because of at the receiver (assumed synchronized), the spread spectrum makes no difference and performance is that of BPSK

E.g., to achieve Pb = 10-6 requires Eb/N0 = 10.54+ dB The spread BW is SF times the modulated signal BW Narrowband interference at the receiver input is suppressed by SF

in power density at the despreader output; because of multiplication by the spreading code, it is wideband at the despreader output

2 2

0

exp / 2 exp / 22 / , , 4

2 2b b z

t zP Q E N Q z dt z

z

ˆ 1d cc t T c t T



6

BPSK/BPSK SS Pb in NB Interference Gaussian approximation (more exact methods in ref.):

Assume narrowband interference of power J at the receiver input Let the single-sided spread signal bandwidth be W:

0

0 0 0

01

0

11

0

/

/ 1 / / /

/

1 / /

1

/ /

where 1/ bit rate

/ processing gain ( )

average signal power

b b b

b

b

b p

b p

b

p

b

E E E N

N N J W J P E N R W

E N

J P E N G

E N P J G

R T

G W R SF

P E R



7

BEP Performance of BPSK/BPSK SS in NB Interference (Gauss Approx.

Note the following: Bit error probability hits

an irreducible floor because of interference

Processing gain can compensate for increased interference - the product J/(PGp) determines the error floor



8

BEP Performance BPSK/BPSK SS with Other Users Present – Gaussian Approximation

For K equal power users present, Pursley has shown that

Approximating the other users’ interference as Gaussian, we get the following rough performance result:

Typical results on next VG

1

01

3 2p b

NKSNR

G E

1

01

3 2bp b

NKP Q SNR Q

G E



9

Multiple User Performance for BPSK/BPSK SS (Gauss Approx.)

Note the following: Higher processing gain means

more users can be accommodated

Performance eventually hits an error floor, which depends on Gp and K

These results are for equal power users - if one has more power than others, it suppresses them (near-far effect)



10

QPSK Spread Spectrum Spreading can be accomplished with a quarternary code More common, however, is to use to binary spreading codes in phase-

quadrature arms as shown below BEP performance in AWGN same as for BPSK/BPSK SS

4-Phasemodulator

Carrier

c1(t)Quadrature

splitter

c2(t)

d(t)+

Phase-modulatedQPSK-spread signal

0cos dP t t

0sin dP t t



11

Other Modulation Options for DSSS Dual-channel QPSK

Two different data streams modulate quadrature carriers Direct sequence spread by two different spreading codes Added to produce a QPSK-spread signal

Any type of phase modulation - Minimum-shift keying, for example



12

Basic Frequency-Hop Spread Spectrum (FHSS) System

DataModulator

FrequencySynthesizer

FH CodeGenerator

BandpassFilter

BandpassFilter

FrequencySynthesizer

FH CodeGenerator

DataDemodulator

Typical modulation: DPSK or NFSKSlow frequency hop: Two or more data symbols per hopFast frequency hop: Several hops per data symbol



13

Typical Hop Pattern for Slow FH (Binary Frequency-Shift Keyed Data)

Tc

Tb

Data sequence: 0 1 1 0 0 1 0 1

Frequecy

T i m e



14

Typical Hop Pattern for Fast FH (Binary Frequency-Shift Keyed Data)

Tb

Tc

Frequecy

T i m e

Data sequence: 0 1 0 1



15

Code Acquisition and Tracking The local code must be generated and properly aligned

with incoming code before data demodulation is possible This involves two steps:

Acquisition - aligning the incoming and local codes to within a fraction of a chip

Tracking - maintaining code alignment to within a small jitter so that data demodulation can take place (uses a phase-lock loop)

Since incoming carrier is data modulated, acquisition must be data independent

The acquisition process may be implemented with a matched filter or a correlator plus stepped search



16

Serial Search Synchronization System – Continuous Linear Sweep

Matchedbandpass

filter

Envelopedetector

Thresholddetector

Referencewaveformgenerator

Referencewaveform

clock

Synchroni-zation logic

Threshold, VT

Sweep stop

r(t)“hit”y’(t)

a(t)

y(t) z(t)

t



17

Equations for Continuous Linear Sweep of the Uncertainty Region

Received signal:

Difference frequency term at mixer output:

02 cos

where signal power

spreading code

noise

dr t Pc t T t n t

P

c t

n t

0

0

ˆ ˆ' 2 cos

ˆ ˆ2 cos

ˆ ˆ reference waveform clock offset

spreading code autocorrelation function

d d d

c d do d

d do

c

y t Pc t T c t T t n t c t T

PR T T Kt t n t c t T

T T Kt

R



18

Equations for Continuous Linear Sweep – continued

Matched filter output (small frequency error):

Peak signal-to-noise ratio at matched filter output:

0 0

0

0 0

/ 2 cos /

ˆ '

ˆwhere cos impulse response of matched filter

ˆ

c

c c c d do

c c

x t P t T K

R K T R T T Kt K d n t

h t R Kt T t

ssmax 0

0

ss

2SNR , AWGN power spectral density

3

where 2 2 / signal duration of matched filter outputc

PTN

N

T T K



19

Equations for Continuous Linear Sweep – continued

Phase of received signal unknown Use square law detector At square law detector output, density function of signal plus

noise is Ricean:

Note that with noise only (i.e., local code not aligned with incoming code), the density function is Rayleigh

Operating curves show probability of detection versus SNRmax with probability of false alarm (VT) as a parameter

2 2

0exp , 02Z

A Ap I

N N N



20

Stepped Serial Search/Fixed Integration Interval Basic idea

Step local code in small increments - usually 1/2 chip Pause after each step and do a trial correlation

From properties of products of m-sequences, can show that output of correlator collapses to narrowband when incoming and local codes are aligned to within 1/2 chip or less

If not aligned to within 1/2 chip, correlator output remains wideband

A bandpass filter and squarelaw device following correlation measures power of correlator output

A comparison with threshold determines if the stepped search should continue or if the receiver should be switched to track



21

Multiple-Dwell Acquisition Basic idea

Uses more than one integration interval - first one to rapidly determine whether codes are within 1/2 chip

If first integration indicates a “hit”, a second integration is tried:

A “hit” here would send receiver into code track;A “miss” would reject the code alignment tried and step code

More than two integrations might be used Analysis is complex and is facilitated by computer

evaluation



22

Sequential Detection Applied to Code Acquisition

Basic Idea Receiver structure similar to the fixed and multiple-

dwell configurations The difference is that two thresholds are employed

If the test of a correlation of a code phase crosses the upper threshold, a “hit” is declared and receiver enters code track

If the test statistic is below the lower threshold, a “miss” is declared and the local code is stepped to a new code delay

If the test statistic is between the thresholds, the integration is continued



23

Convolutional Codes Generated by linear shift-register circuits Example: rate-1/2, constraint length 3 convolutional encoder:

+

+

D DOutputsequence

w(D)

g1(D) = 1 + D + D2

g2(D) = 1 + D2

x1(D)

x2(D)



24

Convolutional Coder Characteristics Completely characterized by generator polynomials Linear - superposition holds Produces more than one output symbol per input symbol

as shown above, rate is 1/n where n is an integer codes of rate k/n, where k is an integer < n, possible

Constraint length is 1 + number of past inputs affecting current inputs (example is 3)

Can be systematic or nonsystematic



25

Output from Convolutional Encoder Output due to example input:

Interlace outputs to get actual output: 00110101001011

2 4w D D D D

2 2 41

2 4 2 3 5 3 4 6

5 6

1

0100011 (mod-2 arithmetic)

x D D D D D D

D D D D D D D D D

D D D

2 2 42

2 4 3 4 6

2 3 6

1

1

1 0111001

x D D D D D

D D D D D

D D D



26

Trellis Diagram Solid line = 0; dashed line = 1:

00 00

10

00

01

10

11

00

01

10

11

00

01

10

11

00

01

10

11

00

01

10

11

00 00 00 00 00

10 10 10

11 11 11 11 11

01 01 01 01

10 10 10 10

00 00 00

11 11 11

01 01 01

Infor. seq.: 0Codeword seq: 00

101

111

001

100



27

Bit Error Probability A Viterbi algorithm implements a maximum likelihood decoder for

convolutional codes The bit error probability is bounded by

where dfree is the free distance defined previously

ck is the weight spectrum to be given for certain codes on the next viewgraph [computed from generating function, T(D, L, N)]:

free

b k kk d

P c P

/ 2/ 2

/ 2 1

1 / 2

0

11 1 , even, hard decisions

/ 22

1 , odd, hard decisions

2, soft decisions

kk e ke k

ke k

kk ee

ke k

bk

k kP p p p p k

e k

kP p p k

e

kREP Q

N



28

Weight Spectra for Rate-1/2 CodesConstr.Lngth,

Codegen.

Freedist., df

ck; d =df df + 1 df + 2 df + 3 df + 4 df + 5 df + 6 df + 7

3 (7,5) 5 1 4 12 32 80 192 448 1024

4 (17,15) 6 2 7 18 49 130 333 836 2069

5 (35,23) 7 4 12 20 72 225 500 1324 3680

6 (75,53) 8 2 36 32 62 332 701 2342 5503

7(171,133) 10 36 0 211 0 1404 0 11633 0

8(371,247) 10 2 22 60 148 340 1008 2642 6748

9(753,561) 12 33 0 281 0 2179 0 15035 0



29

Viterbi Algorithm Example Example trellis

Other details Paths denoted by the trellis state sequences {S1, S2, . . . }

Trellis is truncated by clearing encoder with 0s

1000

1000

1000

1100

1100

1000

0100

1100

Rec’d seq:

Depth: 1 2 3 4 5 6 7 8

State:00

01

10

11 10

11

0101

1000

1111

01

11



30

First and Second Steps in Finding Minimum Distance Path

1000

1000

1000

1100

1100

1000

0100

1100

Rec’d seq:

Depth: 1 2 3 4 5 6 7 8

State:00

01

10

11

11

01

11

1

1

2

1

2

3

10



31

Minimum Distance Paths at Depth 3

1000

1000

1000

1100

1100

1000

0100

1100

Rec’d seq:

Depth: 1 2 3 4 5 6 7 8

State:00

01

10

11

11

01

11

1

1

2

1

2

3

10

11

0010

10

2

2

2

3



32

Typical BEP Performance; Rate-1/2; Hard Decisions



33

Typical BEP Performance; Rate-1/2 Convolutional Code; Soft Decisions



34

Performance of Convolutional Codes with BPSK/DSSS in CW Jamming



35

Performance of Convolutional Codes with BPSK/DSSS in CW Jamming



36

Rate-Compatible Punctured Convolutional Codes

Process Generate rate 1/n convolutional code and increase its rate by

puncturing out symbols periodically If derived from the same mother code for a particular rate,

they are called rate compatible; e.g., example puncturing patterns might be 11011111, 10011111, 10011110 where 0 indicates a punctured bit

Use of rate-compatible punctured codes allow rate and error protection to be changed at any time during transmission as long as decoder is informed of a new puncturing pattern

Same Viterbi algorithm decoder may be used for decoding all punctured codes in a family (insert erasure at puncture)



37

Performance of a Constraint Length 5 Punctured Convolutional Code

Note that performance is best for lowest rates

Free distances are 5, 4, and 3 for rates 4/7, 4/6, and 4/5, respectively

Weight spectra are [1 31 72 175 1003 2697 8214 27032], [2 0 248 0 5444 0 101710], and [21 137 1344 10854 77549 555111] for rates 4/7, 4/6, and 4/5, respectively



38

References R. L. Peterson, R. E. Ziemer, and D. E. Borth, Introduction to Spread Spectrum

Communications, Prentice Hall, 1995 R. E. Ziemer and R. L. Peterson, Introduction to Digital Communication, 2nd

edition, Prentice Hall, 2001 M. B. Pursley, “Performance Evaluation of Phase-Coded Spread-Spectrum

Multiple-Access Communication,” IEEE Trans. Commun., Vol. COM-25, pp. 800-803, Aug. 1977

N. Nazari and R. E. Ziemer, “Computationally Efficient bounds for Performance of Direct-Sequence Spread-Spectrum Multiple-Access Communication Systems in Jamming Environments,” IEEE Trans. Commun., Vol. COM-36, pp. 577-586, May 1988

K. B. Letaief, “Efficient Evaluation of Error Probabilities of Spread-Spectrum Multiple-Access Communications,” IEEE Trans. Commun., Vol. 45, pp. 139-246, Feb. 1997

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Spread Spectrum Modulation