CDMA FOR WIRELESS COMMUNICATIONS

7/29/2019 CDMA FOR WIRELESS COMMUNICATIONS

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One day Tutorial

CDMA FOR

WIRELESS COMMUNICATIONSby Dr. Rodger Ziemer, Fellow IEEE

Organised by

Communications Society Chapter

IEEE Bombay Section, IndiaMay 28, 2002


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An Overview of Spread

Spectrum and Its Use in CDMA

Lecture 1A

Rodger E. ZiemerMay - June, 2002


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COMSOC, IEEEBombay Section

Copyright May 2002; R. E. Ziemer 3

PreliminariesWhat is spread spectrum modulation?

Any modulation scheme that uses a much widertransmission bandwidth than that of the modulatingsignal, independent of the modulating signal bandwidth

Why use spread spectrum?Resistance to interfering signals

Combat multipath

Provide a means for multiple accessAllow for distance measurement

Provide a means for masking the transmitted signal


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Rules for Efficient Multiple Access

Three laws

Know the channel

Minimize interference to othersMitigate interference received from others

Requirements of wireless multiple access

Channel measurementChannel control and modification

Multiple user channel isolation


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What Is Code Division Multiple

Access (CDMA)? Any scheme that uses a form of spread spectrum to allow

multiple users to access the same communications medium

Historically, three common methods for multiple access are Frequency Division Multiple Access (FDMA)

Time Division Multiple Access (TDMA)

Code Division Multiple Access (CDMA)

In cellular radio, two of these are used together; e.g.:

TDMA and FDMA (GSM)

CDMA and FDMA (IS-95 or CDMAone)


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Three Common Multiple Access

Schemes

time

frequency

code

time

frequency

code

time

frequency

code

AMPS GSM CDMA


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Why CDMA? Higher capacity

Improved performance in multipath by diversity

Lower mobile transmit power = longer battery life Power control

Variable transmission rate with voice activity detection

Allows soft handoff

Sectorization gain High peak data rates can be accommodated

Combats other-user interference = lower reuse factors


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Types of Spread Spectrum ModulationDSSS (modulation refers to the spreading)

BPSK (biphase-shift keying)

QPSK (quadriphase-shift keying) balancedQPSK dual channel

Frequency-Hop Spread Spectrum (FHSS)

Noncoherent slowNoncoherent fast

Hybrid


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Basic Direct-Sequence Spread Spectrum (DSSS)

System

d1(t) = 1, Tb s

c1(t) = 1, Tc s A1cos(2pf0t)

s1(t - td)

s1(t - td- D)

c1(t - td)

LPF

Accos[2pf0(t- td)]

Kd1(t - td)

AIcos(2pf0t)

A2d2(t)c2(t)cos(2pf0t), c1(t) c2(t - t) 0

Spreading factor or processing

gain: SF= Gp = Tb/Tc

f, Hz f, Hz

Sdata(f)Sspread(f)

00

d1(t)

t

d1(t)c1(t)

t


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Basic Frequency-Hop Spread Spectrum (FHSS)

System

Data

Modulator

FrequencySynthesizer

FH Code

Generator

Bandpass

Filter

Bandpass

Filter

Frequency

Synthesizer

FH Code

Generator

Data

Demodulator

Typical modulation: DPSK or NFSK

Slow frequency hop: Two or more data symbols per hop

Fast frequency hop: Several hops per data symbol


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Other Points On SS Systems

A challenge is synchronization

Code

Carrier

Symbol

Performance

In Gaussian noise, is the same as the data modulation schemeused

Gives improvement in jamming by the spreading factor orprocessing gain

Can give improved performance in multipath if designedproperly


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Types of Modulation BPSK (biphase shift keying)transmits one bit per symbol period by shifting the phase of a

carrier between 0 to 180o DBPSK (differential BPSK) transmits one bit per symbol period by differential encoding

the data and then shifting the phase of a carrier between 0 to 180o

QPSK (quadrature PSK) transmits two bits per symbol period by shifting the phase of acarrier in steps of 90o

MSK (minimum-shift keying)QPSK with quadrature symbol streams offset symbol

period and then weighted with half cosine or half sine DQPSK (differential QPSK)transmits two bits per symbol period by differential encoding

the data and then shifting the phase of a carrier in steps of 90o

FSK (frequency-shift keying)transmits data by associating blocks of bits with differentfrequency shifts of a carrier (binary = 1 bit per symbol period); may be coherent ornoncoherent, but the latter is most often used

QAM (quadrature-amplitude modulation)

uses the sum of two phase-quadrature carriers ofthe same frequency with amplitudes varied in discrete steps in accordance with a block ofbits at the modulator input; common types are 16- and 64-QAM

OFDM (orthogonal frequency-shift keying)uses a sum of coherently-spaced subcarriers infrequency to send multiple bits per symbol period; modulation on separate subcarriers canbe of varied types as given above; can be implemented with an FFT


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Signal Space Diagrams for BPSK and QPSK

180o 0o Inphase

BPSK

180o 0o Inphase

90o

270o

QuadratureQPSK

Thresholdsand

decision

logic

0

sT

dt

0

sT

dt

02

cos 2s

f tT

p

02

sin 2s

f tT

p

t = nTs

Decision

I

Q

si(t) + n(t)

General Demodulator Structure

sEsE

sE

sE

bEbE


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Signal Space Diagram for 16-QAM

3aa-a-3a

a

3a

-a

-3a

1010

1011

1001

1000

1110(III)

(II)

(II)

(III)

(I)

1111

(II)

1101

1100

0110

0111

0101

0100

0010

0011

0001

0000

Inphase

Quadrature

3

2 1

sEaM


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Signal Space Diagram for 3-FSK

12

cos 2s

f tT

p

22

cos 2s

f tT

p

32

cos 2s

f tT

p

sE

sE

sE


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Minimum-Shift Keying (MSK) and

Gaussian MSK MSK Take OQPSK and weight inphase and quadrature symbol streams

with half sine/cosine

Same BEP and BW efficiency as QPSK and OQPSK

Envelope variations after filtering less severe than OQPSK

Gaussian MSK

produced by passing the bipolar bit stream through a lowpass filter

with Gaussian impulse response

filtered bit stream put into a voltage controlled oscillator (VCO).


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Gaussian MSK BW OccupancyOccupied Bandwidth Tb Containing a Given % Power for GMSK [5]

% Power

BTb

90 99 99.9 99.99

0.2 0.52 0.79 0.99 1.220.25 0.57 0.86 1.09 1.37

0.5 0.69 1.04 1.33 2.08

MSK 0.78 1.20 2.76 6.00


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MSK WaveformsTitle:

e:\icc98\msk.eps

Creator:MATLAB, The Mathworks, Inc.

Preview:

This EPS picture was not saved

with a preview included in it.

Comment:

This EPS picture will print toa

PostScript printer, but not to

other types of pr inters.


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GMSK Waveforms


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Differential Encoding forM-phaseEncoding procedureLet an be the current transmitted signal phase

Desire to convey

(determined by source bits)Send

Decoding procedure

Suppose signal phases received due to an and an-1being transmitted are qn = an + g and qn-1 = an-1 + g

Receiver makes correct decision if

2 1modulo 2 , 1, 2, ,n

ll M

M

p p

1n n na a

1n n n nM M

p p q q


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Symbol Energy to Bit EnergyPR = received signal power

Average bit energy:Eb = PRTb

Average symbol energy:Es = PRTs

Bit time to symbol time: Ts = Tblog2M

Hence, symbol energy to bit energy:

Es = Eb log2M


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Bit Error Probabilities From Symbol

Error Probabilities

Two approximations

Two dimensional signal constellations where Gray

coding used to ensure only 1 bit change in going from a

given signal point to closest adjacent signal point:

Constellations like MFSK where all signal pairs equallydistant

2log

sb

PP

M

2 1b s

MP P

M


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Some Symbol Error Probabilities

BPSK

PSK:

DPSK:

QAM:

CFSK:

NFSK:

11

, NFSK

1 0

1 1exp

1 1

kM

ss

k

M EkP

k k k N

, PSK0

, moderately large2

2 sinss ME

P QN M

p

, asymp, DPSK 0

1 cos / 22 1 cos2cos /

ss

M EP Q

M M N

p p

p

, CFSK0

1 ssE

P M QN

2

, QAM

0

31 24 1 ,

2 1

ss

EaP Q a

N MM

2

, PSK0

exp / 2;

2

2z

bs

tQ z dt

EP Q

N p


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Spreading Codes and Their

Properties

Lecture 1B

May - June, 2002


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Spreading Codes and Their Properties Candidates

Pseudo-noise orm-sequences

Gold codes

Kasami sequences (small, large, and very large sets)

Multiphase codes

Desired properties

Good correlation properties

Narrow zero-delay peak

Low nonzero-delay values

Low cross-correlation with other codes

Family sufficiently large

Security often important


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Linear Feedback Shift-Register

GeneratorsHigh-speed linear FB SR generator structure:

Mathematical description of output (mod 2

arithmetic):

D D+

gr-1

D D+

g1gr

b(D)

21 2

initial SR state

1 rr

a Db D

g D

a D

g D g D g D g D


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Alternative Feedback Shift Register

Configuration Satisfies the same recurrence relationship as

preceding high-speed generator configuration:

D D

+

g1

D D

+

gr-1 gr

b(D)

+

g2

. . .

. . .


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Properties of the FB SR Configuration

Ifg(D) is a primitive polynomial, the sequence generated

by the SR is maximal length [g(D) is a primitive

polynomial if the smallest integern for whichg(D)

dividesDn + 1 is n = 2r

1] The maximum number of states allowed for the SR is 2r

1 (the all-zeros state is not allowed)

2

r

1 is also the maximum length of the output before itrepeats

Ifb(D) is maximum length, it is called an m-sequence


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COMSOC, IEEEBombay Section Copyright May 2002; R. E. Ziemer 29

Properties ofm-Sequences An m-sequence contains one more one than zero

The modulo-2 sum of an m-sequence and any phase shift

of the same m-sequence is another phase of the same m-

sequence (a phase of the sequence is any cyclic shift) If a window of width ris slid along an m-sequence forN

shifts, each r-tuple except the all-zeros r-tuple will appear

exactly once

The periodic autocorrelation function of an m-sequence is

2-valued and is given by (Nis the sequence period)

1, , and 1/ , , integer b bk k lN k N k lN l q q


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Define a run as a subsequence of identical symbols within

the m-sequence. Then, for any m-sequence, there are:

One run of ones of length r

One run of zeros of length r1

One run of ones and one run of zeros of length r2

Two runs of ones and two runs of zeros of length r3

Four runs of ones and four runs of zeros of length r

4 . . .

2r3 runs of ones and 2r3 runs of zeros of length 1

Properties ofm-Sequences - continued


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Autocorrelation of an m-SequenceThe autocorrelation function of a repeated m-

sequence:

1 11 1 ,

1 1,2

c

cc

c c

TT N N

R

NT TN

tt

t

t

NTc

1

1/N

Tc

t

Rc(t


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m-Sequence Power Spectral Density

The Fourier transform of the autocorrelationfunction gives the PSD:

2 2

0 0 2

1 / sinc / , 0, 1/ ;

1/ , 0; sinc sin /c m c m

m

N N m N mS f P f mf f NT P

N m x x x

p p

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

fTc

Sc

(f)

N = 15


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Using Primitive Polynomials to find

the SR Connections Tables of primitive polynomials exist in octal form (next

VG for examples)

As an example, one entry is [4 3 5]8 = [100 011 101]2

We take the right-most entry to beg0 and the left-most

nonzero entry to begr

Thus, the feedback connections in this example areg8 = 1,g7 = 0,g6 = 0,g5 = 0,g4 = 1,g3 = 1,g2 = 1,g1 = 0, andg0

= 1. That is, 2 3 4 81g D D D D D


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Octal Representation of Some

Primitive Polynomials (g0 on right)Deg. Generator Polynomial Deg. Generator Polynomial

2 [7]* 8 [4 3 5], [5 5 1]

3 [1 3]* 9 [1 0 2 1]*, [1 1 3 1]

4 [2 3]* 10 [2 0 1 1]*, [2 4 1 5]

5 [4 5]*

, [7 5], [6 7] 11 [4 0 0 5]*

, [4 4 4 5]6 [1 0 3]*, [1 4 7] 12 [1 0 1 2 3], [1 5 6 4 7]

7 [2 1 1]*, [2 0 3]* 13 [2 0 0 3 3]*, [2 3 2 6 1]*


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Example m-sequence Generation

Take degree 3 entry in table:

[1 3]8 = [0 0 1 1 01]2

Second feedback shift-register configuration:

D D

+

D

SR states:

1 0 0

0 1 0

1 0 1

1 1 0

1 1 10 1 1

0 0 1

1 0 0Output = 1 0 1 1 1 0 0


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Comments on m-Sequences Advantages

Simple to generate

Several exist for a given length; the length can be virtuallyanything

Disadvantages

Poor off-peak partial period correlation properties

Poor cross-correlation properties

Not very secure (estimates of 2m code symbols will suffice,whereN= 2m - 1; e.g., a 15-symbol m-sequence is determined

with the knowledge of 8 symbols) (bi = g1bi-1+g2bi-2+...gmbi-m)

The number of codes for a given length is not sufficient forseveral applications


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Comments on m-Sequences - cont. Synchronization of long codes depends on partial period

correlation properties

Using properties ofm-sequences, can show that the dis-crete partial autocorrelation function of sequence b(D) is

This varies from the ideal value of

considerably, depending on window width and delay (e.g.,for 15-symbol m-sequence with W= 7, it varies between-3/7 and 3/7 whereas the average is -1/15)

1

, ,wt T

c wt

w

R t T c c dT

t t

1

'

0

1, ', , 1 , 0

i

Wb

i q k i

i

k k W a a k qW

q

b b b

, ', 1/k k W N q


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Gold Codes The cross-correlation spectrum for Gold codes:

Constructed by modulo-2 adding a preferred pair* ofm-

sequences delayed relative to each other (each delayproduces another Gold code, for total of 2 +Ncodes)

Example preferred pair:

b = 10101 11011 00011 11100 11010 01000 0

b = 10110 10100 01110 11111 00100 11000 0 t(n) = 1 + 20.5(5 + 1) = 9; permitted values of cross-

correlation are9/31, -1/31, and 7/31.*A preferred pair has the three-valued correlation property given in the first bullet. Finding preferred pairs involves

decimation of certain m-sequences (the decimation gives anotherm-sequence) according to a set of rules beyond the

scope of this discussion.

0.5 1

0.5 2

1 2 , odd1 1 1; ; 2 where

1 2 , even

n

n

nt N t N t n

N N N n


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Other Sequences: The Small Set of

Kasami SequencesConstruction procedure:Let r= 2n, n integer, and d= 2n+ 1

Let b be an m-sequence, and let bbe obtained by

sampling every dth member ofb

The Kasami sequences are b, b + b, b +Db, . . . ,b +Dab, where a = 2n- 2

The result is a family of 2n

sequences:Period 2r- 1

Maximum magnitude cross correlation of (1 + 2n)/N


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Kasami Sequence Example Considerb = 10001 00110 10111 ([2 3]8)

Thus, 2n= 4 orn 2,d= 22 + 1 = 5, a = 22 - 2 = 2

Decimation ofb by d gives b = 10110 11011 01101

The four Kasami sequences are:b = 10001 00110 10111

b + b = 00111 11101 11010

b +Db = 01010 01011 00001

b +D2b = 11100 10000 01100

Checking the cross correlation ofb and b gives -5/15 and

3/15, which obey the bound of (1 + 2n)/N = 5/15


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Other Sequences: Quarternary S(0)

Family

D D D

+ +

2 3

Output

Modulo-4 arithmetic

Examples: Initial load of 001 gives 1001231

Initial load of 010 gives 0103332


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Other Sequences: Quarternary S-series

Parameters of quarternary and Gold sequencescompared:

Family Length Size Bound on

correlation

Gold 2r-1 N + 2 N1/2

S(0) 2r-1 N + 2 N1/2

S(1) 2r-1 > N2 + 3N + 2 (2.6N)1/2

S(2) 2r-1 > N3 + 4N2 + 5N

+ 2

(4.3N)1/2


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Other Sequences: The Walsh Codes Generation: Construct a Hadamard array according to

The rows of the Hadamard array form the Walsh codes,which are orthogonal

For example

Used in 2nd generation CDMA wireless systems forchannelization codes

1

2 2

12

2 2

, integer; 1; overbar denotes complementn n

n

n n

H HH n H

H H

2 4

1 1 1 1

1 1 1 0 1 0;

1 0 1 1 0 0

1 0 0 1

H H


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COMSOC, IEEE

Bombay Section


Other Sequences: Barker Codes Barker codes for various lengths are:

N= 2: (1, -1)

N= 3: (1, 1, -1)

N= 4: (1, 1, -1, 1)

N= 5: (1, 1, 1, -1, 1)

N= 7: (1, 1, 1, -1, -1, 1, -1)

N= 11: (1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1)

N= 13: (1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1)

Barker codes of other lengths are unknown

Barker codes are known for their almost ideal aperiodic autocorrelation functions,given by

aperiodic1, 0

0, 1/ , 1/ , 1 1

nn

N N n Nq


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COMSOC, IEEE

Bombay Section


Complementary Code Keying Used in the 802.11b standard

The sum of their aperiodic autocorrelation functions is zero for all

delays, except 0 delay:

For 11 Mbps standard, they are

Since the phases each take on 4 different values, a code size of 64 isdefined

For the 5.5 Mbps standard,

aperiodic1

, 0

0, otherwise

M

k

M nnq

1 2 3 4 1 3 4 1 2 4

1 2 3 1 31 4 1 2 1

, , ,, phases are QPSK phases

, , , , ,

j j j

j jj j j

e e eC

e e e e e

1 2 3 1 3 1 2 1, , ,j j j jC e e e e


46/46

COMSOC, IEEE Copyright May 2002; R. E. Ziemer 46

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

G. L. Stuber,Principles of Mobile Communication,

2nd edition, Kluwer, 2001

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