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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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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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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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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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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
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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