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April 13, 2005 Topic 4 1
Telecommunications EngineeringTopic 4: Spread Spectrum and CDMAJames K Beard, Ph.D.
http://astro.temple.edu/~jkbeard/
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Topic 4 2April 13, 2005
Attendance
0
5
10
15
20
25
19-J
an
26-J
an
2-F
eb
9-F
eb
16-F
eb
23-F
eb
2-M
ar
9-M
ar
16-M
ar
23-M
ar
30-M
ar
6-A
pr
13-A
pr
20-A
pr
27-A
pr
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Topic 4 3April 13, 2005
Essentials Text: Simon Haykin and Michael Moher, Modern
Wireless Communications SystemView
Use the full version in E&A 603A for your term project Web Site
URL http://astro.temple.edu/~jkbeard/ Content includes slides for EE320 and EE521 SystemView page A few links
Office Hours E&A 349 Hours Tuesday afternoons 3:00 PM to 4:30 PM MWF 10:30 AM to 11:30 AM Others by appointment; ask by email
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Topic 4 4April 13, 2005
Topics
Today we explore the third toolFDMA, uses separate channels for each userTDMA, uses time multiplexing to time
multiplex the channel between usersNow, CDMA with spread spectrum enables
multiple simultaneous users of the channel Direct-sequence modulation Spreading codes Code synchronization
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Topic 4 5April 13, 2005
Direct Sequence Modulation
We begin with BPSK or QPSK We replace the simple pulse shape
Each “pulse” is a more complex wide band pulse The bandwidth of the resulting signal is that of the
new wide band pulse Spectrum of new signal is given by the
convolution theorem
1 2 1 2
1
2s t s t S S d
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Topic 4 6April 13, 2005
Base Performance Equations
0
0
b
b
SignalPowerE
BitRate
NoisePower N Bandwidth
E SignalPower Bandwidth
N NoisePower BitRate
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Topic 4 7April 13, 2005
Performance in Noise
Base equation (Hayken & Moher equations (5.12) page 263, (E.11) page 518)
Adding spreading function -- Eb and N0 are invariant through matched filter
0 0
20.5 erfc b b
e
E EP Q
N N
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Topic 4 8April 13, 2005
Performance in Interference
Consider a tone as interference In base coded signal
Matched filter spreads tone over channelTone energy becomes part of noise floor
In spread spectrum signalMatched filter spreads tone over channelEffective additional noise reduced by
spreading factor
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Topic 4 9April 13, 2005
Spreading Codes and CDMA
Common method is to use a code for each pulse in a signal
This is the spreading code CDMA is achieved when the spreading
code is one of an orthogonal set for each user of the channel
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Topic 4 10April 13, 2005
Spreading Codes and CDMA
Use a coded pulse for each bit in the message The coded pulse is the symbol-shaping function Make the code one of an orthogonal set for each
user of the same broadened channel Result
BER performance is unchanged for each user Users of other spreading codes look like the noise
floor
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Topic 4 11April 13, 2005
The Symbol-Shaping Function
1
number of pulses in spreading code
spreading code , one of orthogonal set
puse of width
Q
k k c cq
c
k
c c
g t c t g t q T
Q
TT
Q
c t k
g t T
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Topic 4 12April 13, 2005
Walsh-Hadamard Sequences
A simple way to formulate orthogonal code sequences
Based on recursive augmentation of Walsh-Hadamard matrices
1
1
1 1
1 1
i ii
i i
H
H HH
H H
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Topic 4 13April 13, 2005
Properties of Walsh-Hadamard Sequences Matrices are symmetrical Matrices are self-orthogonal Each matrix has rows or columns are a
sequence of orthogonal sequences of length 2k
Cross-correlation propertiesExcellent for zero lagPoor for other lags
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Topic 4 14April 13, 2005
Maximal-Length Sequences
Bit sequence is essentially random Pseudo-random noise (PRN) code Codes Construction
Shift registers with feedback Recursive modulo-2 polynomial arithmetic
PRN codes are then selected for good cross-correlation properties
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Topic 4 15April 13, 2005
Desirable PRN Code Properties
Maximal length – 2m codes before repeating
Balance – equal number of (+1) and (-1) pulses
Closed on circular shifts Contain shorter subsequences Good autocorrelation properties
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Topic 4 16April 13, 2005
Galois Field Vector Extensions of Order 2m
Polynomials modulo 2 of order m-1 Arithmetic is done modulo a generating
polynomial of the form
Proper selection of generating polynomialSequence of powers produces all 2m elementsSet is closed on multiplication
1 other powers of xmgg x x
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Topic 4 17April 13, 2005
An Important Isomorphism
Shift registers with feedbackBits in shift register are isomorphic with
polynomial coefficientsShift is isomorphic with multiplication by xModulo the generating polynomial is
isomorphic to multiple-tap feedback Shift registers with feedback can produce
a Galois field in sequence of powers of x These codes are also called m-sequences
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Topic 4 18April 13, 2005
Gold Codes
R. Gold, optimal binary sequences for spread spectrum multiplexing, IEEE Trans. Inform. Theory, Vol. IT-14, pp. 154-156, 1968.
Based on summing the output of two m-sequence generators
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Topic 4 19April 13, 2005
Code Synchronization
Two phasesRecover timingRecover phaseTiming must be recovered first
To recover timingUse code bits known to be 1’sMatched filter for symbol-shaping functionStep timing in increments of Tc until match is
found
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Topic 4 20April 13, 2005
Assignment
Read 5.2, 5.3, 5.5, 5.7, 5.11, 5.15 Do problem 5.7 p. 273 Next time
Power controlFrequency hoppingAn example
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Topic 4 21April 13, 2005
Chinese Remainder Theorem
Over numbers from 0 to 2.3.5=30
The method works when N has no repeated prime factors
Arithmetic advantages?
1
mod ,p
ii i
Nx x p
p
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Topic 4 22April 13, 2005
A Finite Field
Integers mod a prime A reciprocal of a positive integer always
exists Addition, subtraction, multiplication,
division, all defined and commutative
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Topic 4 23April 13, 2005
Power Control and CDMA
The near-far problem The spreading loss will vary up to 70 dB over the
coverage area Code rejection factors are usually less than this Result is that interference can occur between closely-
spaced handsets or near base stations
Solution is power control Reduce handset power to make received power
constant
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Topic 4 24April 13, 2005
Frequency Hopping
Definition: Changing from channel to channel at regular intervals
Mitigates these problems The near-far problem between handsets Narrow band interference
But, non-coherent detection is necessary Advantages also include
Full and best use of available spectrum for QoS Can be combined with spread spectrum (FH-SS)
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April 13, 2005 Topic 4 25
EE320 March 28
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Topic 4 26April 13, 2005
Topics
Term Project Problem 5.1 p. 262 Problem 5.17 p. 299 Theme Example: WCDMA
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Topic 4 27April 13, 2005
The Term Project
Continue with the start that you turned in with the first quiz backup Input
Frequency sweep 1000 Hz to 3500 Hz Noise to obtain 20 dB SNR
Sampling to obtain good performance Do NOT pitch your beginning and pick up the
ADC to bitstream modules as a template Sample and encode/decode as instructed Measure BER vs. Eb/N0 as instructed Compare hard decoding with soft decoding
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Topic 4 28April 13, 2005
Problem 5.1 p. 262
What is the equation for the spectrum of the spreading sequence given by Eq. (5.5) p. 261?
The chips c(q) are +1 or -1 and the chip shape gc(t) is
1
Q
c cq
g t c q g t q T
1
, 0
0, otherwise
cc
t Tg t T
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Topic 4 29April 13, 2005
Use the Convolution Theorem
The spreading sequence is
The Fourier transform of each term in the sum is
1
Q
c cq
g t c q t q T g t
21 1sincq c c
TG f G f f T
Q Q Q
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Topic 4 30April 13, 2005
Problem 5.17 p. 299
Do you expect FEC codes to have a greater or lesser benefit in Rayleigh-fading channels? Discuss your answer
Rayleigh fading channels have higher BER than otherwise similar Gaussian channels – more opportunity for improvement
Interleavers are necessary to make sure that dfree or fewer bits are exposed in a coherency interval
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Topic 4 31April 13, 2005
WCDMA (1 of 3)
From Theme Example 4 pp.323-328 Cell phone technology generations
First: analog cell phonesSecond: TDMA, IS-95, GSMThird: Universal Mobile Terrestrial
Telecommunications systems (UMTS) WCDMA is a UMTS
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Topic 4 32April 13, 2005
WCDMA (2 of 3)
Functional differencesSimultaneous voice and data transmissionOther data such as real-time TV
Performance improvementsThree times the bandwidthFour times the maximum spreading factorOptional turbo codes
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Topic 4 33April 13, 2005
WCDMA (3 of 3)
Other differencesMultiple simultaneous CDMA downlinkDownlink power controlAsynchronous base stations
Bottom lineBroadband or ISDN in a cell phoneNear-far problems mitigatedHigher density of base stations and users
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Topic 4 34April 13, 2005
Problem 5.19 page 305 (1 of 3)
Define the cellular spectral efficiency nu, in bits/second/Hz/cell; this is the total number of bits/second/Hz transmitted by all users in a cell. For a QPSK base modulation, assume that the spectral efficiency of a single CDMA user is 1/Q bits/second/Hz, where Q is the length of the spreading code. Suppose the receiver requires a specified SINR. Using Eq. (5.85) page 304, develop an expression for nu that depends on the received I0/N0, SINR, and f. Whay does the result not depend explicitly on Q? How does it depend implicitly on Q?
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Topic 4 35April 13, 2005
Problem 5.19 page 309 (2 of 3)
The spectral efficiency forK users in the cellEach transmitting 2/Q bits/second/Hz
From Eq. (5.85) page 304
2K
Q
0
0
1 1N
Q f SINR KI
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Topic 4 36April 13, 2005
Problem 5.19 page 309 (3 of 3)
Rolling up these two equations gives nu as
The spreading factor Q influencesThe interference factor fThe interference to noise ratio I0/N0
0
0
2
1 1N
f SINRI
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Topic 4 37April 13, 2005
Theme Example 1: IS-95
Section 5.12 Page 311 Wireless cellular generations
Analog systems Initial digital systems – GSM, IS-54, IS-95 Integrated voice and data systems
Cell bands Uplink 869-894 MHz, downlink 24 MHz lower Uplink 1930-1990 MHz, downlink 80 MHz lower
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Topic 4 38April 13, 2005
IS-95 Specifications and Usage
Most CDMA cell phones use the IS-95 standard Data rate is 9.6 kbps
Mainly voice Some data, trend is increasing amounts
Direct sequence spread to 1.2288 megachips per second
Channel bandwidth is 1.25 MHz Emerging standard based on IS-95 is
CDMA2000
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Topic 4 39April 13, 2005
Channel Protocol of IS-95
Making an IS-95 call – the Mobile Terminal Searches for Pilot channel and synchronizes with it Locks to the Sync channel that is synchronized with
the Pilot channel, and gets system information (spreading code) of the access and paging channels
Sends a request to set up a call to the Access channel
Listens to Paging channel for traffic channel assignment
Transmits up assigned uplink channel, receives on assigned downlink channel
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Topic 4 40April 13, 2005
Channel Protocol of IS-95
Receiving an IS-95 call – the Base StationTransmits a short message on the paging
channelAccepts Mobile Terminal request for call
DifferencesRequest for call has the phone number to
initiate a callPaging channel has Mobile Terminal phone
number in the paging message
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Topic 4 41April 13, 2005
What The Pilot Channel Is
Shared by all users of the base station Transmitted at higher power than the data channels –
about 20% of total power Unmodulated signal – no CDMA here Provides fast synch and reliable channel tracking to
support coherent demodulation and robust CDMA Mobile terminal
Tracks the pilot channel of the current cell Searches for other pilot channels Switches cells when another pilot signal is stronger Transparent to the user
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Topic 4 42April 13, 2005
The Four Downlink Channels
Separated by use of Walsh-Hadamard codes of length 64Pilot used Walsh #0Sync uses Walsh #32Paging using Walsh #1Traffic uses one of the other codes
See Figure 5.29 page 314
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Topic 4 43April 13, 2005
The Traffic Channel
Multiplexed with control bits for power control
Rate ½ FEC encoded and interleaved Scrambling with long code sequence
follows interleaving (42 bits) Block diagram in Figure 5.30 page 315
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Topic 4 44April 13, 2005
Problem 5.2 Page 263
Filtering with an integrate-and-dump filter is equivalent to convolving with a rectangular pulse of length T. Show, by using Parseval’s theorem, that the noise bandwidth of an integrate-and-dump is 1/T.
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Topic 4 45April 13, 2005
Parseval’s Theorem
For Fourier transform pair see Table A.2 p. 482
For Parseval’s theorem see Eq. (A.36) p. 491
2 2h t dt H f df
exp 2
rect , sinc
H f h t j f t dt
th t H f T f T
T
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Topic 4 46April 13, 2005
Noise Bandwidth
Definition: ratio ofThe variance of the output of a transfer
function to a white noise with two-sided power spectral density N0/2
The power spectral density N0
Equation
2
2 2
1
0N
H f dfT
BT TH
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Topic 4 47April 13, 2005
Power Control: The Near-Far Problem Haykin & Moher Section 5.7 pp. 294-297 Received signal from K CDMA
transmitters is, from Eq. (5.38) p. 279
1
propagation loss on path k
signal k
receiver noise
data sequence k X spreading code k
K
c k kk
k
k b k
k k
x t s t w t
s t b E g t
w t
b g t
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Topic 4 48April 13, 2005
SINR of First User
More detail in 5.4.1 pages 279-283
*1 1 1 1 1
10
1 1
2 22 2 20 1 0
2 2
22
2112
2 00
2
1
1
T K
b b k k kk
b
K K
y b k k b kk k
b bgK
yb k
k
y x t g t dt b E E R
y b E
y y N E R N EQ
y E ESINR D
NN E
Q
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Topic 4 49April 13, 2005
Degradation in Multi-User Performance
221
20 1
1
1 11
1
gK
b k
k
DEK
Q N K
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Topic 4 50April 13, 2005
FEC Coding and CDMA
Haykin & Moher Section 5.8 pp. 297-299 Direct Sequence Spread Spectrum (DS-
SS) spreads spectrum without added redundancy
Use of FEC spreads spectrum and adds redundancy
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Topic 4 51April 13, 2005
Spreading Rate and Degradation The maximum spreading rate is
Degradation in multi-user performance is
1, FEC code rateDSQ Q r
r
1 1
0 0
1
0
/1 11 1
/
11
s bg
DS
b
E E rK KD
Q N Q r N
EK
Q N
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Topic 4 52April 13, 2005
Example 5.5 Pages 298-299
Suppose a system has an information rate Rb=4800 bps and Q=Rc/Rb=32. The system is error protected by a rate-1/2 convolutional code. Compare the degradation Db with and without FEC coding at a BER of 10-5 when there are seven interfering users.
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Topic 4 53April 13, 2005
Base Parameters Without FEC Encoding
1 5
0
0
2
g
210 4.265043367=
4.26504336710 log 20 log
2
9.59846903
4.2650433678 1D 1
32 2
0.33449332
b
b
EQ
N
E
N
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Topic 4 54April 13, 2005
Base Parameters With FEC Encoding With rate-1/2 constratin-length 7
convolutional FEC encoding BER improved to 10-5 with Eb/N0
decreased to 4.5 dB Result is Dg increased to 0.62 Improvement is about 2.7 dB
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Topic 4 55April 13, 2005
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April 13, 2005 Topic 4 56
EE320 Telecommunications Engineering
James K Beard, [email protected]&A 349
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Topic 4 57April 13, 2005
Quiz 2
Not a difficult quiz Some problems were a slight variation of
the text material such as substitution of one code for another
I allowed 2 ½ hours for a 50-minute quiz The curve from this quiz should be
definitive
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Topic 4 58April 13, 2005
Crunch Time
We have about four weeks leftLast day of class is Monday May 2Final exam is Monday May 11, 11:00 AM -
1:00 PM Some of you are in trouble
Some quiz grades are lowNot everyone will passDepartment has been notified
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Topic 4 59April 13, 2005
Watch for a Warning
If you are heading toward a grade lower than CYou will receive a warning with your Quiz 2
gradeThe cover page of your quizYour minimum Final Exam grade will be given
Final ExamBy the bookTwo hours, no talking
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Topic 4 60April 13, 2005
The Problem
EE320 Telecommunications Engineering is… A tough course A required course Material packed with new concepts and technology
But the Perception of some is… An easy course A required course that everyone will pass Watch the slides, read the text before each quiz, and
everything will be OK
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Topic 4 61April 13, 2005
The Solution
Take notes Regular class notebook On the slides The act of taking notes helps retention
Study a little Even the best student needs to do two or three
homework problems per chapter The study guide can help you pick them
Do well on the Final Examination A good grade there can bring up your final grade Don’t wait until Study Day to catch up on four courses
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Topic 4 62April 13, 2005
Problem 5.3 page 265
Fill in the missing details of Eq. (5.19) A non-spread link The jammer is on for T seconds Spectrum
After multiplying by de-spreading sequence Development as in Eq. (5.17) Eq. (5.17) with Tc->T, Q->1 because of no spreading
2sincgS f A f f T
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Topic 4 63April 13, 2005
Problem 5.3 page 265
Jammer spectral density at baseband is
The noise bandwidth of an integrate-and-dump is 1/T (see problem 5.2)
The noise variance is
2
1
p pS f S f df
AT
, bandwidthS f A f
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Topic 4 64April 13, 2005
Properties of m-Sequences
Length property: Each m-sequence is of length 2m-1 Balance property: Each m-sequence has 2m-1 ones and
2m-1-1 zeros Shift property: The modulo-2 sum of an m-sequence and
any circularly-shifted version of itself produces another circularly-shifted version of itself
Subsequence property: Each m-sequence contains a subsequence of 1, 2, 3,…,m-1 zeros and ones
Autocorrelation property: See Equations (3.30) and (3.31) pages 272, 272
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Topic 4 65April 13, 2005
Problem 5.7 page 272
Prove the autocorrelation property of Eq. (5.31) for m-sequences (Hint: use preceding Properties 1 through 5 as needed.)
Eq. (5.30) and (5.31) pages 271 and 272
1
0
1mod
1, 0
1, 0
Q
jjq
R k c q c q k QQ
k
kQ
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Topic 4 66April 13, 2005
Proof of Autocorrelation Property of m-Sequences By the Shift property, the circular
autocorrelation, a modulo-2 sum of an m-sequence and a circularly-shifted version of itself, is another circularly-shifted version of iteslf
From the Balance property an m-sequence has one more 1 than zeros.
QED
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Topic 4 67April 13, 2005
Course Material Overview
The problemMake a cell phone system workDeal with mobile terminalsDeal with urban fading
The solutionConstruct the network layer infrastructureDispense the data link layer mobile terminalsExploit the physical layer successfully
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Topic 4 68April 13, 2005
Designing the Data Link Layer
The problemAddressing multiple users
Data push – making calls Data pull – accepting calls SINR
Dealing with urban fading The solution
IS-95 and other 2nd generation standardsThird generation standards
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Topic 4 69April 13, 2005
How IS-95 Meets the Challenges 64 Walsh-Hadamard codes Uplinks 45 MHz below downlinks Synchronization
The pilot channel (Walsh code 0) allows coherent detection
The synchronization channel (Walsh code 32) provides spreading codes of access and paging channels
Paging channel (Walsh code 1) assigns access channel
Access channels (other Walsh codes)
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Topic 4 70April 13, 2005
Meeting the Challenge of Fading Forward Error Correction Codes (FECs)
Allows robust operation with high bit error rates (BER)
Spread spectrum Allows higher BER in frequency-selective fading
Interleaving Helps bridge dropouts from fading and interference
over intervals of a few milliseconds
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Topic 4 71April 13, 2005
Meeting the Challenge of Higher Traffic and New Uses Use of CDMA to allow channel sharing Use of power control to limit SINR at the base
station In next-generation standards such as Universal
Mobile Terminal Terrestrial Telecommunication Systems (UMTSs) Base station power control to limit SINR at the mobile
station Higher bandwidths and data rates More sophisticated coding to approach Shannon
channel limit More versatile data formats for text, video, etc.
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Topic 4 72April 13, 2005
Problem 5.8 Page 274
To show that scramblers based on m-sequences are not very good encryption devices, determine the minimum number of consecutive bits that would need to be known to reconstruct the initial state.
The generating polynomial is known. Use Figure 5.10, f(x)=x7+x3+1 as an
example
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Topic 4 73April 13, 2005
Solution to Problem 5.8
If the generating polynomial is known then the entire m-sequence is known
The problem is reduced to determining how many successive bits in the m-sequence are necessary to uniquely determine the position in the sequence
From Figure 5.10 m, the number of lags – seven for this example – bits in a row determines the state of the shift register
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Topic 4 74April 13, 2005
RAKE Receiver
RAKE Not an acronym Based on signal flow diagram that looks like a garden
rake
Receiver architecture used for CDMA systems Concept addresses multipath environments Consists of
An array of up to Q parallel receiver Timing between these receivers varies in steps of Tc
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Topic 4 75April 13, 2005
RAKE Signal Flow
Each channelMultiplied by spreading code g(t) Integrate and dump filter of length T=Q.Tc
Weight by expected corresponding multipath channel amplitude
All are then summed into a single-channel processor
Result is “matched filter” to multipath channel
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Topic 4 76April 13, 2005
Example 5.5 Pages 298-299
Given BPSK Information rate Rb=4800 bps
Spreading factor Q=Rc/Rb=32
Rate ½ convolutional code BER is 10-5
Number of interfering users is 7 (K=8) Compare degradation Dg with and without FEC
Use Eqs. Page 272 and (5.72) just preceding1
0
11 b
g
EKD
Q N
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Topic 4 77April 13, 2005
Example 5.5 (Continued)
The BER of 10-5 indicates single-user
The degradation factor is
0 0
9.12 10 dBb sE E
N N
1
8 11 9.12 0.33 -4.8 dB
32gD
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Topic 4 78April 13, 2005
Example 5.5 (Continued)
With rate ½ constraint length 7FEC encoding Spreading factor Qs=16, total Q=32
Single-user
Degradation factor is
0 0
2.82 4.5 dBb sE E
N N
1
8 11 2.82 0.62 -2.1 dB
32gD
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Topic 4 79April 13, 2005
Example 5.5 (Concluded)
Degradation improves 2.7 dB with FEC Degradation vs. loading for rate ½ codes
shown in Figure 5.23 page 298No improvement for single userGains of about 2 dB for K near Q Improvement doesn’t vary much with BER
Conclusion: BER is important power-bandwidth tradeoff with multiple users
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Topic 4 80April 13, 2005
Problem 5.49 Page 336
Describe how the use of a rate ¼ FEC doe would affect the implementation and performance of a RAKE Receiver
Effects of change in FEC code Delay-line parallelism is not affected Channel tracking (see 5.6 pages 292-294) is affected
because algorithm operates before FEC and Eb/N0 is lower with better codes
Measures for use with better codes include Use a known pilot signal, as with IS-95 Use training sequences (standard messages) for
channel tracking, as with WCDMA
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April 13, 2005 Topic 4 81
EE320 Telecommunication Engineering
Wireless Architectures
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Topic 4 82April 13, 2005
Open System Interconnection (OSI) Model Seven-layer model
Physical layer (modem)Data link layerNetwork layerTransport layer (packetizing, ACK/NAK)Session layer (Service selection and access)Presentation layer (encryption, compression)Application layer (HMI)
Layers designed together as a system
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Topic 4 83April 13, 2005
Power Control Architectures
Open Loop Mobile terminals measure strength of pilot channel Transmit power decreased for strong pilot channels Fast and simple, but must be approximate
Closed Loop Base station measures mobile terminal signal strength Mobile station receives signal strength by downlink Accurate but delay and averaging must be smaller than channel
coherence time Outer Loop Control
Base station uses expected signal strength in control algorithm Complexity can result in a slow loop
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Topic 4 84April 13, 2005
Power Control: Summary
Power control minimizes SINR in busy cells Handset power control minimizes SINR in the
base station but not at the mobile terminal Methods still evolving Next generation standards will implement
Newer techniques such as outer-loop control Base station power control for SINR control at the
mobile station
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Topic 4 85April 13, 2005
Next Time
Assignment: Read parts of Chapter 77.3, OSI7.6, Power Control7.7, Handover7.8, Network Layer