Communications - IB Paper 6 Handout 5: Multiple Access
Transcript of Communications - IB Paper 6 Handout 5: Multiple Access
CommunicationsIB Paper 6
Handout 5: Multiple Access
Jossy Sayir
Signal Processing and Communications LabDepartment of Engineering
University of [email protected]
Lent Term
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Outline
1 Introduction and Motivation
2 Multiple Access TechniquesFrequency-Division Multiple AccessTime-Division Multiple AccessCode-Division Multiple AccessExample: GSM
3 Course SummaryImportant TopicsRelevant Past Tripos Questions
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Introduction and Motivation
So far...We have studied techniques for single user point-to-pointcommunications.
Source
Destination
Channel
received
signal
transmitted
signal
message
received
message
Transmitter
Receiver
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Introduction and Motivation
Remember (Handout 4)If we have one user we have that
y(t) = x(t) + z(t)
x(t), y(t) are the transmitted and received signals of bandwidth Bz(t) is the noise with flat power spectral density N0
the channel capacity is given by
C = B log2
(1 +
PN0B
)
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Multiple Access Techniques
What is Multiple Access?Multiple access techniques
are special modulation techniques to accommodate multiple usersin a communications channelallow multiple users to share a finite amount of bandwidth
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Multiple Access Techniques
Modulator
Sourcemessage
Transmitter
Sourcemessage
Transmitter
..
.
Channel DestinationReceiverreceived
signal
transmitted
signal
transmitted
signal
User 1
User K
Multiple
Access
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Multiple Access Techniques
ExampleImagine that all of you (multiple users) have a question (which may ormay not be the same) to ask me (receiver). What techniques can weuse, such that I understand all questions?
One after the other (time-division multiple access), each using thewhole bandwidth for a fraction of the time.All at the same time, but each with a different frequency(frequency-division multiple access), using a fraction of thebandwidth all the timeAll at the same time using the whole bandwidth, each with adifferent signature (code-division multiple access), i.e., a differentlanguage (known to the receiver)
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Multiple Access Techniques
B
Signature
Time
Frequency
Tf
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Multiple Access Techniques
ExampleOther real-life examples include
Multiple cell phones desiring to call at the same timeMultiple computers accessing the internetMultiple satellites transmitting to earth
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Multiple Access TechniquesFrequency-Division Multiple Access
FDMAMultiple users are multiplexed in the frequency domain, such that theydo not interfere with each other, using a fraction of the total bandwidth.Essentially DSB-SC modulation for each user, such that spectrums donot overlap.
User K
ffc,1
...
fc,2 fc,Kfc,K−1
Bu
B
User K − 1User 1 User 2
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Multiple Access TechniquesFrequency-Division Multiple Access
user
2
Signature
Time
Frequency
Tf
Bu
B
user
K
user
1
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Multiple Access TechniquesFrequency-Division Multiple Access
FDMAThe time-domain signals get mixed together though...
xK(t)
..
. ..
.cos(2πfc,Kt)
cos(2πfc,1t)
User 1
User K
sFDMA(t)
x1(t)
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Multiple Access TechniquesFrequency-Division Multiple Access
Capacity of FDMAAssuming no overlap nor guard bands, i.e., B = KBu (see Figure) thecapacity of each user is
CFDMAk =
BK
log2
(1 +
PN0
BK
)
= Bu log2
(1 +
PN0Bu
)
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Multiple Access TechniquesTime-Division Multiple Access
TDMAMultiple users are multiplexed in time, so that they transmit one afterthe other, using the whole bandwidth B. We divide the frame durationTf into K time slots of duration Tu = Tf
K .
. . .
Tu
User 2 User KUser 1 User K − 1
Tf
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Multiple Access TechniquesTime-Division Multiple Access
user
K
Signature
Time
Frequency
TuTf
B
user
1 user
2
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Multiple Access TechniquesTime-Division Multiple Access
Capacity of TDMAAssuming no overlap nor guard intervals, i.e., Tf = KTu (see Figure)and users transmit with power KP when active (so that the averagepower per user is P), the capacity of each user is
CTDMAk =
1K
B log2
(1 +
PKN0B
)
= Bu log2
(1 +
PN0Bu
)
= CFDMAk
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Multiple Access TechniquesCode-Division Multiple Access
CDMAMultiple users are multiplexed in code or signature, and transmit usingthe whole bandwidth B over the whole time frame of duration Tf .
... but what is a signature?A signature is a signal characteristic to each user, and known to thereceiver. We denote the K signatures by ck (t) for k = 1, . . . ,K .
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Multiple Access TechniquesCode-Division Multiple Access
Signature user 3 c3(t)
t
t
t
t
+1
+1
Signature user 1 c1(t) Signature user 2 c2(t)
Signature user 4 c4(t)
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Multiple Access TechniquesCode-Division Multiple Access
cos(2πfct)
..
. ..
.
User 1
User K
c1(t)
cK(t)
s1(t)
sK(t)xK(t)
x1(t)
sCDMA(t) =
K∑
k=1
ck(t)xk(t) cos(2πfct)
cos(2πfct)
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Multiple Access TechniquesCode-Division Multiple Access
Orthogonal SignaturesThe received CDMA signal is given by
y(t) =K∑
k=1
ck (t)xk (t) cos(2πfc t) + z(t)
where z(t) is the noise signal. Assuming we have no noise (i.e.,z(t) = 0) and perfect carrier demodulation we have
y(t) =K∑
k=1
ck (t)xk (t)
where y(t) is the demodulated signal.
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Multiple Access TechniquesCode-Division Multiple AccessOrthogonal SignaturesIf we chose the signatures to be orthogonal, i.e.,
〈ck (t), cj(t)〉 =1T
∫ T
0ck (t)cj(t)dt =
{0 j 6= k1 j = k
we can recover the transmitted information by each user, by simplyperforming the following operations for all j = 1, . . . ,K (assuming thatxk (t) are rectangular pulses)
〈y(t), cj(t)〉 =1T
∫ T
0y(t)cj(t)dt
=1T
∫ T
0
K∑
k=1
ck (t)xk (t)cj(t)dt =
{0 j 6= kxk (t) j = k
assuming xk (t) does not vary within the period T .
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Multiple Access TechniquesCode-Division Multiple Access
Orthogonal Signatures: SummaryIf we chose the signatures to be orthogonal, the signals can overlap inboth time and frequency and we are still able to recover the informationof each user.
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Multiple Access TechniquesCode-Division Multiple Access
user 2
Signature
Time
Frequency
B
Tf
user K
user 1
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Multiple Access TechniquesExample: GSM
GSMGSM uses a combination of both TDMA and FDMA, and assigns atime slot and a frequency carrier to each.
GSMIn order to minimise the distortion due to fading (mobility, multipathpropagation) GSM changes the time-frequency allocations assigned todifferent users during transmission.
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Multiple Access TechniquesExample: GSM
user K
Signature
Time
Frequency
TuTf
Bu
B
user 1
user 2
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Course SummaryImportant Topics
1 Communications ChannelsI ConvolutionI NoiseI Multipath and Doppler (coherence bandwidth and time)
2 Analogue ModulationI AM, DSB-SC, SSB-SC (properties, differences, spectrum, power)I FM: Carson’s rule
3 DigitisationI SamplingI Quantisation (quantisation noise)I Representation of digital signals and spectrum
4 Digital modulation ASK, FSK, BPSK (spectrum, error probability)5 Channel capacity
I Concept of rate and channel codingI Channel capacity
6 Multiple-Access (FDMA, TDMA, CDMA)
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Course SummaryRelevant Past Tripos Questions
2012 Paper 6, Questions 5 and 62011 Paper 6, Questions 5 and 62010 Paper 6, Questions 5 and 62009 Paper 6, Questions 5 and 62008 Paper 6, Questions 5 and 62007 Paper 6, Questions 4 and 52006 Paper 6, Question 52005 Paper 6, Question 52004 Paper 6, Question 62003 Paper 6, Question 5 excluding the final two lines of part (d).2002 Paper 6, Question 52002 Paper 6, Question 6 except part (c).2001 Paper 6, Question 6
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