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

Jossy Sayir (CUED) Communications: Handout 5 Lent Term 1 / 27

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


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


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

)


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



Modulator

Sourcemessage

Transmitter

Sourcemessage

Transmitter

..

.

Channel DestinationReceiverreceived

signal

transmitted

signal

transmitted

signal

User 1

User K

Multiple

Access



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)



B

Signature

Time

Frequency

Tf



ExampleOther real-life examples include

Multiple cell phones desiring to call at the same timeMultiple computers accessing the internetMultiple satellites transmitting to earth


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



user

2

Signature

Time

Frequency

Tf

Bu

B

user

K

user

1



FDMAThe time-domain signals get mixed together though...

xK(t)

..

. ..

.cos(2πfc,Kt)

cos(2πfc,1t)

User 1

User K

sFDMA(t)

x1(t)



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

)


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



user

K

Signature

Time

Frequency

TuTf

B

user

1 user

2



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


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 .



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)



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)



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.


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 .



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.



user 2

Signature

Time

Frequency

B

Tf

user K

user 1


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.


Multiple Access TechniquesExample: GSM

user K

Signature

Time

Frequency

TuTf

Bu

B

user 1

user 2


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)


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


communications - ib paper 6 handout 5: multiple access

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