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Multiplexing

• The combining of two or more information channels onto a common transmission medium.

• Basic forms of multiplexing: – Frequency-division multiplexing (FDM). – Time-division multiplexing (TDM)– Code-division multiplexing (CDM)

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FDM

• Frequency Division Multiplexing – The deriving of two or more simultaneous,

continuous channels from a transmission medium by assigning a separate portion of the available frequency spectrum to each of the individual channels.

• FDMA (frequency-division multiple access): The use of frequency division to provide multiple and simultaneous transmissions.

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• Transmission is organized in frequency channels, assigned for an exclusive use by a single user at a time

• If the channel is not in use, it remains idle and cannot be used by others

• There are channeling frequency plans elaborated to avoid mutual co-channel and adjacent-channel interference among neighboring stations

• The use of a radio channel or a group of radio channels requires authorization (license) – for each individual station or for group of stations

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FDM (Frequency Division Multiplexing)F

requ

ency

TimeFrequency channel

Bm

Bc

Example: Telephony Bm = 3-9 kHz

Frequen

cyTime

Power FDMA

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FDD

• Frequency division duplexing – 2 radio frequency channels for each duplex

link (1 up-link & 1 down-link or 1 forward link and 1 reverse link)

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Transmitter Emissions

• Transmitter output components– Fundamental (wanted)

signal– Harmonic emissions– Master oscillator

(fundamental & harmonics)– Non-harmonically related

spurious– Noise

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10

Frequency (relative)

Out

put s

pect

rum

Ideal Real

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Receiver response

• Fundamental channel• Spurious channels

– Intermediate frequency

– Image frequency– Channels received via

LO harmonics– Intermodulation

channels

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10Frequency

Res

pons

e

Ideal

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Intermodulation

• 2 or more signals, nonlinear circuit

• Intermodulation products: Fi = SCkFk

• {Ck} positive/negative integers or zero

• {Fk} frequencies of signals applied

• Order of Intermod. Product = S|Ck|• 3rd order (2F1-F2, 2F2-F1), also 5th and 7th

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• Non-ideal wideband linear systems are frequently treated by expressing the output (Y) of the system as a power series:

• where X is the total input signal, and the coefficients a are presumed to be real and independent on X.

• Assume, for simplicity, that input consists of three elementary signals:

Y a a X a X a X a Xnn 0 1 2

23

3 ... ...

X A t t B t t C t t ( ) cos( ) ( ) cos( ) ( ) cos( ) 1 2 3

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• Some simple calculations will show that the output of the system Y, in addition to the linearly transposed input signals, contains the following spectral components:

• 1st order

Multiplied version of the input signal

1 1 2 3[ ( ) cos( ) ( ) cos( ) ( ) cos( )]a A t t B t t C t t

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• 2nd order• a) Distorted version of the modulating signals

• b) 2nd harmonics

• c) Sum and difference

aA t

aB t

aC t2 2 2 2 2 2

2 2 2( ); ( ); ( )

2 2 22 2 21 2 3( ) cos(2 ); ( ) cos(2 ); ( ) cos(2 )

2 2 2

a a aA t t B t t C t t

ttCtBa

ttCtAa

ttBtAa

)cos()()(

)cos()()(

)cos()()(

132

322

212

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3rd ordera) Distorted modulating signal

b) 3rd harmonics

c) Crossmodulation

d) Intermodulation

3 3 33 1 3 2 3 3

3 3 3( )cos( ); ( ) cos( ); ( ) cos( )

4 4 4a A t t a B t t a C t t

3 3 33 1 3 2 3 3

1 1 1( )cos(3 ); ( ) cos(3 ); ( ) cos(3 )

4 4 4a A t t a B t t a C t t

2 2 23 2 3 1 3 1

2 2 23 3 3 2 3 3

3 3 3( ) ( ) cos( ); ( ) ( ) cos( ); ( ) ( ) cos( )

2 2 23 3 3

( ) ( ) cos( ); ( ) ( ) cos( ); ( ) ( ) cos( )2 2 2

a A t B t t a A t B t t a A t C t t

a A t C t t a B t C t t a B t C t t

2 2 23 2 1 3 1 2 3 3 1

2 2 23 1 3 3 3 2 3 2 3

3 3 3( ) ( ) cos ( 2 ; ( ) ( ) cos ( 2 ; ( ) ( ) cos ( 2

4 4 43 3 3

( ) ( ) cos ( 2 ; ( ) ( ) cos ( 2 ; ( ) ( ) cos ( 24 4 4

a A t B t a A t B t a A t C t

a A t C t a B t C t a B t C t

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Non-essential channels

F

Y

X

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F-D Separation Concept

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Theoretical Cells & Cell Clusters

Various combinations possible

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Frequency and Distance Separation

Separation acceptable

Separation unacceptable

L+FDR=

Frequency separation

Dis

tanc

e se

para

tion

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F-D Separation: 1D (Line)

1 2 1 2 1 2

Separation by (reuse distance) 1 zone 2 channels

1 2 3 1 2 3 1

2 zones 3 channels

n zones (n +1) channels

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F-D Separation: 2D (Surface)

Reuse distance = 1 4 channels Reuse distance = 2 9 channels

n zones (n +1)2 channels

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Cell clusters

Various combinations possible

37

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F-D Separation: 3D (Space)

n zones (n+1)3 channels

9

9

9 > 27 4 4 > 8

1 zone 8 channels 2 zone 27 channels

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Ideal Lattices

• Bound-less, regular, plane lattice• Each station located at a node• All nodes occupied (no "holes")• All stations identical (omnidirectional)• Uniform propagation (no terrain

obstacles)• Uniform EM environment • One set of channels regularly re-used

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Equipment deficiency: example Spectrum “blocked” by typical UHF-TV terrestrial transmitter due to receiver’s deficiencies (“FCC

Taboos”)

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350Distance from transmitter, km

No

of

chan

nel

s d

enie

d

Ideal

Real

Dixon64

Area * No. of channelsideal: 1%co-ch: 23%other: 77%

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OFDM• Orthogonal Frequency Division

Multiplexing (OFDM)– The channel is split into a

number of sub-channels– Each sub-channel transmits a

part of the original information– Each sub-channel adjusted to

its environment (S/N)– Reduces multipath & selective

fading– Allows for higher speeds– Requires smart signal

processing – Used in 802.11a(USA),

DTTB(Eu), Hyperplan(Eu), Power Line Coms. standards.

Ser

ial-t

o-P

aral

lel C

onve

rter F1

F2

FN

Dem

odul

atio

n S

igna

l Pro

cess

ing

Ser

ial-t

o-P

aral

lel C

onve

rter

Digital Modulation

Sub-Ch 1

Sub-Ch 2

Sub-Ch N

Delogne P, Bellanger M: The Impact of Signal Processing on an Efficient Use of the Spectrum, Radio Science Bulletin June 1999, 23-28LeFloch B, Alard M, Berrou C: Coded Orthogonal Frequency Division Multiplex, Proc of IEEE June 1995, 982-996

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TDM

• Time Division Multiplex: A single carrier frequency channel is shared by a number of users, one after another. Transmission is organized in repetitive “time-frames”. Each frame consists of groups of pulses - time slots.

• Each user is assigned a separate time-slot.• TDD – Time Division Duplex provides the

forward and reverse links in the same frequency channel.

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TDMF

requ

ency

TimeTime slot

Time-frame

Example: DECT (Digital enhanced cordless phone) Frame lasts 10 ms, consists of 24 time slots (each 417s)

Time

Power densityTDM

Frequen

cy

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SDM

• Space Division Multiple Access controls the radiated energy for each user in space using directive antennas– Sectorized antennas – Adaptive antennas

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CDMA or SS • Code Division Multiple Access or Spread

Spectrum communication techniques– FH: frequency hoping (frequency synthesizer controlled by pseudo-random sequence of

numbers)

– DS: direct sequence (pseudo-random sequence of pulses used for spreading)

– TH: time hoping (spreading achieved by randomly spacing transmitted pulses)

– Other techniques• Hybrid combination of the above techniques (radar and other

applications) • Random noise as carrier

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CDMA - FH SSF

requ

ency

TimeTime-frequency slot

Transmission is organized in time-frequency “slots”. Each link is assigned a sequence of the slots, according to a specific code. Used e.g. in Bluetooth system

BmBc

CDMA

Time

Power density

Frequen

cy

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DS SS communications basics

Originalinformation

Propagation effects Transmission

Reconstructedinformation

Original signal Spread signal

Spread signal+ Reconstr. signal

Spreading

De-spreading

Unwanted signals + Noise

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SS: basic characteristics

• Signal spread over a wide bandwidth >> minimum bandwidth necessary to transmit information

• Spreading by means of a code independent of the data

• Data recovered by de-spreading the signal with a synchronous replica of the reference code– TR: transmitted reference (separate data-channel and reference-channel,

correlation detector)

– SR: stored reference (independent generation at T & R pseudo-random identical waveforms, synchronization by signal received, correlation detector)

– Other (MT: T-signal generated by pulsing a matched filter having long, pseudo-randomly controlled impulse response. Signal detection at R by identical filter & correlation computation)

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DS SS: transmitter

Modulator X Antenna

[A(t), (t)] Information

[g1(t)]

Carriercos(0t)

Modulated signalS1(t) = A(t) cos(0t + (t))band Bm Hz

Spread signal g1(t)S1(t)band Bc HzBc >> Bm

gi(t): pseudo-random noise (PN) spreading functions that spreads the energy of S1(t) over a bandwidth

considerably wider than that of S1(t): ideally gi(t) gj(t) = 1 if i = j and gi(t) gj(t) = 0 if i j

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DS SS-receiver

Spreading function

[g1(t)]

Correlator &

bandpassfilter

Xantenna

Linearcombinationg1(t)S1(t)g2(t)S2(t)…….gn(t)Sn(t)N(t) (noise)S’(t)

g1(t) g1(t)S1(t)g1(t) g2(t)S2(t)…….g1(t) gn(t)Sn(t)g1(t) N(t)g1(t) S’(t)

S1(t)

To d

emod

ulat

or

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SS-receiver’s Input

Wanted (spread) signal: g1(t)S1(t)

Unwanted signalsSS s.: g2(t)S2(t); …;

gn(t)Sn(t)Other s. : S’(t)Noise: N(t)

Bc

W/Hz

Hz

Signal-to-interference ratio (S/ I)in = S/ [I()*Bc]Bc = Input correlator bandwidthI() = Average spectral power density of unwanted signals in BcS = Power of the wanted signal

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SS-correlator/ filter output

Bm

Bc

(S/ I)out = S/ [I()*Bm]

Bc = Input correlator bandwidth Bm = Output filter bandwidthI() = Average spectral power density of unwanted signals & noise in BmS = power of the wanted signal at the correlator output

Signal-to-interference ratio

Wanted (correlated) signal: de-spread to its original bandwidthas g1(t) g1(t)S1(t) = S1(t) with g1(t) g1(t) = 1

Uncorrelated (unwanted) signalsspread & rejected by correlator + noiseg1(t) S’(t); g1(t) N(t); g1(t) gj(t)Sj(t) = 0

as gi(t) gj(t) = 0 for i j

Spreading = reducing spectral power density

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SS Processing Gain =

= [(S/ I)in/ (S/ I)out ] = ~Bc/ Bm

Example: GPS signalRF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz

Processing gain ~20’000 (+43 dB)

Input S/N = -20 dB (signal power = 1% of noise power)

Output S/N = +23 dB (signal power = 200 x noise power)

(GPS = Global Positioning System)

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SS systems attributes (1)

• Low spectral density of the signal – LPI: low probability of intercept– LPPF: low probability of position fix– LPSE: low probability of signal exploitation– Privacy– Covert operations capabilities – Low interference potential

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SS systems attributes (2)

• AJ: anti-jamming/ anti-interference capability • Security• Natural cryptographic capabilities• Multiple-user random access communications

with selective addressing (CDMA)• High time resolution (~1/B; multi-path suppression)

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Summary

• To illustrtae the nature of the multiple access techniques consider a number of guests at a cocktail party. The aim is for all the guests to hold an intelligible conversation. In this case the resource available is the house itself

• FDMA: each guest has a separate room to talk to their partner

• TDMA: everyone is in a common room and has a limited time slot to hold the conversation

• FH-CDMA: the guests run from room to room to talk• DS-CDMA: everyone is in a common room talkim at the

same time, but each pair talks in a different language

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Access Control to Radio Resources

• Distributed wireless networks (e.g. packet radio, ad hoc networks) have no central control.

• Centralized wireless networks (e.g. WLAN, Cellular) control the use of radio channel; various approaches exist

• Slotted systems (e.g. TDMA) require wide network synchronization for use of discrete time slots

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Packet Radio Protocols

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Packet Radio

• In packet radio access techniques, many user attempt to access a single channel, which may led to collisions.

• Protocols aim at limiting collisions• ALOHA is the oldest, classic protocol,

developed in 1970 in Hawaii as an extension of TDMA and FDMA

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ALOHA• If 2 or more users transmit at the same time so that receiver

receives more than one packet, the receiver is unable to separate the packets since they are not orthogonal in time (like in TDMA) or in frequency (like in FDMA).

• The vulnerable period is the time interval during which the packets are susceptible to collisions with transmissions from other users

Packet B

Packet A

Packet CTransmitter 1

Transmitter 2

t1 T1+2

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• In pure ALOHA, the vulnerable period is 2 packet durations. A user transmits whenever it has a packet to deliver. If no acknowledgment (ACK) is received, the user waits a random time and retransmit the packet. The throughput is T = Re-2R, R being the normalized channel traffic in Erlangs (Tmax = 0.184 at R = 0.5)

• In slotted ALOHA, time is divided into equal time slots of length greater than the packet duration. The users have synchronized clocks and transmit messages only at the beginning of a new time slot. This prevent partial collisions where one packet collides with a portion of another. The vulnerable period is only one packet duration. The throughput is T = Re-R (Tmax = 0.368 at R = 1)

• ALOHA protocols do not listen to the channel before transmission, and do not exploit information about the other users.

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• Carrier Sense Multiple Access (CSMA) protocols base on monitoring the channel. If the channel is idle (no carrier is detected), then the user is allowed to transmit. Important are detection delay and propagation delay.

• Reservation protocols – certain packet slots are assigned with priority

5428/01/2003

References

• Coreira LM, “Wireless Flexible Personalized Communications”, J Wiley

• Dunlop J, Smith DG, “Telecommunication Engineering”, Chapman & Hall

• Reed JH, “Software Radio”, Prentice Hall• Taub H, Shilling DL, “Principles of

Communication Systems”, McGraw Hill