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Communications Theory and Engineering

Master's Degree in Electronic Engineering

Sapienza University of Rome

A.A. 2020-2021

Multiple Access

TDMA, FDMA, CDMA

From the single link to the network

• In a digital communication network many users simultaneously communicate with one another

• A key issue is how to provide access to a single transmission medium for two or typically many more users

Domains of application

• Full-duplex transmission on a single medium: the two directions of transmission must share one medium such as a wire pair (example the digital subscriber loop for the telephone channel)

• Multiple communications over a common high-speed link, such as the optical fiber: this is called multiplexing

• Many users share a wireless channel and broadcast information: cellular communications, wireless local area networks, satellite networks

Multiple Access

• Multiple access refers in general to any situation where two or more users share a common transmission medium

• Messages corresponding to different users must be separated in some fashion

• They should not interfere with one another

• This is usually obtained by making the messages orthogonal to one another in the signal space

Messages separated in time

• In Time Division Multiple Access (TDMA) each user is allowed to transmit only within specified time intervals (Time Slots). Different users transmit in differents Time Slots

• When users transmit, they occupy the whole frequency band; separation among users is performed in the time domain

TDMA : Frame Structure

• TDMA requires a centralized control node, whose primary function is to transmit a periodic reference burst that defines a frame and forces a measure of synchronization of all users

• This frame is divided into Time Slots, and each user is assigned a Time Slot for transmitting information

TF

TS

Frame

Time Slot

Refe

renc

e Bu

rst

TDMA : Frame Structure

User 1 User 2 User 3

TDMA : guard intervals

• Since the distance between users and central unit may vary, users may receive the reference burst with different phases, and correspondingly transmit misaligned traffic bursts

• There is therefore a need for guard intervals to take into account this variability and avoid overlaps

• The Time Slot is therefore longer than strictly needed, thereby avoiding the overlap in presence of unknown propagation delays

misalignment misalignment

with guard time without guard time

TDMA : preamble

• Since traffic bursts are transmitted with uncertain phases relative to the reference burst, a preamble is needed at the beginning of each traffic burst

• The preamble allows the receiver to acquire, on top of coarse synchronization provided by the reference burst, a fine estimate of timing and carrier phase

preamble information

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

-100

-50

0

50

100

TIME [s]

AMPLITUDE [V]

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

-15

-10

-5

0

5

10

15

Time [s]

Amplitude [V]

sRX

j( ) t( )sTXj( ) t( )

Received signal afterpropagation over a two-paths channel

BEWARE!

At risk of multiuserinterference!

TDMA and channels with multipath

Frequency DivisionMultiple Access (FDMA)

• Each user transmits with no limitations in time, but using only a portion of the whole available frequency bandwidth.

• Users are separated in the frequency domain.

User 1

User 2

User 3

Time

Frequency

Power

FDMA vs. TDMA

• Frequency division is very simple: all transmitters sharing the medium have output power spectra in non-overlapping bands.– Many of the problems experienced in TDMA due to different

propagation delays are eliminated in FDMA

• A major disadvantage of FDMA is the need for expensive and sophisticated bandpass filters– TDMA is realized primarily with much cheaper logic functions

• Another disadvantage of FDMA is sensitivity towards channelnon-linearity

TDMA + FDMA

FDMA TDMA + FDMA

Frequency

Time Time

Frequency

Power

CarriersUsers

User 1

User 2

User 3

Power

TDMA + FDMA in the GSM900 standard

Code Division Multiple Access (CDMA)

CDMA and Spread Spectrum

• CDMA is based on a technique called spread-spectrum

• As its name indicates this technique consists in “spreading” the spectrum over the whole set of available frequencies

• All users transmit then over all frequencies but are separated from one another thanks to coding

x yPN-Spreadingsequence

Px

frequencyBandwidth of the input signal Bandwidth of the coded signal

frequency

“Direct Sequence” Spread Spectrum

Original signal(band related to bit rate=1/Tb)


Tbbit time

Tcchip time

PN Sequence: 0110001001called “spreading sequence”



Tbbit time


Tcchip time



Tbbit time

Tcchip time

DSSS signal(band related to chip rate=1/Tc)


Signal 1 DSSS signal 1


XX

Integrator

- - + -0 0 1 0

0 0 1 0

The DS-CDMA coded signal

Digital binary signal

𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"

𝑝 & 𝑚 𝑟𝑒𝑐𝑡,# 𝑡 −𝑚𝑇# − 𝑘𝑇

DS-CDMA-coded signal

𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍" = ∫ 𝑎"! 𝑟𝑒𝑐𝑡# 𝑡

𝑟𝑒𝑐𝑡# 𝑡𝑇

𝑑𝑡 = 𝑎"(!)

Received signal after unspreading

Decision variable after correlator



𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"



𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍" = ∫ 𝑎"! %$%&

'"#

𝑝 ! 𝑚 𝑟𝑒𝑐𝑡#$ 𝑡 − 𝑚𝑇( . %$%&

'"#

𝑝 ! 𝑚𝑟𝑒𝑐𝑡#$ 𝑡 − 𝑚𝑇(

𝑇𝑑𝑡 = 𝑎"

(!)


Decision variable after correlator:



𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"



𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍' = ∫ 𝑠!"#!$%& 𝑡 + 𝑘𝑇 . $

()*

+!"

𝑝 & 𝑚𝑟𝑒𝑐𝑡,# 𝑡 −𝑚𝑇#

𝑇 𝑑𝑡 = 𝑎'(&)



Sign

al1

Sign

al2

Codedsignal 1

Codedsignal 2

Adding codedsignals 1 and 2


PN Sequence: 0110001001

PN Sequence: 1111101100

Signal 2 DSSS signal 2


XX

Integrator Contributionfrom signal 2 disappears asPN1 and PN2 are orthofonal!

PN2 PN1


Received signal 1+2

Spreading sequence used to encode signal 1

multiplier

Signal 2 removed

X

It works if codes are orthogonal!

Signal 1: 0 0 1 0 Integrator



𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"



𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍" = ∫ 𝑎"! 𝑟𝑒𝑐𝑡# 𝑡

𝑟𝑒𝑐𝑡# 𝑡𝑇

𝑑𝑡 = 𝑎"(!)


Decision variable after correlator



𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"



𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍" = ∫ 𝑎"! %$%&

'"#

𝑝 ! 𝑚 𝑟𝑒𝑐𝑡#$ 𝑡 − 𝑚𝑇( . %$%&

'"#

𝑝 ! 𝑚𝑟𝑒𝑐𝑡#$ 𝑡 − 𝑚𝑇(

𝑇𝑑𝑡 = 𝑎"

(!)





𝑠 ! 𝑡 = $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%& 𝑡 =$

'𝑎'& $()*

+!"



𝑟 ! 𝑡 = $"𝑎"! $$%&

'!"

𝑝 ! 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

= $"𝑎"! 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇 𝑎𝑠 (𝑝 ! 𝑚 . 𝑝 ! 𝑚 = 1)

𝑍' = ∫ 𝑠!"#!$%& 𝑡 + 𝑘𝑇 . $

()*

+!"


𝑇 𝑑𝑡 = 𝑎'(&)




If we have another signal(i)

𝑠 + 𝑡 = $"𝑎"+ 𝑟𝑒𝑐𝑡# 𝑡 − 𝑘𝑇

𝑠!"#!$%/ 𝑡 =$

'𝑎'/ $()*

+!"

𝑝 / 𝑚 𝑟𝑒𝑐𝑡,# 𝑡 −𝑚𝑇# − 𝑘𝑇

With another orthogonal spreadingsignal

𝑟 + 𝑡 = $"𝑎"+ $$%&

'!"

𝑝 + 𝑚 . 𝑝 ! 𝑚 . 𝑟𝑒𝑐𝑡## 𝑡 − 𝑚𝑇( − 𝑘𝑇

𝑍$% = ∫ 𝑎$% 4&'(

)!"

𝑝 % 𝑚 . 𝑝 * 𝑚 . 𝑟𝑒𝑐𝑡+# 𝑡 − 𝑚𝑇, .𝑟𝑒𝑐𝑡+ 𝑡

𝑇𝑑𝑡 = 𝑎$%

𝑇-𝑇4&'(

)!"

𝑝 % 𝑚 . 𝑝 * 𝑚 = 0

Passing through the receiver of signal j


𝑝 +as and are orthogonal𝑝 !


𝑠!"#!$%& 𝑡 + 𝑠!"#!$%

' 𝑡

So, if we received two signals with orthogonalscodes

𝑍' = ∫ 𝑠!"#!$%& 𝑡 + 𝑠!"#!$%

/ 𝑡 . $()*

+!"


𝑇 𝑑𝑡

Passing through the receiver of signal j , the decision variable after the correlator is

= ∫ 𝑠./,.01* 𝑡 . ∑&'(

)!" 𝑝 * 𝑚23-4$# 45&+#

+𝑑𝑡+ ∫ 𝑠./,.01

% 𝑡 . ∑&'()!" 𝑝 * 𝑚

23-4$# 45&+#+

𝑑𝑡

= 𝑎$* + 0 = 𝑎$

*

CDMA and MUI

• Multi-user Interference happens when PN are not orthogonal (itmay happen in case of unsynchronization for instance)

CDMA : the partial correlation problem

• Partial correlations prevent the receiver to totally cancel the contributions of other users even in the presence of spreadingcodes having low cross-correlation

• In presence of partial correlations, the received signal is thereforeaffected by Multi User Interference

• The partial correlations can be reduced by proper choice of the spreading codes, but sometimes cannot be totally eliminated

• CDMA system capacity is thus tipically limited by Multi User Interference, rather than by thermal noise.

Device #2

RX

What is Multi User Interference (MUI)?

Device #1

Device #3

Device #4

wireless transmission

TX

TX

RX

• MUI is generated by the presence of several users sharing a same resource

• Ideally, if multiple access was well-defined this interference would not exist since all users would be “orthogonal” in the resource space

• The presence of MUI depends on the robustness of the multiple access scheme to phenomena that cause loss of orthogonality between users

What is Multi User Interference (MUI)?

CDMA : the near-far problem

• If all users transmit at the same power level, then the received power ishigher for transmitters closer to the receiving antenna

• Thus, a transmitter that is far from the intended receiver may be strongly at risk due to interference from other users that are close to that receiver

• This problem can be mitigated by introducing powercontrol by which transmitters adjust their transmissionpower so that power arriving at a receiving antenna is equalfor all transmitters

• In other words, the nearby transmitters are assigned with a lowertransmit power level than the far away transmitters

• Power control can be easily achieved in centralized access schemes (e.g. cellular networks), and is a challenging issue in distributed systems

MUI in TDMA-based networks

• TDMA is usually adopted in centralized network organizations

• In these networks one can reasonably suppose that MUI can be neglected by proper design of the guard times between time slots

packet

timeTSj TSj+1 TSj+2

guard time

MUI in FDMA-based networks

• If not well-designed FDMA suffers from inter-channel interference between adjacent channels that is a form of MUI

• Thus the need for guard bands and consequently loss in efficiency of use of the frequency resource

• With frequency guard bands one can suppose as in TDMA that MUI is negligible

• Note that here users do not need to be coordinated and that this scheme applies to distributed topology of access and distributed network organization

• In the case of an access point transmitting to Nu mobile receivers, signals may be encoded using orthogonal signature codes

• The Nu signals are perfectly synchronized at TX, so that basically they arrive synchronous at each mobile receiver

• Each receiver can demodulate its own signal with negligible interference from the other signals sharing the same bandwidth.

The downlink in a centralized network

MUI in CDMA-based networks

• Case of an access point receiving from Nu mobile nodes, that use orthogonal signature codes.

• The Nu signals may be perfectly synchronized at TX, as in synchronous networks, and perfectly orthogonal thanks to a good design of the code space

• These signals may arrive out of phase as in TDMA: this effect can be adjusted by the RX, based on an exchange with the transmitters during which the RX asks (as in TDMA) to adjust clock phases

• Different signals experience, however, different channel conditions and this provokes a loss of orthogonality that cannot be easily recovered

• The above effect is the main reason for MUI in CDMA networks and is present regardless of network organization

MUI for uplink CDMA

The uplink in a centralized network

System model for MUI analysis

Data sequence

a1[n] Encoder &Transmitter

s1(t)

code 1

Encoded signal

h1(t)PTX1

+sRX1(t)Received useful signal

Transmitter 1 Receiver

PRX1

Transmitter 2

Transmitter K

…

h2(t)

hK(t)

…

s2(t)PTX2

sK(t)PTXK

+

sRX2(t)

sRXK(t)

PRX2

PRXK… … si(t)

MUI signal

code 2

code K

n(t)Thermal noise

r(t)

MUI estimation under the SGA

• System performance can be easily evaluated under the Standard Gaussian Approximation (SGA) hypothesis: the cumulative noise term (Zmui + Zn) is treated as an additive white Gaussian noise term

Z = Zu + Zmui + Zn

Decision variable

Cumulative

noise term

( )totSNRerfcBER ⋅γ=21

γ

22muin

btot

ESNR

σ+σ=Average BER at receiver

output under the SGA

depends on the modulation format

( )2ub ZE =2nσ2muiσ Variance of Zmui

Variance of Zn

Capacity of Multiple Access Techniques

• A reminder: what is channel capacity according to Shannon.• Channel capacity C in bits/s for a band-limited Additive White

Gaussian Noise (AWGN) ideal channel with a band-limited and average power-limited input is given by:

!!"

#$$%

&+=

0NWP

1logWC 2

P: average power

W : band of the input signal

WN0 : noise power

N0 : unilateral thermal noise density power

Capacity of Multiple Access Techniques

• Note that P is an average power and therefore:

where Eb is the energy per bit under the condition that the transmission rate matches the channel capacity.

bECP =

W/C2

W/C12E W/CW/C

b ≈−=0N

• Given the expression of channel capacity, one can easily find:

Capacity of Multiple Access Techniques : FDMA

• Suppose Nu FDMA users. Each user is allocated with a bandwidth W/Nu andtransmits power Pn=P/Nu. Therefore capacity Cn for user n is:

( ) !!"

#$$%

&+=!!

"

#$$%

&+=

00 NN W

PN1log

N

W

NW

P1log

N

WC nu

2uu

n2

un

• System capacity C for the network of Nu users is:

!!"

#$$%

&+=!!

"

#$$%

&+==

00 NN W

P1logW

W

PN1logWCNC 2

nu2nu

which shows that total capacity is equivalent to the case of a single user usingpower P = NuPn and all bandwidth W.

• Note that C increases with Nu but bandwidth allocation for a single userbecomes smaller.

Capacity of Multiple Access Techniques : TDMA

• In TDMA, each user is allocated with a Time Slot of normalized duration1/Nu. Each user transmits within its allocated time over the overallbandwidth W using total power P.

• The capacity per user is therefore the same as in FDMA:

!!"

#$$%

&+=!!

"

#$$%

&+=

00 NN W

P1log

N

W

W

P1logW

N

1C 2

u2

un

• When compared to FDMA: note that each user transmits with power PP = NuPn

although for a shorter time• When Nu increases, there is a practical limit for P beyond which a single user

cannot reasonably operate.

Capacity of Multiple Access Techniques : CDMA

In CDMA, each user transmits over the total bandwidth W with power Pn.

Let us consider two cases:

Case A - Users are non-cooperative (they ignore each other)

Case B - Users are cooperative (they know each other and coordinatewith one another)

Non-cooperative CDMA

• In this case at each receiver the signal originating from the (Nu-1) non-usefulusers are perceived as interfering noise.

• The capacity per user is thus:

( ) !!"

#$$%

&

−++=

nu

n2n P1NW

P1logWC

0N

• The total capacity is:

( ) !!"

#$$%

&

−++==

uu

u2unu N/P1NW

N/P1logWNCNC

0N

• Note that the relation of C to Nu is more complex than in FDMA andTDMA.

Power control

Cooperative CDMA

• In the case of cooperative users we can suppose that all users aresynchronized.

• The receiver knows all codes of all users and can jointly detect all signals withno interference between users.

• The total channel capacity is therefore:

!!"

#$$%

&+=!!

"

#$$%

&+=

00 NN W

P1logW

W

PN1logWC 2

nu2

which is the same of TDMA and FDMA.

• However, there is a fundamental difference in the present case whencompared to TDMA and FDMA

Cooperative CDMA

• The capacity of the single user is not in this case equal to a fraction C/Nu ofthe total capacity, rather, it is equal to:

!!"

#$$%

&+=

0NWNP

1logWC u2n

which can be shown to be greater than in the TDMA / FDMA case

!!"

#$$%

&+>!!

"

#$$%

&+=

00 NN W

P1logW

N

1

W

NP1logWC 2

u

u2n

Cooperative CDMA

while the rates of the single users must satisfy:

!!"

#$$%

&+<

0NWNP

1logWR u2i

• The aggregate rate R is thus bound by C:

!!"

#$$%

&+=<=∑

= 0NWP

1logWCRR 2

N

1ii

u

Comparison of capacity regions

• Example: N=2