Multiplexing Techniques

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Contents

1. Overview2. Multiple Access Protocols3. Multiplexing Techniques4. TDMA5. FDMA6. CDMA7. SDMA8. Others9. Example of GSM

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Multiple Access protocols single shared communication channel two or more simultaneous transmissions by nodes:

interference only one node can send successfully at a time

multiple access protocol: distributed algorithm that determines how stations share

channel, i.e., determine when station can transmit communication about channel sharing must use channel itself! what to look for in multiple access protocols:

• synchronous or asynchronous • information needed about other stations • robustness (e.g., to channel errors) • performance

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Ideal Multiple Access Protocol

Broadcast channel of rate R bps1. When one node wants to transmit, it can send

at rate R.2. When M nodes want to transmit, each can

send at average rate R/M3. Fully decentralized:

no special node to coordinate transmissions no synchronization of clocks, slots

4. Simple

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MAC Protocols: a taxonomy

Three broad classes: Channel Partitioning TDMA, FDMA, CDMA

divide channel into smaller “pieces” (time slots, frequency)

allocate piece to node for exclusive use Random Access ALOHA, CSMA, CSMA/CD, CSMA/CA

allow collisions “recover” from collisions

“Taking turns” Polling, Token passing tightly coordinate shared access to avoid collisions

Goal: efficient, fair, simple, decentralized

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Channel Partitioning MAC protocols: TDMA

TDMA: time division multiple access access to channel in "rounds" each station gets fixed length slot (length = pkt trans time) in each round unused slots go idle example: 6-station LAN, 1,3,4 have pkt, slots 2,5,6 idle

TDM (Time Division Multiplexing): channel divided into N time slots, one per user; inefficient with low duty cycle users and at light load.

FDM (Frequency Division Multiplexing): frequency subdivided.

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Channel Partitioning MAC protocols: FDMA

FDMA: frequency division multiple access channel spectrum divided into frequency bands each station assigned fixed frequency band unused transmission time in frequency bands go idle example: 6-station LAN, 1,3,4 have pkt, frequency bands 2,5,6 idle

TDM (Time Division Multiplexing): channel divided into N time slots, one per user; inefficient with low duty cycle users and at light load.

FDM (Frequency Division Multiplexing): frequency subdivided.

frequ

ency

bands time

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Channel Partitioning (CDMA)

CDMA (Code Division Multiple Access) unique “code” assigned to each user; i.e., code set

partitioning used mostly in wireless broadcast channels (cellular,

satellite, etc) all users share same frequency, but each user has own

“chipping” sequence (i.e., code) to encode data encoded signal = (original data) X (chipping sequence) decoding: inner-product of encoded signal and chipping

sequence allows multiple users to “coexist” and transmit

simultaneously with minimal interference (if codes are “orthogonal”)

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CDMA Encode/Decode

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CDMA: two-sender interference

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Random Access Protocols

When node has packet to send transmit at full channel data rate R. no a priori coordination among nodes

two or more transmitting nodes -> “collision”, random access MAC protocol specifies:

how to detect collisions how to recover from collisions (e.g., via delayed

retransmissions)

Examples of random access MAC protocols: slotted ALOHA ALOHA CSMA, CSMA/CD, CSMA/CA

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Slotted Aloha

time is divided into equal size slots (= pkt trans. time)

node with new arriving pkt: transmit at beginning of next slot

if collision: retransmit pkt in future slots with probability p, until successful.

Success (S), Collision (C), Empty (E) slots

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Slotted ALOHA

Assumptions all frames same size time is divided into

equal size slots, time to transmit 1 frame

nodes start to transmit frames only at beginning of slots

nodes are synchronized if 2 or more nodes

transmit in slot, all nodes detect collision

Operation when node obtains fresh

frame, it transmits in next slot

no collision, node can send new frame in next slot

if collision, node retransmits frame in each subsequent slot with prob. p until success

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Slotted ALOHA

Pros single active node can

continuously transmit at full rate of channel

highly decentralized: only slots in nodes need to be in sync

simple

Cons collisions, wasting

slots idle slots nodes may be able to

detect collision in less than time to transmit packet

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Slotted Aloha efficiency

Suppose N nodes with many frames to send, each transmits in slot with probability p

prob that 1st node has success in a slot = p(1-p)N-1

prob that any node has a success = Np(1-p)N-1

For max efficiency with N nodes, find p* that maximizes Np(1-p)N-1

For many nodes, take limit of Np*(1-p*)N-1

as N goes to infinity, gives 1/e = .37

Efficiency is the long-run fraction of successful slots when there’s many nodes, each with many frames to send

At best: channelused for useful transmissions 37%of time!

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Pure (unslotted) ALOHA unslotted Aloha: simpler, no synchronization when frame first arrives

transmit immediately

collision probability increases: frame sent at t0 collides with other frames sent in [t0-

1,t0+1]

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Pure Aloha efficiencyP(success by given node) = P(node transmits) .

P(no other node transmits in [p0-1,p0] .

P(no other node transmits in [p0-1,p0]

= p . (1-p)N-1 . (1-p)N-1

= p . (1-p)2(N-1)

… choosing optimum p and then letting n -> infty ...

= 1/(2e) = .18 Even worse !

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CSMA: (Carrier Sense Multiple Access)

CSMA: listen before transmit:

If channel sensed idle: transmit entire pkt If collision occurs has to retransmit again

If channel sensed busy, defer transmission P-Persistent CSMA: (for slotted channels) retry immediately with

probability p when channel becomes idle (may cause instability) Non-persistent CSMA: (for nonslotted channels) retry after random

interval human analogy: don’t interrupt others!

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CSMA collisions

collisions can occur:propagation delay means two nodes may not hear each other’ transmissioncollision:entire packet transmission time wasted

spatial layout of nodes along ethernet

note:role of distance and propagation delay in determining collision prob.

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CSMA/CD (Collision Detection)CSMA/CD: carrier sensing, deferral as in CSMA

collisions detected within short time colliding transmissions aborted, reducing channel

wastage collision detection:

easy in wired LANs: measure signal strengths, compare transmitted, received signals

difficult in wireless LANs: receiver shut off while transmitting

human analogy: the polite conversationalist

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CSMA/CD collision detection

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“Taking Turns” MAC protocolschannel partitioning MAC protocols:

share channel efficiently and fairly at high load

inefficient at low load: delay in channel access, 1/N bandwidth allocated even if only 1 active node!

Random access MAC protocols efficient at low load: single node can fully

utilize channel high load: collision overhead

“taking turns” protocolslook for best of both worlds!

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“Taking Turns” MAC protocolsPolling: master node

“invites” slave nodes to transmit in turn

concerns: polling overhead latency single point of

failure (master)

Token passing: control token passed

from one node to next sequentially.

token message concerns:

token overhead latency single point of failure

(token)

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Frame Relay (more)

Flag bits, 01111110, delimit frame address:

10 bit VC ID field 3 congestion control bits

• FECN: forward explicit congestion notification (frame experienced congestion on path)

• BECN: congestion on reverse path• DE: discard eligibility

addressflags data CRC flags

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Frame Relay -VC Rate Control Committed Information Rate (CIR)

defined, “guaranteed” for each VC negotiated at VC set up time customer pays based on CIR

DE bit: Discard Eligibility bit Edge FR switch measures traffic rate for each VC;

marks DE bit DE = 0: high priority, rate compliant frame;

deliver at “all costs” DE = 1: low priority, eligible for congestion discard

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Frame Relay - CIR & Frame Marking Access Rate: rate R of the access link

between source router (customer) and edge FR switch (provider); 64Kbps < R < 1,544Kbps

Typically, many VCs (one per destination router) multiplexed on the same access trunk; each VC has own CIR

Edge FR switch measures traffic rate for each VC; it marks (i.e. DE = 1) frames which exceed CIR (these may be later dropped)

Internet’s more recent differentiated service uses similar ideas

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Example: GSM

Frequency Band 935-960, 890-915 MHz Two pieces of 25 MHz band

(same as AMPS) AMPS has 833 user channels How about GSM?

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Different Generations

1G analog

2G digital

3G higher data rate for multimedia applications

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1G Cellular Systems

Many Different Standards: AMPS (US) NMT (Northern Europe) TACS (Europe) NTT (Japan) many others...

Spectrum around 800 and 900 MHz

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2G Cellular Systems

Four Major Standards: GSM (European) IS-54 (later becomes IS-136, US) JDC (Japanese Digital Cellular) IS-95 (CDMA, US)

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Frequency Division Duplex (FDD)

Forward Link

Reverse Link

Two separate frequency bands are used for forward and reverse links.

Typically, 25 MHz in each direction.

AMPS: 824-849 MHz (forward) 869-894 MHz (reverse)

mobile

base station

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Frequency Division Multiple Access (FDMA)

The spectrum of each link (forward or reverse) is further divided into frequency bands

Each station assigned fixed frequency band

frequ

ency

bands

idle

idle

idle

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Number of User Channels in AMPS Bandwidth allocated to each user in each link

(forward or reverse) is 30 KHz.

No. of user channels = Total bandwidth / user bandwidth = 25 MHz / 30 kHz

= 833 Is it enough?

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Frequency Reuse

f

f

The same frequency can be reused in different cells, if they are far away from each other

Radio coverage, called a cell.

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Cellular ArchitectureMS – Mobile StationBSC – Base Station ControllerMSC – Mobile Switching CenterPSTN – Public Switched

Telephone Network

MSC PSTN

BSC

segmentation of the area into cells

MS

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Time Division Multiple Access (TDMA)

The mobile users access the channel in round-robin fashion.

Each station gets one slot in each round.

Slots 2, 5 and 6 are idle

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FDMA/TDMA, example GSM

1 2 3 7 8

f

t

124

1

124

1

20 MHz

200 kHz

890.2 MHz

935.2 MHz

915 MHz

960 MHz

Each freq. carrier is divided into 8 time slots.

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Number of channels in GSM

Freq. Carrier: 200 kHz TDMA: 8 time slots per freq carrier

No. of carriers = 25 MHz / 200 kHz = 125

No. of user channels = 125 * 8 = 1000

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Capacity Comparison

Reuse factor 7 for AMPS 3 for GSM (why smaller reuse factor?)

What’s the capacity of GSM relative to AMPS?

A. one half of AMPS B. the sameC. 3 times larger D. 10 times larger

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Answer

AMPS reuse factor = 7 no. of users / cell = 833 / 7 = 119

GSM reuse factor = 3 no. of users / cell = 1000 / 3 = 333 almost 3 times larger than AMPS!

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Multiple Access Methods

Three major types: Frequency Division Multiple Access

(FDMA) Time Division Multiple Access (TDMA) Code Division Multiple Access (CDMA)

• Frequency hopping (FH-CDMA)• Direct sequence (DS-CDMA)

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Frequency-Time Plane

Time

Frequency

Partition of signal space into time slots and frequency bands

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FDMA

Time

Frequency

Different users transmit at different frequency bands simultaneously.

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TDMA

Time

Frequency

Different users transmit at different time slots.

Each user occupy the whole freq. spectrum.

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Frequency Hopping CDMA

Frequency

Time

At each successive time slot, the frequency band assignments are reordered.

Each user employs a code that dictates the frequency hopping pattern.

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Synchronization

The previous figure implies that each signal synchronizes with each of the other signals.

In practice, this is not the case. Frequency hops may collide, but it does

not occur frequently. How often collisions occur depends on the

choice of codes.

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Direct Sequence CDMA

Time

Frequency

All users occupy the whole bandwidth all the time.

Signals of different users overlap with one other.

How can it be done?

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CDMA Encoding

Each user is assigned a unique signature sequence (or code), denoted by (c1,c2,…,cM). Its component is called a chip.

Each bit, di, is encoded by multiplying the bit by the signature sequence:

Zi,m = di cm

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Encoding Example

Data bit d1 = –1

Signature sequence (c1,c2,…,c8) = (+1,+1,+1,–1,+1,–1,–1,–1)

Encoder Output(Z1,1,Z1,2,…,Z1,8) = (–1,–1,–1,+1,–1,+1,+1,+1)

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Bandwidth

Note that the chip rate is much higher than the data rate.

Consider our previous example. Suppose the original data signal occupies a

bandwidth of W. What is the bandwidth of the encoded

signal?

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Spread Spectrum Technique

Time

Frequency

Time

Frequency

Encoding

The bandwidth expands by a factor of M.

M is called spreading factor or processing gain.

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CDMA Decoding

Without interfering users, the receiver would receive the encoded bits, Zi,m , and recover the original data bit, di, by computing:

M

mmmii cZ

Md

1,

1

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CDMA Decoding Example

(c1,c2,…,c8) = (+1,+1,+1,–1,+1,–1,–1,–1)

(Z1,1,Z1,2,…,Z1,8) = (–1,–1,–1,+1,–1,+1,+1,+1)

(–1,–1,–1,–1,–1,–1,–1,–1)

di = –1

multiply

add and divide by M

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Multiuser Scenario

If there are N users, the signal at the receiver becomes:

How can a CDMA receiver recover a user’s original data bit?

N

n

nmimi ZZ

1,

*,

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Multiplied by the signature sequence of user 1

2-user example

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Signature Sequences

In order for the receiver to be able to extract out a particular sender’s signal, the CDMA codes must be of low correlation.

Correlation of two codes, (cj,1,…, cj,M) and (ck,1,…, ck,M) , are defined by inner product:

M

mmkmj cc

M 1,,

1

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The Meaning of Correlation

What is correlation? It determines how much similarity one sequence

has with another. It is defined with a range between –1 and 1.

Correlation Value

Interpretation

1 The two sequences match each other exactly.

0 No relation between the two sequences

–1 The two sequences are mirror images of each other.

Other values indicate a partial degree of correlation.

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Generation of Signature Sequences How to generate signature sequences of

low correlation?

There are two classes of signature sequences that are widely used in CDMA systems. Orthogonal Codes Pseudo Noise Sequences (PN Sequences)

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Orthogonal Codes

Two codes are said to be orthogonal if their correlation is zero. no interference between the two users.

In our previous two-user example, the codes are orthogonal.

How to generate orthogonal codes?

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Walsh Codes

The most common orthogonal codes used in CDMA systems.

A set of Walsh codes of length n is defined by the rows of an n n Hadamard matrix.

Hadamard matrix can be constructed by an iterative method.

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Iterative Construction

Example:

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1121 0

nn

nnn HH

HHHH

0110

1100

1010

0000

10

0042 HH

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Signature Sequences

The signature sequences can be found by Taking the rows out Replacing 0 by –1

10

002

H )1,1(

)1,1(

2

1

s

s

Are they orthogonal?

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IS-95 Forward Link

Walsh Codes of length 64 is used for spreading in the forward link (base-to-mobile) of IS-95.

It is NOT suitable for the reverse link (mobile-to-base). (Why?) PN sequences are used instead.

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PN Sequences

What is Pseudo-Noise Sequences? They are deterministic. But they look like random noise.

How to generate PN sequences? One common way is to use linear feedback

shift register.

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Shift Register Implementation: An Examplex1 x2 x3

x1 x2 x3 Output

1 0 0 ---

0 1 0 0

1 0 1 0

1 1 0 1

1 1 1 0

0 1 1 1

0 0 1 1

1 0 0 1

Initial state: 1 0 0

Output: 0 0 1 0 1 1 1 …

(Periodic with period 7)

The output sequence must be periodic (why?)

The period cannot be greater than 7. (why?)

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2.2 Multiple Access protocols

single shared communication channel two or more simultaneous transmissions by nodes: interference

only one node can send successfully at a time multiple access protocol:

distributed algorithm that determines how stations share channel, i.e., determine when station can transmit

communication about channel sharing must use channel itself!

type of protocols:• synchronous or asynchronous • information needed about other stations • robustness (e.g., to channel errors) • performance

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2.3 Multiple Access Control Protocols

Three broad classes: Channel Partitioning

divide channel into smaller “pieces” (time slots, frequency, code)

allocate piece to node for exclusive use TDMA, FDMA, CDMA

Random Access allow collisions “recover” from collisions CSMA, ALOHA

Taking turns tightly coordinate shared access to avoid collisions Token ring

Goal: efficient, fair, simple, decentralized

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2.4 Random Access protocols

When node has packet to send transmit at full channel data rate R. no a priori coordination among nodes

two or more transmitting nodes -> “collision”, random access MAC protocol specifies:

how to detect collisions how to recover from collisions (e.g., via delayed

retransmissions) Examples of random access MAC protocols:

slotted ALOHA ALOHA CSMA and CSMA/CD

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2.5 CSMA: Carrier Sense Multiple Access

CSMA: listen before transmit: If channel sensed idle: transmit entire pkt If channel sensed busy, defer transmission human analogy: don’t interrupt others!

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2.6 CSMA/CD (Collision Detection)

CSMA/CD: carrier sensing, deferral as in CSMA collisions detected within short time colliding transmissions aborted, reducing channel wastage persistent or non-persistent retransmission

collision detection: easy in wired LANs: measure signal strengths, compare

transmitted, received signals difficult in wireless LANs: receiver shut off while transmitting

human analogy: the polite conversationalist

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CSMA/CD collision detection

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Thank You