Multiplexing and Demultiplexing

Question

• Why cannot Verizon users get an iPhone from AT&T and get it work in Verizon's network?

iPhone@AT&T vs. iPhone@Verizon

• GSM vs. CDMA– Two primary systems in cellular phones.

• How do they differ from each other?– Why cannot you use your GSM phone in CDMA networks?

Multiplexing and Demultiplexing • Multiplexing: A network word for sharing– Combining information streams from multiple sources for

transmission over a shared medium– Multiplexor: a method/device to implement this.– Demultiplexing: Separating a combined stream back into

individual streams

The Basic Types of Multiplexing

• Four basic approaches– Frequency Division Multiplexing (FDM)• Combination in the frequency domain

– Time Division Multiplexing (TDM)• Combination in the temporal domain

– Wavelength Division Multiplexing (WDM)• A form of FDM used for optical fiber

– Code Division Multiplexing (CDM)• Combination with pure math magic

Frequency Division Multiplexing

• FMD: Each pair of sender and receiver use a particular carrier frequency.

Example: FM broadcasting

• 101 channels between 87.8 MHz – 108.0 MHz in North America– NYC: http://www.nyradioguide.com/freqlist.htm– SC: http://www.statecollege.com/music/radio.php

• Each channel is assigned a frequency band– 200KHz

• Each channel has a center frequency– Majic 99: 99.5 MHz

Frequency Division Multiplexing• Advantage: A dedicated frequency channel for each

pair.

• Limitation: Frequency interference • Requiring adequate spacing between channels.• Guard band

Use of an FM Radio Channel

• If a carrier uses a single frequency, why does FDM allocates blocks of frequencies?

• Usually divided the range of frequencies into multiple sub-channels.– Increase the data rate• Each carrier for different piece of information.

– Increase immunity/reliability to interference• Each carrier for the same piece of information.

Hierarchical FDM

• FM signals can be further modulated to a different frequency band!

Source

Carrier 1

Carrier 2

11

Hierarchical FDM

New York Los Angeles

Street Block

Neighborhood

District

City

For each pair of telephone numbers, knowing their path in theFDM hierarchy is good enough to determine which frequency band to use in multiplexing.• Analogy: Your mailing address

Wavelength Division Multiplexing (WDM)

• FDM in optical fiber– l: wavelength

• Prism: multiplexing and demultiplexing device– a multiplexor: combines beams of light of various

wavelengths into a single beam– a demultiplexor: separate a single beam into beams

with different wavelengths.

f *l = c (speed of light)

Time Division Multiplexing (TDM)

• A simple trick: an item from one source per unit time slot

Synchronous TDM

Unfilled Slots in Synchronous TDM

Statistical TDM • Also called asynchronous TDM by some– Eliminating unused slots– Statistical TDM takes less time to send the same amount of data

• Extra overhead– ID of the receiver in each slot MAC address (Ch. 13)

Code Division Multiplexing (CDM)• Unlike FDM/TDM, CDM does not rely on any

physical property of signals.– Uses an interesting mathematical idea

• CDMA: Code Division Multiple Access– A CDM version for cellular phones

Orthogonal Vector Spaces• Vector– (x,y), (x,y,z), (a1, a2, …, an)

• Dot product of two vectors a = (a1, a2, …, an) and b = (b1, b2, …, bn)– Must have the same number of elements.– Multiplying the corresponding pairs and adding up

the products

• Two vectors are said to be orthogonal if their dot product is zero– a b = 0∙

a b= ∙ a1 b1 + a2 b2 + … + an bn

Exercise: Orthogonal or Not?

• (1,-1) and (1,1)– yes

• (1,1,1,1) and (1, -1, -1, -1)– no

• (0, 0) and (1, 1)– yes

• (-2, -1, 1) and (1, 1, 3)– yes

a b = 0∙

Example: Two Vector CDM• A sender is assigned a vector, chip sequence,

that is orthogonal to all other senders’ chip sequences.– Information from this sender (digitized voice) is

processed with this vector.

Code Division Multiplexing

• The first step consists of converting the binary values into vectors that use -1 to represent 0:

• Multiplying C1 x V1 and C2 x V2

• The final signal to be sent will be the sum of the two signals

Code Division Multiplexing• On the receiving side– Use the sender A’s vector (1, -1) – chip sequence– Treat the sequence as a vector– Compute the dot product of the vector and the chip

sequence

• Interpreting the result as a sequence produces: (2 -2 2 -2)– In binary: (1 0 1 0)

Can Other Senders Extract Information?

• Suppose Sender B does not send anything.

• One receiver uses B’s chip sequence to extract information.– (1, 1) ( (1, -1), (-1, 1), (1, -1), (-1, 1) ) ∙ ( 0, 0, 0, 0)

• Implication: A’s information cannot be intercepted by others.

CDM Signals Still Require Frequency Modulation

• CDM combines different signals into one.• FM shifts the original signal to a higher frequency

band for transmission

Back to the Previous Questions• GSM phones vs. CDMA phones

– Using very different multiplexing/demultiplexing techniques– GSM: TDM (early version), TDM + FDM

• GSM phones in different countries– May using different frequency bands.

• Quad-band: 850, 900, 1800, 1900 MHz

– Phones must be able to pick up a right frequency band.

• Impact on consumers– Natural technology monopoly/barrier– Consumers are locked into a particular system.– More versatile phones?