15-441Communications and Networking

Gregory KesdenGregory Kesden

Copper WireUnshielded twisted pair

»Two copper wires twisted, often unshielded

»Twisting avoids capacitive coupling – the cause of cross-talk

»Grouped into cables: multiple pairs with common sheath

»Category 3 versus category 5/5e (more twists)

»100 Mbps up to 100 m, 1 Mbps up to a few km

Coax cables.»One connector is placed inside the other connector

»Holds the signal in place and keeps out noise

»Gigabit up to a km

Signaling processing research pushes the capabilities of a specific technology.

1000

wavelength (nm)

loss(dB/km)

1500

0.0

0.5

1.0

tens of THz

1.3

1.55

Light Transmission in Silica Fiber

lower indexof refraction

core

cladding

(note: minimum bend radius of a few cm)

Ray Propagation

Multimode fiber.»62.5 or 50 micron core carries multiple “modes”

»used at 1.3 microns, usually LED source

»subject to mode dispersion: different propagation modes travel at different speeds, depending on where source reflects bounces within cable – different paths are different lengths

»Mode dispersion can be combated with a graded refraction index. Cable has variable refraction index to squeeze things back together.

»typical limit: 1 Gbps at 100m

Single mode»Narrow cable so that it holds only “one beam” of light

»8 micron core carries a single mode

»used at 1.3 or 1.55 microns, usually laser diode source

»typical limit: 1 Gbps at 10 km or more

»still subject to chromatic dispersion

Fiber Types

Wireless - Satellite

•Typically geostationary orbit•High latency•High bandwidth (500MHz)•High latency (240ms – 540ms) •Microwave frequencies (108 – 1011 Hz)•Interestingly enough, water (rain, &c) absorbs a great deal of microwave energy – that’s why we use it to cook.

Radio - terrestrial• Below microwave frequency range (104 – 109 Hz)• Still absorbed by water, but less so than microwave• Higher frequencies tend to “bounce” off obstacles• Lower frequencies tend to be penetrate• Lower frequencies can “bounce” off ionosphere. • As frequency approaches microwave band, this doesn’t happen.

For comparison: Twisted pair 104 – 106 Hz, Fiber optic 1014-1015 Hz

Maximum Data Rate

Different media (even assuming no outside Different media (even assuming no outside interference) have different ability to hold a interference) have different ability to hold a signalsignal

For example, copper tends to be limited by For example, copper tends to be limited by capacitancecapacitance

Fiber optic media limited by electronics on Fiber optic media limited by electronics on either sideeither side

Bandwidth

Bandwidth is literally that – the width of the band, Bandwidth is literally that – the width of the band, or range of frequencies, supported by the media. or range of frequencies, supported by the media.

Bandwidth is usually given in terms of a Bandwidth is usually given in terms of a frequency – the number of times per unit time that frequency – the number of times per unit time that a recognizable sine wave can be transmitted over a recognizable sine wave can be transmitted over the media.the media.

Depending on the encoding, a different number of Depending on the encoding, a different number of bits might be transmitted per cycle. bits might be transmitted per cycle.

An Example Encoding:Sine Waves and Bits

0

1

1

1

01

11

This particular encoding transmits two bits per cycle.

Nyquist’s Theorum

How is the data rate constrained by bandwidth?How is the data rate constrained by bandwidth? Maximum data rate(bits/second) = Maximum data rate(bits/second) =

2 * bandwidth (hz)2 * bandwidth (hz)

Nyquist’s Theorum considers Nyquist’s Theorum considers only the limit only the limit imposed by the bandwidth imposed by the bandwidth not noise, encoding, or not noise, encoding, or other factors. other factors.

We saw one such encoding on the previous slideWe saw one such encoding on the previous slide

Nyquist’s Theorum Why Double The Bandwidth? In addition to looking at a signal in the time domain, we can view it in In addition to looking at a signal in the time domain, we can view it in

the frequency domain. the frequency domain.

In other words, instead of asking the question, “What is the amplitude In other words, instead of asking the question, “What is the amplitude at time X?”, we can ask the question, “How much energy is present at time X?”, we can ask the question, “How much energy is present every X units of time?”every X units of time?”

For some signals this is a meaningless measure – but many are For some signals this is a meaningless measure – but many are periodic. For discrete signals (like data signals), we just assume that periodic. For discrete signals (like data signals), we just assume that they repeat forever. they repeat forever.

Ene

rgy

Frequency

A (periodic) signal can be viewed as a sum of sine waves of different A (periodic) signal can be viewed as a sum of sine waves of different strengths.strengths.

Every signal has an equivalent representation in the frequency domain.Every signal has an equivalent representation in the frequency domain. What frequencies are present and what is their strengthWhat frequencies are present and what is their strength Similar to radio and TV signalsSimilar to radio and TV signals

TimeFrequency

Am

plit

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The Frequency Domain

Nyquist’s Theorum Why Double The Bandwidth?

As an analog signal is transmitted through some media, it As an analog signal is transmitted through some media, it is filtered by that media.is filtered by that media.

Not only is noise introduced, but energy at certain Not only is noise introduced, but energy at certain frequencies is lost – and nearly completely so above and frequencies is lost – and nearly completely so above and below some threshold frequencies.below some threshold frequencies.

As a result, the signal has no harmonics above a certain As a result, the signal has no harmonics above a certain frequency or below another. frequency or below another.

A fundamental theoretical finding is that to reproduce an analog signal A fundamental theoretical finding is that to reproduce an analog signal accurately at a certain frequency, we must sample it twice as accurately at a certain frequency, we must sample it twice as frequently. Otherwise, we could lose information.frequently. Otherwise, we could lose information.

If we sample less often, we might miss an event – we sample just If we sample less often, we might miss an event – we sample just before it happens. before it happens.

If we sample more often, we just sample the same thing twice – we If we sample more often, we just sample the same thing twice – we can’t get more information than is there – and the data has already can’t get more information than is there – and the data has already been limited to a certain bandwidth of information. been limited to a certain bandwidth of information.

Nyquist’s Theorum Why Double The Bandwidth?

Nyquist’s Theorum Why Double The Bandwidth?

We need to have two points within the same period to know exactly which sine function we have. More points provide no additional information.

Nyquist’s Theorum Why Double The Bandwidth?

Reversing this, we find that, given an analog signal of a Reversing this, we find that, given an analog signal of a certain frequency, we can have binary samples at twice the certain frequency, we can have binary samples at twice the frequency. frequency.

Better Than Nyquist’s Limit

If clocks are If clocks are synchronized synchronized sender and sender and receiver, we only need one point per period.receiver, we only need one point per period.

This is because the synchronized starting This is because the synchronized starting point counts as one of the two points. point counts as one of the two points.

Noisy Channel

Consider ratio of signal power to noise Consider ratio of signal power to noise power.power.

Consider noise to be super-imposed signalConsider noise to be super-imposed signal Decibel (dB) = 10 Log (S/N)Decibel (dB) = 10 Log (S/N) S/N of 10 = 10 dBS/N of 10 = 10 dB S/N of 100 = 20 dBS/N of 100 = 20 dB S/N of 1000 = 30 dBS/N of 1000 = 30 dB

Shannon’s Theorum Maximum data rate (bits/second) = Maximum data rate (bits/second) =

bandwidth (Hz) Log bandwidth (Hz) Log 22 (1 + S/N) (1 + S/N)

As before, this only gives us the limit on the data As before, this only gives us the limit on the data rate imposed by the noise, itself. rate imposed by the noise, itself.

It does not consider the encoding or bandwidth It does not consider the encoding or bandwidth limitations.limitations.

The bandwidth parameter can be confusing. It is The bandwidth parameter can be confusing. It is there because it governs the effect that the noise there because it governs the effect that the noise has. More bandwidth either dilutes the noise, or has. More bandwidth either dilutes the noise, or gives the data more places to hide, or both.gives the data more places to hide, or both.

• Increased bandwidth decreases the effects of noise.• One way to think of this is that the signal has either more frequency space to call its own, or the noise gets diluted across the frequency space, or some combination of the two.

noise signalShannon’s Theorum

Higher Frequency = Higher Energy

frequency = frequency =

speed of light (m/s)/wavelength (m)speed of light (m/s)/wavelength (m) Energy (Joules) = frequency * Plank’s Energy (Joules) = frequency * Plank’s

constantconstant Planck’s constant (Energy in a photon) is Planck’s constant (Energy in a photon) is

6.626 X 10 6.626 X 10 –34–34

Magnetic Media

Hauling a big-rig of DAT along I-79 may Hauling a big-rig of DAT along I-79 may appear to be high bandwidth, but how are appear to be high bandwidth, but how are you going to load them at the other side?you going to load them at the other side?

Even if the bandwidth can be achieved, I-79 Even if the bandwidth can be achieved, I-79 has a very high latencyhas a very high latency

Throughput vs. Latency Throughput is the amount of work (data transfer) per unit timeThroughput is the amount of work (data transfer) per unit time Latency is the delay before the first unit of work (data) arrivesLatency is the delay before the first unit of work (data) arrives Consider highway analogy: Throughput is a function of the number of lanes. Consider highway analogy: Throughput is a function of the number of lanes.

Latency is a function of the speed limit.Latency is a function of the speed limit. In networks, throughput is often related to bandwidth. Latency is often related In networks, throughput is often related to bandwidth. Latency is often related

to distance (number of hops across networks). to distance (number of hops across networks).

Amplitude Modulation

Frequency Modulation

Baseband modulation: send the “bare” signal.

Carrier modulation: use the signal to modulate a higher frequency signal (carrier).

»Can be viewed as the product of the two signals

»Corresponds to a shift in the frequency domain

Baseband vs. Carrier Modulation

Am

plitu

de

Signal CarrierFrequency

Am

plitu

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ModulatedCarrier

Amplitude Carrier Modulation

Multiple channels can coexist if they transmit at a different frequency, or at a different time, or in a different part of the space.

– Compare with planes: height, (horizontal) space, time

Space can be limited using wires or using transmit power of wireless transmitters.

Frequency is controlled by standards or law.

Supporting Multiple Channels

Frequency Division Multiplexing (FDM)

Channels shifted to occupy different frequency space

Any single channel

Time Division Multiplexing (TDM)

User 1 User 2 User 3

Send multiple wavelengths through the same fiber.

– Multiplex and demultiplex the optical signal on the fiber

Each wavelength represents an optical carrier that can carry a separate signal.

– E.g., 16 colors of 2.4 Gbit/second Like radio, but optical and much faster

OpticalSplitter

Frequency

Wavelength Division Multiplexing