Transcript Tuesday, January 25, 2007 (Physical layer

15-441
Communications and Networking
Gregory Kesden
Copper Wire
Unshielded
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.
Light Transmission in Silica Fiber
1.0
tens of THz
loss
(dB/km)
0.5
1.3
1.55
0.0
1000
1500
wavelength (nm)
Ray Propagation
cladding
core
lower index
of refraction
(note: minimum bend radius of a few cm)
Fiber Types
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
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
interference) have different ability to hold a
signal
 For example, copper tends to be limited by
capacitance
 Fiber optic media limited by electronics on
either side

Bandwidth

Bandwidth is literally that – the width of the band,
or range of frequencies, supported by the media.

Bandwidth is usually given in terms of a
frequency – the number of times per unit time that
a recognizable sine wave can be transmitted over
the media.

Depending on the encoding, a different number of
bits might be transmitted per cycle.
An Example Encoding:
Sine Waves and Bits
1
1
11
0
1
01
This particular encoding transmits two bits per cycle.
Nyquist’s Theorum

How is the data rate constrained by bandwidth?

Maximum data rate(bits/second) =
2 * bandwidth (hz)

Nyquist’s Theorum considers only the limit
imposed by the bandwidth not noise, encoding, or
other factors.

We 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
the frequency domain.

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
every X units of time?”

For some signals this is a meaningless measure – but many are
periodic. For discrete signals (like data signals), we just assume that
they repeat forever.
Energy

Frequency
The Frequency Domain

A (periodic) signal can be viewed as a sum of sine
waves of different strengths.
Every signal has an equivalent representation in the
frequency domain.
 What frequencies are present and what is their
strength
 Similar to radio and TV signals
Amplitude

Time
Frequency
Nyquist’s Theorum
Why Double The Bandwidth?

As an analog signal is transmitted through some media, it
is filtered by that media.

Not only is noise introduced, but energy at certain
frequencies is lost – and nearly completely so above and
below some threshold frequencies.

As a result, the signal has no harmonics above a certain
frequency or below another.
Nyquist’s Theorum
Why Double The Bandwidth?

A fundamental theoretical finding is that to reproduce an analog signal
accurately at a certain frequency, we must sample it twice as
frequently. Otherwise, we could lose information.

If we sample less often, we might miss an event – we sample just
before it happens.

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
been limited to a certain bandwidth of information.
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
certain frequency, we can have binary samples at twice the
frequency.
Better Than Nyquist’s Limit

If clocks are synchronized sender and
receiver, we only need one point per period.

This is because the synchronized starting
point counts as one of the two points.
Noisy Channel
Consider ratio of signal power to noise
power.
 Consider noise to be super-imposed signal
 Decibel (dB) = 10 Log (S/N)
 S/N of 10 = 10 dB
 S/N of 100 = 20 dB
 S/N of 1000 = 30 dB

Shannon’s Theorum

Maximum data rate (bits/second) =
bandwidth (Hz) Log 2 (1 + S/N)

As before, this only gives us the limit on the data
rate imposed by the noise, itself.

It does not consider the encoding or bandwidth
limitations.

The bandwidth parameter can be confusing. It is
there because it governs the effect that the noise
has. More bandwidth either dilutes the noise, or
gives the data more places to hide, or both.
Shannon’s Theorum
noise
signal
• 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.
Higher Frequency = Higher Energy
frequency =
speed of light (m/s)/wavelength (m)
 Energy (Joules) = frequency * Plank’s
constant
 Planck’s constant (Energy in a photon) is
6.626 X 10 –34

Magnetic Media
Hauling a big-rig of DAT along I-79 may
appear to be high bandwidth, but how are
you going to load them at the other side?
 Even if the bandwidth can be achieved, I-79
has a very high latency

Throughput vs. Latency




Throughput is the amount of work (data transfer)
per unit time
Latency is the delay before the first unit of work
(data) arrives
Consider highway analogy: Throughput is a
function of the number of lanes. Latency is a
function of the speed limit.
In networks, throughput is often related to
bandwidth. Latency is often related to distance
(number of hops across networks).
Amplitude Modulation
Frequency Modulation
Baseband vs. Carrier 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
Amplitude
Amplitude
Amplitude Carrier Modulation
Signal
Carrier
Frequency
Modulated
Carrier
Supporting Multiple Channels



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.
Frequency Division Multiplexing
(FDM)
Any single channel
Channels shifted to occupy different frequency space
Time Division Multiplexing
(TDM)
User 1
User 2
User 3
Wavelength Division Multiplexing



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
Optical
Splitter
Frequency