Physical Layer

Sending signals

pressure and flow analogy
a means of encoding signals in a conductive medium (copper)
at very high frequencies (or very short wavelengths) we send "light" energy (fiber optics)
in either case we encode our binary data into some change or the state of a time varying signal
every signal can be looked at in two ways: the time and frequency domain

periodic signals
value of signal must repeat after a certain time T (the period)
amplitude
size of the signal
frequency
inverse of the period
phase
position within the period of the signal
Example: a sinusoid is a sine function wave
s(t) = A sin(2 pi f t + theta)

A - amplitude

f - frequency

theta - phase

T = 1/ f - period of the sine wave

every component of a time domain signal has a period
the frequency domain representation of the signal shows what frequencies are present in the signal.
Spectrum
the range of frequencies contained in a signal
Bandwidth
the width of the spectrum (possibly infinite)
most of the energy of a signal is concentrated in a range we call the bandwidth
every signal has a bandwidth (range of frequencies it covers)
every medium has a bandwidth it will pass (range of frequencies it passes)

Data rate and bandwidth

The rate at which the signal can change is the baud rate. Baud means signals per second.

Example of human speech

Suppose one word is a signal. Someone from the southern US signals at about 0.5 - 1 baud. Someone from Uppsala signals at 3-5 baud.

Example of human speech

Suppose I have an extremely limited vocabulary of 1024 Swedish words. If I use these words with equal probability, then we could devise an encoding scheme for my Swedish vocabulary of 10 bits per word. Or looked at the other way, each time I say a Swedish word to you I'm transmitting 10 bits. If I could speak quickly, like someone from Uppsala, then I could transmit 4 signals/second * 10 bits/signal = 40 bits per second. My data rate would be higher than my signalling or baud rate.

Fourier Analysis

Since the bandwidth of a signal is determined by the difference between the highest and lowest frequencies, and the Fourier series for a waveform may have an infinite number of frequency terms, do we need infinite bandwidth to transmit certain waveforms? Luckily no, because the amplitudes of the individual components are decreasing with frequency. Include just a few of the lower harmonics and you get a pretty good representation of the signal being sent.

<figure 2-1>

Square waves

A square wave is composed of the sum of an infinite number of sinusoidal waves, its Fourier series.

A square wave with frequency f has a positive pulse and a negative pulse in each period. So each pulse lasts 1/2f seconds long (since each is 1/2 the period). Since each pulse can represent a bit, 2f bits are being transmitted per second on this waveform.

To get a square wave from sinusoids, we add sinusoids of frequencies f and 3f. This gives us a crude approximation. Note that the amplitude of the frequency components is not constant. The higher frequencies contribute less to the signal than does the main frequency.

If we keep adding frequencies, we get a better and better square wave. We need an infinite number of them for a perfect square wave. But this gives us infinite bandwidth.

s(t) = sum {n=1, infinity} Dn sin(2 pi k f t)

where Dn = A/n for odd n, Dn = 0 for even n

<frequency domain picture of signal>

Example

Send an approximate square wave (just the first three components) so we don't need infinite bandwidth to the receiver.

If the carrier frequency is f =1 MHz then the highest frequency component of the transmitted signal is 5 f Hz = 5 MHz

The bandwidth of this approximate square wave signal is 5 - 1 = 4Mhz.

How many bits are being sent every second? The carrier frequency f tells us the period of the signal T = 1/f  = 1 us. The square wave has 2 halves each period, each of which can represent a bit, so a single bit is only 0.5us, and thus 2 Mbps are being transmitted in 4 MHz.

If we could make an even grosser approximation (lower bandwith, fewer frequency components) to the square wave we could send more bits per second in the same bandwidth.

Both the media and the tranmistter/receiver limit the bandwidth of the signal.

Does the bandwidth of the signal depend on the number of signals in the message?
Does the bandwidth of the signal depend on the amplitude of the signal?
If I decrease the period of the signal, what happens to the data rate? how about the bandwidth?

Channel Capacity

A band-limited signal of W Hz can be perfectly reconstructed from a set of samples taken at frequency 2W. This is known as the Sampling Theorem.

Since the signal may have any number of different levels M, and we can encode our binary data into those levels, we can transmit
    log2 M bits per signal
using our sampled signal of 2W Hz, so the maximum data capacity of this noiseless channel is
   C =  2W log2 M bps

Questions

Does Nyquists theorem mean that I can make the data rate arbitrarily high for a given baud rate just by increasing M?

Signal Strength

Expressed in decibels (logarithmic relation) because power often falls exponentially in real media. Using a log scale means that cascaded amplifiers and losses become simiple add/subtract power in dB. The ratio of power P1 to power P2 in dB is

power ratio of P1 to P2 in dB = 10 log10 P1/P2

40 dB loss (-40dB gain) in a media means that if we put 1 W into the media, at the receiver we will only get 10^(-40/10) = 1/10,000th of that power out (0.1 milliwatt)

An amplifier with a gain of 20dB gives us a factor of 100 in power gain.

If we put our 1 W signal through a 40dB loss, then amplifiy it 20dB with an amplifier, we get (-40 + 20) = -20dB gain, or a factor of 1/100 reduction, so 0.010 watts = 10 milliwatts.

Signal/Noise ratio (SNR)

power of signal divided by power of noise, usually stated in dB

Noise

Shannon extended Nyquist's work to determine a channel capacity for noisy channels. The only sort of noise his formula considers is thermal, or white, noise.

Data rate for error-free communication down a noisy channel

C = W log2 (1 + S/N)

Does not account for anything but thermal (white) noise, so this is a best-case sort of limit. Applying this result to a voice-grade telephone channel you have W=3000Hz, SNR = 35dB and S/N = 3160, so C is about 35,000 bps.

What does this say about 56kbps modems?

Analog versus digital signals

Analog signals are continuous; they may take any of an infinite number of possible values within some range. An analog signal is like the sound pressure wave that comes from a musical instrument.

Since any kind of signal (analog or digitial) degrades in strength during trasmission, signals must be amplified or boosted after some distance. Noise also creeps into the signal as it travels along. With analog signals the boosting is an amplifier. The amplifier can't know anything about the original signal, so it has no choice but to amplifiy both the signal and the noise.

A digital signal can be re-generated to be a perfect copy of the original. Digital transmission systems use repeaters, rather than amplifiers. This gives digital signals one big advantage over analog signals: noise is not cummulative as it travels from point to point in a multihop transmission.

An example of this can be seen by taking a picture and making a copy of it on a photocopy machine. Then make a copy of the copy, then a copy of the copy of the copy, etc. Each copy gets a litle worse, a little noisier. The SNR decreases with each copy. This is like an analog signal and amplifier. In contrast to this, think of how many times you could ftp a digital representation of the same image without any degradation.

<example copies>

Media

telephone voice: 300-3400 Hz
co-axial cable: 100KHz - 1GHz
AM radio: 100 kHz - 1MHz
FM radio, TV: 10MHz - 1000 MHz
microwave: 1 GHz - 100 GHz
infrared: 1000 GHz - 100 THz
visible: 100 THz - 1000 THz
ultraviolet: 1000 THz - 10,000 THz

Guided

Two open wires

Twisted pair

Coaxial cable

Optical fiber

Single-mode (more expensive, higher bandwidth, narrower hence one angle) vs Multi-mode (cheaper, lower bandwidth, thicker hence multiple angles transmitted)
Attenuation of light in glass (of course frequeny dependent) determines wavelengths used (0.85, 1.30, 1.55 microns)
Light source: cheap LED or semiconductor laser
Used for 100s of Mbps (lab demos to 5Gbps, 100km repeater)
Used to be hard to join
Immune to electrical noise - tapping, interference properties

Dispersion (pulses spread due to dealy being frequency dependent) can be fought using specially shaped pulses known as solitons.

By comparison to copper, fiber is much lighter (like 100x), much smaller (100x ?), much higher capacity. Size and weight make it much easier to install, so no new copper is being installed anywhere.

The cost of fiber is very cheap. The manufacture of the fiber cable, and the installation of the cable is what is expensive.
40,000 km installed in 1999

Optical amplifiers

short loop of doped Erbium fiber
no electrical components, no repeating signal
100 - 1000 times amplification
enables long fibers, undersea
go 100s of km with these
terrestial links use electronic repeaters every 250km, all optical in between

30 year old fiber works just fine - compare that to other media, IT infrastructure
increase capacity of previously installed fiber
combine with optical amplifier - saves lots of money since you would need N separate repeaters, one for each wavelength
32 available 1999, 64 and 128 are coming soon
160 x 10 G bps = 1.6 Tbps for sale from Nortel 2000

cables all over the world
WDM
2 T bps on a single cable

50 THz of bandwidth on fiber, if you go up to 0.4 dB/km - 50-100 Tbps
once the limit is hit, go for better spectral efficiency
the limit will be reached in 10 years(?)
new weird fibers with holes like Swiss cheese to reduce losses

when the electronics can't keep up
wavelength converters

complete optical repeater is possible

available 5-10 years from now

250 M bps, easy to handle, cheap, short distances - home networks

Unguided

• mobile users,
• difficult or hostile terrain,
• sparse density of nodes

Another possibility is to spread the energy over many frequencies. There are several ways of doing this, all known as spread spectrum techniques. Advantages include privacy, since the signal at any particular frequency isn't any higher than the background noise (frequency domain picture helpful here), and channel sharing, since many simultaneous conversations may occupy the same spectrum without interference.

The frequency of the energy used determines many of the characteristics and problems involved. For instance, low frequency energy goes through obstacles like walls, but is attenuated very strongly in air (say proportional to the cube of the distance travelled). At higher frequencies energy is blocked by obstacles, or bounces off, but doesn't attenuate as rapidly, so travels further.

Radio Frequency

Microwave

Infrared

Satellites

uplink/downlink frequencies vary to avoid interference
downlinks may be focused or broad
typical satellite has 12-20 transponders, each with around 50MHz bandwidth for a 50Mbps capacity

low earth orbit satellites aren't geostationary, so you need lots of them to always have on in view
various proposals, Motorola Iridium is typical
66 LEO satellites
uses of idea of cellular radio, but both the users and the cells are moving
spot beams on the satellites sweeping the earth are equivalent to cells
six polar orbit necklaces of 11 satellites each cover the entire earth
each satellite has 48 spot beams (cells), each cell has 174 full-duplex channels, each channel would be TDMd so that multiple users can share each channel
satellites would communicate between themselves to relay messages between end users

being stationary wrt to Earth ( orbit at 22,200 miles, 36,000 km) means you don't have to move the antenna
number of satellites limited by spacing in orbit
latency is large due to round-trip distance (say 270ms)

• direct connection (avoid local loop),
• mobile communication,
• expensive right-of-way or hostile terrain,
• rapid deployment

Cellular Radio

References

http://www.cdg.org/a_ross/MultipleAccess.html

Analog cellular phones

first modern mobile phone system, 1982
cells of 10-20km in diameter divide a region
each cell has a low power transmitter/receiver base station with multiple frequency channels
the low power allows frequency re-use in cells which are separated by other cells (non adjacent)
cells may be made smaller with lower power used when more capacity is needed

Crucial for the cellular concept to work is the re-use of frequencies in non-neighboring cells. This in turn, relies on the fact that transmitted power decays like R^-n, with 3 < n < 5.  Free space decay is only n = 2.

each base station has a connection to the PSTN via a packet switching network
each cellular phone is in one cell at a time
when a phone moves the base station asks its neighbors who has the clearest signal from this phone, and a handoff then ocurrs
handoffs mean a change of frequencies, since frequencies aren't shared between adjacent cells

the entire system has 832 full duplex channels, each of which is 2 separate simplex channels
the channels are separated from each other by FDM
channels are used for

• control,
• paging - alerting phones to incoming calls,
• access (making calls),
• voice/data
since neighboring cells can't share frequencies, the number of voice/data channels is only around 45 per cell

phones register with the system by broadcasting their unique id when powered on
registering with a cellular system causes your home cellular system to know where you are
to make a call involves negotiating with the the base station on an access channel
a voice channel is granted in the cell, then the phone waits for the connection

to receive a call each phone monitors the paging channel
information is sent on a control channel to tell the phone which voice channel has a call for it

security is a big problem since none of the channels are encrypted
thieves can steal phone ids and make calls spoofing other phones
conversations are easily monitored

Capacity

The capacity of a K-way reuse pattern (the mapping of frequencies to cells to avoid neighbors sharing frequencies) is simply the total number of available channels divided by K. With K=7 and 416 channels, there are approximately 57 channels available per cell. At a typical offered load of 0.05 Erlangs (a phone company measurement which characterizes the load each subscriber puts on the system, or a probability of a person using the phone) per subscriber, each site supports about 1140 subscribers.

Digital cellular phones

US

Two competing digital cellular systems. The first is compatible with AMPS and the second is based on spread spectrum techniques.

GSM deployed before US digital systems. Starting to appear in the US.
"more than 100 operators in 70 countries through Asia Pacific and Africa as well as Europe. MTA-EMCI forecasts 118 million cellular subscribers in 120 countries by 1999, 45 million of them digital."

Market shares likely to be
    GSM 58% of the market by 2000
    Japan's Personal Digital Cellular Standard 21%
    US's two contending systems-CDMA and TDMA together 16%

GSM is described fully in the Wireless Access notes.

Microcell approach merges cordless phones with digital cellular phones.
Cells are tiny (50 to 100 meters) and use very low power (good for size of phone, battery time).
The "base stations" for PCS are small as well, but there needs to be many of them for good coverage.

Telephone System

Architecture: local loop - end office - toll office - switching office

<figure 2-37, telephone switch network hierarchy>

All but the local loop is now digital. The system used is called PCM (pulse code modulation).

PCM

Analog data -> Sampler -> Quantizer

The analog data is sampled and the amplitude of a narrow pulse is set to the sample value (PAM).  If the values of the signal are rounded off to an integer, then you have PCM.  Each pulse represents log2M bits where M is the number of levels.

The quantizer introduces noise, since it is approximating the value of each pulse by rounding it off to the nearest integer level.  This noise can be expressed as a formula involving the number of bits used and a constant:

SNR = 6*n - a dB
where n = number of bits in samples
a = constant between 0 and 1

Good voice reproduction can be done with 128 levels (7 bits) of PCM data.  8000 samples/second * 7 bits/sample = 56k bps. Another bit is used by each channel for signalling, so the total data rate is 64kbps per voice channel.

Modems

The fact that your modem converts a digital signal into an analog signal for the benefit of the PSTN, only to have the modern PSTN equipment re-convert it into a digital PCM signal isn't just ironic, it introduces quantization noise. Even if you had a perfectly noiseless local loop this quantization process puts a "noise floor" on the SNR of 35 to 36 dB. This means with a 3000Hz spectrum Shannon's limit is 34,822 bps.

V.32

2400 baud x 4 bits/baud = 9600 bps

echo cancellation - subtract out your own signal from what you received
provides for full duplex, full bandwidth in each direction (need a fast DSP)

V.32bis

Compression: V.42bis/MNP5

looks for patterns of 32 bits, encodes as a single character, adds to library
receiving modem learns library and decompresses
transparent to software and kernel

V.34

USRobotics X2

Recently introduced by USRobotics (aka 3Com) to get 56kbps over analog phone lines. The key to getting passed the theoretical limit of around 30kbps on a 3kHz phone line was recognizing that only the local loop was still analog, and that it was generally short and of high quality so that it could pass a digital PAM signal in 4kHz.

56k modems works by having the ISPs modems skip the digital to analog conversion (avoids the noise of quantization) by sending PCM encoded signals directly through the network and to the line card connecting the home modem to the end office. This gives the full, digital, 64kbps data rate from the ISP to the house, and is possible when the ISP buys special equipment that let it connect directly to the switching trunks (and hence do the digital signalling). The signalling technique being used downstream is therefore not a phase or frequency modulation technique like V.34, but PAM (pulse amplitude modulation) where each of the 8 bit symbols is assigned one of 256 particular voltage levels.

To achieve 56kbps requires only that 128 levels of the possible 256 are used, so the max is 56kbps. If the phone lines don't allow for even 128 levels to be distinguished, then the modems fall back to using fewere levels (and hence fewer bits per symbol). The typical speed is in the mid 40s kbps. This has not hindered USR marketing efforts.

Going the other direction all digital is impossible, since the local loops go to the end offices which expect to receive an analog signal from the homes, so V.34 is used for upstream traffic. This is a good match to current uses of temporary Internet connections (think of how you use the Web).

N-ISDN

ISDN Services

• voice communication is key, enhanced features expected
• instant access to other phones (no call set-up)
• tied to computers to display number, database entry
• call transfer, forwarding, conference calls
• data communication standard needed for world-wide service
• closed user group - lets public network work like a private network
• airline reservations, yellow pages, bank access, etc
• email
• fax - email for images
• automated meter reading, alarms, medical monitoring

ISDN Evolution

Available capacity is only 2Mbps for 80% of short loops, less for rest.

To use ISDN your switching office must be ISDN capable, you must have an ISDN terminal or computer, and the place you are calling must have ISDN.

ISDN Architecture

<picture of ISDN exchange, network terminating device, home bus>

network terminating device is smart
assigns addresses automatically
supports 8 devices on bus
does contention resolution
monitors performance, does maintenance
adaptors can be used to connect RS232 terminals to ISDN PBXs

A - 4KHz analog phone
B - 64kbps digital channel for voice or data
C - 8 or 16 kbps digital
D - 16 or 64 kbps digital for out-of-band signalling
E - 64 kbps for internal ISDN signalling
H - 384, 1536, 1920 kbps digital channel

Standard combinations are

basic rate - 2B + 1D
primyary rate - 23B + 1D

Digital Subscriber Line (DSL)

http://www.adsl.com/
"DSL: Broadband by Phone", George Hawley, Scientific American.

1980s Lechleider proposed using the actual bandwidth available from copper pair phone lines and using multilevel encoding to achieve 800 kbps in each direction over 4000 m. This symmetric scheme was known as HDSL (high bandwidth DSL).

At about the same time Cioffi at Stanford proposed a discrete multitone signalling scheme of dividing the channel into 256 discrete subchannels of approximately 4 k Hz each. The result was 8 M bps over 1600 meters.

The discrete multitone system became an international standard and was used to give 6 M bps "downstream" or coming into the house, and 0.6 M bps for the upstream connection for Asymmetric DSL.

ADSL can avoid using the 300 - 3300 Hz used by a voice channel, so you can have data and voice on a single line, something not true of symmetrical or HDSL.

By trading off speed for distance you can reach more houses (up to 5500 m from the CO) and still achieve high data rates. G.Lite is an international standard of ADSL that yields 1.5 Mbps downstream and 0.5 Mbps upstream.

From the CO DSL lines are multiplexed onto OC-3 155 Mbps lines.

Broadband ISDN & ATM

ATM switching

ATM also allows for permanent virtual circuits where a reservation is made by contract with the PSTN and the circuit is dedicated to a particular customer. This eliminates the set-up time for the virtual circuit.

Pros

Possible to reserve resources in switches and guarantee performance.
No wasted resources due to idle connections (like packet).
Better match to bursty traffic (like packet).
Circuits are grouped together for faster re-routing when links/switches fail.
Less addressing info in each cell (like circuit).
Small amount of switching time for each cell (like circuit).
Cell ordering is preserved (like circuit).
Does wormhole routing (like circuit, like packet).

Connection set-up time (like circuit).
Congestion is not eliminated if resource reservation is not used (like packet).
Link/switch failure may destroy connection (like circuit).

Transmission

<figure 2-44>

ATM links are always point-to-point and are unidirectional. Two lines must be used for bi-directional traffic. ATM may be carried on fiber or short turns of UTP. The details are taken care of by the PMD sublayer.

The initial ATM speeds of 155M and 622M were chosen to be compatible with a signalling standard for fiber called SONET.

ATM switches are tricky things to design because they must operate very quickly, provide virtual circuit services, and be able to guarantee various quality of service parameters.

Controller Area Network (CAN)

Two wire interface running over S-TP, UTP or ribbon cable. Data rates between 20 kbps and 1 Mbps. Lengths up to 1 km (40m at 1 Mbps).

Asycnronous signalling is NRZ and bit-stuffing is used as necessary to guarantee enough bit transitions to maintain synchronization.

Start and stop bits are sent around each character of data.

Frame format is: Arbitration, Control, Data, CRC, ACK.

The data frame is 0-8 bytes. Frame is defined by start of frame, end of frame symbols.

11 bit identifier for each message (Control field?). 7 bits of this are address for total of 128 devices. 4 bits are for the message type (SYNC, TIME STAMP, EMERGENCY, PDO TX, PDO RX, etc).

The 8 bytes of data are process data objects (PDOs).

Supports synchronous polling of devices for data. High priority SYNC message causes modules to respond with data.