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Networks - Physical Layer Cheat Sheet by

First of a series of Cheat Sheets on Computer Networks. This cheat sheet breaks down the Physical Layer aspect of a network, the various forms of transmission, the different forms of modulation, and more.

Nyquist Theorem

Equation expressing maximum data rate for a finite bandwidth noiseless channel
If signal is run through a low-pass filter of bandwidth B
The filtered signal can be completely recons­tructed by making only 2B samples per second
Sampling faster than 2B x per second is pointless
Higher frequency components have already been filtered out.
B = channel bandwidth
V = discrete levels the signal consists of
Max data rate = 2B log₂ V bits/sec

Twisted Pair

A form of transm­ission media
Two insulated copper wires (1mm thick)
Twisted in helical form (like DNA)
Wires are twisted so the waves cancel out
Used for transm­itting analog or digital inform­ation
Bandwidth depends on wire thickness and distance traveled
Several megabi­ts/sec for a few kilometers
Widely used
Adequate perfor­mance and cheaper
Unshielded Twisted Pair
Cat 5 UTP cable, mostly in office buildings:
4 pairs of twisted insulated wires in a single plastic sheath.
Links can be used in both directions at the same time, like a two-way road
Link can be used in either direction, only one way at a time
Links that allow traffic in only one direction.

Digital Modulation

Process of converting between bits and signals
To send digital inform­ation, we must devise analog signals to represent bits

Baseband Transm­ission

Signals occupies frequency from zero up to a maximum
The maximum frequency depends on the signaling rate.

Clock recovery

The process of extracting timing inform­ation from a data stream for the receiver to decode
To encode bits into symbols, receiver must know when one symbol ends and the next begins
Receiver needs to reference a clock of the same frequency
Accurate clocks are expensive
Another strategy must be used

Overhead Defini­tion

Overhead is any combin­ation of excess or indirect comput­ation time, memory, bandwidth, or other resources that are required to perform a specific task.


Non-return to zero
Simplest, literal line code
-V for 0
+V for 1
A long run of 0's or 1's leaves the signal unchanged
Differ­ent­iating between bits become difficult. A long line of 15 0's looks like 16 without a very accurate clock


Bandwidth Efficiency

For NRZ, it moves between + and - levels every 2 bits
Requires bandwidth of at least B/2 when the bit rate is B bits/sec
This limits the speed, as more bandwidth is required to run faster.
Using more than two signalling levels, the limited bandwidth can be used for effici­ently
e.g. using 4 voltages, 2 bits can be sent at once, as a single symbol
Effective only if the receiver can distin­guish the 4 levels
The signal change rate is now half the bit rate, thus reducing the required bandwidth.
The rate the signal changes is the symbol rate
the bit rate is the symbol rate multiplied by the number of bits per symbol


The inverted vesion of NRZ
transition for 1
no transition for 0
Used by USB
Universal Serial Bus

NRZI Image


Used for classic Ethernet
low to high = 0
high to low = 1
Requires twice as much bandwidth as NRZ because of the clock
Adds 100% overhead
Guarantees clock recovery and balanced signal because:
-Each bit is modulated in a balanced signal

Manchester Image

Bipolar Encoding (AKA Alternate Mark Inversion)

0 = logical zero
Encodes 0's with a zero-s­ignal
1 = + or -
Encodes 1 with positive or negative level
In telephone networks, it is know as Alternate Mark Invers­ion­(AMI), where "­mar­k" is 1 and "­spa­ce" is 0.
Guarantees a balanced signal because:
-1's are encoded in altern­ating +V, - V signal levels
If -V is a logical zero, and the two voltages +1V and -1V represents a logical zero, to send "­1", the transm­itter alternates between +1V and -1V.

Bipolar Encoding Image


Balanced Signal

Base-band signal averages zero
As much + voltage as -, even after short period of time
No DC electrical components
Advant­ang­eous, as some channels (coaxial or lines with transf­ormers) attenuate a DC component due to their physical properties
DC component filtered out
Avoids energy waste
Provides better clock recovery
Through transi­tions, due to mix of + and - volatages.
Allows measuring the signal average
For error detection and receiver calibr­ation. Impossible with an unbalanced signal

Link Failure

Instances for possible link failure:
Sequence used for scrambling could be the same as the signal
Transm­itting all 0's, consti­tuting a link failure
With unbalanced signals, the average may drift from the true decision level due to a density of 1s, for example, which would cause more symbols to be decoded with errors.

Capacity Coupling

Method of connecting the reciever to the channel.
Passes only the AC portion of the signal.


A form of line code
Maps groups of 4 bits of data onto groups of 5 bits for transm­ission
Used to prevent more than 3 consec­utive 0's
Every data (4B) has a fixed codewo­rd(5) that it is translated to
This scheme adds 25% overhead
Better than the 100% overhead of Manchester encoding
Non-data codes can represent physical layer control signals
e.g: "­111­11" - idle line
"­110­00" = start of a frame
Produces at least two transi­tions per 5 bits of output code, regardless of input data.

4B/5B Encoding Table


Maps 8 bits input onto 10 bits output
80% efficient
Achieves DC signal balance, never far from balanced
At most 2 bit disparity
8 bits of data are transm­itted as a 10-bit entity called a symbol
Low 5 bits are encoded into a 6 bit group
5b/6b portion
Top 3 bits encoded into a 4-bit group
3b/4b portion
These groups are concat­enated together to form a 10-bit symbol that is transm­itted.
Standards also define up to 12 symbols that can be sent in place of a data symbol
These indicate start-­of-­frame, end-of­-frame, link idle, etc.
Helps clock recovery, never more than 5 consecuive 1s or 0s

Passband Transm­ission

Signals that are shifted to occupy a higher range of freque­ncies, (all wireless transm­iss­ions)
Scheme that regulates the amplitude, phase or frequency of a carrier signal to convey bits.
Occupies a band of freque­ncies around the frequency of the carrier signal.
Common for wireless and optical channels.
Regulatory constr­aints and intere­ference prevention dictates choice of freque­ncies.
Modulating the amplitude, freque­ncy­/phase of a carrier signal sends bits in a (non-zero) frequency range

Passband Transm­ission Image


Regula­tin­g/m­odu­lating a carrier

Amplitude Shift Keying (ASK)
-Two different amplitudes represent 0 and 1
-More levels can represent more sumbols
Frequency Shift Keying (FSK)
-Two or more tones used
Phase Shift Keying(PSK)
- Carrier wave system­aticaly shifted 0 or 180 dgrees at each symbol period.
Schemes can be combined and more levels used to transmit more bits per symbol. However, only one of frequency and phase can be modulated as they are related.


Frequency Shift Keying (FSK)

Two freque­ncies used
one symbol for 0, another for 1

FSK Image

Phase Shift Keying - PSK

Only Phase is modulated through time
to identify points on the plane
Amplitude stays constant, not modulated
Each point corres­ponds to one of four symbols.
2 bits per symbol transm­itted

To indentify 4 vertic­es(­"­qua­dra­tur­e") of a square centered plane. Each point corres­ponds to 4 symbols.
As there are 4 symbols, 2 bits per symbol are transm­itted.


Conste­llation Diagrams

Shorthand to capture the amplitude and phase modula­tions symbols
The points give the legal amplitude and phase combin­ations of each symbol.
The phase of a dot is indicated by the angle a line from it to the origin makes with the positive x-axis
The amplitude of a dot is the distance from the origin

Conste­llation Diagram Image



Quadrature Amplitude Modulation
16 combin­ations of amplitudes and phase used
Can transmit 4 bits per symbol
A denser modulation scheme with 64 different combin­ations is called QAM-64. There are even higher­-order QAMs used.


Assign­s(maps) bits to symbols so that adjacent symbols differ in only 1 bit position
If a receiver decodes the symbol in error
It will make only a single bit in error

Gray-c­oding Image

Gray-coded QAM-16 conste­llation


Channels shared by multiple signals
More convenient than using a single wire to carry several signals than to install a wire for every signal.

Frequency Division Multip­lex­ing­(­FDM)

Divides the spectrum into frequency bands. e.g. AM radio
Shares the channel by placing users on different freque­ncies
Freque­ncies are allocated different logical channels, with interc­hannel separation great enough to prevent interf­erence
Subcar­riers are coordi­nated to be tightly packed
Filters limit the useable bandwidth to 3100hz p/voic­e-grade channel.
Many channels multip­lexed together, 4000hz allocated per channel
Different freque­ncies encode different values, while phase and amplitude remain constant.
Higher frequency is associated to 1 bit, and a lower to 0
Separa­tio­ns(the excess) are called guard bands. Even though there is a large gap, some adjacent channels do overlap because filters do not have ideal 'sharp edges', therefore a strong spike at the edge of one channel will be felt in jacanet as nonthermal noise

Frequency Division Multip­lexing Image

(a) The original bandwidths
(b) The bandwidths raised in frequency
(c) The Multip­lexed channel

Orthogonal FDM (OFDM)

OFDM (Ortho­gonal FDM) is an efficient FDM technique used for 802.11, 4G cellular and other commun­ica­tions that does not use guard bands.
The channel is divided into many subcar­riers that indepe­ndently send data.
Subcar­riers are tightly packed in the frequency domain.
Frequency response of each subcar­rieris zero at the center of adjacent subcar­riers, therefore subcar­riersbe sampled at their center freque­ncies without interf­erence from neighbours
Guard time required to repeat ports of symbol signals so that they have the desired frequency

Time Division Multip­lexing

Shares a channel over time
Users take turns on a fixed schedule
Not packet switching
Each gets the entire badwidth for a little burst of time
Bits from each input stream are taken in a fixed time slot and output to the aggregate stream.
This stream runs the sum rate of individual streams.
Streams must be synchr­onized in time.
Widely used in teleph­one­/ce­llular systems
Small intervals of guard time analoguous to a requency guard band may be added to accomodate small timing variations

Time Division Multip­lexing Image

Three streams being multip­lexed with TDM.

Code Divison Multiple Access

Shares the channel by giving users a code
Codes are orthogonal
Can be sent at the same time
Widely used as part of 3G networks
Scalar Product (example):
A ● B = (a₁, a₂, a₃) ● (b₁, b₂, b₃) = a₁b₁ + a₂b₂ + a₃b₃
Walsh Codes (example):
A = (a₁ , a₂, a₃) = (-a₁ , -a₂, -a₃)
B =(b₁ , b₂, b₃) = (-b₁ , -b₂, -b₃)

Properties of CDMA codes:
For all A, B with AB
AA = +1
A = -1
AB = A B = 0

A, B and C transmit 1, 1 and 0 respec­tively
A, B and C send codes A, B and respec­tively
The receiver sees A + B +

Code Division Multiple Access­(­CDMA)

A form of spread spectrum commun­ication
Narrowband signal spread out over a wider frequency band
Tolerant of interf­erence.
Allows multiple signals from different users to share the same frequency band.
CDMA shares the channel by giving users a code
Codes are orthog­onal;
Can be sent at the same time
Widely used as part of 3G networks
Each station can transmit over the entire frequency spectrum all the time
Can also be called "Code Division Multip­lex­ing­", but because it is used mostly to allow the same frequency band to be shared by different users by multiple signals, it was commonly called Code Division Multiple Access


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