Computer Networks Group Universität Paderborn Computer Networks Chapter 2: Physical layer Holger...

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Computer Networks Group Universität Paderborn Computer Networks Chapter 2: Physical layer Holger Karl

Transcript of Computer Networks Group Universität Paderborn Computer Networks Chapter 2: Physical layer Holger...

Computer Networks GroupUniversität Paderborn

Computer Networks Chapter 2: Physical layer

Holger Karl

WS 05/06, v 1.1 Computer Networks - Physical layer 2

Goals of this chapter

Answer the basic question: how can data be transported over a physical medium?

Understand the basic service provided by a physical layer Different ways to put “bits on the wire” Reasons why performance of any physical layer is limited Reasons for errors A few examples of important physical layers

Note: This is vastly simplified material

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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Basic service of physical layer: transport bits

Physical layer should enable the transport of bits between two locations A and B

Abstraction: Bit sequence – correct, in order delivery

Layer 0 ”Physical connection”

Pair of copper wires

Layer 1 “Bit ! voltage conversion”

Layer 1 “voltage ! Bit conversion”

SAP of Layer 1

Bits Bits

SAP of Layer 1

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A bit ! signal conversion rule

A simple conversion rule For a “1” bit, apply voltage to the pair of wires For a “0” bit, no voltage

Layer 0 ”Physical connection”

Layer 1 “Bit ! voltage conversion”

Layer 1 “voltage ! Bit conversion”

Bit=1: Close switchBit=0: Open switch

If voltage: Indicate a “1” bitIf no voltage: Indicate a “0” bit

This is called “Non return to

zero” NRZ

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Example: Transmit bit pattern for character “b”

Character “b” needs a representation as a sequence of bits One option: Use the ASCII code of “b”, 98, as a binary

number 01100010 Resulting

voltage put on the wire:

Note: Abstract data is represented by physical signals – changes of a physical quantity in time or space!

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What arrives at the receiver?

Typical pattern at the receiver:

What is going on here?

Note: this and the following examples are exaggerated!

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Some background: Fourier analysis

To understand signal propagation on a physical medium, some background is required how such signals can be analyzed/treated mathematically

First: Fourier’s theoremAny periodic function g(t) (with period T) can be written as a (possibly infinite) sum of sine and cosine functions; the frequencies of these functions are integer multiples of the fundamental frequency f = 1/T.

Constants c, an, bn are to be determined.

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Fourier analysis – computing coefficients

Coefficients c, an, bn in the Fourier series can be computed:

Because of orthogonality of sines and cosines as basis functions

The nth summary terms are called harmonics The sum of the squares of the nth coefficients – an

2 + bn2 –

is proportional to the energy contained in this harmonic Usually, root of it is shown - (an

2 + bn2)1/2

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Applying Fourier analysis to example

The transmitted waveform of ‘b’ is not a periodic signal – Fourier not applicable directly

Use a trick: Suppose waveform is repeatedinfinitely often, resulting in a periodic waveform with period 8 bit times

0 5 10 15 20 250

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Repeated waveform for bit pattern 'b'

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rent

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Applying Fourier analysis to example

Result of computing an, bn, c and using 512 terms to represent the signal:

Almost no discernible difference between original signal and Fourier series

Curves overlap

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Fact 1: Signals are attenuated in a physical medium

Attenuation : Ratio of transmitted to received power High attenuation ! little power arrives at receiver

Attenuation depends on Actual medium Distance between

sender and receiver … other factors

Normalized, typically given in dB

0 1 2 3 4 5 6 7 80

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Received attenuated signal

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Fact 2: Not all frequencies pass through a medium

Previous picture assumed that all frequencies travel unhindered through a physical medium

This is not the case for real media! Simplified behavior: frequencies up to given upper bound fc

can pass; higher frequencies are suppressed Mathematically: the Fourier series is cut off at a certain harmonic High frequencies are attenuated to zero

This frequency fc is called the bandwidth of a physical medium (or channel)

Smaller fc means fewer harmonics can pass through

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Bandwidth-limited medium – example

Result when fewer and fewer harmonics are transported

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Fourier series with 128 harmonics

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1.2Fourier series with 32 harmonics

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Fourier series with 8 harmonics

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Fourier series with 4 harmonics

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Fourier series with 2 harmonics

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Fourier series with 1 harmonic

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Fact 3: Attenuation depends on frequency

Model just used: Cutoff Attenuation is 1 below

bandwidth, infinite above

More realistic: attenuation depends on frequency

Attenuation close to 1 below bandwidth limit and increases for higher frequencies

Both are examples of a bandwidth-limited medium / channel

1

fc

1

fc

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Example with frequency-dependent attenuation

Suppose attenuation is 2, 2.5, 3.333… , 5, 10, 1 for the 1st, 2nd, … harmonic

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We have to explainthis behavior:

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Received signal with frequency-dependent attenuation

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Fact 4: Media not only attenuates, but also distorts

In a physical medium other than vacuum, different frequencies have different propagation speed

Some wave lengths travel faster than others

Apparent result: Waves arrive at receiver out of phase Recall: a sine wave is determined by amplitude a, frequency f, and

phase

Amount of phase shift in the medium depends on frequency

This is called distortion

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Example with frequency-dependent attenuation and jitter

Behavior of “real” medium already well matched! What about the “wriggling”?

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Received signal with frequency-dependent attenuation

and phase change

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We have to explainthis behavior:

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Fact 5: Real media are noisy

A physical medium, in combination with the receiver, exhibits random (thermal) noise

Fluctuations in the receiver circuitry, interference from nearby transmissions, etc.

Materializes as random fluctuations around the (noise-free) received signal

Typical model: noise as a Gaussian random variable of zero mean, uncorrelated in time

More sophisticated models exist

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Example with frequency-dependent attenuation and distortion, random noise

When taking all five facts into account, the received wave form can be satisfyingly explained:

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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Is it so simple? WHEN is the

middle of a bit? HOW does

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Converting signals to data: Sampling

Suppose we have a channel with “sufficient” bandwidth available, free of noise

How does a receiver convert the signal back to data? Simple: Look at the signal

If high, bit is a 1 If low, bit is a 0

0 1 1 1 0000

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Fourier series with 8 harmonics

Sampling over a noisy or bandwidth-limited channel

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In presence of noise or limited bandwidth (or both), signal will not likely be exactly 0 or 1

Or whatever 0 and 1 amounts to after attenuation

Instead of comparing to these precise values, receiver has to use some thresholds within which a signal is declared as a 0 or a 1

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Fourier series with 2 harmonics

Sampling & low bandwidth

What happens when little bandwidth is available?

Assuming same thresholds as before

At some sampling points, the signal will be outside the thresholds!

No justifiable decision possible

What are possible ways out?

0 ? 1 ? 0??0

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Possible way out: Make thresholds wider?

Wide thresholds would (apparently) reduce opportunity for confusion

E.g., +/- 0.4

But: what happens in presence of noise?

Wider thresholds lead to higher probability of incorrect decisions!

! Not good!

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Fourier series with 2 harmonics

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Way out 2: Increase time for a single bit

If bandwidth is limited, received signal cannot track very steep raises and falls in the signal

Hence: give the signal more time to reach the required level for a 0 or a 1 detection.

This means: Time for a single bit has to be extended! Useable data rate is reduced!

This is a fundamental limitation and cannot be circumvented

Formally: maximum data rate · 2H bits/s

where H is the channel bandwidth Basic reason: need to sample sufficiently often

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Way out 3: Use more than just 0 and 1 in the channel

Who says we can only use 0 and 1 as possible levels for the transmitted signal?

Suppose the transmitter can generate signals (current, voltage, …) at four different levels, instead of just two

Then: to determine one of four levels, two bits are required Distinction:

“Bits” are 0 or 1, used in “higher” layers “Symbols” can have multiple values, are transmitted over the

channel Symbol rate: Rate at which symbols are transmitted

Measured in baud Data rate: Rate at which physical layer processes incoming data

bits Measured in bit/s

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Way out 3: Use four-level symbols to encode two bits

Example: Map 00 ! 0, 01 ! 1, 10 ! 2, 11 ! 3 Symbol rate is then only half the data rate as each symbol

encodes two bits

0 1 1 0 0 0 1 0

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Data rate with multi-valued symbols – Nyquist

Using symbols with multiple values, the data rate can be increased

Nyquist formula summarizes:

where V is the number of discrete symbol values

maximum data rate · 2H log2 V bits/s

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Unlimited data rate with many symbol levels?

Nyquist’s theorem appears to indicate that unlimited data rate can be achieved when only enough symbol levels are used

Is this plausible? More and more symbol levels have to be spaced closer

and closer together What then about noise?

Even small random noise would then result in one symbol being misinterpreted for another

So, not unlimited?

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Shannon limit on achievable data rate

Achievable data rate is fundamentally limited by noise More precisely: by the relationship of signal strength S compared

to noise N The relatively fewer noise there is at the receiver, the easier it is

for the receiver to distinguish between different symbol levels Relationship characterized by Shannon, 1948

where S is signal strength, N is noise level

This theorem formed the basis for information theory

maximum data rate · H log2 (1 + S/N) bits/s

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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When to sample the received signal?

How does the receiver know WHEN to check the received signal for its value?

One typical convention: in the middle of each symbol But when does a symbol start?

The length of a symbol is usually known by convention via the symbol rate

The receiver has to be synchronized with the sender at the bit level

The link layer will have to deal with frame synchronization There is also “character” synchronization – omitted here

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Overly simplistic bit synchronization

One simple option: Assume that sender and receiver at some point in time are

synchronized That both have an internal clock that tics at every symbol step

Usually, this does not work Clock drift is major problem – two different clocks never stay in

perfect synchrony

Errors if synchronization is lost:

01 1 1 1 10 0 0

Sender:

Channel

Receiver with a slightly fast clock:

0 1 01 1 1 0 1 0

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Options to tell the receiver when to sample

Relying on permanently synchronized clocks does not work Provide an explicit clock signal

Needs parallel transmission over some additional channel Must be in synch with the actual data, otherwise pointless

! Useful only for short-range communication

Synchronize the receiver at crucial points (e.g., start of a character or of a block)

Otherwise, let the receiver clock run freely Relies on short-term stability of clock generators (do not diverge

too quickly)

Extract clock information from the received signal itself Treated next in more detail

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Extract clock information from signal itself

Put enough information into the data signal itself so that the receiver can know immediately when a bit starts/stops

Would the simple 0 ! low, 1 ! high mapping of bit! symbol work?

It should – after all, receiver can use 0-1-0 transitions to detect the length of a bit

But it fails depending on bit sequences: think of long runs of 1s or 0s – receiver can loose synchronization

Not nice not to be able to transmit arbitrary data

1 0 1 1 0 0 0 1 1 0 1Daten:

NRZ-L

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Extract clock information from signal itself – Manchester

Idea: At each bit, provide indication to receiver that this is where a bit {starts/stops/has its middle}

Example: Manchester encoding For a 0 bit, have the symbol change in the bit middle from low to

high For a 1 bit, have the symbol change in the bit middle from high to

low

Ensures sufficient number of signal transitions Independent of what data is transmitted!

1 0 1 1 0 0 0 1 1 0 1Daten:

Manchester

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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Baseband versus broadband transmission

The transmission schemes described so far: Baseband transmission

Baseband transmission directly puts the digital symbol sequences onto the wire

At different levels of current, voltage, … essentially, direct current (DC) is used for signaling

Baseband transmission suffers from the problems discussed above

Limited bandwidth reshapes the signal at receiver Attenuation and distortion depend on frequency and baseband

transmissions have many different frequencies because of their wide Fourier spectrum

Possible alternative: broadband transmission More correct name: bandpass transmission

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Broadband transmission

Idea: get rid of the wide spectrum needed for DC transmission

Use a sine wave as a carrier for the symbols to be transmitted

Typically, the sine wave has high frequency But only a single frequency!

Pure sine waves has no information, so its shape has to be influenced according to the symbols to be transmitted

The carrier has to be modulated by the symbols (widening the spectrum)

Three parameters that can be influenced Amplitude a Frequency f Phase

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Amplitude modulation

Given a sine wave f(t) and a time-varying signal s(t) Signal can be analog (i.e., a continuous function of time) or digital

(i.e., a discrete function of time) Signal can be e.g. the symbol levels discussed above

The amplitude modulated sine wave fA(t) is given as:

I.e., the amplitude is given by the signal to be transmitted

Receiver can extract s(t) from fA(t)

Special cases: s(t) is an analog signal – amplitude modulation s(t) is a digital signal – also called amplitude keying s(t) only takes 0 and 1 (or 0 and a) as values – on/off keying

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Amplitude modulation – example

Question: How to solve bit synchronization here? Is Manchester applicable?

Binarydata

On/off modulated

carrier

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Frequency modulation

The frequency-modulated sine wave fF(t) is given by

Modulation/keying terminology like for AM Example

Binarydata

Frequency-modulated

carrier

Note: s(t) has an additive constant in this example to avoid having frequency zero

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Phase modulation

Similarly, a phase modulated carrier is given by

Modulation/keying terminology again similar Example:

s(t) is chosen such that there are phase changes when the binary data changes

Typical example for differential coding

Binarydata

Phase-modulated

carrier

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Phase modulation with high multiple values per symbol

A receiver can usually quite well distinguish phase shifts Hence: Use phase shifts of 0, /2, , 3/2 to encode two

bits per symbol Even better: Use /4, 3/4, 5/4, 7/4 phase shifts for each bit Why better? Clock extraction! Result: Data rate is twice the symbol rate

Technique is called Quadrature Phase Shift Keying (QPSK)

Visualization as constellation diagram:

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Combinations of different modulations

Amplitude, frequency, and phase modulations can be fruitfully combined

Example: 16-QAM (Quadrature Amplitude Modulation) Use 16 different combinations of phase change and amplitude for

each symbol Per symbol, 24 = 16 bits are encoded and transmitted in one step Constellation diagram:

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Bit error rate as function of SNR

The higher the SNR, the better the reception The more reliably can be signals converted to bits at receiver Actually: Energy per bit – takes into account data rate,

#bits/symbol

Concrete bit error probability/rate (BER) depends on SNR and used modulation

Example: DPSK, data rate corresponds to bandwidth

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Examples for SINR ! BER mappings

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

-10 -5 0 5 10 15

Coherently Detected BPSKCoherently Detected BFSK

BER

SNR

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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Digital vs. analogs signals

A sender has two principal options what types of signals to generate1. It can choose from a finite set of different signals – digital transmission

2. There is an infinite set of possible signals – analog transmission

Simplest example: Signal corresponds to current/voltage level on the wire In the digital case, there are finitely many voltage levels to choose from In the analog case, any voltage is legal

More complicated example: finite/infinitely many sinus functions In both cases, the resulting wave forms in the medium can well be

continuous functions of time!

Advantage of digital signals: There is a principal chance that the receiver can precisely reconstruct the transmitted signal

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Structure of digital communication systems

How to put these functions together into a working digital communication system?

How to structure transmitter and receiver? How to bridge from a data source to a data sink? Essential functions for baseband transmission

Data source

FormatSourceencode

Channelencode

Physical

transmit

Physical medium

Data sink

FormatSourcedecode

Channeldecode

Physical

receive

Channelsymbols

Sourcebits

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Functions

Format: Bring source information in digital form E.g., sample and quantize an analog voice signal, represent text

as ASCII

Source encode: Remove redundant or irrelevant data E.g., lossy compression (MP3, MPEG 4); lossless compression

(Huffmann coding, runlength coding)

Channel encode: Map source bits to channel symbols Potentially several bits per symbol May add redundancy bits to protect against errors Tailored to channel characteristics

Physical transmit: Turn the channel symbols into physical signals

At receiver: Reverse all these steps

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Structure of a (digital) broadband system

Previous example assumed a simple physical transmission in baseband

Using broadband transmission adds complexity to signal generation

Data source

FormatSourceencode

Channelencode

Physical

transmit

Physical medium

Data sink

FormatSourcedecode

Channeldecode

Physical

receive

Channelsymbols

Sourcebits

Modu-late

Demo-dulate

Discrete set of analog waveforms

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Tricky part: Receiver!

Difficult: How to decide, given an incoming, noisy version of a channel symbol (=a waveform) what the originally sent symbol/waveform was?

Receiver (channel decoder) knows, for each channel symbol

All legal waveforms s1(t), …, sm(t)

The actual, incoming, distorted waveform r(t) = si(t) + n(t) Where n(t) is noise, i is unknown index of transmitted channel symbol

How to determine i?

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Coherent receiver

Coherent receiver: Receiver has perfect time synchronization with transmitter, perfect phase

Not true in practice, a simplification

Conceptually: Receiver compares r(t) with all si(t), computes distance measure

T is length of a channel symbol

Result is i that minimizes this distance measure This waveform is assumed to be the one that the transmitter has

sent

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Receiver as correlator/matched filter

Alternative: Compute the correlation of received signal with legal waveforms

Result is i that maximizes the correlation with the actually received channel symbol

Practical implementations have many additional constraints

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Overview

Baseband transmission over physical channels Limitations on data rate: Nyquist and Shannon Clock extraction Broadband versus baseband transmission Structure of digital communication systems Examples

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Example physical layers

Guided transmission media Copper wire – twisted pair Copper wire – coaxial cable Fiber optics

Wireless transmission Radio transmission Microwave transmission Infrared Lightwave

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Electromagnetic spectrum

Hz

103 105 107 109 1011 1013 1015

leitungsgebundene Übertragungstechniken

verdrillte DrähteKoaxialkabel Hohlleiter optischeFasern

sichtbaresLicht

InfrarotMikrowellen

Fernsehen

KurzwelleMittelwellen

-Radio

Langwellen-Radio

nicht-leitungsgebundene Übertragungstechniken

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Conclusion

The physical layer is responsible for turning a logical sequence of bits into a physical signal that can propagate through space

Many different forms of physical signals are possible Signals are limited by their propagation in a physical

medium (limited bandwidth, attenuation, dispersion) and by noise

Bits can be combined into multi-valued symbols for transmission

Gives rise to the difference in data rate and baud rate

Baseband transmission is fraught with problems, partially overcome by modulating a signal onto a carrier (broadband transmission)

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Compute Fourier transform for square wave

Consider a square wave as function g(t)

t

1

-1

T

Compute Fourier coefficients!