Unit 2 Fundamentals of Signal Transmission

Introduction to Communication Networks Spring 2007

©EECS 122 SPRING 2007

Unit 2Fundamentals of Signal Transmission

2 of 46Prof. Adam Wolisz

Acknowledgements• For this unit I have used mostly slides from theBook by WIliam

Stallings (our supplementary texbook)

• Some figures/tables have been taken from „Communication Networks“ by Leon_Garcia and Widjaja – marked GW

• Other sources are referenced...


Inputdevice Transmitter Transmission

mediumOutputdeviceReceiver

g g(t) s(t) r(t) gr(t) g

Sending Receiving

Input g: information

Input represen-tation:

Transmitted signaldigital or analog

Received signal generallydifferent from transmitted

gr(t) ideally (but notnecessarily) identical to g(t)

Information Transmission• Important transformations:

– Source coding

– Channel coding

Source information: Files, Pictures, Speech, Video....Input signal: a representation of the data (a time function)Transmitted signal: another representation of the data, proper for transmission


Input information ...see examples for speech... [GW]


Continuous & Discrete


Sinusoidal Signals

• s(t) = A sin(2 π f t + Θ)

– A: Amplitude (max strength of signal)

– f: frequency (rate of change of signal [Hz] repetitions/s)

– Θ: Phase (relative position in time)

• Two signals with 90o phase shift:


Transmission of Sinusoidal Signals • Sender

– Sender signal

s(t) = As sin(2 π f t )

– The transmitter has a given power Ps [mW]

– Power to Amplitude relation is Ps ≈ As2

• Receiver

– Received signal:

r(t) = Ar sin(2 π f t - τ), τ = Distance/ (Velocity of propagation)

– In most cases: Ar < As

– The receiver receives a power Pr [mW] < Ps [mW]

During the transmission signals are always attenuated. The attenuation is strongly frequency dependent.

The delay may also be frequency dependent...


Attenuation of Signals • The attenuation for the transmission is

– af [dB] = 10 log ( Ps /Pr ) = 20 log (As/Ar)

• Decibel (dB) – is a ratio (not a value)

– expresses a logarithmic relationship

– is used to indicate relative magnitude (gain or loss)

– dB = 10 log(P1/P2)

• Power ratio n of: (n=2) => 3 dB, (n=10) => 10 dB,(n=100) =>20 dB (n=0.1) => -10 dB

• For expressing power, frequently dBW is used, expressing the signal strength with reference to 1 W

– Power [dBW] = 10 log ( Power [W] /1 W )


Power Equations• The transmitter has a given power Ps [dBW]

• The medium has an attenuation of af [dB/km] for a unitary distance

• The receiver has a sensitivity Sf [dBW]

– The smallest incoming power which it will detect with acceptable error -see discussion later...

• To receive a signal properly the power equation (in dB) must be considered

Ps - afx - Sf > 0

where x: distance [km]

What can be influenced? Ps- sometimes... X - usually...


Fourier Analysis of Signals• Every signal s(t) can be represented as a (possibly infinite!)

sum of component sinusoidal signals with different frequencies

Example in the next slide…:

• We do ususally ignore sinusoids with rather small amplitude (thus carrying little energy) – consider only SIGNIFICANT sinusoids.

• Signals with QUICK changes of amplitude will contain significant sinusoids with HIGHER frequencies than signals with slow changes....


Square Wave Frequency Components


Spectrum and Bandwidth• There is a clear and unique equivalence between time representation and

frequency spectrum representation s(t) ≡ S(f)

• rapid signal changes ⇒ bigger bandwidth has to be used: smaller rectangles => higher basic frequency...

• Spectrum

– range of frequencies contained in signal

• Absolute bandwidth

– width of spectrum

• Effective bandwidth

– Often just bandwidth

– Band of frequencies containing most of the energy

• DC Component

– Component of zero frequency


Example: Spectrum with DC Component


Acoustic Spectrum (Analog)


Low-pass Filter- Any transmission system supports a limited band of

frequencies- A frequent system:

- low-pass filter

• af = a for f < flim ,

• af → ∞ for f ≥ flim

– flim = upper limiting frequency

– Gf = 1/af = transmission gain

Be careful: We will mix gain and attenuationsince both are popular!


Characteristics of a Typical Voice Channel

• Attenuation:

• 1 - unequalized

• 2 - equalized

Atte

nuat

ion

-re

lativ

e to

at

tenu

atio

n at

100

0 H

z!

Frequency [Hz]

Note: Attenuation relative to attenuation at 1000 Hz!


Transmission of Digital SignalsTransmitting a rectangular pulse over a low-path filter with different bandwidth (the R-C System).

The Response of an R-C Transmission System to a Rectangular Input Pulse for Several Values of β =1/(RC)


Even cloaser to reality... [from Comer]


Transmission of Complex Signals

• Analog signals subject to distortion by noise

• Digital signals reconstructed in spite of noise

• Regeneration possible for digital signals


Evailable bandwidth influences signal quality!!! [GW]


Digital Representation of Analog Information (1)Source coding

Sampling (discretizationin time)

- The Nyquist sampling theorem says that any signal s(t), where the spectrum has no frequency components at a frequency higher than B[Hz] can be precisely reconstructed from sample values taken 2B times per second !

For voice we assume that : B=4000 Hz, corresponding to 8000 samples/second.


Digital Representation of Analog Signals(2)• Quantization (discretization in value)

– A proper quantization unit has to be chosen. For voice (not CD quality !!!) 256 levels give an excellent quality (8 bits coding, usually sign plus 7 bits value).

– This is PCM (Pulse Code Modulation) coding

– The discretization can be linear (left side) or nonlinear…

Effect of nonlinear coding


Transmission Media and their FeaturesWe will shortly discuss some of them…

• Guided Media:

– Twisted Pair

– Coaxial cable

– Fiber

• Unguided Media:

– Radio


Twisted Pair (TP) • 2 parallel wires -> simple antenna

• A way to limit electromagnetic influence ⇒ twisted pair


Twisted Pair (TP) (2)• UTP- Unshielded TP (speed limited by radiation)

considerations • STP- Shielded TP (speed limited by higher capacity)


Comparison of Shielded and Unshielded TP

Attenuation (dB per 100 m) Near-end Crosstalk (dB)

Frequency(MHz)

Category 3UTP

Category 5UTP 150-ohm STP

Category 3UTP

Category 5UTP 150-ohm STP

1 2.6 2.0 1.1 41 62 58

4 5.6 4.1 2.2 32 53 58

16 13.1 8.2 4.4 23 44 50.4

25 — 10.4 6.2 — 41 47.5

100 — 22.0 12.3 — 32 38.5

300 — — 21.4 — — 31.3


Attenuation of typical twisted pair cables [GW]


Coaxial Cable [GW]

• Used for analog and digital transmission

• Low noise

• Huge bandwidth (several 100 MHz)


Attenuation of the Coax. [GW] ..


Fiber optics... [GW]


Attenuation of the fiber... [GW]

Attractive „windows“ in the Wavelengths: 1.3, 1.5


Fiber optics (3)

Refractive index and some representative light path in a multimode stepped-index optical fiber

Refractive index and some representative light path in a multimode graded-index optical fiber. The light is continually refocused as it travels along the fiber.

Single-mode optical fibers has a core that is so thin that only one ray (only the fundamental mode) of light travels along it. In this way, all the rays of light arrive at the end at the same time, and modal dispersion is nonexistent.


A comparison of the guided media.


Electromagnetic Spectrum The light wave region is expanded for further detail.


Radio propagation (1)


Radio Propagation (2)


RadioPropagation (3) - the relevant for us...


Propagation path attenuation – the theory…

( )2

2

4 dPP t

r πλ

=

• Attenuation in free space is inverse proportional to the square of distance…

• Attenuation is stronger for higher frequencies… lower frequencies cover bigger distances with the same transmission power…

• Other environments introduce even stronger attenuation

Pr – received power [mW]

Pt – transmitted power [mW]

αdPPr /0=


The simplification and the reality... [Kotz & al]

In addition: -Reciprocity does not hold (your hear me but I do not read you-Individual „identical“ radios are NOT identical See additional reading for details!


Multipath Fading

• The received signal is the sum of the signals arriving along different paths,

• Except for the LOS path all paths are the result of reflection and diffraction,

• Equalization

• Diversity


Rayleigh fading: Received Signal

6km/h50 km/h

-35

-30

-25

-20

-15

-10

-5

0

5

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

rece

ived

sig

nal [

dB]

time [s]


Doppler Shift

• As the transmitter moves towards the receiver, the propagation time τwill change with time t as (1)

• The original frequency fc changes to fc+fd (2)

• fd is a shift in the frequency observed at the receiver (Doppler frequency shift)

• fd is positive if the receiver and sender move towards each other, else negative

• The Doppler effect constitutes a source of signal fading.

ctvd

ctdt m−

== 0)()(τ (1)

cm

d fcvf = (2)


REMEMBER: the transmissions my interfere! [FCC]

• Main issue: Interfering with others....

• Licencing of the frequencies .....

• Competition in (few!) bands dedicated to unlicenced sharing• Recent research: secondary usage of licenced frequencies,

temporarily not used by the „owner“


Fiber, radio... Something in common? • In both cases only specific frequency bands are used, different

form the „natural spectrum of the signal“. Think of voice....

• The „useful“ signl has to be „shifted“ where desired...

• We will call this „pass-band transmission“

• We do this, using modulation ...


Pass-band Transmission (Analog Data and Signals!)• We shift the frequency spectrum

elsewhere...

• The different kinds of modulation can be combined


Why to Modulate Analog on Analog?• Take Amplitude Modulation AM: If the modulated signal is a

sinusoid with frequency fc, and data are within [0 , B] Hz then the resulting spectrum is from fc to (fc +B) or from (fc -B) to fc

• One possible justification: smaller differences in attenuation...


Digital Data / Digital Signal Encoding• Digital Data:

– Sequence of bits to transmit

• Physical signal:Physical value e.g. voltage, changing in discrete time epochs.

• Encoding (channel coding): Mapping of bit sequences to signals. This can be done in many ways...

• Example:

Unipolar (unbalanced) signaling

Polar (balanced) signaling

1 0 1 1 0 0 1 0 0 1


Digital Signal Encoding (2)• Signaling period - T

• Number of signal levels - M

• Within the signaling period K changes of the signal level arepossible, the number of changes per second = baud rate !

• There are MK signal shapes possible. Usually only some N < MK signal shapes are permitted.

• Achievable bit rate R=(lg2N)/T

• Bit rate is not necessarily equal to baud rate


Digital Signal Encoding (3)• Criteria for selection

– Signal spectrum :

• lack of high-frequency component

• lack of dc component (transformers!)

• transmitted power concentrated in the middle of bandwidth

– Clocking reconstruction at the receiver

• long periods of constant values avoided

– Some error detection features

– Polarity of the signal negligible

• (only the change counts)

– Noise immunity


Digital Signal Encoding (4a)• NRZ-L(Nonreturn-to-Zero-Level)

– 0 = high level

– 1 = low level

• NRZI (Nonreturn-to-Zero-Inverted)

– 0 = no transition at beginning of interval

– 1 = transition at beginning of interval

• Bipolar -AMI

– 0 = no line signal

– 1 = positive or negative level, alternating

•Note: 3 level of signal, bit rate=baud rate

Thus: the possible bit rate could be log2 (3)= 1.58, but really only one bit /signaling time is send....


The Discussed Codes..


Digital Signal Encoding (4b)• Pseudoternary

– 0 = positive or negative level, alternating zeros

– 1 = no line signal

• Manchester

– 0 = transition high > low in middle of interval

– 1 = transition low > high in middle of interval

Note: Bit rate lower than baud rate!!

• Differential Manchester

– Always a transition in middle of interval

– 0 = transition at beginning of interval

– 1 = no transition at beginning of interval


NRZ vs. Manchester...


• Consider a simple pulse like:

• The distribution of the signal energy over the frequency spectrum is:

Spectral Efficiency


Spectral Efficiency of Codes


Note: The bit rate is twice (or 3 times !) the baud rate...

Multilevel Schemes


Digital goes also on analog


Also in multilevel way...• Think in terms of having multiple

– Amlitudes

– Frequencies

– Phase changes

• Think in term of mixing them

(e.g. Amplitude and Phase)


Which Bandwidth is needed?• Nyquist result: Using M signal levels, In absence of noise; we could get at most :

C [Bps] = 2B log2 M – where B is the bandwidth in Hz.

• Great idea: just increase the number of signal levels? Not really... There is noise...

• Shannon result: In presence of noise, theoretical upper bound is:

C [Bps] = B log2 (1 + SNR) for error free transmission without limits on delay!


The reality... • Unfortunately – limits are usually not achievable....

• And we DO have time limits...

• As result: there are errors in transmission.

• We do ususally look at the measure expressed as

BIT ERROR RATE – the ratio of bits in error....

• We plot it usually as a function of :

Eb/No the ratio of (signal energy / bit)

to (noise power density/ Hz)


Prob

abilit

y of

err

or (B

ER)

Bit Error Rate for Multilevel PSK (example)

Average energy-per-bit to noise density ratio (Eb/E0) in dB

Documents

Unit 2 Fundamentals of Signal Transmission