Ilenia Tinnirello

Lecture 0:

Basic Concepts

(Stallings, Chapter 2)

Ilenia Tinnirello

Fundamentals of

Communication Systems

�Which topics?

�Converting data into signals

�Characterizing statistical signals

�Transporting signals in real channels

�Studying the effects of the noise

Electrical Communications

Ilenia Tinnirello

Fundamentals of

Communication Systems

�Which topics?

�Organizing the data into information units

�Setting a path along a network of nodes between source and destination

�Defining rules (i.e. protocols) for communication among devices

�Sharing resources among multiple devices

Networks

Ilenia Tinnirello

Electromagnetic Signal

�The transfer of information over a medium is performed by electromagnetic signals

�e.g. voice cannot be sent very far by screaming. To extend the range of sound, we need to convert it

�Each medium offers different attenuations and distortions, which imply the use of specific carriers. The carrier is a sinusoid of a given frequency.

�e.g. light, microwave, etc.

�Each signal can be represented in time and frequency domain

Ilenia Tinnirello

Time Representation

�Analog signal - signal intensity varies in a smooth fashion over time

�No breaks or discontinuities in the signal

�Digital signal - signal intensity maintains a constant level for some period of time and then changes to another constant level

�Periodic signal - analog or digital signal pattern that repeats over time

� s(t +T ) = s(t ) where T is the period of the signal

Ilenia Tinnirello

Frequency Representation (1)

�Any electromagnetic signal can be shown to

consist of a collection of periodic analog

signals (sine waves) at different amplitudes,

frequencies, and phases

�The period of the total signal is equal to the

period of the fundamental frequency

�e.g. sin(t)+1/3sin(t*3)+1/5sin(t*5)

Ilenia Tinnirello

Frequency Representation (2)

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

Ilenia Tinnirello

Frequency-Domain Concepts

�Fundamental frequency - when all frequency components of a signal are integer multiples of one frequency, it’s referred to as the fundamental frequency

�Spectrum - range of frequencies that a signal contains

�Absolute bandwidth - width of the spectrum of a signal

�Effective bandwidth (or just bandwidth) -narrow band of frequencies that most of the signal’s energy is contained in

Ilenia Tinnirello

Data Communication Terms

�Data - entities that convey meaning,

or information

�analog (video/audio); digital (integer,

text )

�Signals - electric or electromagnetic

representations of data

�analog/digital

�Transmission - communication of

data by the propagation and

processing of signals

Ilenia Tinnirello

Analog Signals

�A continuously varying electromagnetic wave that may be propagated over a variety of media, depending on frequency

�Examples of media:

�Copper wire media (twisted pair and coaxial cable)

�Fiber optic cable

�Atmosphere or space propagation

�Analog signals can propagate analog and digital data

Ilenia Tinnirello

Analog Signaling

Ilenia Tinnirello

Digital Signals

�A sequence of voltage pulses that may

be transmitted over a copper wire

medium

�Generally cheaper than analog

signaling

�Less susceptible to noise interference

�Suffer more from attenuation

�Digital signals can propagate analog

and digital data

Ilenia Tinnirello

Digital Signaling

Ilenia Tinnirello

Data and Signal Combinations

�Digital data, digital signal

�Equipment for encoding is less expensive than digital-to-analog equipment

�Analog data, digital signal

�Conversion permits use of modern digital transmission and switching equipment

�Digital data, analog signal

�Some transmission media will only propagate analog signals

�Examples include optical fiber and satellite

�Analog data, analog signal

�Analog data easily converted to analog signal

Ilenia Tinnirello

Data Rate and Bandwidth

� There is a relation between the information-carrying capacity of a signal and its bandwidth

� Consider a square wave, in which the positive pulse represents 0 and the negative one represents 1

� The duration of each pulse is 1/2f; the data rate is 2f bits per second (bps)

� What are the frequency components? Adding sin waves at frequencies f, 3f, 5f.. Suitably scaled, we approach the square wave

� It can be shown that this waveform has an infinite number of frequency components and hence an infinite bandwidth (each discontinuity implies infinite bandwidth).

� HOWEVER, we can limit the bandwidth (i.e. consider only a subset of frequencies) and obtain a waveform close to the original one. (physical medium have limited bandwidth)

Ilenia Tinnirello

Example

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

� f=1MHz, B=4MHz

3 frequencies:1,3,5 MHz

0101010101 @ 2Mbps

� f=2MHz, B=8MHz

3 frequencies:2,6,10 MHz

0101010101 @ 4Mbps

� f=2MHz, B=4MHz

2 frequencies: 2,6 MHz

0101010101 @ 4Mbps

�By doubling B, we double the potential rate

�For a given bandwidth, we can support various data rate

depending of the ability of the receiver to discern 0 and 1 in

presence of noise.

Ilenia Tinnirello

Relationship between Data

Rate and Bandwidth

�The greater the bandwidth, the higher the

information-carrying capacity

�Conclusions

�Any digital waveform will have infinite

bandwidth

�BUT the transmission system will limit the

bandwidth that can be transmitted

�AND, for any given medium, the greater the

bandwidth transmitted, the greater the cost

�HOWEVER, limiting the bandwidth creates

distortions

Ilenia Tinnirello

Digital Modulations

http://www.complextoreal.com/chapters/mod1.pdf

Ilenia Tinnirello

Modulation

� The process of converting information so that it can

be successfully sent through a medium is called

modulation

� A digital signal is a sequence of voltage pulses that

can be transmitted over a copper wire medium

(strong attenuations at high frequencies)

� Some transmissions medium (optical fiber and

satellite) only propagate analog signals: for wireless

communications is then required a digital to analog

conversion

Ilenia Tinnirello

From digital signal to analog signal

�The analog signal is built starting from

sinusoid. Information is carried by varying

some sinusoid parameters:

�Amplitude, Frequency, Phase

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

Baseband signal

1 1 0 1 1 0 0 0 1 0

Binary modulations

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

Ilenia Tinnirello

Signal Spaces

�Study of signal spaces provide o geometric

method of conceptualizing the modulation

process

�As in normal spaces, all the modulated

signals can be expressed as linear

combination of orthogonal base signals

� e.g. in a date interval, the signal modulated via ASK

or PSK is an cos(2π f t), where an is 1 or 0.5 for ASK, 1

or -1 for BPSK

� cos(2π f t) can be considered a base vector of a mono-

dimensional space

cos(2ππππft) cos(2ππππft)

Ilenia Tinnirello

Signal Spaces (2)

�Starting with cos(2ππππ f t) we cannot represent

cos(4ππππ f t) or cos(2ππππ f t + φφφφ). For general

modulation waveforms we need more

dimensions and more base functions

�e.g. cos(4π f t), cos(2π f t) for FSK

cos(2ππππft)

cos(4

ππ ππft

)

Ilenia Tinnirello

M-ary modulations

�Instead of using two waveforms for 0

and 1, we can use more waveforms for

aggregated data

�e.g. cos(2πft) 00

sin(2πft) 01

-cos(2πft) 10

-sin(2πft) 11 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

Ilenia Tinnirello

Bi-dimensional Modulations

� All the waveforms Acos(2ππππft+φφφφ) can be expressed as a

combination of cos(2ππππft) and sin(2ππππft)

� Using cos(2ππππft) and sin(2ππππft) as base functions we can

represent these modulation waveforms in a bi-

dimensional space

� e.g. QPSK: we can see this modulation as two BPSK for

cos(2 π ft) and sin(2 πft)

cos(2ππππft)

sin

(2ππ ππft

)

Ilenia Tinnirello

Bi-dimensional Modulations (2)

� We can add further waveforms in order to transmit more

bits with a single signal.

� e.g. 8PSK: 8 different waveforms for groups of 3 bits

si = cos(2πft+2 π/8*i) i=0,1,...7

000

001

010

011

100

101

110111

Ilenia Tinnirello

QAM: Quadrature Amplitude

Modulation

� It is another bi-dimensional modulation. We can vary

simultaneously the amplitude and the phase of the

signals in order to derive more waveforms.

� e.g. 8-QAM, 16 QAM

if M is the total # of signals, the # of bits carried by each

singal is log2M

Ilenia Tinnirello

Symbols & bauds

� According to the total # of waveforms, each

waveform, which represents a unit of transmission

energy, carries a different # of bits.

� The waveform which stands for a group of bits is

called symbol

� The number of symbols in the unit time (seconds) is

defined as bauds = symbols/second

� e.g. BPSK vs. QPSK: 1 bit/symbol vs. 2 bits/symbol

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

-1

-0 . 8

-0 . 6

-0 . 4

-0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

Suppose to have a symbol

rate of 106/s:

1 Mbps with BPSK

2 Mbps with QPSK

Ilenia Tinnirello

More symbols, more rate?

� Given the bandwidth B, with maximum symbol rate 2B, we can transmit C = 2B log2M bps

� We can expect to increase the bit rate by simply choosing an high number of different symbols M..

� However, we have to take into account the noise effects: the received signal does not correspond with the red spots

� a M grows, it is more and more difficult at the receiver to distinguish the symbols (given the symbol energies)

Ilenia Tinnirello

Shannon Limit

� For a given level of noise, a greater signal strength improve the ability to correctly receive data.

� The key parameter involved in this reasoning is the Signal-to-Noise-Ratio (SNR), which is the ratio of the power in a signal to the power of the noise.

� It has been proved by Shannon that the maximum bit rate C possible in a given bandwidth obeys to the following equation: C = B log2(1 + SNR)

� C is called Shannon Capacity

Ilenia Tinnirello

Shannon Capacity Formula

�Equation:

�Represents theoretical maximum that can

be achieved

�In practice, only much lower rates achieved

�Formula assumes white noise (thermal noise)

�Impulse noise is not accounted for

�Attenuation distortion or delay distortion not

accounted for

( )SNR1log2 += BC

Ilenia Tinnirello

Example

�Spectrum of a channel between 3 MHz and 4

MHz ; SNRdB = 24 dB

�Using Shannon’s formula

( )

251SNR

SNRlog10dB 24SNR

MHz 1MHz 3MHz 4

10dB

=

==

=−=B

( ) Mbps88102511log10 6

2

6 =×≈+×=C

( )

16

log4

log102108

log2

2

2

66

2

=

=

××=×

=

M

M

M

MBC

Ilenia Tinnirello

Bandwidth improvements

� Given M different waveforms, the data modulation in

general creates a signal with discontinuities (which

imply great bandwidth consumptions, such as the

square wave)

� It is possible to use some shape functions to mitigate

the discontinuities; the symbols are recognized

sampling opportunely at the receiver

� e.g. the root raised cosine is often used with QPSK

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hamming

window

Ilenia Tinnirello

� In principle equal to the previous case, with different

shaping functions: half-sin for MSK and gaussian

pulse for GMSK

� e.g. MSK using sin pulses

MSK and GMSK Modulations

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

BPSK

MSK