Principles of communication systems 6th edition

Principles of communication systems 6th edition là tài liệu hữu ích cho tất cả các bạn trong ngành viễn thông. Đã học cũng như đang học ngành viễn thông nâng cao kiến thức và khả năng làm việc của mình.

Introduction

2

Signal Retrieval and Communication

 Theory of systems for the conveyance of

information

 Characteristics of communication systems

 Noise and “information” (deterministic vs probabilistic)

 Communication (only particular type of signal retrieval

problem)

 Usually two resources to consider

Innovation in microelectronics and

signal processing have led to the

proliferation of communication systems

Components of Block Diagram

 Couple the message to the channel

 Modulation, filtering, amplification, and coupling

 Modulation

 For the ease of radiation

 To reduce noise and interference

 For channel assignment

 For multiplexing or transmission of several messages over a single channel

 To overcome equipment limitations

8

Channel Characteristics

 Noise generated from sources outside a communication

system, including atmospheric, man-made, and extraterrestrial sources

Channel Characteristics

 Convolutive noise (usu very troublesome)

10

802.11a/b/g

802.11n/ac

802.11ad

Traditional Cellular Network

• Low system capacity

• Poor performance for

cell edge users

MBS

MBS

B4G Objectives

Spectrum Efficiency

Spectrum Extension /Utilization

Network Density

1000x Capacity

Required capacity (bps/km 2 = bps/Hz/cell × Hz × cell/km 2 )

Current capacity Spectrum extension

Existing cellular bands

Hybrid access using coverage and

New cellular concept for cost/energy efficient dense deployment

Cellular network assists local area radio access

Home/office

Dense urban Shopping mall

Traffic offloading

(alternative means for communications)

WiFi offload, D2D, etc

In a Nutshell…

14

Pico-BS Relay

backhaul D2D

Operator-Major Issues

• Neighbor discovery

• Offloading traffic

Major Issues

• Femto-to-femto interference and femto-to-macro interference Femto-BS

Macrocells: 20-40 watts

(large footprint)

Systems Analysis Techniques

 Time and frequency domain analyses

 Modulation and communication theories

 Modulation theory employs time and frequency domain analyses to analyze and design systems for modulating and demodulating of information-bearing signals

and design of systems to counteract their effects are

modulation theory

16

Probabilistic Approaches to System

Optimization

convolutive) noise (incl interference) is important

 Probabilistic models are often used

 Why?

 Optimal design is crucial

 Many “optimal” design are not optimal – depends on perspective

 How do we do it? (We are engineers, this is important!)

 Statistical signal detection and estimation theory

 Wiener optimum filter, matched filter, adaptive filter, and many more…

 Information theory and coding

 Shannon says it can be done, but didn’t tell us how it can be done

Signal and Linear System Analysis

 Take on random values at any given time instant and

characterized by pdf: not completely predictable, with

uncertainty E.g x(n) = value of a die shown when tossed at time index n

 If the signal is random, how do we describe (model) it?

= − ∞ < < ∞

Signal Model and Classifications

 Periodic signal

such that x(t + T0) = x(t), ∀t The smallest such T0 is called fundamental period or simply period

 Aperiodic signal

4

Signal Model and Classifications

 Phasor signal and spectra

 Key part of modulation theory

 Construction signal for almost any signal

 Easy mathematical analysis for signal

 Phase carries time delay information

( )

, rotating phasor, phasor, ,

Signal Model and Classifications

 Information is contained in A and t (given a fixed f0 or ω0)

 The related real sinusoidal function

 In vector form graphically

Signal Model and Classifications

: Defines a precise sample point of at time (or if - )

t

x t x t t t dt

x t x t d

at t t t a

8

Signal Model and Classifications

( )( )( )

0

2 0

5 What is precisely? Some intuitive ways of realizing it:

1 lim , , E.g 1 2

0, otherwise

1 E.g 2 lim sin

Any signal having unit area an

t

t t

t t

Signal Model and Classifications

10

Signal Classifications: Energy & Power

( ) ( )

2

2

This classification will be needed for the later analysis of

deterministic and random signals

T T T

Signal Classifications: Energy & Power

T

T

t T

T T

α

α

α α

2 2

Example 2:

lim lim

1 lim

2

2

T T T

T

T T T

Signal Classifications: Energy & Power

2 0

0

0 2

t T t T

2

2

1 lim

t T t T

T A

14

Signal Classifications: Energy & Power

we only need to check its power

and mostly is an energy signal

mutually exclusive, i.e cannot be both at the same time But a signal can be neither energy nor power signal

Signals and Linear Systems

Linear and Time-Invariant (LTI) System

Linear System satisfies superposition principle:

Complete Characterization of LTI Systems

Convolution Using Matrices and Vectors (Digression on DT convolution)

T h





20

BIBO Stability

 BIBO Stability

bounded output sequence

BIBO Stability Examples

<

22

Causality

 A system is causal if current output does not

depend on future input, or current input does not contribute to the output in the past

Eigenfunctions of LTI System

Consider

x(t) y(t)

What is the relation to eigenvalues and eigenvectors?

jst

LTI, h(t)

24

System Transmission Distortion and

System Frequency Response

combination of orthogonal sinusoidal basis functions

ej2πft, we only need to inject Aej2πft to the system to

characterize the system’s properties, and the eigenvalue

primary concern in high-quality transmission of data

Hence, the proper representation for the transmission

channel (remember, convolutive noise is troublesome)

3 Types of Distortion of a Channel

 Amplitude distortion

constant

 Phase distortion

 Linear system but the phase shift is not a linear function of frequency

 Nonlinear distortion

0 0

2

2 0

2 2

0

Complex exponential respresentation

1

Sinusoidal respresentation

j nf t n

n

j nf t n

• n = 1 term is called the fundamental

• n = 2, 3, … terms are called the 2 nd ,

3 rd , …harmonics, respectively

0 0

0

0 0

0 0

0 0

0

2 0

0 0

2 0

t

t T t

t T

j nf t n

t

t T t

X x t e dt T

T

X x t e dt T

0 0

Properties of Fourier Series

( ) ( )

0

Linearity: ,

30

Properties of Fourier Series

( )

( ) ( )

0

0 0

0

2 0

2

* ,

0

2

* 0

Parseval's Theorem:

Power in time domain = power in frequency domain

1

1

1

j m n f t

m n T

m n

j m n f t

m n

P x t dt T

X X e dt T

X X e T

2 0

0 2

1

1

, ,

0,

n n

dt

X X m n f t j m n f t dt T

T X m n T

m n X

Fourier Series for Several Periodic Signals

, 4

1

1

Im tan

Re

n n

n

n

X X

Example 1

34

Example 2

1 2

n

t nT

x t A

τ τ

2

0, else

t t

+π and –π added to account for the fact

that |sinc(nf0τ)| = -sinc(nf0τ) when

sinc(nf0τ) < 0 Choice of + or – are arbitrary, as long as the phase function

is odd

36

Fourier Series and Fourier Transform

Good orthogonal basis functions for a periodic function

1 Intuitively, basis functions should also be periodic

2 Intuitively, periods of the basis functions should be equal to

the period or integer fractions of the target signal

3 Fourier found that sinusoidal functions are good and smooth

functions to expand a periodic function

Good orthogonal basis functions for an aperiodic function

1 Already know sinusoidal functions are good choice

2 Sinusoidal components should not be in a

“fundamental & harmonic” relationship

3 Aperiodic signals are mostly finite duration

4 Consider aperiodic function as a special case of

periodic function with infinite period

Synthesis & analysis (reconstruction & projection) Synthesis & analysis (reconstruction & projection)

is the spectra coefficient, spectra amplitude response

To synthesize, it must first analyze it and find

jn t n n n

x t T f f

0

By orthogonality

1

n

t T

jn t n

2 0

2 2

Given aperiod with period 1/ ,

2 , it can be synthesized as

1 lim

2

By orthogonality (FT/freq response of )

d n

j ft t

π π

ω ω π

ω ω π

Fourier Series and Fourier Transform

1 Decompose an aperiodic signal into

uncountable frequency components

2 No fundamental frequency and contain all

possible freqs

3 Continuous spectral density

: amplitude : phase of

X f

 A specific case of projection of vectors

 Sinusoidal/exponential functions (of different ω ’s) form the basis

j ft f

π π

0 0

0

0

2 0

/ 2 2 / 2

/ 2 2

t

j ft t

t

j ft t

τ π τ

π

π τ π τ

τ τ

π π

x

x

π π

40

Fourier Transform of Singular Functions

(pronounced dir ric clay) conditions, i.e signal must be

bounded, must be absolutely integrable,

However, its FT can be obtained by formal

2 0

sifting property 2

j nf t

n T

j nf t j nf t n

42

Fourier Transform of Periodic Signals

(Signals that are not energy signals)

s n

Poisson Sum Formula

( ) ( )

Taking the inverse CTFT of

s

s

s n

2 0

sifting property 2

Since is periodic, it can be

represented by its CTFS coefficients

n

j nf t n

t n

2 0

2

Using the Poisson sum formula

Time-Average Correlation of Energy

Signal (Deterministic Signals)

( ) ( )

x t

Time-Average Correlation of Power Signal (Deterministic Signals)

2

*

,1

2

T

f

R x t x t

x t x t dt T

x t x t dt T

S f F R

τ τ

S f = F R τ = ∑ X δ f −nf

48

Interpretation of Time-Average

Correlation

 φ ( τ ) and R( τ ) measure the similarity between the

signal at time t and t+ τ

per unit frequency at frequency f

Properties of Time-Average Correlation

R(0)

 R( τ ) is even for real signals: R(- τ ) = <x(t),x * (t- τ )>

= R( τ )

 If x(t) does not contain a period component, then

 If x(t) is periodic with period T 0 , then R( τ ) is

periodic in τ with the same period

T T T

xy t

xy yx

x t y t dt T

I/O Relationships of LTI Systems for

Discrete-time signal: x[n] = x c (nT), -∞ < n < ∞, T: sampling period

In theory, we break the C/D operation in two steps:

1 Ideal sampling using “analog delta function (Dirac delta function)”

• Can be modeled by equations

2 Conversion from impulse train to discrete-time sequence

• Only a concept, no mathematical model

Conversion from impulse train to discrete-time sequence

(more when you learn DSP)

We shall use Ω = 2 πF to denote analog normalized frequency,

and

ω = 2 πf to denote “digital” normalized frequency

(F = previous f, and f here is now “digital frequency”)

Ideal sampling signal

Continuous - time signal Sampled (continuous - time) signal

( ) ( ) ( ) ( ) ( )

( ) ( )

n

c n

c n

δδ

Ideal Sampling – Frequency Domain

Remark: : analog frequency (radians/sec) : discrete (normalized) frequency (radians/sample)

: Ideal sampling (all in analog domain)

2

1 (*)

c

c

s k

s k

X j k T

s

s

j t s

n

j t c

t n

j nT c

Step 2: Analog to Sequence (Analog to

1 Since , thus

Nyquist Sampling Theorem

(Nyquist, Shannon)

 Nyquist frequency = ΩN, the bandwidth of signal

 Nyquist rate = 2 ΩN, the minimum sampling rate without

distortion (In some books, Nyquist frequency = Nyquist rate.)

 Undersampling: Ωs < 2ΩN

 Oversampling: Ωs > 2ΩN

we can achieve perfect reconstruction For example, ideal

Conversion from seqence

to impulse train

x[n] x s (t) Reconstruction

Signal Reconstruction Derivation

t

x r (t)

H r (jΩ)

T

Modulation I

Types of Modulation Techniques

 Message sampled at discrete time

 Amplitude, width, or position of pulse is varied corresponding the value of the information-bearing sample

cos 2 , : carrier frequency (fixed), : amplitude, : phase

Assuming the receiver knows exactly the phase

and frequency of the received signal

Coherent (synchronous) demodula

BPF

Amplitude Modulation (AM)

 Non-coherent detection is a major problem

 Squaring operation for DSB to extract carrier frequency

 Makes use of envelope detector

 Tradeoff:

 Power vs ease of design at Rx

 Less efficient use of power (carrier doesn’t carry any information about the message)

 DC component of m(t) cannot be actually recovered as it is mixed with the carrier

x t A am t f t

t

π δ

usu 1 1

min

: modulation index : DC bias

Example

( ) sin 2 1 , ( ) c 1

To measure the efficiency of the modulator, compute the

time-average value of :

1

21

11

AM – Power Efficiency

( )

( ) ( )

2

zero 2

Assuming has zero average value, and taking time average

T T

T nd

c n T

T

T c

n T T

m t

A dt A T

A am t dt T

A a

m t dt T

AM – Power Efficiency

( ) ( )

( ) ( )

( ) ( )

carrier power information-bearing

signal power (sideband)

( ) ( )

n

t n

2

c

T T T

T

T T

ff

12

12

c c

15

Single-Sideband Modulation

 Not necessary to send both sidebands

Upper sideband

Lower sideband Lower

sideband

SSB Modulation

Method 1: Hilbert transform

• easy to understand, but hard to implement

• Requires ideal BPF

• Message m(t) does not have very low frequency

components

low freq components

Method 2: Phase-shift modulator

Hilbert Transform

( ) ( )

j

f t

1 0

42

sgn

Hilbert Transform Properties

( ) ( )( ) ( )

compute the Hilbert transform of the pro

1 sgn

0,

n n

Natural Envelope Representation of

Natural envelope: : magnitude of

If constant (no active information), then all the message information is represented by

In general, a BP signal can carry two message

I R

x t t

x t

a t x t t

25

Complex Envelope Representation of

Bandpass Signals

( ) ( ) ( ),Remark: The complex envelope of an arbitrary BP signal is an equivalent

expression that contains two messa

j f t

j f t

e R

P I

x t jx t e

P

Complex-valued LP signal

Bandpass, Lowpass, Analytic Signal,

j f t

j f t

e R

P I

x t jx t e

27

Complex Envelope Representation of

Bandpass Signals

 A physical system in passband (e.g a channel)

may have different in-phase and quadrature

Complex Envelope Representation of

Complex envelope

Complex Envelope Representation of

Physical Implementation of Bandpass

2 Envelope

SSB-LB Modulation – Hilbert Transform Approach

2 Part-B :

2

1 ˆ

ˆ sin 2

4 1

SSB-UB Modulation – Hilbert Transform Approach

SSB-UB Modulation – Analytic Signal

39

Upper- and Lower-Sideband and SSB

Upper sideband

Lower sideband

Lower sideband

If 0, 2 -term represents crosstalk, and distorts

Carrier Insertion With Envelope Detector

cos 2

2

c c

ˆ 2

where

ˆ tan The instantaneous frequency of is

ˆ

2 2 tan

c c

Example 3.2: Time-Domain SSB

Waveform

 Transmit small amount

(vestige) of unwanted sideband

 Pros: Simplified receiver

design

 With carrier reinsertion,

envelope detector can be used

1 cos 2

2

After demodulation by 4 cos 2

and LPF (removal of 2 )

1

2 cos 2

c

c c

f t f

VSB Modulation – Phase Response

( )

2

Demodulation: ( 2 and take real part)

For the first two terms to combine:

phase response has odd symmetry around

Distortionless response requires

From : 1 and with denoting delay

VSB Demodulation Via Carrier

51

Frequency Translation and Mixing

 Signal received, e.g at radio frequency (RF), needs to be moved/translated to a (fixed) intermediate frequency (IF) for processing

 Hard to perform signal processing, like amplification, BPF, and detection at high frequency

 Easier to build filters and detectors to operate at a fixed (IF) invariant to the carrier frequency

 Easier to build tunable oscillators

 Improvement to frequency selectivity

 Separates and extract out signals that are close together in frequency

 E.g TV channels that are closed together

 This is done by a mixer

 Process of multiplying a bandpass signal (message) by a periodic signal is called mixing or