DCT_1.pdf

TC 503 Digital Communication Theory

Course Teacher: Dr. Muhammad Imran Aslam

TEXT BOOK

Communication System

Main purpose of a communication system is to transfer information from a source to a recipient via a channel or medium.

Basic block diagram of a communication system:

Source Transmitter Receiver

Recipient

Channel

Dr. M. Imran Aslam 2

Brief Description Source: analog or digital Transmitter: transducer, amplifier, modulator, oscillator, power amp.,

antenna Channel: e.g. cable, optical fibre, free space Receiver: antenna, amplifier, demodulator, oscillator, power amplifier,

transducer Recipient: e.g. person, (loud) speaker, computer


Types of information Voice, data, video, music, email etc. Types of communication systems Public Switched Telephone Network (voice,fax,modem) Satellite systems Radio,TV broadcasting Cellular phones Computer networks (LANs, WANs, WLANs)


Information Representation Communication system converts information into electrical

electromagnetic/optical signals appropriate for the transmission medium.

Analog systems convert analog message into signals that can propagate through the channel.

Digital systems convert bits(digits, symbols) into signals Computers naturally generate information as characters/bits Most information can be converted into bits Analog signals converted to bits by sampling and quantizing (A/D

conversion)


Phenomena affecting signals

Phenomena affecting signals during propagation / transmission Distortion: Due to non-ideal response of

transmission line/ circuits

Noise: Unwanted electrical signals in the system Interference: Unwanted signals from other sources


Digital Vs Analog Communication System

Signal comes from a finite set of waveform shapes

Objective is to determine which waveform from the finite set was sent.

Signal comes from set of infinite waveform shapes (with theoretically infinite resolution)

Exact reproduction of signal at destination is required.


Why digital? Digital techniques need to distinguish between discrete symbols

allowing regeneration versus amplification Use of regenerative receivers is easy Easy to regenerate distorted signals Regenerative repeaters prevent accumulation of noise

Good processing techniques are available for digital signals, such

as medium. Data compression (or source coding) Error Detection / Error Correction (or channel coding) Equalization Security

Immunity to distortion and interference

Digital circuits are less subject to distortion and interference than an analog circuit


Why digital? Advantages of digital circuitry

Reliable Low-cost Flexible Shorter design and production cycle

Different types of digital signals (voice, video, telegraph, etc.) can

be treated as identical signals A bit is a bit

Easy to mix signals and data using digital techniques

TDM/CDM is easier than FDM

Digital signals Low error rate High fidelity


Disadvantages of Digital Communication System

Intensive signal processing (compared to analog) Requires reliable synchronization

Significant resources are allocated to the task of synchronization at various levels

Requires A/D conversions at high rate Requires larger bandwidth Nongraceful degradation

If SNR drops certain threshold, the quality of service (QOS) can change from very good to very poor.


Performance Metrics Analog Communication Systems

Metric is fidelity: want SNR typically used as performance metric

Digital Communication Systems

Metrics are data rate (R bps) and probability of bit error

Symbols already known at the receiver Without noise/distortion/sync. problem, we will never make

bit errors

( ) ( )m t m t

( )( )bP p b b=


Important Points Transmitters modulate analog messages or bits in case of a DCS for

transmission over a channel.

Receiver recreate signals or bits from received signal (mitigate channel effects)

Performance metric for analog systems is fidelity, for digital it is the bit rate and error probability.


Goals in Digital Communication System Design

To maximize transmission rate, R To maximize system utilization, U To minimize bit error rate, Pe To minimize required systems bandwidth, W To minimize system complexity, Cx To minimize required power, Eb/No


Basic Block Diagram of Digital Communication System


Description

The source output may be digital or analog. In case of analog signal source encoder generates an equivalent digital signal using sampling and quantization and removes any redundancy in the signal. The output of source encoder is stream of bits. The channel encoder take k information bits, adds (n - k) non-information bits in the signal to generate code word of length n. Additional non-information bits are used to exercise control over errors. The amount of redundancy introduced is measured by the ratio n/k. Code rate is defined as reciprocal of the redundancy i.e. k/n.


Description

The digital modulator takes the binary sequence from channel encoder and produces a corresponding signal waveform appropriate for transmission over channel. The channel is the physical medium between transmitter and the receiver. While transmitting through channel signal gets affected by different random phenomena such as noise, fading, attenuation etc. The receiver antenna collects the signal form the channel and the receiver reverses all the process performed at the transmitter end to get output signal.


Description of Each Block 1. Format:

Transforms source information into bits Ensure compatibility between source information and DCS

2. Source Encoder: Remove redundant bits from message 3. Encrypt:

To maintain privacy i.e. Preventing unauthorized extraction of information (eavsdropping)

To establish authentication i.e. preventing unauthorized injection of spurious signals (Spoofing)

4. Channel Encoder: Takes k information bits, adds (nk) non-information bits in the signal to generate code word (or channel symbol) of length n. Additional bits are used for error detection / error correction. [Redundancy = n/k, code rate= k/n]

5. Multiplexing: Provides resource sharing by combining different signals/symbols.


Description of Each Block 6. Pulse Modulation:

Define Pulse waveform (pulse shaping) Generate baseband (low-frequency) waveform Filtering to minimize transmission bandwidth When pulse modulation is applied to binary symbols the resulting waveform

is called pulse-code-modulation (PCM) waveform. In telephone applications these waveforms are called line-cods.

7. Bandpass Modulation: Baseband signal is frequency translated by a carrier wave Required to meet transmission characteristics of channel

8. Synchronization (and clock signal): is involved in the control of all signal processing within DCS. It plays a role in regulating operation of every block.

9. Frequency Spread: Spread spectrum techniques are important for interference and privacy. Share bandwidth resources.


Description of Each Block 10. Multiple Access: Provide resource sharing for remote users 11. Transmitter Front End (Channel Coupler): Injects signal into the channel 12. Channel: Actual propagation medium

If channel impulse response is (), Transmitted signal is and noise is () then the received signal is = + ().

13. Equalizer: is implemented to compensate for signal distortion 14. Receiver: All the steps (except detect) preformed at transmitter are

reversed at the receiver side. 15. Detect: Use decision theory to decide which symbol was transmitted.

Example: For binary symbols, compare received power/amplitude to decide whether zero or one was tranmistted.


Basic DCS Transformations


Basic Digital Communication Nomenclature Information Source: Device producing information

Discrete output values e.g. Keyboard Analog signal source e.g. output of a microphone

Character Member of an alphanumeric/symbol (A to Z, 0 to 9) Characters can be mapped into a sequence of binary digits using one of the

standardized codes such as ASCII: American Standard Code for Information Interchange EBCDIC: Extended Binary Coded Decimal Interchange Code

Textual Message: Sequence of characters Binary Digit (Bit): Unit information content. (Fundamental information

unit for all digital systems) Bit Stream: Sequence of bits.


Basic Digital Communication Nomenclature

Digital Message: Messages constructed from a finite number of symbols Printed language consists of 26 letters, 10 numbers, space and several

punctuation marks. Hence a text is a digital message constructed from about 50 symbols

Morse-coded telegraph message is a digital message constructed from two symbols Mark and Space

M ary: A digital message constructed with M symbols Digital Waveform: Current or voltage waveform that represents a digital

symbol A pulse for baseband transmission A sinusoid for bandpass transmission

Bit Rate: Actual rate at which information is transmitted per second


Basic Digital Communication Nomenclature

Baud: When transmitting a sequence of pulses, the unit Baud is sometimes used to express pulse rate (or symbol rate)

Baud Rate: Refers to the rate at which the signaling elements are transmitted, i.e. number of signaling elements per second.

Data Rate: This quantity in bits per second (bits/s) is given by =

=2

bits/s, where bits identify a symbol from = 2 -symbol alphabet,

and is the -bit symbol duration. Bit Error Rate: The probability that one of the bits is in error or simply the

probability of error


Classification Of Signals

Signals can be classified in various ways. 1. Deterministic and Random Signals 2. Periodic and Non-Periodic Signals 3. Continuous Time and Discrete Time Signals 4. Analog and Digital Signals 5. Real and Complex Signals 6. Energy and Power Signals 7. Even and Odd Signals


1. Deterministic and Random Signals

Deterministic Signal: A signal is deterministic if there is no uncertainty with respect to its value at any time. Deterministic waveforms are modeled by explicit mathematical

expressions, example: = 2cos (10 + 30) Random Signal: A signal is random if there is some degree of

uncertainty before the signal actually occurs. Random waveforms/ Random processes when examined over a long

period may exhibit certain regularities that can be described in terms of probabilities and statistical averages.

Example if random signals: Noise Dr. M. Imran Aslam 28

2. Periodic and Non-periodic Signals

A signal is called periodic in time if there exists a constant 0 > 0 such that

= + 0 The smallest value of 0 satisfying this condition is called period of .

A signal for which there is no value of 0 that satisfies the abovementioned condition is called a nonperiodic signal.


2. Periodic and Non-periodic Signals Examples of Periodic Signals


3. Continuous Time and Discrete Time Signals Continuous Time Signal: A signal x(t) is a continuous-time

signal if t is a continuous variable; that is, x(t) is uniquely defined for all t Example: An electrical analog at output of a microphone

Discrete Signal: A discrete signal x(kT) is one that exists only at discrete times; it is characterized by a sequence of numbers defined for each time, kT, where k is an integer and T is a fixed time interval. Example: A sampled signal


4. Analog and Digital Signals

Analog Signal: If a continuous-time signal x(t) can take on any value in the continuous interval (a, b), then the continuous-time signal x(t) is called an analog signal

Digital Signal: If a discrete-time signal x[n] can take on only a

finite number of distinct values, then we call this signal a digital signal.


5. Real and Complex Signals

Real Signal: A signal x(t) is a real signal if its value is a real number.

Complex Signal: a signal x(t) is a complex signal if its value is a

complex number

A general complex signal is a function of the form = 1 + 2

where 1 and 2 are real signals and = 1.


6. Energy and Power Signals Recall

An electrical signal is described either by its voltage or by current

Power across a resistor () is = 2()

= 2 For communication systems power is normalized by taking = 1.

Therefore, = 2() = 2 Regardless signal [()] is voltage or current, instantaneous power is

= 2(). Actual power can be obtained by de-normalization.

Energy dissipated in time interval (2

, 2

) by a real signal is

= /2/2 = 2 /2/2

Power is the rate at which energy is delivered Power dissipated during this interval is

=

= 1 2 /2/2


6. Energy and Power Signals Energy Signal

The performance of a communication system depends on the received signal energy; higher energy signals are detected more reliably (with fewer errors) than are lower energy signals

() is classified as an energy signal if, and only if, it has nonzero but finite energy (0 < < ) for all time, where:

= lim 2()/2/2 = 2()

An energy signal has finite energy but zero average power. Signals that are both deterministic and non-periodic are

classified as energy signals


6. Energy and Power Signals Power Signal

A signal is defined as a power signal if, and only if, it has finite but nonzero power (0 < < ) for all time, where

= lim

1 2 /2/2

Power signal has finite average power but infinite energy. As a general rule, periodic signals or random signals are classified as

power signals


7. Even and Odd Signals Even Signal: A signal x(t) or x[n] is referred to as an even signal

if = ; = []

Odd Signal: A signal x(t) or x[n] is referred to as an odd signal if

= ; = [] Any signal x(t) or x[n] can be expressed as a sum of two

signals, one of which is even and one of which is odd. i.e. = + (); = + []

the product of two even signals or of two odd signals is an even signal and that the product of an even signal and an odd signal is an odd signal


7. Even and Odd Signals Examples


Problem


Solution


The Unit Impulse Function

Dirac delta function (t) or impulse function is an abstractionan infinitely large amplitude pulse, with zero pulse width, and unity weight (area under the pulse), concentrated at the point where its argument is zero.

Sifting or Sampling Property

(t) dt = 1

(t) = 0 for t 0(t) is bounded at t 0

=

0 0( ) (t-t )dt = x(t ) x t


The Unit Impulse Function

Some Properties of impulse function


The Unit Impulse Function Problems

Evaluate following integrals 1. 10()(1 + )1 2. 10()(1 + )121 3. ( + 4)(2 + 6 + 1) 4. ( + 4)(2 + 6 + 1)21 Answers

1. 10 2. 10 3. 7 4. 0


TC 503 Digital Communication Theory Communication SystemBrief DescriptionSlide Number 4Information RepresentationPhenomena affecting signalsDigital Vs Analog Communication SystemWhy digital?Slide Number 9Why digital?Disadvantages of Digital Communication SystemPerformance MetricsImportant PointsGoals in Digital Communication System DesignBasic Block Diagram of Digital Communication SystemDescriptionDescriptionSlide Number 18Description of Each BlockDescription of Each BlockDescription of Each BlockBasic DCS TransformationsBasic Digital Communication NomenclatureBasic Digital Communication NomenclatureBasic Digital Communication NomenclatureSlide Number 26Classification Of Signals1. Deterministic and Random Signals 2. Periodic and Non-periodic Signals2. Periodic and Non-periodic SignalsExamples of Periodic Signals3. Continuous Time and Discrete Time Signals4. Analog and Digital Signals5. Real and Complex Signals6. Energy and Power Signals6. Energy and Power SignalsEnergy Signal6. Energy and Power SignalsPower Signal7. Even and Odd Signals7. Even and Odd SignalsExamplesProblemSolutionThe Unit Impulse FunctionThe Unit Impulse FunctionThe Unit Impulse FunctionProblems

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