Objective This course covers some of the fundamental concepts

and the key advanced topics related to the transmitter, channel and receiver in digital communication. It also introduces some of the advanced research areas in the field.

Pre requisites Required:

Signals and Systems

Recommended:

Stochastic Processes

Communication It is the transmission of information from a source to

one or more recipients via a channel or a medium.

Communication system: A system that allows transfer of information reliably.

Basic block diagram of a communication system

Information

Source Transmitter Receiver

Information

Sink

Channel

Information Source The source of data.

Data could be: human voice, data storage device CD, video etc.

Data types: Discrete: Finite set of outcomes Digital

Continuous : Infinite set of outcomes Analog

Transmitter Converts the source data into a suitable form for

transmission. Telephone converts voice into electric current Modem converts bits into tones

After some signal processing techniques it transmit the information over the channel.

Channel

The physical medium used to send the signal.

The medium where the signal propagates till arriving to the receiver.

Physical Mediums (Channels): Wired : twisted pairs, coaxial cable, fiber optics

Wireless: Air, vacuum and water

Each physical channel has a certain limited range of frequencies ,( fmin fmax ), that is called the channel bandwidth.

Physical channels have another important limitation which is the noise.

SarahHighlight

SarahHighlight

Noise is undesired random signal that corrupts the original signal and degrades it.

Noise sources: Electronic equipments in the communication system. Thermal noise. Atmospheric electromagnetic noise (Interference with

another signals that are being transmitted at the same channel).

Another Limitation of noise is the attenuation. Weakens the signal strength as it travels over the

transmission medium.

Receiver

Extracts the information from the received signal. Telephone converts electric current into voice

Modem converts tones into bits

SarahHighlight

SarahHighlight

Information Sink

The final stage.

The user.

Types of communication

Analog communication: The information bearing signal is continuously varying both in time and amplitude, and it is used directly to modify some characteristics of a sinusoidal carrier wave, such as amplitude, phase or frequency.

Digital communication: The information bearing signal is discrete in time and amplitude.

Why digital

Less distortion and interference as compared to analog.

Regeneration of digital signal is easy, it is impossible in analog signal. Amplification doesnt work.

SarahHighlight

SarahHighlight

SarahHighlight

Costs of going digital It is more signal processing intensive compared to

analog

Synchronization is a major step in digital comms, unlike analog

SarahHighlight

SarahHighlight

Classification Of Signals Deterministic and Random Signals

A signal is deterministic means that there is no uncertainty with respect to its value at any time.

Deterministic waveforms are modeled by explicit mathematical expressions,

A signal is random means that 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.

SarahHighlight

SarahHighlight

SarahHighlight

SarahHighlight

Periodic and Non-periodicsignals A signal x(t) is called periodic in time if there exists a

constant To> 0 such that

x(t) = x(t + T) for - < t <

t denotes time

T0is the period of x(t).

A signal for which there is no T0is called non periodic.

Analog and Discrete Signals An analog signal x(t) is a continuous function of time;

that is, x(t) is uniquely defined for all t.

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

T is a fixed time interval.

SarahHighlight

Energy and Power signals 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

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

An energy signal has finite energy but zero average power.

Signals that are both deterministic and non-periodic are classified as energy signals

SarahHighlight

SarahHighlight

SarahHighlight

SarahHighlight

SarahHighlight

Power is the rate at which energy is delivered.

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

Power signal has finite average power but infinite energy.

As a general rule, periodic signals and random signals are classified as power signals.

SarahHighlight

SarahHighlight

SarahHighlight

SarahHighlight

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.

SarahHighlight

SarahHighlight

SarahHighlight

Spectral Density The spectral density of a signal characterizes the

distribution of the signals energy or power in the frequency domain.

This concept is particularly important when considering filtering in communication systems while evaluating the signal and noise at the filter output.

The energy spectral density (ESD) or the power spectral density (PSD) is used in the evaluation

SarahHighlight

SarahHighlight

Energy Spectral Density (ESD) Energy spectral density describes the signal energy per

unit bandwidth measured in joules/hertz.

Represented as x(f), the squared magnitude spectrum

Power Spectral Density (PSD)

The power spectral density (PSD) function Gx(f ) of the periodic signal x(t) is a real, even, and non-negative function of frequency that gives the distribution of the power of x(t) in the frequency domain.

Autocorrelation Autocorrelation of an Energy Signal

Correlation between two phenomenon refers to how closely they correspond in behavior or appearance. Correlation is a matching process; autocorrelation refers to the matching of a signal with a delayed version of itself.

Autocorrelation function of a real-valued energy signal x(t) is defined as:

SarahHighlight

SarahHighlight

SarahHighlight

The autocorrelation function Rx() provides a measure of how closely the signal matches a copy of itself as the copy is shifted units in time.

Rx() is not a function of time; it is only a function of the time difference between the waveform and its shifted copy.

SarahHighlight

SarahHighlight

Autocorrelation of an Energy Signal The autocorrelation function of a real-valued energy

signal has the following properties

Autocorrelation of a Power Signal Autocorrelation function of a real-valued power signal

x(t) is defined as:

When the power signal x(t) is periodic with period T0, the autocorrelation function can be expressed as

The autocorrelation function of a real-valued periodic signal has the following properties similar to those of an energy signal:

Random Signals All useful message signals appear random; that is, the

receiver does not know, a priori, which of the possible waveform have been sent.

Random Processes In probability theory a stochastic process or

sometimes random process (widely used) is a collection of random variables

This is often used to represent the evolution of some random value, or system, over time.

Random Processes A random process X(A, t) can be viewed as a function

of two variables: an event A and time.

Each of sample function can be regarded as the output of different noise generator.

Totality of sample function is called ensemble.

For a specific time tk, X(A,tk) is random variable.

For specific event, A=Aj and specific time t=tk, X(Aj,tk) is simply a number.

SarahHighlight

SarahHighlight

SarahHighlight

Pdf of random process will be different for different times, mostly it is not practical to determine empirically pdf of random process.

A partial description consisting of the mean and autocorrelation function are often adequate for the needs of communication systems.

So we define mean of random process X(t) as

Autocorrelation function of the random process X(t)

Autocorrelation function is measure of the degree to which two time samples of same random process are related.

SarahHighlight

SarahHighlight

SarahHighlight

SarahHighlight

Noise in Communication Systems The term noise refers to unwanted electrical signals

that are always present in electrical systems; e.g. spark-plug ignition noise, switching transients, and other radiating electromagnetic signals.

Man made noise ..

Natural noise

One natural noise i.e. thermal noise cannot be eliminated caused due to motion of electrons in all components

Can describe thermal noise as a zero-mean Gaussian random process

A Gaussian process n(t) is a random function whose amplitude at any arbitrary time t is statistically characterized by the Gaussian probability density function

SarahHighlight

The normalized or standardized Gaussian density function of a zero-mean process is obtained by assuming unit variance.

SarahHighlight

We will often represent the random signal as the sum of Gaussian noise random variable and a dc signal.

z=a+n

z is random signal, a is dc component and n is Gaussian noise random variable.

White noise The primary spectral characteristic of thermal noise is

that its power spectral density is the same for all frequencies of interest in most communication systems .

Thermal noise source emanates an equal amount of noise power per unit bandwidth of all frequencies-from dc to about 1012 Hz.

Power spectral density Gn(f

SarahHighlight

AWGN (Add White Gaussian Noise)????