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
Channel
Receiver
Information
Sink
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.
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
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.
Costs of going digital
It is more signal processing intensive compared to
analog
Synchronization is a major step in digital comms,
unlike analog
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.
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)
t denotes time
T0is the period of x(t).
for - < 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.
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
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.
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.
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
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:
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.
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.
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.
Noise in Communication Systems
The term noise refers to unwanted electrical signals
that are always present in electrical systems; e.g. sparkplug 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
The normalized or standardized Gaussian density
function of a zero-mean process is obtained by
assuming unit variance.
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 frequenciesfrom dc to about 1012 Hz.
Power spectral density Gn(f
AWGN (Add White Gaussian Noise)????
