A Report on
Noise in communication system
Report submitted in partial fulfillment of the
requirement for the degree of
M.Tech
In
Electronics and
communication
Under the Supervision of
Prof. Pravin Chandra
By
Ashish Kumar
(05316412819)
To
Guru Gobind Singh Indraprastha University
GGSIPU, Golf Course Rd, Sector 16 C,
Dwarka, Delhi-110078
Certificate
This is to certify that the term paper report entitled ”Noise in communication
system” submitted by Ashish Kumar in partial fulfillment of the requirement for the
award of the degree M.Tech ECE at USICT, GGSIP University, Dwarka, Delhi, is
to the best of my knowledge, a record of the candidate’s own work conducted under my
supervision.
Date:
Supervisor
1
Declaration
This is to certify that the term paper report titled “Noise in communication
system” which is submitted by me in partial fulfillment of the requirement for the
award of degree M.Tech. in Electronics and communication to USICT, GGSIP
University, Dwarka, Delhi, comprises only my original work, and due acknowledgment
has been made in the text to all other material used.
Date:
Ashish Kumar
2
Contents
1 Definiton of Noise
6
1.1 Time-Averaged Noise Representations . . . . . . . . . . . . . . . . . . . .
7
1.2 Noise in linear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3 Naturally occuring noise........................................................................................... 10
References
11
3
List of Figures
1
2
Natural Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noise Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
6
8
Abstract
The purpose of a communication system is to convey information from a source point
to a destination point, which may be separated by a few metres or by thousands of
kilometres [1]. This chapter helps the readers learn how to determine noise power and
signal-to-noise ratio at various points in a communication system. It begins with a
discussion on the physical sources of noise, which includes quantitative estimates of noise
level. The chapter builds on the foundation of Gaussian noise to discuss the important
concepts of white and narrowband noise before proceeding to a treatment of system noise
calculations, including noise power, noise temperature, and noise factor in single- and
multiple-stage systems. The impact of noise in various analogue and digital transmission
systems is discussed, which equips us to make an informed choice of modulation technique
in each situation.
5
Introduction
1
Definiton of Noise
Noise can be defined as any unwanted signals, random or deterministic, which interfere
with the faithful reproduction of the desired signal in a system. Stated another way, any
interfering signal [2], which is usually noticed as random fluctuations in voltage or current
tending to obscure and mask the desired signals is known as noise. These unwanted
signals arise from a variety of sources and can be classified as man-made or naturally
occurring. Man-made types of interference (noise) can practically arise from any piece
of elec- trical or electronic equipment and include such things as electromagnetic pick-up
of other radiating signals, inadequate power supply filtering or alias terms. Man-made
sources of noise all have the common property that their effect can be eliminated or at
least minimised by careful engineering design and practice[3, 4]. Interference caused by
naturally occurring noise are not controllable in such a direct way and their characteristics
can best be described statistically. Natural noise comes from random thermal motion of
electrons, atmospheric absorption and cosmic sources. [?].
Figure 1: Natural Noise
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1.1
Time-Averaged Noise Representations
In forming averages of any signal, whether random or deterministic, we find parameters
which tell us something about the signal. But much of the detailed information about
the signal is lost through this process. In the case of random noise, however, this is the
only useful quantity[2]. Suppose n(t) is a random noise voltage or current.[?]. We now
define the following statistical quantities of n(t): 0 50 100 150 200 0
Time t [ms]n(t)
0 50 100 150 200
Time t [ms]
mean n(t)
T= 5 ms
T= 50 ms
T= 400 ms
The mean value of n(t) will be refered to as n(t), T or En(t). It is given by:
n(t) = En(t) = T = limT→
1
T
! T /2
T /2
n(t)dt
where n(t) is often referred to as dc or average value of n(t). For practical calculation
of the mean value, the averaging time T has to be chosen large enough to smooth the
fluctuations of n(t) adequately. Fig. 4.1 shows the averages n(t) calculated by sliding
a window centred at t and extending from t T/2 to t + T/2 over n(t). It is seen that
for small averaging time T = 5 ms there is still a considerable amount of fluctuation
7
present whereas for T = 400 ms the window covers the whole time signal which results
in a constant average value [5].
Figure 2: Noise Dominance
8
1.2
Noise in linear systems
When designing and characterizing communication systems, noise is an important parameter which must be accounted for. In general, the different physical noise sources in
addition to other man-made noise sources contribute to the total noise in the system. In
the following, noise in linear time invariant (LTI) systems is investigated.
Overview// The power spectral density shall be used to describe noise. Knowing that
random noise tends to have rapid fluctuations, we assume a noise voltage n(t) having the
auto-correlation function: Rn( ) = No 2 ( ) (4.22) where ( ) is the impulse function. Thus,
Rn( ) is zero for all = 0, which indicates completely uncorrelated noise signal except
for zero time shift. Taking the Fourier transform of Rn( ) the power spectral density
is: Sn(f) = FRn( ) = No/2 [Watt/Hz] (4.23) The power spectral density is constant for
all frequencies, thus it contains all fre- quency components with equal power weighting.
This type of noise is designated as white noise in analogy to white light. The factor of
one-half in (4.23) is necessary to have a two-sided power spectral density.
9
1.3
Naturally occuring noise
Natural radio noise in telecommunication systems is both picked up by the antenna as
well as generated within the system itself. The first effect can be accounted for by the
contribution which it makes to the antenna noise temperature. Attenuation due to water
vapor and oxygen, clouds and precipitation is accompanied by thermal noise, lightening
and other atmospherics which further degrades the applicable signal-to-noise ratio. In
addition, extraterrestrial noise of thermal or non-thermal origin may be picked up by
the receiving antenna. This section gives an overview of the different types of naturally
occurring noise and defines appropriate quantities for modelling the effect of this noise.
To start with, we state Planck’s radiation law, which is the the basis for other types of
noise. Planck’s Law In 1900, Max Planck found the law that governs the emission of
electromagnetic radi- ation from a black body in thermal equilibrium [Planck, 1900]. A
black body is simply defined as an idealized, perfectly opaque material that absorbs all
the incident radia- tion at all frequencies, reflecting none. A body in thermodynamic
equilibrium emits to its environment the same amount of energy it absorbs from its
environment. Hence, in addition to being a perfect absorber, a blackbody also is a
perfect emitter. The essential point of Planck’s derivation is that energy can only be
exchanged in discrete portions or quanta equal to hf, where h is Planck’s constant h =
6.626 × 1034 J s and f is the frequency in Hertz. Then, the energy of the ground level
(or state) is 0, of the first level hf, of the second level 2hf and so on. In general:
Ev = n · hf for v = 0, 1, 2 ... (4.36)
where v is the level or state number. Given the number Nv of energy quanta (in Planck’s
publications these are referred to as energy elements) occupying level v results in an
energy of vNvhf for that level. The total energy is obtained by summing up over all
states, thus
Etot = N0 · 0 + N1hf + N2 · 2hf + N3 · 3hf + ... (4.37)
Now according to quantum mechanics, the probability of occupying an energy level goes
down with eE/kT where k = 1.38 × 1023 J K1 is the Boltzmann constant, T is the
absolute temperature in Kelvin, and E the excess energy. Then, the number of energy
quanta N1 at the first level is given by the number at ground state N0 multiplied by
the probability ehf/kT . Similarly N2 = N1ehf/kT = N0e2hf/kT and so on. The total
number of quanta is :
Ntot = N0
(
1 + ehf /kT + e2hf /kT + e3hf /kT + ... ) (4.38)
To determine the average energy, we divide the total energy by the total number of energy
quanta. The expression can be simplified to give:
E(f) = hf
ehf /kT 1 (4.39)
Using the density of modes we find Planck’s law for the black body radiation. Ex- pressed
in terms of the brightness of the radiated energy from a blackbody this is given by:
Bf (f) = 2hf 3
c2
1
ehf /kT 1 (4.40)
10
References
References
[1] H. V. Poor, An Introduction to Signal Detection and Estimation.
& Business Media, 1994.
Springer Science
[2] S. O. Rice, “Mathematical analysis of random noise,” Bell System Technical Journal,
vol. 23, no. 3, pp. 282–332, 1944.
[3] J. G. Proakis and M. Salehi, Communication Systems Engineering.
2001.
Prentice Hall,
[4] C. E. Shannon, “A mathematical theory of communication,” Bell System Technical
Journal, vol. 27, no. 3, pp. 379–423, 1948.
[5] W. Yang and H. Li, “Characterization of noise in communication systems,” in 2017
IEEE International Conference on Communications (ICC). IEEE, 2017, pp. 1–6.
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