Noise in Communication Systems
Professor Z Ghassemlooy
Electronics and IT Division
School of Engineering
Sheffield Hallam University
U.K.
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Contents
• Interference
• Types of noise
• Electrical noise
• Gaussian noise
• White noise
• Narrow band noise
• Noise equivalent bandwidth
• Signal-to-noise ratio
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Interference
Is due to:
• Crosstalk
• Coupling by scattering of signal in the atmosphere
• Cross-polarisation: two system that transmit on the same frequency
• Interference due to insufficient guard bands or filtering
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Types of Noise
1- Manmade (artificial): These could be eliminated via better design
- Machinery
- Switches
- Certain types of lamps
2- Natural
- Atmospheric noise: causing crackles on our radios
- Cosmic noise (space noise):
Noise in Electrical Components
• Thermal noise: Random free electron movement in a conductor (resistor) due to
thermal agitation
• Shot noise: Due to random variation in current superimposed upon the DC value.
It is due to variation in arrival time of charge carriers in active devices.
• Flicker noise: Observed at very low frequencies, and is thought to be due to
fluctuation in the conductivity of semiconductor devices.
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Gaussian Noise
Each noise types outlined before (except flicker noise) is the result of a
large number of statistically independent and random contributions. The
distribution of such random noise follow a Gaussian distribution with zero
mean.
p(vn)
1
p(vn ) 
e
 2
0.4/
 v 2n 


2
 2 


Where 2 is the variance of noise voltage vn
-3 -2
-
0

For zero mean, normalised noise power or
vn mean square voltage:
2
3
Probability density function of zero mean
and standard deviation 
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Pn  vn2   2
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White Noise
vn
The time-average autocorrelation
function of the noise voltage is:
T
t
t+
t
Rv ()  lim
T 
1
vn (t )vn (t  ) dt

T0
Assumptions:
• vn(t+) is random value that does not depend on vn(t).
• The above condition holds no matter how small  is, provided it is not zero.
White noise w(t)
(i.e perfect randomness, which can not be attained in real systems)
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White Noise - cont.
Pn
Rw (t )  
0
The autocorrelation of white noise is:
0
0
Rw(t) is a zero width of height Pn with an area under the pulse = o/2
Rw ( ) 
o
 ( )
2

Sw(f)
Sw(f)
o/2
o
f
f
Double-sided power spectral density
Single-sided power spectral density
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Narrowband Noise
White noise
w(t)Sw(f)
Communication Receiver
H(f)
Narrow band noise
vn(t)  Sv(f)
Sv ( f )  S w ( f ) H ( f ) 2
Sv(f)
Sw(f)
o
B
Ideal LPF
o
B
Sv(f)
f
Ideal BPF
f
o
f
fc-B/2
fc
fc+B/2
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fc-B/2
fc
fc+B/2
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Narrowband Noise - cont.
White noise
w(t)Sw(f)
Bandpass Filter
H(f)
Narrow band noise
vn(t)  Sv(f)
Sw(f)
Sv(f)
o
o
1
f
f
fc-B/2
fc
fc+B/2
fc-B/2
fc
fc+B/2
Bandlimited noise vn (t )  x(t ) cosct  y(t ) sin ct
x(t) and y(t) have the same power as the band pass noise vn(t)
B/2
Px (t )  Py (t ) 
 Sv ( f ) df 
B / 2
B/2

2
o H ( f ) df  o
B / 2
B/2
2
1
df


B

P


o
n

B / 2
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Narrowband Noise - Phasor diagram
Bandlimited noise vn (t )  x(t ) cosct  y(t ) sin ct
y(t)
Quadrature
component
R(t)
(t)
R (t )  x (t )  y (t )
2
2
x(t) Inphase component
1 
y (t ) 

(t ) tan 
 x(t ) 
and
x(t) and y(t) have the same power as the band pass noise vn(t)
2
2
2
x
(
t
)
y
(
t
)
R
(t )




2
Pn  vn (t )  
 
 
2
 2  2 
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Noise Equivalent Bandwidth
• The power Pn of the band limited noise vn(t) is given bt the area
under its power spectral density as:
Sv(f)
w(t)
o
Realisable filter
H(f)


0
0
Ideal filter
vn(t)
Beq
Pn   S v ( f ) df   o H ( f ) df  o Beq
2

2
Noise equivalent bandwidth Beq   H ( f ) df
0
We replace realisable filter H(f) with a unit-gain ideal filter of bandwidth Beq.
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Noise - Example: a simple RC low-pass filter
A simple RC low-pass filter is shown in figure below:
R = 300 
Vin(t)
C=
132.63 nF
Vout(t)
• Find the noise equivalent bandwidth Beq?
• Find the 3-dB bandwidth B of the filter?
• Calculate the noise power Pn at its output when connected to a matched antenna
of noise temperature Ta = 80 K? (Assuming the filter is noise free)
• How much error is incurred in noise power calculation by using the 3-dB
bandwidth in place of the Beq?
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Solution
• The transfer function of the filter is:
H( f ) 
Vout (t )
1 jC
1
1  jCR



Vin (t ) R  1 jC 1  jCR 1  jCR
1
CR

j
 H ( f ) exp jf 
2
2
1  (CR)
1  (CR)
where | H ( f ) |
1
1  (CR )
2
( f )  t an1 (CR ) 

Equivalent bandwidth Beq 

0
Note: = 2f and a = 2RC

Amplitude response
Phase response
2

1
df
2 2
0 1 a f
H ( f ) df  
The form of integral suggest the to use
substitution of af = tan 
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System Signal-to-Noise Ratio (SNR)
Incoming Si
signal
+
BPF
(fc)
Ni
So & No
Output
signal
Demodulator
(Gd)
SNRi
SNRo
White noise w(f)
The SNR at the demodulator output is: SNR0  SNRi  Gd
Where - SNRi is the input signal (modulated carrier) to noise ratio
- Gd is the demodulator gain.
- Si = Total power in the received modulated signal
- So = Power in the recovered message signal m(t)
- Band limited noise power Ni = Pn = 2
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