Double Side Band Supressed Carrier

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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.
Where ?2 is the variance of noise voltage vn
For zero mean, normalised noise power or mean
square voltage
Probability density function of zero mean and
standard deviation ?
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White Noise
The time-average autocorrelation function of the
noise voltage is
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.
The autocorrelation of white noise is
Rw(t) is a zero width of height Pn
with an area under the pulse ?o/2
?o/2
Double-sided power spectral density
Single-sided power spectral density
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Narrowband Noise
Communication Receiver H(f)
B
Ideal LPF
Ideal BPF
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Narrowband Noise - cont.
Bandpass Filter H(f)
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Bandlimited noise
x(t) and y(t) have the same power as the band
pass noise vn(t)
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Narrowband Noise - Phasor diagram
Bandlimited noise
and
x(t) and y(t) have the same power as the band
pass noise vn(t)
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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

Realisable filter H(f)
Noise equivalent bandwidth
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

• 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

Amplitude response
where
Phase response
Equivalent bandwidth
Note ? 2?f and a 2?RC
The form of integral suggest the to use
substitution of af tan ?
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System Signal-to-Noise Ratio (SNR)
Si
Ni
BPF (fc)
Demodulator (Gd)

The SNR at the demodulator output is
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