Chapter 5 Effect of Noise on Analog Communication Systems. Outline. Chapter 5 Effect of Noise on Analog Communication Systems 5.1 Effect of Noise on linear-Modulation Systems 5.1.1 Effect of noise on a baseband system 5.1.2 Effect of noise on DSB-SC AM 5.1.3 Effect of noise on SSB AM
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Note that :
with ideal-phase coherent demodulator
for synchronous demodulation (similar to DSB, except using
instead of m(t) )
by a dc block
In practical application :
After removing the dc component,
The same as y(t) for the synchronous demodulation, without the ½ coefficient
Notes: i) Signal and noise components are no longer additive.
ii) Signal component is multiple by the noise and is no
iii) no meaningful SNR can be defined.
==> threshold effect
assume , zero-mean (i.e. no dc component)
the average power at the output of a narrow band filter
tuned to the carrier frequency fc is zero.
There is signal power at the frequency , which can
be used to drive a PLL.
VCO is , represents the estimate of , then
where is a gain constant in radians/ volt-sec.
and its transfer function is .
PLL can be represented by the closed-loop system model as follows.
closed-loop transfer function
where the factor of ½ has been absorbed into the gain parameter k
where : loop-damping factor
: natural frequency of the loop
which is corrupted by additive narrowband noise
, are assumed to be statistically independent stationary Gaussian noise.
i.e. xc(t) and xs(t) have exactly the same statistical characteristics as nc(t) and ns(t).
is additive at the input to the loop, the variance of the phase error , which is also the variance of the VCO output phase is
Bneq : one-sided noise equivalent bandwidth of the loop, given by
where is defined as the SNR
Thus, the variance of is inversely proportional to the SNR.
where SL is called the squaring loss and is given as
since SL<1 , we have an increase in the variance of the phase error caused by the added noise power that results from the squaring operation.
Gaussian process M(t) with autocorrelation
is the difference between two jointly Gaussian random variables.
where and G(f) is its Fourier transform.
the resulting SY(f) has almost a flat spectrum for , the bandwidth of the message.
i.e. for | f |<W , the spectrum of the noise components in the PM and FM.
( ) does not hold, a phenomenon known as the threshold effect will occur, and the signal will be lost in the noise.
is the 3-dB frequency of the filter
where h is Planck’s constant, k is Boltzmann’s constant, and T is the temperature of the resistor in degree Kelvin, i.e., T=273+C, where C is in degrees Centigrade.
L = PT / PR
Ldb=10log L = 10log PT – 10log PR
L communication systems5.5.4 Repeaters for signal transmission