Noise in FM Receivers

1
Noise in FM Receivers
Noise at the output of BPF is
expressing n(t) in terms of its envelope and
phase, we have
envelope
phase
2
Noise in FM Receivers

• The envelope r(t) is Rayleigh distributed and
  phase is uniformly distributed over
  radians.

• The FM signal is defined as

where
the noisy signal at the output of BPF is
using a phasor diagram with the signal term as
the reference
is the angle of the resultant phasor
3
Noise in FM Receivers

• The envelope of x(t) is of no interest to us as
  any envelope variations at the output of the BPF
  will be removed by the limiter circuit. Our
  motivation is to determine the error in
  instantaneous frequency of the carrier wave
  caused by the filtered noise n(t). Assuming ideal
  discriminator with its output proportional to
  where is the derivative of
• with respect to time. We also
  assume that the carrier-to-noise ratio at the
  discriminator output is large as compare to
  unity. Hence, we have

ignoring the term as Ac is the dominant term.
4
Noise in FM Receivers
Discriminator output is
where
Since is uniformly distributed over
radians the phase difference is
also uniformly distributed over
radians. Hence, we have
we know that
Hence,
5
Noise in FM Receivers

• The additive noise appearing at the discriminator
  output is determined effectively by carrier
  amplitude and the quadrature component nQ(t) of
  the narrowband noise n(t).

• Average noise power at the output can be found as

Hence, we have
6
Noise in PM Receivers

• The PM signal is defined as

where

• The output for PM is

where
Hence
7
Noise in PM Receivers

• The average noise power can be found as

8
Capture Effect

• The FM system also has the ability to minimize
  the effects of interference (unwanted signals).
  However, interference suppression in an FM
  receiver works well only when the interference
  signal is weaker than the desired FM input. When
  interference is stronger, the receiver locks onto
  the stronger signal and hence suppresses the
  desired FM input. When they are of nearly equal
  strengths, the receiver fluctuates back and forth
  between them, This phenomenon is called capture
  effect.

9
Threshold Effect

• The formula defining the output signal-to-noise
  ratio of an FM receiver is valid only if
  carrier-to-noise ratio measured at the
  discriminator input is large as compared to
  unity. Experimentally it has been found that as
  the input noise power is increased the
  carrier-to-noise power is decreased and the FM
  receiver breaks. Near the breaking point (SNR)O,
  FM fails by predicting the values of output
  signal-to-noise ratio larger than the actual
  ones. This phenomenon is called threshold effect.
• Threshold effect in FM receivers can be avoided
  in most practical cases of interest if is
  greater than or equal to 20, i.e. 13dB.

where is the transmitter power.
10
FM Demodulation with Negative Feedback

• In FM receivers it is required to reduce the
  noise threshold so that the receiver operates
  satisfactorily with the minimum possible signal
  power. Threshold reduction in FM receivers is
  achieved by using a FM demodulator with negative
  feedback (FMFB).

11
Pre-Emphasis and De-Emphasis in FM

• The PSD of the noise at the output of an FM
  receiver has a square law dependence on the
  operating frequency whereas, the PSD of a typical
  message source audio and video signals have
  spectra of this form

• Around the relative spectral density
  of the message is quite low whereas, that of the
  output noise is quite high in comparison. An
  approach to efficiently use the allowed frequency
  band is based on the use of pre-emphasis in the
  transmitter and de-emphasis in the receiver.

12
Pre-Emphasis and De-Emphasis in FM

• In this method, we artificially emphasize the
  high frequency components of the message signal
  before modulation. In effect the low frequency
  and high frequency portions of the PSD of the
  message are equalized. Then, at the discriminator
  output we perform the inverse operation by
  de-emphasizing the high frequency components to
  restore the original signal power distribution of
  the message. In this process the high frequency
  components are also reduced, thereby, effectively
  increasing the output signal-to-noise ratio of
  the system.

13
Pre-Emphasis and De-Emphasis in FM

• The frequency response of the de-emphasis filter
  must ideally be

where W is the bandwidth of the message

• For high carrier-to-noise ratio the PSD of the
  noise nd(t) at the discriminator output is given
  bt

• The average output noise power with de-emphasis is

14
Pre-Emphasis and De-Emphasis in FM

• Since, the average message power at the receiver
  output is ideally unchanged due to the
  pre-emphasis and de-emphasis the improvement in
  (SNR)O is defined by