Digital communication

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Digital communication
H V KUMARASWAMY
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Topics in this session

• Optimum transmitter receiver
• Correlative receiver
• Matched filter

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Optimum transmitter receiver

• Probability of error depends on signal to noise
  ratio
• As the SNR increases the probability of error
  decreases
• An optimum transmitter and receiver is one which
  maximize the SNR and minimize the probability of
  error.

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Correlative receiver
Observation Vector x
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Receiver consists of a bank of M
product-integrator or correlators F1(t) ,F2(t)
.FM(t) orthonormal function The bank of
correlator operate on the received signal x(t) to
produce observation vector x
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Implemented in the form of maximum likelihood
detector Operates on observation vector x to
produce an estimate of the transmitted
symbol Inner products (x,sk) k 1, 2 ..M The
largest in the resulting set of numbers is
selected The optimum receiver is commonly
referred as a correlation receiver
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MATCHED FILTER
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Yj(t) xj where xj is the j th correlator output
The impulse response of the matched filter is
time-reversed and delayed version of the input
signal For causal system
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MAXIMIZATION OF OUTPUT SNR
h(t) impulse response input
signal W(t) white noise
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MATCHED FILTER
Sample At t T
Impulse Response h(t)
Output
f(t) Known Signal

White Noise w(t)
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Schwarzs inequality
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Rayleighs energy theorem
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conclusion