Elements of a Digital Communication System

1
Elements of a Digital Communication System

• Block diagram of a communication system

2
Mathematical Models for Communication Channels

• Additive Noise Channel
• In presence of attenuation

3
Mathematical Models for Communication Channels

• The Linear filter channel

4
Mathematical Models for Communication Channels

• Linear Time-Variant Filter Channel
• Are charachterized by a time-variant channel
  impulse response

5
Representation of Band-Pass Signals and Systems

• Representation of Band-Pass Signals
• Energy of the signal
• Representation of Linear Band-Pass Systems
• Response of a Band-Pass System to a Band-Pass
  Signal

6
Orthogonal Expansion of Signals

• We can express M orthonormal signals
  as a Linear combination of basis functions
  and hence can be defined as
• Linear digitally modulated signals can be
  expanded in terms of two orthonormal basis
  functions given by
• and

7
Representation of Digitally Modulated Signals

• Pulse-amplitude-modulated Signals (PAM)
• Phase-modulated signals (PSK)
• Quadrature amplitude modulation (QAM)

m1,2,M
m1,2,..,M,
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Representation of Digitally Modulated Signals

• Orthogonal multidimensional signals
• Biorthogonal signals
• Simplex signals
• m1,
  2,, M..
• Signal waveforms from binary codes

9
Optimum Receivers Corrupted by additive White
Gaussian Noise- I

• General Receiver
• Receiver is subdivided into
• 1. Demodulator.
• (a) Correlation Demodulator.
• (b) Matched Filter Demodulator.
• 2. Detector.

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Optimum Receivers Corrupted by additive White
Gaussian Noise- II

• Correlation Demodulator
• Decomposes the received signal and noise into a
  series of linearly weighted orthonormal basis
  functions.
• Equations for correlation demodulator

11
Optimum Receivers Corrupted by additive White
Gaussian Noise- III

• Matched Filter Demodulator
• Equation of a matched filter
• Output of the matched filter is given by
• k1,2, N

12
Optimum Receivers Corrupted by additive White
Gaussian Noise- IV

• Optimum Detector
• The optimum detector should make a decision on
  the transmitted signal in each signal interval
  based on the observed vector.
• Optimum detector is defined by
• 
  m1,2, M
• or

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OFDM

• It is a block modulation scheme where data
  symbols are transmitted in parallel by employing
  a large number of orthogonal sub-carriers.
• Equation of complex envelope of the OFDM signal
• where

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General FFT based OFDM system-I

• Block diagram of FFT based OFDM transmitter
• Equations at the transmmitter end

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General FFT based OFDM system-II

• Block diagram of FFT based OFDM receiver
• At the demodulator

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General FFT based OFDM system-II

• Merits of OFDM
• 1. the modulation and the demodulation can be
  achieved in the frequency-domain by using a DFT.
• 2. the effects of ISI can be eliminated with the
  introduction of the guard interval.

17
IMPLEMENTATION OF OFDM SYSTEM-I

• Basic implementation of OFDM system

18
SIMULATION RESULTS.

• Perfomance charachteristics were obtained for the
  simulated OFDM system.

19
Conclusion.

• 1. OFDM communication system exhibits better Pe
  Vs SNR curves in case of Non-Fading channel as
  compared to the Fading channel.
• 2. As the value of the SNR is increased the value
  of Pe gradually decreases.
• 3. Perfomance charachteristics of simulated OFDM
  communication system are consistent with the
  performance charachteristics of the general OFDM
  communication system.