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
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):
m=1,2,…M
m=1,2,..,M,

8. Representation of Digitally Modulated Signals
Orthogonal multidimensional signals:
Biorthogonal signals:
Simplex signals:
m=1, 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.

10. 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:
k=1,2, …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:
m=1,2,… M or

13. 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

14. General FFT based OFDM system-I
Block diagram of FFT based OFDM transmitter :
Equations at the transmmitter end:

15. General FFT based OFDM system-II
Block diagram of FFT based OFDM receiver:
At the demodulator:

16. 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.