1. Q-Function Alternative Representation of the Gaussian Q Function

2. 2 Q - Function

3. 3 Major Problem BER

4. 4 Craig Solution

5. 5 2-D Q-Function

6. 6 Example M-QAM SER

7. 7 Simon Solution

8. 8 Alternative Formulaton of Q(x)

9. 9 Alternative Approach

10. 10 Alternative Approach

11. 11 Prove

12. 12 Alternative Approach

13. 13 Alternative Approach,

14. 14 2-D Q-Function

15. 15 Alternative Approach of Q(x,y)

16. 16 Alternative Approach of Q(x,y)

17. 17 Alternative Approach of Q(x,y)

18. 18 Alternative Approach of Q(x,y)

19. 19 Conclusion New Formulation for Q function Use of step Function Replace Step by its Fourier Transform Change of variables Better for Average BER

20. 20 Questions ?

21. 21 Resources [1] M.K Simon and M.S. Alouini, “A Unified Approach to the Performance Analysis of Digital Communications over Generalized Fading Channels”, Proc. IEEE, vol. 86, no. 9, Sep. 1998, pp. 1860 – 1877. [2] T.Y. Al-Naffouri, B. Hassibi, “On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables” under preparation. [3] Gradshteyn and Ryzhik, Table of Integrals, Series and Products. Alan Jeffrey and Daniel Zwillinger(eds), 5th edition, 1996 [4] M.K. Simon and M.S. Alouini, Digital Communication over Fading Channels, 2nd edition. Wiley, N.J. 2002