Q-Function Alternative Representation of the Gaussian Q Function

2 Q - Function

3 Major Problem BER

4 Craig Solution

5 2-D Q-Function

6 Example M-QAM SER

7 Simon Solution

8 Alternative Formulaton of Q(x)

9 Alternative Approach

10 Alternative Approach

11 Prove

12 Alternative Approach

13 Alternative Approach,

14 2-D Q-Function

15 Alternative Approach of Q(x,y)

16 Alternative Approach of Q(x,y)

17 Alternative Approach of Q(x,y)

18 Alternative Approach of Q(x,y)

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 Questions ?

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 – [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