1. Optimizing PSK for Correlated Data Blake Borgeson Rice University Clemson SURE Project Advised by Dr. Carl Baum Clemson University

2. Basic Road Map Background Ideas  Correlated data transmission  Phase Shift Keying (PSK) Altering the receiver Altering the transmitter Conclusions, directions

3. Basic Road Map Background Ideas  Correlated data transmission  Phase Shift Keying (PSK) Altering the receiver Altering the transmitter Conclusions, directions

4. Correlated Data--Introduction Goal: transmit, receive correlated data Markov state machine: models real data  Yields desired correlation values, e.g.,

5. Correlated Data—Example Analysis in MATLAB: p=0.03, q=0.59 “Mr. PSK”

6. Phase Shift Keying (PSK) M-ary PSK: Optimum receiver correlates with sine and cosine:

7. PSK Representation Traditional transmitter: evenly spaced points on the circle Traditional receiver: corresponding equal pie wedges

8. Basic Road Map Background Ideas  Correlated data transmission  Phase Shift Keying (PSK) Altering the receiver Altering the transmitter Conclusions, directions

9. Altering the Receiver: MAP MAP, maximum a posteriori probability: choose s m to maximize probability that s m was transmitted, given received r, i.e., Other gains: take into account previous bit, next bit, or both p = q = 0.001

10. Gains from Altering Receiver Traditional receiver never gains

11. Gains from Altering Receiver MAP algorithm: prior probabilities

12. Gains from Altering Receiver Algorithm: prior probabilities plus guess of preceding (previous) bit

13. Gains from Altering Receiver Algorithm: prior probabilities plus guess of following (next) bit

14. Gains from Altering Receiver Algorithm: prior probabilities plus guesses of both preceding and following bits

15. Putting Gains into Perspective All decision algorithms: higher correlation  more gain Even playing field: set p, q for comparison

16. Basic Road Map Background Ideas  Correlated data transmission  Phase Shift Keying (PSK) Altering the receiver Altering the transmitter Conclusions, directions

17. Altering the Transmitter Idea: equation gives angle for each symbol Requirements  Use prior probabilities  For all, limit is traditional receiver Resulting formula:

18. The Altered Transmitter Resulting transmission points: shifted Here: beta =.000001 p=0.01, q=0.5 000 001 011 010 110 111 101 100

19. The Altered Transmitter Resulting transmission points: shifted Here: beta =.1 p=0.01, q=0.5 000 100 101 111 110 010 011 001

20. Gains from Altering Transmitter Moderate correlation values  moderate gains for MAP

21. Gains from Altering Transmitter Moderate correlation values  moderate gains for MAP ~.5-1dB gain over best MAP at reasonable P e values

22. Conclusions A successful alternative  Correlated data, PSK transmission  Source coding impractical Future directions  Simplified algorithms  Bandwidth tradeoffs

23. References Proakis and Salehi. Communications Systems Engineering. Prentice Hall, 2002. Komo, John J. Random Signal Analysis in Engineering Systems. The Academic Press, 1987. Hogg and Tanis. Probability and Statistical Inference. Prentice Hall, 2001.