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Optimizing PSK for Correlated Data

Optimizing PSK for Correlated Data. Blake Borgeson Rice University Clemson SURE Project Advised by Dr. Carl Baum Clemson University. Basic Road Map. Background Ideas Correlated data transmission Phase Shift Keying (PSK) Altering the receiver Altering the transmitter

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Optimizing PSK for Correlated Data

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

  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=0.5 011 001 010 110 000 111 100 101

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

  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 Pe 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.

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