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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 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 • Conclusions, directions
Basic Road Map • Background Ideas • Correlated data transmission • Phase Shift Keying (PSK) • Altering the receiver • Altering the transmitter • Conclusions, directions
Correlated Data--Introduction • Goal: transmit, receive correlated data • Markov state machine: models real data • Yields desired correlation values, e.g.,
Correlated Data—Example • Analysis in MATLAB: p=0.03, q=0.59 “Mr. PSK”
Phase Shift Keying (PSK) • M-ary PSK: • Optimum receiver correlates with sine and cosine:
PSK Representation • Traditional transmitter: evenly spaced points on the circle • Traditional receiver: corresponding equal pie wedges
Basic Road Map • Background Ideas • Correlated data transmission • Phase Shift Keying (PSK) • Altering the receiver • Altering the transmitter • Conclusions, directions
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
Gains from Altering Receiver • Traditional receiver never gains
Gains from Altering Receiver • MAP algorithm: prior probabilities
Gains from Altering Receiver • Algorithm: prior probabilities plus guess of preceding (previous) bit
Gains from Altering Receiver • Algorithm: prior probabilities plus guess of following (next) bit
Gains from Altering Receiver • Algorithm: prior probabilities plus guesses of both preceding and following bits
Putting Gains into Perspective • All decision algorithms: higher correlation more gain • Even playing field: set p, q for comparison
Basic Road Map • Background Ideas • Correlated data transmission • Phase Shift Keying (PSK) • Altering the receiver • Altering the transmitter • Conclusions, directions
Altering the Transmitter • Idea: equation gives angle for each symbol • Requirements • Use prior probabilities • For all , limit is traditional receiver • Resulting formula:
The Altered Transmitter • Resulting transmission points: shifted • Here: beta = .000001 p=0.01, q=0.5 011 001 010 110 000 111 100 101
The Altered Transmitter 011 • Resulting transmission points: shifted • Here: beta = .1 p=0.01, q=0.5 001 010 110 111 000 100 101
Gains from Altering Transmitter • Moderate correlation values moderate gains for MAP
Gains from Altering Transmitter • Moderate correlation values moderate gains for MAP • ~.5-1dB gain over best MAP at reasonable Pe values
Conclusions • A successful alternative • Correlated data, PSK transmission • Source coding impractical • Future directions • Simplified algorithms • Bandwidth tradeoffs
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.