230 likes | 330 Vues
Explore the optimization of Phase Shift Keying for correlated data, altering receiver and transmitter methods for improved transmission. Conclusions and future directions discussed.
E N D
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.