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 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

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 = p=0.01, q=

The Altered Transmitter Resulting transmission points: shifted Here: beta =.1 p=0.01, q=

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 P e 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, Komo, John J. Random Signal Analysis in Engineering Systems. The Academic Press, Hogg and Tanis. Probability and Statistical Inference. Prentice Hall, 2001.