optimizing psk for correlated data
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Optimizing PSK for Correlated Data
Blake BorgesonRice UniversityClemson SURE Project
Advised by Dr. Carl BaumClemson 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.,
qp
qpRxx
)1()1(
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:
)2
2cos()( mEMtcfAts
xT
yT
Decision
algorithm 321ˆˆˆ bbb
Received bits
s(t)+n(t)
T
dt0
)(
T
dt0
)(
)2sin(1
tfc
s
)2cos(1
tfc
s
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 sm to maximize probability that sm was transmitted, given received r, i.e.,
Other gains: take into account previous bit, next bit, or both
)|(.maxargˆ rsPs ms
mm
p = q = 0.001
Gains from Altering Receiver
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.01
Traditional rcvr
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
Traditional receiver never gains
Gains from Altering Receiver
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.01
Traditional rcvr
MAP receiver
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
MAP algorithm:
prior probabilities
Gains from Altering Receiver
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.01
Traditional rcvr
MAP receiver
MAP, Prev. bit
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
Algorithm:
prior probabilities plus guess of preceding (previous) bit
Gains from Altering Receiver
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.01
Traditional rcvr
MAP receiver
MAP, Prev. bit
MAP, Next bit
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
Algorithm:
prior probabilities plus guess of following (next) bit
Gains from Altering Receiver
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.01
Trad. rcvrMAP receiverMAP, Prev. bitMAP, Next bitMAP, Both prev, next
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
Algorithm:
prior probabilities plus guesses of both preceding and following bits
Putting Gains into Perspective
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK MAP, Both prev. and next bits
p=q=0.5p=q=0.1p=q=0.01p=q=0.001p=q=0.0001
Pe:
prob. o
f bit
err
or
Eb/N
0 (dB)
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:
)(i
)(i
8
1i
)ln(
)ln(
48
1
ii
The Altered Transmitter
Resulting transmission points: shifted
Here:
beta = .000001
p=0.01, q=0.5
000
001
011
010
110
111
101
100
The Altered Transmitter
Resulting transmission points: shifted
Here: beta = .1
p=0.01, q=0.5000
100101
111
110
010
011001
Gains from Altering Transmitter
Moderate correlation values moderate gains for MAP
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.5"Morgan's drawing"
Trad, no MAP
MAP receiver
MAP using prev, next
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
Gains from Altering Transmitter
10-6
10-5
10-4
10-3
10-2
10-1
0 5 10 15
8-PSK Receivers, p=.01, q=.5"Morgan's drawing"
Trad, no MAP
MAP receiver
MAP using prev, next
Altered, beta=.000001
Pe: p
rob.
of b
it er
ror
Eb/N
0 (dB)
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.