By Topic

On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference--II: The randomized decision rule solution (Corresp.)

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solution \phi^{0} uses an equaUy likely mixed strategy to chose one of N Bayesian single-threshold decision rules \phi_{i}^{0}, i = 1,\cdots , N having been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability density f_{0} , where f_{0} is a picket fence function with N pickets on its domain. Thee pair (\phi^{0}, f_{0}) is shown to satisfy the saddlepoint condition for probability of error, i.e., P_{e}(\phi^{0} , f) \leq P_{e}(\phi^{0} , f_{0}) \leq P_{e}(\phi, f_{0}) holds for all f and \phi . The decision rule \phi^{0} is also shown to be an eqoaliir rule, i.e., P_{e}(\phi^{0}, f ) = P_{e}(\phi^{0},f_{0}) , for all f , with 4^{-1} \leq P_{e}(\phi^{0},f_{0})=2^{-1}(1-N^{-1})\leq2^{-1} , N \geq 2 . Thus nature can force the communicator to use an {em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.

Published in:

IEEE Transactions on Information Theory  (Volume:27 ,  Issue: 1 )