Adaptive Detection of Known Signals in
Additive Noise by Means of Kernel Density Estimators
Responsor AB, Odengatan 5, SE-164 92 Kista, Sweden
Dept of Mathematical Statistics, Lund University
Box 118, SE-221 00 Lund, Sweden
IEEE Trans. on Information Theory,
vol 43, pp 1192-1204, July 1997. © 1997 IEEE.
We consider the problem of detecting known signals contaminated
by additive noise with a completely unknown probability density
To this end, we propose a new adaptive detection rule.
It is defined by plugging a kernel density estimatior of f
into the maximum a posteriori (MAP) detector.
The estimate can either be computed off-line from a training
sequence or on-line simultaneously with the detection.
For the off-line detector, we prove that the (asymptotic) error
probability for weak signals converges to the minimal error
probability of the MAP detector as the number of
training data tends to inifinity, and we establish rates of convergence
and the optimal choice of bandwith order for a certain class of
In a Monte Carlo study, the off-line plug-in MAP detectors
are compared with the L1 and
L2-detecors for various noise distributions.
When the training sequence is long enough, the plug-in detectors
have excellent performance for a wide range of distributions,
whereas the L2-detecor
breaks down for heavy-tailed distributions and the
L1-detector for distributions with
little mass around the origin.
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