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Estimation of multilevel digital signals in the presence of arbitrary impulsive interference

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2 Author(s)
Jun Shen ; Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA, USA ; C. L. Nikias

We first study the a posteriori probability density function of the state of a discrete-time system given the measurement data. By applying the Bayesian law to the state and measurement equations of the stochastic system, the a posteriori density is obtained in closed-form and computed recursively for arbitrary i.i.d. state noise and any discrete-type measurement noise (or multilevel digital signal). Then, our effort concentrates on the estimation of impulsive noise which interferes the multilevel signal of interest. By considering the Lp -metric performance criterion, where 0<p<2, the corresponding estimators are obtained. Using a new damping function scheme, the performance of the new estimators is improved even further. As an example, a highly impulsive state process driven by noise with symmetric ∩-stable distribution is estimated and then removed from the measurement data; after that, the multilevel digital signal is recovered

Published in:

IEEE Transactions on Signal Processing  (Volume:43 ,  Issue: 1 )