On-line order selection for communications

Abstract

We address the problem of on-line order determination for communications and show that penalized partial likelihood criterion provides a suitable likelihood framework for the problem by allowing correlations among samples and online processing ability. An on-line, efficient order selection scheme is developed assuming that the observations can be modeled by a finite normal mixture model without imposing any additional conditions on the unknown system, such as linearity. Channel equalization by finite normal mixtures is considered as an example for which correct order determination is critical and examples are presented to show the application and effectiveness of the approach.

Partial likelihood for signal processing

“…As we have noted in Section VI-C, the FNM equalizer can be very efficient if the order specification in terms of the number of normal components is made properly. In [20], we show that PL theory can be used to derive a penalized partial likelihood criterion for determining the effective model/filter order online.…”

“…We establish its information-theoretic connection and give examples of its application. We have shown a number of ways this framework can be exploited, such as in the derivation of efficient algorithms [14], to study the tradeoffs in signal processing within a likelihood framework with different types of posing the problem (pmf versus pdf type modeling) [16] and for online order selection [20]. There are a number of other important advantages of a flexible likelihood framework that naturally allows processing of dependent observations that can be further explored.…”

“…In addition, by the definition of , we have for . We can write , which is defined in (10) as (20) Similarly, since is always bounded, the first term in (20) is bounded. We have also noted the boundedness of .…”