Expansions of the likelihood ratio and applications

The likelihood ratio receiver, although optimal, is oftentimes difficult to realize. To overcome this difficulty, suboptimal approximations have been studied in the past. One of the simplest approaches is to expand the likelihood ratio and truncate this expansion under the weak signal assumption. In this paper, we first study the relations between the Taylor expansion and the Volterra expansion. Under a weak signal assumption, we emphasize the links between the Taylor expansion with respect to the SNR and the detection criteria on one hand, and with robustness on the other. In particular, using two criteria derived from deflection, we show that the minimax robust filter is the matched filter. Finally, an application to underwater signal detection is studied, showing that the degradation resulting from the use of the locally optimal receiver is small.