Some Considerations on the Design of Adaptive Digital Filters Equipped with the Sign Algorithm

In this paper we present some tools that can be helpful in the design of adaptive digital filters operating with the so-called sign algorithm. Although theoretical results with respect to the convergence behavior of such filters are available, it may be hard to derive practical design criteria from them. We introduce a new type of design graph, which characterizes the convergence pretty well and which we call "the elephant\´s ear," due to its typical shape. We also consider some effects of non-Gaussian statistics of the received signal and show how the preceding analysis can be extended to include the effects of dithering. Finally, we pay attention to the digital word lengths required in a finite precision implementation. The subject of this paper is restricted to adaptive digital echo cancellers (EC), but the results can be generalized to include other adaptive filters like decision feedback equalizers (DFE) or combinations of EC and DFE.