Multistage RAM: An FIR filter for echo cancellation in a digital two-wire subscriber loop

In a two-wire full-duplex ISDN transmission unit, a transversal filter or a lookup table are generally proposed for echo cancellation. Both structures have their advantages and disadvantages. This paper presents a little-known intermediate solution, the multistage RAM (
m
- RAM), which is investigated analytically for the two most common least-mean-square (LMS) adaptive algorithms: the stochastic iteration algorithm (SIA) and the sign algorithm (SA). We try to develop a theory that covers not only these structures and algorithms but also, in general, nonbinary codes. This theory relies on a number of assumptions, the validity of which is discussed. Finally, our results are compared with computer simulations.