Analysis of the Convergence Behavior of Adaptive Distributed-Arithmetic Echo Cancellers

Abstract

Adaptive distributed-arithmetic echo cancellers are well suited for full-duplex High-speed data transmission. They allow a simpler implementation than adaptive linear transversal filters, since multiplications are replaced by table lookup and shift-and-add operations. Various tradeoffs between the number of operations and the number of memory locations of the lookup tables can be achieved by segmenting the echo canceller delay line into sections of shorter length. Adaptivity is achieved by a decisioNDirected stochastic gradient algorithm to adjust the contents of the lookup tables. In this paper, we adopt the mean-square error criterion to investigate the convergence behavior of adaptive distributed-arithmetic echo cancellers. Under the assumption that the lookup values are statistically independent of the symbols stored in the echo canceller delay line, we obtain an analytical expression for the mean-square error as a function of time. The maximum speed of convergence and the corresponding optimum adaptation gain are also determined. Simulation results for a full-duplex quaternary partial response class-IV system are presented and compared with theoretical results. © 1993 IEEE.