ANALYSIS OF THE CONVERGENCE BEHAVIOR OF ADAPTIVE DISTRIBUTED-ARITHMETIC ECHO CANCELERS

Adaptive distributed-arithmetic echo cancellers are well suited for fu ll-duplex high-speed data transmission. They allow a simpler implement ation than adaptive linear transversal filters, since multiplications are replaced by table look-up and shift-and-add operations. Various tr adeoffs between the number of operations and the number of memory loca tions of the look-up tables can be achieved by segmenting the echo can celler delay line into sections of shorter length. Adaptivity is achie ved by a decision-directed stochastic gradient algorithm to adjust the contents of the look-up tables. In this paper, we adopt the mean-squa re error criterion to investigate the convergence behavior of adaptive distributed-arithmetic echo cancellers. Under the assumption that the look-up 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 con vergence and the corresponding optimum adaptation gain are also determ ined. Simulation results for a full-duplex quaternary partial response class-IV system are presented and compared with theoretical results.