Analysis of the convergence behavior of adaptive distributed-arithmetic echo cancellers

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 look-up and shift-and-add operations. Various trade-offs between the number of operations and the number of memory locations of the look-up tables can be achieved by segmenting the echo canceller into filter sections of shorter length. Adaptivity is achieved by a decisiondirected stochastic gradient algorithm to adjust the contents of the look-up 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 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 convergence and the corresponding optimum adaptation gain are also determined. Simulation results for a fullduplex quaternary Partial-Response Class-IV communications system are presented and compared with the theoretical results.