Recurrent canonical piecewise linear network: Theory and application

Recurrent Canonical Piecewise Linear (RCPL) network is defined by combining the canonical piecewise linear function with the autoregressive moving average (ARMA) model such that an augmented input space is partitioned into regions where an ARMA model is used in each. Properties of RCPL network are discussed. Particularly, it is shown that RCPL function is a contractive mapping and is stable in the sense of bounded input and bounded output stability. By generalizing Donoho's minimum entropy deconvolution approach [5] to the nonlinear case, it is shown that RCPL network can achieve blind equalization. RCPL network is applied to both supervised and blind equalization and results are presented to show that it is computationally efficient and with a very simple structure, can deliver highly satisfactory performance.