Recurrent canonical piecewise linear network and its application to adaptive equalization

We present a recurrent canonical piecewise linear (RCPL) network based on canonical piecewise-linear (CPL) function and autoregressive moving average model, and apply it to adaptive channel equalization. It is shown that a recurrent neural network with piecewise linear activation function realizes an RCPL network. RCPL network has several advantages. First, it can make use of standard linear adaptive filtering techniques to perform training tasks. Second, it allows for efficient selection of the partition boundaries and the corresponding RCPL of appropriate complexity using CPL techniques. Third, being a generalized IIR filter, RCPL equalizer has a distinct dynamic behavior which is much more powerful than that attained by the use of finite duration impulse response feedforward structures. Overall, it is computationally efficient and conceptually simple. As an application, the learning algorithm for a simple RCPL network is derived and applied to multilevel equalization. The numerical experiments demonstrate the superior performance of RCPL network for adaptive equalization.