Experimental Setup

The nonlinear Wiener system is a well-known and simple nonlinear system which consists of a series connection of a linear filter and a memoryless non-linearity (see Fig. 1). Such a nonlinear channel can be encountered in digital satellite communications [9] and in digital magnetic recording [10]. Traditionally, the problem of blind nonlinear equalization or identification has been tackled by considering nonlinear structures such as MLPs [11], recurrent neural networks [12], or piecewise linear networks [13].

Here we consider a supervised identification problem, in which moreover at a given time instant the linear channel coefficients are changed abruptly to compare the tracking capabilities of both algorithms: During the first part of the simulation, the linear channel is $H_1(z) = 1 + 0.0668z^{-1} -0.4764^{-2} + 0.8070^{-3}$ and after receiving $500$ symbols it is changed into $H_2(z) = 1 - 0.4326z^{-1} - 0.6656z^{-2} + 0.7153^{-3}$. A binary signal is sent through this channel and then the nonlinear function $y = \tanh(x)$ is applied on it, where $x$ is the linear channel output. Finally, white Gaussian noise is added to match an SNR of $20$dB. The Wiener system is then treated as a black box of which only input and output are known.

Figure 1: A nonlinear Wiener system.