Time-varying Wiener System

A third setup is presented to test the tracking capability of the online K-CCA algorithm. The analyzed Wiener system has a minimum phase linear filter whose coefficients change linearly from $H(z) = 1 + 0.3551z^{-1} + 0.4587z^{-2} - 0.1708z^{-3}$ to $H(z) = 1 + 0.0563z^{-1} - 0.3677z^{-2} - 0.2046z^{-3}$ over $2000$ input samples, and nonlinearity $f(x) = x + 0.1x^3$. The input signal is a white zero-mean Gaussian with unit variance and additive white Gaussian noise with zero-mean is added to the output, matching an SNR of $25$dB. The online K-CCA algorithm is applied with $N=150$. As an example we present the evolution of the third coefficient of $\hat{H}(z)$ compared to the third coefficient of $H(z)$ (see Fig. 9). After an initialization period of length $N$ in which the initialization data in the kernel matrix are replaced by real data, it can be observed that the algorithm is capable of functioning in a time-varying environment.

Figure 9: Tracking capability of the online K-CCA algorithm. The dotted line represents a coefficient of the linear filter of a time-varying Wiener system. The straight line represents the estimated filter coefficient.