System Equalization

While performing system identification of the Wiener system, an estimate is made of the inverse nonlinearity $g(.)$, which compensates for the nonlinearity $f(.)$. A linear equalizer $W(z)$ is proposed to compensate for $H(z)$, as shown in Fig. 3. A wide range of techniques are available to estimate this linear filter, among others the least mean squares algorithm (LMS), RLS, linear Wiener filter estimation, etc. We opted for the RLS algorithm with convergence speed in mind.

Figure 3: Diagram for supervised equalization: Sliding-window K-CCA is applied on the input $x_1[n]$ and output $x_2[n]$ of the Wiener system. This estimates the nonlinear function $g(.)$ and its output $y_2[n]$. Using $y_2[n]$ and a time-delayed version of the system input $x_1[n-d]$, an equalizer $W(z)$ is estimated.