Blind Equalization in Neural Networks

Figure 2.7: The structure of the three-layer feed-forward neural network.

$u_i^I\left(n\right)=y_i\left(n\right)\left(2.53\right)$

$v_i^I\left(n\right)=u_i^I\left(n\right)=y_i\left(n\right)\left(2.54\right)$

$u_j^J\left(n\right)={\displaystyle \sum _{i=1}^I{W}_{ij}\left(n\right)v_i^I\left(n\right)}={\displaystyle \sum _{i=1}^I{W}_{ij}\left(n\right)y_i\left(n\right)}\left(2.55\right)$

$v_j^J\left(n\right)=f_1\left(u_j^J\left(n\right)\right)=f_1\left({\displaystyle \sum _{i=1}^I{W}_{ij}\left(n\right)y_i\left(n\right)}\right)\left(2.56\right)$

$u_k^K\left(n\right)={\displaystyle \sum _{j=1}^J{W}_{jk}\left(n\right)}{v}_j^J\left(n\right)\left(2.57\right)$

${\widehat{\chi }}_k\left(n\right)=v_k^K\left(n\right)=f_2\left(u_k^K\left(n\right)\right)=f_2\left({\displaystyle \sum _{j=1}^J{w}_{jk}\left(n\right)v_j^J\left(n\right)}\right)\left(2.58\right)$

In eqs. (2.56) and (2.58), f₁(n) and f₂(n) are the transfer function of the hidden layer and the output layer, respectively. ...