Blind Equalization in Neural Networks

$\tilde{x}\left(n\right)=f\left(v_R\left(n\right)\right)+if\left(v_I\left(n\right)\right)\left(7.31\right)$

According to the steepest descent method, an iterative formula of network weights can be obtained

$W\left(n+1\right)=W\left(n\right)-\mu \frac{\partial J\left(n\right)}{\partial W\left(n\right)}\left(7.32\right)$

where μ is the iteration step-size factor

$\frac{\partial J\left(n\right)}{\partial W\left(n\right)}=\left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]\left|\tilde{x}\left(n\right)\right|\left(\frac{\partial \left|\tilde{x}\left(n\right)\right|}{\partial W_R\left(n\right)}+j\frac{\partial \left|\tilde{x}\left(n\right)\right|}{\partial W_I\left(n\right)}\right)\left(7.33\right)$

And the real situation is similar; because the three-layer complex-valued feed-forward neural network has the hidden layer unit and the output layer, so the weight of the iterative formula is different.

The weight iterative formula of output layer

For the hidden layer of complex-valued FFWNN, the connection weights between the hidden layer and the output layer are ...