Blind Equalization in Neural Networks

where μ is the weight iterative step size.

Because there are two hidden layers and an output layer in the four-layer FFNN, the weight iteration formulas are different.

Weight iterative formula of the output layer

The connection weight between the output layer and the second hidden layer is w_k(n), so

$w_k\left(n=1\right)=w_k\left(n\right)-2{\mu }_1\tilde{x}\left(n\right)\left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]\frac{\partial \tilde{x}\left(n\right)}{\partial w_{k}0n}\left(3.46\right)$

$\frac{\partial \tilde{x}\left(n\right)}{\partial w_k\left(n\right)}=f_3^{\prime }\left({\displaystyle \sum _{k=1}^K{w}_k\left(n\right)v_k^K\left(n\right)}\right)v_k^K\left(n\right)\left(3.47\right)$

$w_k\left(n+1\right)=w_k\left(n\right)-2{\mu }_1\tilde{x}\left(n\right)\left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]f_3^{\prime }\left({\displaystyle \sum _{k=1}^K{w}_k\left(n\right)v_k^K\left(n\right)}\right)v_k^K\left(n\right)\left(3.48\right)$

where μ₁ is the weight iterative step size of the output layer.

Weight iterative formula between the first hidden layer and the second hidden layer

The connection weight between the ...