Blind Equalization in Neural Networks

The DRNN has the input layer, the hidden layer, the self-feedback layer, and the output layer. So there are different weight iterative formulas.

4.3.2.1Weight iteration formula of the output layer

The connection weight between the output layer and the hidden layer is , so

$w_j^o\left(n+1\right)=w_j^o\left(n\right)-2{\mu }_1\tilde{x}\left(n\right)\left[|\tilde{x}\left(n\right){|}^2-R_2\right]\frac{\partial \tilde{x}\left(n\right)}{\partial w_j^o\left(n\right)}\left(4.30\right)$

$\frac{\partial \tilde{x}\left(n\right)}{\partial w_j^o\left(n\right)}={f^{\prime }}_2\left({\displaystyle \sum _{j=1}^J{w}_j^o\left(n\right)v_j^J\left(n\right)}\right)v_j^J\left(n\right)\left(4.31\right)$

$w_j^o\left(n+1\right)=w_j^o\left(n\right)-2{\mu }_1\tilde{x}\left(n\right)\left[|\tilde{x}\left(n\right){|}^2-R_2\right]{f^{\prime }}_2\left({\displaystyle \sum _{j=1}^J{w}_j^o\left(n\right)v_j^J\left(n\right)}\right)v_j^J\left(n\right)\left(4.32\right)$

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

4.3.2.2Self-feedback weight iteration formula of the hidden layer

The self-feedback ...