Blind Equalization in Neural Networks

Appendix D:Iterative Formula Derivation of Blind Equalization Algorithm Based on DRFNN

In the blind equalization algorithm based on dynamic recurrent fuzzy neural network, the connection weights of the feedback unit, the connection weights of the output layer (i.e., defuzzification layer), the center, and width of the Gauss membership function need to adjust. Their iterative formulas are shown as follows:

(1) w_j(n) iterative formula

According to eq. (5.13), we obtain

$w_j\left(n+1\right)=w_j\left(n\right)-2\mu \left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]\tilde{x}\left(n\right)\frac{\partial \tilde{x}\left(n\right)}{\partial w_i\left(n\right)}\left(\text{D}\text{.1}\right)$

$\frac{\partial \tilde{x}\left(n\right)}{\partial w_j\left(n\right)}=\frac{\partial O^{\left(5\right)}\left(n\right)}{\partial w_j\left(n\right)}=\frac{\partial I^{\left(5\right)}\left(n\right)}{\partial w_j\left(n\right)}=O_j^{\left(4\right)}\left(n\right)\left(\text{D}\text{.2}\right)$

$w_j\left(n+1\right)=w_j\left(n\right)-2{\mu }_1\left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]\tilde{x}\left(n\right)O_j^{\left(4\right)}\left(n\right)\left(\text{D}\text{.3}\right)$

where μ₁ is the connection ...