Blind Equalization in Neural Networks

There are feed-forward unit, feedback unit, and linear feedback unit in BLRWNN. The following are weight iterative formula derivations.

The feed-forward weight iterative formula

The connection weight of feed-forward unit and output unit is c_j(n)

$\frac{\partial \left|\tilde{x}\left(n\right)\right|}{\partial c_j}=f\text{'}\left(v\left(n\right)\right){\psi }_{a,b}^{\text{'}}\left[{\displaystyle \sum _{j=0}^k{c}_j\left(n\right)y\left(n-j\right)}\right]y\left(n-j\right)\left(7.74\right)$

Plug eq. (7.74) into eqs. (7.73) and (7.72),

$c_j\left(n+1\right)=c_j\left(n\right)-2{\mu }_c\left[{\left|\tilde{x}\left(n\right)\right|}^2-R_2\right]f\text{'}\left(v\left(n\right)\right){\psi }_{a,b}^{\text{'}}\left({\displaystyle \sum _{j=0}^k{c}_j\left(n\right)y\left(n-j\right)}\right)\tilde{x}\left(n\right)y\left(n-j\right)\left(7.75\right)$

where μ_c is feed-forward iterative step factor.

The recurrent unit weight iterative formula

The connecting weight of recurrent unit and output unit is a_i(n):

$\frac{\partial \left|\tilde{x}\left(n\right)\right|}{\partial a_i\left(n\right)}=f\text{'}\left(v\left(n\right)\right)\tilde{x}\left(n-i\right)\left(7.76\right)$

Plug eq. (7.76) into eqs. ...