Blind Equalization in Neural Networks

$\begin{array}{l}{w}_{ij}^h\left(n+1\right)=w_{ij}^h\left(n\right)-2{\mu }_5\tilde{x}\left(n\right)\left[|\tilde{x}\left(n\right){|}^2-R_2\right]{f^{\prime }}_2\left({\displaystyle \sum _{j=1}^J{w}_j^o\left(n\right)v_j^J\left(n\right)}\right)\\ \times \left({\displaystyle \sum _{i=1}^I{w}_{ij}^h\left(n\right)v\left(n-i\right)+w_j^d\left(n\right)v_j^J\left(n-1\right)+w_{j,j+1}^d\left(n\right)v_{j+1}^J\left(n-1\right)}\right)\left(4.59\right)\\ +w_{j-1,j}^d\left(n\right)v_{j-1}^J\left(n-1\right))w_j^o\left(n\right)y\left(n-i\right)\end{array}$

where μ₅ is the weight iteration step size of the hidden layer.

4.4.3Computer simulation results

The input signals are 4PAM and 8PAM. The additive Gauss white noise is zero mean and unit variance. The simulation channels adopt the typical telephone channel and the ordinary channel. Their z-transforms are shown in eqs. (2.84) and (3.13).

When 4PAM and 8PAM signals go through the typical digital telephone channel, the iterative step sizes are μ₁ = μ₂ = μ₃ = μ₄ = μ₅ = 0.00016 and μ₁ = μ₂ = μ₃ = μ₄ = μ₅ = 0.0000055, ...