Table 1 Recursion steps for RR MWF algorithm

$\begin{array}{l}\mathrm{for}i=1,2,\dots ,D\\ {\mathit{t}}_i={\displaystyle \sum _{n=0}^{K-1}{d}_{i-1}^{*}\left[n\right]{\mathit{X}}_{i-1}\left[n\right],{\mathit{t}}_i-{\mathit{t}}_i/{‖{\mathbf{t}}_i‖}_2}\\ d_i\left[n\right]={\mathit{t}}_i^H{\mathit{X}}_{i-1}\left[n\right],n=0,1,\dots ,K-1\\ {\mathit{X}}_i\left[n\right]={\mathit{X}}_{i-1}\left[n\right]-d_i\left[n\right]{\mathit{t}}_i,n=0,1,\dots ,K-1\\ \mathrm{end}\\ {\epsilon }_D\left[n\right]=d_D\left[n\right]\end{array}$

$\begin{array}{l}\mathrm{for}i=D-1,D-2,\dots ,0\\ {\omega }_{i+1}=\left\{{\displaystyle \sum _{n=0}^{K-1}{d}_i^{*}\left[n\right]{\epsilon }_{i+1}^{*}\left[n\right]}\right\}/\left\{{\displaystyle \sum _{n=0}^{K-1}{\left|{\epsilon }_{i+1}^{*}\left[n\right]\right|}^2}\right\}\\ {\epsilon }_i\left[n\right]=d_i\left[n\right]-{\omega }_{i+1}{\epsilon }_{i+1}\left[n\right],n=0,1,\dots ,K-1\\ \mathrm{end}\\ {\mathit{w}}_0^{\left(D\right)}={\displaystyle \sum _{i=1}^D{\left(-1\right)}^{i+1}\left\{{\displaystyle {\prod }_{l=1}^i{\omega }_l}\right\}{\mathit{t}}_i}\end{array}$