Table 2 JO-NLMS algorithm
From: An overview on optimized NLMS algorithms for acoustic echo cancellation
Initialization: | |
\(\widehat {\mathbf {h}}(0)=\mathbf {0}_{L \times 1} \) | |
m(0)=ε>0 | |
\(\widehat {\sigma }_{w}^{2}(0) = 0 \) | |
Parameters: | |
\({\sigma _{v}^{2}},\) noise power known or estimated | |
For time index n=1,2,…: | |
\(\widehat {\sigma }_{x}^{2}(n) = \frac {1}{L}\mathbf {x}^{T}(n)\mathbf {x}(n) \) | |
\(e(n) = d(n)-\mathbf {x}^{T}(n)\widehat {\mathbf {h}}(n-1) \) | |
\(p(n) = m(n-1)+ L\widehat {\sigma }_{w}^{2}(n-1)\) | |
\(q(n) = \frac {p(n)}{L{\sigma _{v}^{2}} + (L+2)p(n)\widehat {\sigma }_{x}^{2}(n)} \) | |
\(\widehat {\mathbf {h}}(n) = \widehat {\mathbf {h}}(n-1)+q(n)\mathbf {x}(n)e(n) \) | |
\(m(n) = \left [1 - q(n)\widehat {\sigma }_{x}^{2}(n) \right ] p(n) \) | |
\(\widehat {\sigma }_{w}^{2}(n)=\frac {1}{L}\left \| \widehat {\mathbf {h}}(n) - \widehat {\mathbf {h}}(n-1) \right \|_{2}^{2}\) |