From: Asymptotic equivalent analysis of the LMS algorithm under linearly filtered processes
Variable | Dimension | Meaning |
---|---|---|
d _{ k } | IR | Desired output of unknown system |
w | IR^{M×1} | Impulse response of unknown system |
w _{ k } | IR^{M×1} | Estimate of w |
u _{ k } | IR^{M×1} | Regression vector |
u _{ k } | IR^{1×1} | Elements of the regression vector |
v _{ k } | IR | Additive noise |
R _{uu} | IR^{M×M} | Autocorrelation matrix of u _{ k } |
Λ _{u} | IR^{M×M} | Diagonal matrix =Q R _{uu} Q ^{T} |
K _{ k } | IR^{M×M} | Covariance matrix of w−w _{ k } |
x _{ k } | IR | White generating process |
\(m_{\mathrm {x}}^{(2)}\) | IR | Second-order moment of x _{ k } |
\(m_{\mathrm {x}}^{(2,2)}\) | IR | Joint fourth-order moment of x _{ k } |
μ | IR | Step-size |
A | IR^{M×(M+P)} | upper right Toeplitz matrix |
I | IR^{M×M} | Identity matrix of dimension M |
I _{ P } | IR^{P×P} | Identity matrix of dimension P |
1 | IR^{M×1} | Vector with ones as entries |