Table 1 The proposed algorithm

Initialization

\(w = \vec{0}\)

Beginning computation

Iterate for n > k

\(d\left( n \right) = h^{T} x\left( n \right) + v\left( n \right)\)

\(e\left( n \right) = d\left( n \right) - w^{T} x\left( n \right)\)

\(f_{e} \left( n \right) = k_{{{\text{ap}}}} \sqrt {\sum\limits_{i = n - k + 1}^{n} {\left| {e\left( i \right)} \right|}^{2} }\)

\(\mu \left( {f_{e} \left( {n + 1} \right)} \right) = \beta \mu \left[ {f_{e} \left( n \right)} \right] + \left( {1 - \beta } \right)af_{e} \left( {n + 1} \right)e^{{ - bf_{e} \left( {n + 1} \right)}}\)

\(w\left( {n + 1} \right) = w\left( n \right) + \mu \left[ {f_{e} \left( n \right)} \right]\left| {e\left( n \right)} \right|^{p - 1} {\text{sgn}} \left( n \right)x\left( n \right)\)

end