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Table 4 Computational complexity of SSLM algorithm

From: Family of state space least mean power of two-based algorithms

Equation number

Operation

Multiplication

Additions

6

\(\bar {\mathbf {x}}[k]_{n\times 1} = \mathbf {A}[k-1]_{n\times n}\hat {\mathbf {x}}[k-1]_{n\times 1}\)

n 2

n 2n

8

\({\mathbf {\varepsilon }}[k]_{m\times 1} = \mathbf {y}[k]_{m\times 1}\bar {\mathbf {y}}[k]_{m\times 1}\)

0

m

9

\(\bar {\mathbf {y}}[k]_{m\times 1} = \mathbf {C}[k]_{m\times n}\bar {\mathbf {x}}[k]_{n\times 1}\)

mn

n mm

7

\(\hat {\mathbf {x}}[k]_{n\times 1} = \bar {\mathbf {x}}[k]_{n\times 1} + \textbf {K}[k]_{n\times m}{\mathbf {\varepsilon }}[k]_{m\times 1}\)

mn

nm

15

K[k] n×m =μ 1×1||ε[k] m×1||2L−2 G n×n C T[k] n×m

m n 2+m n+m+L−1

m n 2m n+m−1

Total for the SSLM algorithm

 

3m n+n 2+m n 2+m+L−1

m+m n 2+n 2+m nn−1