Smooth Approximation 𝑙₀-Norm Constrained Affine Projection Algorithm and Its Applications in Sparse Channel Estimation

Table 1

Computational complexity.

Algorithms	Additions	Multiplications	Divisions
NLMS	3𝑁	3𝑁+1	1
ZA-NLMS	𝑁+3𝐾	𝑁+3𝐾+1	1
RZA-NLMS	𝑁+4𝐾	𝑁+4𝐾+1	𝑁+1
APA	𝑁𝑄^2+𝑁𝑄+𝐾−𝑁+𝑂(𝑄^3)	𝑁𝑄^2+𝑄^2+𝑁𝑄+𝑄+𝑂(𝑄^3)	𝑄
ZA-APA	𝑁𝑄^2+𝑄^2+3𝑁𝑄−2𝑄−2𝑁+3𝐾+𝑂(𝑄^3)	𝑁𝑄^2+2𝑄^2+3𝑁𝑄+2𝑄+𝐾+𝑂(𝑄^3)	𝑄
RZA-APA	𝑁𝑄^2+𝑄^2+3𝑁𝑄−2𝑄−2𝑁+4𝐾+𝑂(𝑄^3)	𝑁𝑄^2+2𝑄^2+3𝑁𝑄+𝑄+𝑁+2𝐾+𝑂(𝑄^3)	𝑁+𝑄
SL0-APA	𝑁𝑄^2+𝑄^2+3𝑁𝑄−2𝑄−2𝑁+4𝐾+𝑂(𝑄^3)	𝑁𝑄^2+2𝑄^2+3𝑁𝑄+𝑄+𝑁^2−𝑁+2𝐾+𝑂(𝑄^3)	𝑁+𝑄