Table 1 Comparison of computational complexity between the CE, conventional and the exhaustive search scheme

(N _d ,N _p )

$\mathcal{U}$

$\mathcal{J}$

β

Conventional method

CE method

Exhaustive search method

$\mathbf{\left|}\mathcal{K}\mathbf{\right|}\mathbf{/}{\mathit{N}}_{\mathit{a}}$

$\mathcal{O}\mathbf{(}{\mathit{N}}_{\mathit{a}}^{\mathbf{2}}\mathbf{+}{\mathit{N}}_{\mathit{a}}{\mathit{N}}_{\mathit{p}}\mathbf{)}$

$\mathcal{O}\mathbf{\left(}\mathbf{\right[}\mathbf{2}\mathbf{\ast }{\mathit{N}}_{\mathit{d}}{\mathit{N}}_{\mathit{p}}\mathbf{+}{\mathit{N}}_{\mathit{p}}\mathit{L}\mathbf{\left]}\mathcal{U}\mathcal{J}\mathbf{\right)}$

$\mathcal{O}\mathbf{\left(}\mathbf{\right[}\mathbf{2}\mathbf{\ast }{\mathit{N}}_{\mathit{d}}{\mathit{N}}_{\mathit{p}}\mathbf{+}{\mathit{N}}_{\mathit{p}}\mathit{L}\mathbf{\left]}\mathcal{U}\left(\genfrac{}{}{0.0pt}{}{\mathbf{\left|}\mathcal{K}\mathbf{\right|}}{{\mathit{N}}_{\mathit{p}}}\right)\mathbf{\right)}$