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Table 1 ODN naïve (O)SIC FNSA, ODN ZF-(O)SIC FNSA, ODN MMSE-(O)SIC FNSA, RDN LRA-ZF-(O)SIC FNSA, RDN LRA-MMSE-(O)SIC FNSA, and ML formulas

From: A simplified hard output sphere decoder for large MIMO systems with the use of efficient search center and reduced domain neighborhood study

Technique designation

Corresponding metric

ODN naïve (O)SIC FNSA

\( \parallel {\boldsymbol{Q}}^H\boldsymbol{y}-\boldsymbol{R}\boldsymbol{x}{\parallel}^2,\ \boldsymbol{x}\in {\xi}^{n_{\mathrm{T}}} \)

ODN exact ZF-(O)SIC FNSA

\( \parallel \boldsymbol{R}\left({\boldsymbol{y}}_{\mathrm{ZF}}-\boldsymbol{x}\right){\parallel}^2,\ \boldsymbol{x}\in {\xi}^{n_{\mathrm{T}}} \) [14]

ODN equivalent MMSE-(O)SIC FNSA

\( {\left({\boldsymbol{y}}_{\mathrm{MMSE}}-\boldsymbol{x}\right)}^H\left({\boldsymbol{H}}^H\boldsymbol{H}+{\sigma}^2\boldsymbol{I}\right)\left({\boldsymbol{y}}_{\mathrm{MMSE}}-\boldsymbol{x}\right),\ \boldsymbol{x}\in {\xi}^{n_{\mathrm{T}}} \) [38]

RDN exact LRA-ZF-(O)SIC FNSA

\( \parallel \tilde{\boldsymbol{R}}\left({\boldsymbol{z}}_{\mathrm{LRA}\hbox{-} \mathrm{Z}\mathrm{F}}-\boldsymbol{z}\right){\parallel}^2,\ \boldsymbol{z}\in {\mathrm{\mathbb{Z}}}_{\mathrm{\mathbb{C}}}^{n_{\mathrm{T}}} \)

RDN equivalent LRA-MMSE-(O)SIC FNSA (proposed)

\( {\left({\boldsymbol{z}}_{\mathrm{LRA}\hbox{-} \mathrm{MMSE}}-\boldsymbol{z}\right)}^H\left({\tilde{\boldsymbol{H}}}^H\tilde{\boldsymbol{H}}+{\sigma}^2{\boldsymbol{T}}^H\boldsymbol{T}\right)\left({\boldsymbol{z}}_{\mathrm{LRA}\hbox{-} \mathrm{MMSE}}-\boldsymbol{z}\right),\ \boldsymbol{z}\in {\mathrm{\mathbb{Z}}}_{\mathrm{\mathbb{C}}}^{n_{\mathrm{T}}} \)

ML

\( \parallel \boldsymbol{y}-\boldsymbol{H}\boldsymbol{x}{\parallel}^2,\ \boldsymbol{x}\in {\xi}^{n_{\mathrm{T}}} \)