4 Errata for Publications 4.1 Uplink and Downlink MIMO-NOMA with Simultaneous Triangularization 5 License

4.2 Downlink MIMO-RSMA with Successive Null-Space Precoding

This errata is for the publication [13], which is also available on arXiv here: https://arxiv.org/abs/2107.08294. In the first-order expansion of equation (14), which is given in equation (21), the loop over $k^{\prime}$ must be between $1$ and ${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}k}$ (instead of $k-1$ ). The correct equation is given below.

\displaystyle\tilde{R}_{k,\mathrm{c}}

\displaystyle=\mathrm{logdet}\left(\boldsymbol{I}_{M_{k}}+\frac{1}{L_{k}\sigma% ^{2}}\boldsymbol{H}_{k}\boldsymbol{Q}_{\mathrm{c}}\boldsymbol{H}_{k}^{\mathrm{% H}}+\frac{1}{L_{k}\sigma^{2}}\boldsymbol{H}_{k}\Big{(}\sum_{k^{\prime}=1}^{k}% \boldsymbol{Q}_{k^{\prime}}\Big{)}\boldsymbol{H}_{k}^{\mathrm{H}}\right)-% \mathrm{logdet}\left(\boldsymbol{I}_{M_{k}}+\frac{1}{L_{k}\sigma^{2}}% \boldsymbol{H}_{k}\breve{\boldsymbol{Q}}_{k+1}^{(l-1)}\boldsymbol{H}_{k}^{% \mathrm{H}}\right)-\frac{1}{L_{k}\sigma^{2}\log_{\mathrm{e}}(2)}\sum_{k^{% \prime}=1}^{\leavevmode\hbox to17.91pt{\vbox to17.91pt{\pgfpicture% \makeatletter\hbox{\hskip 8.95634pt\lower-8.95634pt\hbox to0.0pt{% \pgfsys@beginscope\pgfsys@invoke{ }\definecolor{pgfstrokecolor}{rgb}{0,0,0}% \pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@invoke{ }\pgfsys@color@rgb@fill{0}{0}% {0}\pgfsys@invoke{ }\pgfsys@setlinewidth{0.4pt}\pgfsys@invoke{ }\nullfont\hbox to% 0.0pt{\pgfsys@beginscope\pgfsys@invoke{ } {{}}\hbox{\hbox{{\pgfsys@beginscope% \pgfsys@invoke{ }\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{% 1,0,0}\pgfsys@color@rgb@stroke{1}{0}{0}\pgfsys@invoke{ }\pgfsys@color@rgb@fill% {1}{0}{0}\pgfsys@invoke{ }\definecolor[named]{pgffillcolor}{rgb}{1,0,0}{{}{{{}% }}{{}}{}{}{}{}{}{}{}{}{}{\pgfsys@beginscope\pgfsys@invoke{ }\color[rgb]{1,0,0}% \definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\pgfsys@color@rgb@stroke{1}{0}{% 0}\pgfsys@invoke{ }\pgfsys@color@rgb@fill{1}{0}{0}\pgfsys@invoke{ }% \definecolor[named]{pgffillcolor}{rgb}{1,0,0}{}\pgfsys@moveto{8.75635pt}{0.0pt% }\pgfsys@curveto{8.75635pt}{4.83606pt}{4.83606pt}{8.75635pt}{0.0pt}{8.75635pt}% \pgfsys@curveto{-4.83606pt}{8.75635pt}{-8.75635pt}{4.83606pt}{-8.75635pt}{0.0% pt}\pgfsys@curveto{-8.75635pt}{-4.83606pt}{-4.83606pt}{-8.75635pt}{0.0pt}{-8.7% 5635pt}\pgfsys@curveto{4.83606pt}{-8.75635pt}{8.75635pt}{-4.83606pt}{8.75635pt% }{0.0pt}\pgfsys@closepath\pgfsys@moveto{0.0pt}{0.0pt}\pgfsys@stroke% \pgfsys@invoke{ } \pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope}{{{{}}\pgfsys@beginscope% \pgfsys@invoke{ }\pgfsys@transformcm{1.0}{0.0}{0.0}{1.0}{-1.93228pt}{-2.43054% pt}\pgfsys@invoke{ }\hbox{{\definecolor[named]{.}{rgb}{1,0,0}\definecolor[% named]{pgfstrokecolor}{rgb}{1,0,0}\pgfsys@color@rgb@stroke{1}{0}{0}% \pgfsys@invoke{ }\pgfsys@color@rgb@fill{1}{0}{0}\pgfsys@invoke{ }\hbox{{% \definecolor[named]{.}{rgb}{1,0,0}\color[rgb]{1,0,0}\definecolor[named]{% pgfstrokecolor}{rgb}{1,0,0}$k$}} }}\pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope}}} \pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope}}} \pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope{}{}{}\hss}% \pgfsys@discardpath\pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope\hss}}% \lxSVG@closescope\endpgfpicture}}}\mathrm{tr}\left(\boldsymbol{\Psi}_{k^{% \prime}}^{\mathrm{H}}\boldsymbol{H}_{k}^{\mathrm{H}}\Big{[}\boldsymbol{I}_{M_{% k}}+\frac{1}{L_{k}\sigma^{2}}\boldsymbol{H}_{k}\breve{\boldsymbol{Q}}_{k+1}^{(% l-1)}\boldsymbol{H}_{k}^{\mathrm{H}}\Big{]}^{-1}\boldsymbol{H}_{k}\boldsymbol{% \Psi}_{k^{\prime}}\Big{(}\boldsymbol{X}_{k^{\prime}}-\breve{\boldsymbol{X}}_{k% ^{\prime}}^{(l-1)}\Big{)}\right)

(21)

Thanks to Rajashekhar from Indian Institute of Science, Bangalore, for bringing this error to my attention.

4.2.1 Version History

1.

First published: 3rd Mar. 2024.