Table 2 Comparison of the minimum Euclidean distances

Beamforming

$\frac{4}{M_s}{E}_s{\rho }_1$

Water-filling

$\frac{4}{M_s}{\left({\rho }_b\frac{E_s+\sum _{j=1}^{b}1/{\rho }_j}{b}-1\right)}^{+}$

MMSE

$\frac{4}{M_s}{\left(\sqrt{{\rho }_b}\frac{E_s+\sum _{j=1}^{b}1/{\rho }_j}{\sum _{j=1}^{b}1/\sqrt{{\rho }_j}}-1\right)}^{+}$

max−λ _min

$\frac{4}{M_s}\frac{E_s}{\sum _{j=1}^{b}1/{\rho }_j}$

Our proposed

$\left\{\begin{array}{c}\frac{4}{M_s}{E}_s{\rho }_1\text{for}{\mathbf{F}}_1\\ \frac{4}{M_s}{E}_s\frac{2{\rho }_1{\rho }_2}{{\rho }_1+3{\rho }_2}\text{for}{\mathbf{F}}_2\\ \dots \dots \dots \end{array}\right.$