Table 2 Coefficients of the PDF, the MGF, the BEP, and the P _out for DF sharing scheme

A^(DF)

$\sum _{k=3}^N{\lambda }_{\text{RD}}{c}_k{(1-\beta )}^{k-1}\left(\beta +\frac{1-\beta }{k-2}\right)$

a^(DF)

$\frac{1}{2{\lambda }_{\text{RD}}}\left(\frac{2A^{\text{(DF)}}{\lambda }_{\text{SD}}}{-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}}}-\frac{4B^{\text{(DF)}}{\lambda }_{\text{SD}}}{{(-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}})}^2}\right)$

+ c₂(1−β)βλ_RD

B^(DF)

$\frac{c_2}{2}{(1-\beta )}^2{\lambda }_{\text{RD}}^2$

b^(DF)

$\frac{1}{4{\lambda }_{\text{RD}}^2}\left(\frac{4B^{\text{(DF)}}{\lambda }_{\text{SD}}}{-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}}}\right)$

D^(DF)

$\sum _{k=2}^N{c}_k{\beta }^2{(1-\beta )}^{k-2}$

f^(DF)

$\frac{2A^{\text{(DF)}}}{2{\lambda }_{\text{RD}}-{\lambda }_{\text{SD}}}+\frac{4B^{\text{(DF)}}}{{(2{\lambda }_{\text{RD}}-{\lambda }_{\text{SD}})}^2}+$

$\sum _{k=3}^N\frac{2E_k^{\text{(DF)}}}{{\lambda }_{\text{RD}}k-{\lambda }_{\text{SD}}}+D^{\text{(DF)}}$

$E_k^{\text{(DF)}}$

$\frac{c_k}{2}{(1-\beta )}^k\left(\frac{-2}{k-2}\right){\lambda }_{\text{RD}}$

$E_k^{\text{(DF)}}$

$\frac{1}{{\lambda }_{\text{RD}}k}\left(\frac{2E_k^{\text{(DF)}}{\lambda }_{\text{SD}}}{-{\lambda }_{\text{RD}}k+{\lambda }_{\text{SD}}}\right)$