## 4 Joint Power Allocation for Co3P JDT
\[\cdot\frac{\log_{2}\left(e\right){\tilde{\gamma}}_{2}}{\left({P _{2}^{*}}{\tilde{\gamma}}_{2}-{P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}\right) \left({P_{2}^{*}}{\tilde{\gamma}}_{2}-{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{ 3}\right)}{{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}}\]9 \[+\left\{{2P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-\frac{{P_{3}^{ *}}^{2}{\tilde{\gamma}}_{3}\left({\tilde{\gamma}}_{3}-{\tilde{P}_{1}^{*}}^{ \prime}{\tilde{\gamma}}_{1}\right)}{{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{ P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}}-\frac{{P_{3}^{*}}^{2}{\tilde{\gamma}}_{3} \left({\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}\right)}{{P _{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{ 2}}-1\right\} \tag{23}\]0 \[+\left\{{2P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-\frac{{P_{3}^{ *}}^{2}{\tilde{\gamma}}_{3}\left({\tilde{\gamma}}_{3}-{\tilde{P}_{1}^{*}}^{ \prime}{\tilde{\gamma}}_{1}\right)}{{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{ P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}}-\frac{{P_{3}^{*}}^{2}{\tilde{\gamma}}_{3} \left({\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}\right)}{{P _{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{ 2}}-1\right\} \tag{23}\]1 \[+\left\{{2P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-\frac{{P_{3}^{ *}}^{2}{\tilde{\gamma}}_{3}\left({\tilde{\gamma}}_{3}-{\tilde{P}_{1}^{*}}^{ \prime}{\tilde{\gamma}}_{1}\right)}{{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{ P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}}-\frac{{P_{3}^{*}}^{2}{\tilde{\gamma}}_{3} \left({\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}\right)}{{P _{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{ 2}}-1\right\} \tag{23}\]2 \[+\left\{{2P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-\frac{{P_{3}^{ *}}^{2}{\tilde{\gamma}}_{3}\left({\tilde{\gamma}}_{3}-{\tilde{P}_{1}^{*}}^{ \prime}{\tilde{\gamma}}_{1}\right)}{{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{ P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}}-\frac{{P_{3}^{*}}^{2}{\tilde{\gamma}}_{3} \left({\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}\right)}{{P _{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{ 2}}-1\right\} \tag{23}\]3  
Furthermore, using \(\chi\), we obtain the LLA CTP power expression for \(P_{3}^{*}\) versus \(\tilde{\tau}_{3}[\mathrm{dB}]\) along the settled points as  
\[+\left\{{2P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-\frac{{P_{3}^{ *}}^{2}{\tilde{\gamma}}_{3}\left({\tilde{\gamma}}_{3}-{\tilde{P}_{1}^{*}}^{ \prime}{\tilde{\gamma}}_{1}\right)}{{P_{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{ P_{1}^{*}}^{\prime}{\tilde{\gamma}}_{1}}-\frac{{P_{3}^{*}}^{2}{\tilde{\gamma}}_{3} \left({\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{2}\right)}{{P _{3}^{*}}^{\prime}{\tilde{\gamma}}_{3}-{P_{2}^{*}}^{\prime}{\tilde{\gamma}}_{ 2}}-1\right\} \tag{23}\]4  
In Figure 4a-c, the dotted and dashed lines, respectively, indicate the CTP3 powers when the LQA and LLA CTP power expressions are used, in the condition \(\tilde{\tau}_{3}=\tilde{\tau}_{2}\). From Figure 4a-c, we see that the CTP3 power using the LQA CTP power expression is closer to the corresponding optimum CTP3 power over the Co3P JDT region than that using the LLA CTP power expression.