Table 1 Optimized values of \(P_{s_{u_{[k]}},n}^{k}\)

\(P_{p,(n-1)}^{k}= 0\) any value for a ^k and c ^k

Interweave

\(\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}\)

\(P_{p,(n-1)}^{k}\neq 0\) {a ^k=0;c ^k=0}

Int = noise

\(\text {min}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)

\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} <0; c^{k} > 0\right \}\)

SIC

0

SC

\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\hat {\mu _{s,n}}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {n_{0}\left (|h^{k}_{pp}|^{2} - |h^{k}_{sp}|^{2}\right)}{|h^{k}_{sp}|^{2} |h^{k}_{ps_{u_{[k]}}}|^{2}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)

\( P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} >0; c^{k} < 0\right \}\)

SIC

\(\text {min}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)

SC

0

\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} <0; c^{k}<0\right \}\)

SIC

\(\text {min}\left \{\frac {c^{k}}{a^{k}}; \left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)

SC

\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\hat {\mu _{s,n}}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {n_{0}\left (|h^{k}_{pp}|^{2} - |h^{k}_{sp}|^{2}\right)}{|h^{k}_{sp}|^{2} |h^{k}_{ps_{u_{[k]}}}|^{2}}; \frac {c^{k}}{a^{k}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)

\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} >0; c^{k}>0\right \}\)

SIC \(\text {if} \frac {c^{k}}{a^{k}}\leq \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}} \)

\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {c^{k}}{a^{k}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)

otherwise

0

SC

\(\min \left \{\max \left \{\left [\frac {1}{\mu ^{\wedge }_{s,n}}-\frac {1}{b^{k}_{s,(n-1)}}\right ]^{+} ;\frac {n_{0}\left (\left |h^{k}_{pp}\right |^{2}-\left |h^{k}_{sp}\right |^{2}\right)}{\left |h^{k}_{sp}\right |^{2}\left |h^{k}_{ps_{u_{[k]}}}\right |^{2}}\right \}; \frac {c^{k}}{a^{k}};\frac {I^{k}_{\text {th}}}{\left |h^{k}_{ps_{u_{[k]}}}\right |^{2}}\right \}\)