Fig. 4

The achievable rate regions and sum-capacities of the BDF relaying mode for four conditions. a \({\beta _{1}} < \gamma \left [ {{P_{\mathrm {B}}}{{\left | {{h_{{\text {BR}}}}} \right |}^{2}}/(\sigma _{\mathrm {R}}^{\mathrm {2}} + {P_{\mathrm {M}}}{{\left | {{h_{{\text {MR}}}}} \right |}^{2}})} \right ]\), \(\beta _{2} > \gamma ({P_{\mathrm {M}}}{\left | {{h_{{\text {MR}}}}} \right |^{2}}/\sigma _{\mathrm {R}}^{\mathrm {2}})\). b \({\beta _{1}} > \gamma ({P_{\mathrm {B}}}{\left | {{h_{{\text {BR}}}}} \right |^{2}}/\sigma _{\mathrm {R}}^{\mathrm {2}})\), \({\beta _{2}} < \gamma \left [ {{P_{\mathrm {M}}}{{\left | {{h_{{\text {MR}}}}} \right |}^{2}}/(\sigma _{\mathrm {R}}^{\mathrm {2}} + {P_{\mathrm {B}}}{{\left | {{h_{{\text {BR}}}}} \right |}^{2}})} \right ] \). c \({\beta _{1}} < \gamma \left [ {{P_{\mathrm {B}}}{{\left | {{h_{{\text {BR}}}}} \right |}^{2}}/(\sigma _{\mathrm {R}}^{\mathrm {2}} + {P_{\mathrm {M}}}{{\left | {{h_{{\text {MR}}}}} \right |}^{2}})} \right ] \), \( {\beta _{2}} < \gamma \left [ {{P_{\mathrm {M}}}{{\left | {{h_{{\text {MR}}}}} \right |}^{2}}/(\sigma _{\mathrm {R}}^{\mathrm {2}} + {P_{\mathrm {B}}}{{\left | {{h_{{\text {BR}}}}} \right |}^{2}})} \right ] \). d \({\beta _{1}} + {\beta _{2}} > \gamma \left [ {({P_{\mathrm {M}}}{{\left | {{h_{{\text {MR}}}}} \right |}^{2}} + {P_{\mathrm {B}}}{{\left | {{h_{{\text {BR}}}}} \right |}^{2}})/\sigma _{\mathrm {R}}^{\mathrm {2}}} \right ]\)