Table 1 Symbol definition

\(h_0\)

The complex channel coefficient of \(S \rightarrow {D_2}\)

\(h_1\)

The complex channel coefficient of \(S \rightarrow {D_1}\)

\(h_2\)

The complex channel coefficient of \({D_1} \rightarrow {D_2}\)

\(|h_0|^2\)

Power gain of \(S \rightarrow {D_2}\)

\(|h_1|^2\)

Power gain of \(S \rightarrow {D_1}\)

\(|h_2|^2\)

Power gain of \({D_1} \rightarrow {D_2}\)

\(P_S\)

Transmission power at S

\(\beta\) \((0<\beta <1)\)

The power splitting ratio

\(P_r\)

The transmission power at \(D_{1}\)

E[.]

Expectation operation

\(E[|h_0|^2]=\Omega ^{-1}_0\)

Expectation operation of the complex channel coefficient of \(S \rightarrow {D_2}\)

\(E[|h_1|^2]=\Omega ^{-1}_1\)

Expectation operation of the complex channel coefficient of \(S \rightarrow {D_1}\)

\(E[|h_2|^2]=\Omega ^{-1}_2\)

Expectation operation of the complex channel coefficient of \({D_1} \rightarrow {D_2}\)

T

The total time block

\({\alpha _1}\)

Power allocation coefficient for data symbol \(x_{1}\)

\({\alpha _2}\)

Power allocation coefficient for data symbol \(x_{2}\)

\({n_{{D_1}}}\)

Additive white Gaussian noise (AWGN) at \(D_{1}\) with zero mean and variance \({\sigma ^2}\)

\(\eta\) \((0<\eta <1)\)

The energy harvesting efficiency at the energy receiver

\(\rho \buildrel \Delta \over = \frac{{{P_S}}}{{{\sigma ^2}}}\)

The transmit signal-to-noise ratio (SNR)

\({\psi _I} = \left( {1 - \beta } \right)\)

The IP coefficient

\({\psi _E} = \,\beta \eta\)

The EH coefficient

\(R_{1}\)

The target rate for detecting \(x_1\)

\(R_{2}\)

The target rate for detecting \(x_2\)

R

The total network throughput