η

The energy conversion efficiency

E
_{
D
}

The maximum transmission power of UE1, UE2, and UE3.

E
_{
C
}

The circuit power of UE1,UE2, and UE3.

E
_{
R
}

The transmit power of R

X^{2}, r
_{
X
}, and P
L
_{
X
}

The channel power gain, the distance, and the path loss model for the link from UE1 to R, respectively.

Y^{2}, r
_{
Y
}, and P
L
_{
Y
}

The channel power gain, the distance, and the path loss model for the link from R to UE2, respectively.

Z^{2}, r
_{
Z
}, and P
L
_{
Z
}

The channel power gain, the distance, and the path loss model for the link from R to UE3, respectively.

W^{2}, r
_{
W
}, and P
L
_{
W
}

The channel power gain, the distance, and the path loss model for the link from UE2 to UE3, respectively.

Ω
_{
k
}

The exponential parameters corresponding to k^{2}, k∈[X,Y,Z,W].

α
_{1}
T

Time switching (TS) fraction used for EH from UE1 to R

α
_{2}
T

TS fraction used for IT from EU1 to R

(T−α
_{1}
T−α
_{2}
T)

TS used for IT from R to UE2 and UE3

β
E
_{
D
}

Power spitting (PS) fraction used for EH at R

(1−β)E
_{
D
}

Information transmission (IT) from UE1 to R in PS protocol

λ

The power allocation at R used to transmit signals to UE2

(1−λ)

The power allocation at R used to transmit signals to UE3

κ

The aggregate level of hardware impairments

H
I
_{1}

The distortion noise caused by HWIs in the communication between UE1 and R with variance, H
I
_{1}∼C
N(0,κ
E
_{
D
}
P
L
_{
X
}X^{2})

H
I
_{2}, H
I
_{3}, and H
I
_{4}

The distortion noise HWIs from R to UE2, R to UE3, and between UE2 and UE3 with variance H
I
_{2}∼CN(0,κ
λ
E
_{
R
}
P
L
_{
Y
}Y^{2}), H
I
_{3}∼CN(0,κ(1−λ)E
_{
R
}
P
L
_{
Z
}Z^{2}), and H
I
_{4}∼CN(0,κ
E
_{
D
}
P
L
_{
W
}W^{2}), respectively.

n
_{0}

The additive white Gaussian noise (AWGN) at UEs and R with mean power, Ω
_{0},

F
_{
x
}, f
_{
x
}

The cumulative distribution function (CDF)/the probability density function (PDF) of the RV x is \({F_x}(z) = Pr(x<z)=1  {e^{\frac {z}{{{\Omega _x}}}}}\), \({f_x}(z) = Pr(x<z)={\frac {z}{{{\Omega _x}}}}{e^{\frac {z}{{{\Omega _x}}}}}\), respectively, in which Ω
_{
x
} is the mean of the exponential RV x.

Pr{.}

The probability distribution function.

K
_{
n
}{.}

The n order modified Bessel function of the second kind with the last equality

\(\mathbb {E}\left \{ {.} \right \}\)

The expectation operator.

\(\gamma _{i}^{AF}\), \(\gamma _{i}^{DF}\)

The signaltonoiseplusdistortion ratio (SNDR) at UEi for AF scheme and DF scheme, respectively

Γ
_{
D
}

The SNDR threshold
