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Table 1 Important notations

From: Successful transmission probability of cognitive device-to-device communications underlaying cellular networks in the presence of hardware impairments

Symbols Meanings
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
(Tα 1 Tα 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 1C 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 2CN(0,κ λ E R P L Y |Y|2), H I 3CN(0,κ(1−λ)E R P L Z |Z|2), and H I 4CN(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 signal-to-noise-plus-distortion ratio (SNDR) at UEi for AF scheme and DF scheme, respectively
Γ D The SNDR threshold