Table 2.

List of Parameters and Operators—Definitions.

Notation	Definition
a	Coefficient associated with increase of path loss with distance
$\mathcal{B}$	Overall bandwidth
b	Coefficient associated with the offset value of path-loss
c	Coefficient associated with increase of path loss with frequency
d	Distance between the transmitting and receiving stations (in meters)
${\mathcal{E}}^{\prime }$	Maximum harvested energy obtained on the saturation of the EH circuit
$\mathcal{E}\left(x\right)$	Non-linear EH (sigmoidal) expression with input power x
${\mathcal{E}}^{\mathrm{PS}}(x,\rho )$	Non-linear EH expression for PS scheme
${\mathcal{E}}^{\mathrm{TS}}(x,\tau )$	Non-linear EH expression for TS scheme
$E_U^{\mathrm{PS}}$	Harvested energy at the end-user with PS scheme in the PGN/AGN scenario
$E_U^{\mathrm{TS}}$	Harvested energy at the end-user with TS scheme in the PGN/AGN scenario
$E_U$	Parameter to refer to $E_U^{\mathrm{PS}}$ or $E_U^{\mathrm{TS}}$ according to the chosen scheme
$E_{U,PR}^{\mathrm{PS}}$	Overall harvested energy at the end-user with PS scheme in the HAP scenario
$E_{U,PR}^{\mathrm{TS}}$	Overall harvested energy at the end-user with TS scheme in the HAP scenario
$E_{U,PR}$	Parameter to refer to $E_{U,PR}^{\mathrm{PS}}$ or $E_{U,PR}^{\mathrm{TS}}$ according to the chosen scheme
$\mathbb{E}[·]$	Expectation value operator
f	Operational frequency of the system
$h_{1,D}$	Channel coefficient for the direct link between transmit source and end-user
$h_{1,P}$	Channel coefficient for the first phase of indirect link pertaining to PR device
$h_{1,R}$	Channel coefficient for the first phase of indirect link pertaining to AR device
$h_1$	Parameter to refer to $h_{1,P}$ or $h_{1,R}$ according to the chosen scheme
$h_{2,P}$	Channel coefficient for the second phase of indirect link pertaining to PR device
$h_{2,R}$	Channel coefficient for the second phase of indirect link pertaining to AR device
$h_2$	Parameter to refer to $h_{2,P}$ or $h_{2,R}$ according to the chosen scheme
$J(·)$	Lagrange Dual Function
$\mathcal{L}(·)$	Lagrangian function operator
n${}_P$	AWGN introduced at the PR device
n${}_R$	AWGN introduced at the AR device
$n_1$	Parameter to refer to $n_P$ or $n_R$ according to the chosen scheme
$n_{u_a}$	AWGN introduced due to the antenna element of the end-user
$n_{u_{ID}}$	The noise introduced by the baseband processing circuit at the end-user
$P_{\mathcal{T}}$	Transmit power at the source
$P_R$	Maximum overall power available at the relay
$P^{\star }$	Overall power limitation for the transmitter-relay system
$R_U^{\mathrm{PS}}$	Data throughput at the end-user with PS scheme in the PGN/AGN scenario
$R_U^{\mathrm{TS}}$	Data throughput at the end-user with TS scheme in the PGN/AGN scenario
$R_U$	Parameter to refer to $R_U^{\mathrm{PS}}$ or $R_U^{\mathrm{TS}}$ according to the chosen scheme
$R_{U,PR}^{\mathrm{PS}}$	Overall data throughput at the end-user with PS scheme in the HAP scenario
$R_{U,PR}^{\mathrm{TS}}$	Overall data throughput at the end-user with TS scheme in the HAP scenario
$R_{U,PR}$	Parameter to refer to $R_{U,PR}^{\mathrm{PS}}$ or $R_{U,PR}^{\mathrm{TS}}$ according to the chosen scheme
$R_{1,D}^{\mathrm{PS}}$	Data throughput at the end-user with PS scheme via direct link
$R_{1,D}^{\mathrm{TS}}$	Data throughput at the end-user with TS scheme via direct link
$R_1$	Parameter to refer to $R_{1,D}^{\mathrm{PS}}$ or $R_{1,D}^{\mathrm{TS}}$ according to the chosen scheme
$r_{1,P}$	Transmit signal seen at the PR device
$r_{1,R}$	Transmit signal seen at the AR device
$r_1$	Parameter to refer to $r_{1,P}$ or $r_{1,R}$ according to the chosen scheme
s	Symbol tranmsitted from the source
T	Time period
w	Complex amplification coefficient of the AR device
$y_{1,D}$	Signal received by the end-user via direct link
$y_{2,P}$	Signal received by the end-user via PR device over the second phase
$y_{2,R}$	Signal received by the end-user via AR device over the second phase
$y_2$	Parameter to refer to $y_{2,P}$ or $y_{2,R}$ according to the chosen scheme