## 5 Parametric Modeling of System Characteristics  
### Energy Consumption  
In [8,14], the energy consumed in baseband signal processing blocks were neglected to keep the energy consumption model simple. However, in this paper, we have also computed the energy consumed by baseband (Digital) signal processing blocks. The DGN (often a more resourceful node serving as a sink) is considered to have no energy constraints unlike the DSNs and DANs [14]. _RF (Analog) Energy Consumption_: The total energy consumption in RF section is due to long-haul communication (from DSNs to receiving side DANs and DGN itself) and receiver side local communication (from DANs to DGN). The total average power consumption along the signal path for long-haul can be divided into two main components: power consumption of all power amplifiers \(P_{PA}^{L}\), and power consumption of all other circuit blocks \(P_{c}^{L}\)[8]. As in [27], we assume that the power consumed by power amplifiers is linearly dependant on the transmit power \(P_{out}^{L}\):  
\[P_{PA}^{L}=(1+\alpha)P_{out}^{L} \tag{9}\]  
where \(\alpha=\mu/\varsigma\) with \(\varsigma\) being the drain efficiency of the RF power amplifier, and \(\mu\) being the peak-to-average power ratio (PAPR) [28], which depends on the modulation scheme and associated constellation size [8]. \(P_{out}^{L}\) can be calculated according to link budget relationship [29] as follows:  
\[P_{out}^{L}=\bar{E}_{b}^{L}R_{b}\frac{(4\pi d^{L})^{2}}{G_{t}G_{r}\lambda^{2}} M_{t}N_{f} \tag{10}\]  
where \(\bar{E}_{b}^{L}\) is the required energy per bit for a given BER \(\bar{P}_{b}^{L}\) at receiver side, \(R_{b}\) is the bit rate of the system, \(d^{L}\) is the distance between transmitting and receiving side cluster, \(G_{t}\) and \(G_{r}\) are the transmitter and receiver antennas gains respectively, \(\lambda\) is the carrier wavelength, \(M_{t}\) is the link margin for compensating the hardware process variations and other additive background noise or interference, and \(N_{f}\) is the receiver noise figure. The power consumption in all circuit blocks for long-haul communication with \(N_{t}\) transmitter circuits and \(N_{r}\) receiver circuits using WOFDM transmitter and receiver architecture as shown in Figure 5, can be calculated as:  
\[ \begin{split} P_{c}^{L}\approx N_{t}\big{[}P_{DAC}&+ P_{mix}+\big{(}2\times P_{fil}\big{)}+P_{LO}\big{]}\\ &+N_{r}\big{[}P_{LNA}+P_{mix}+\big{(}2\times P_{fil}\big{)}+\ P_{LO}+P_{IFA}+P_{ADC}\big{]}\end{split}  \tag{11}\]  
where \(P_{DAC}\), \(P_{mix}\), \(P_{fil}\), \(P_{LO}\), \(P_{LNA}\), \(P_{IFA}\) and \(P_{ADC}\) are the power consumption values for the digital-to-analog convertor (DAC), the mixer, filter, local oscillator, low-noise amplifier (LNA), intermediate-frequency amplifier (IFA) and analog-to-digital convertor (ADC), respectively. In addition, the energy models developed in [27] can be used to estimate the values for \(P_{DAC}\) and \(P_{ADC}\). Total power consumption in all circuit blocks for long-haul communication with \(N_{t}\) transmitter circuits and \(N_{r}\) receiver circuits using In-Phase/Quadrature-Phase (FOFDM and QAM) transmitter and receiver architecture as shown in Figure 6, can be calculated as:  
\[ \begin{split} P_{c}^{L}\approx N_{t}\big{[}(2\times P_{DAC})+(2 \times P_{mix})+\big{(}3\times P_{fl}\big{)}+P_{LO}+P_{PS}+P_{Add}\big{]}\\ +N_{r}\big{[}P_{LNA}+(2\times P_{mix})+\big{(}3\times P_{fl}\big{)}+ P_{LO}+P_{PS}+\ (2\times P_{IFA})\\ +(2\times P_{ADC})\big{]}\end{split}  \tag{12}\]  
where \(P_{PS}\) and \(P_{Add}\) are the power consumption values for phase shifter, and adder respectively. The total energy consumption per bit for long-haul communication can then be obtained as follows:  
\[E_{b}^{L}=\frac{P_{PA}^{L}+P_{c}^{L}}{R_{b}} \tag{13}\]  
where \(R_{b}\)is the data rate in bits per second (bps).