# Flexible, Brain-Inspired Communication in Massive Wireless Networks
## 2 System Model
### Digital Communication Power Consumption Model  
Let us now consider digital transmissions system with Quadrature Amplitude Modulation (QAM) presented in Figure 3, where the analog input signal \(x_{\text{m}}\left(t\right)\) is sampled with sampling frequency \(f_{\text{s}}\) and quantized using \(N_{\text{b}}\) bits. Then, the data in the digital form are processed in the forward error correction (FEC) encoder, mapped to QAM symbols, which modulate the complex carrier. For the signal at the output of the digital to analog converters (DAC), the pulse is shaped using the raised-cosine pulse shaping filter with roll-off factor \(\beta\). Finally, the signal converted to the radio frequency is amplified in PA and fed to the antenna. These processes have to be inverted at the receiver in order to get the estimate of the original signal. The bandwidth of the transmitted signal can be calculated as:  
\[B_{\text{sigD}}=\frac{\left(1+\beta\right)R_{\text{s}}}{2}, \tag{6}\]  
where \(R_{\text{s}}\) is the symbol rate of the transmitted signal, and is given by:  
\[R_{\text{s}}=\frac{f_{\text{s}}N_{\text{b}}}{R_{\text{cod}}\log_{2}\left(M \right)}. \tag{7}\]  
In the above equation, \(R_{\text{cod}}\) determines the code rate (in the case of an uncoded scheme \(R_{\text{cod}}=1\)), and \(M\) is the QAM constellation order. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Name** & **Description** & **Type.** & **Max.** \\  & **[mW]** & **[mW]** \\ \hline Niigata Seimitsu Co. NS73M-61 LU & FM transmitter, full CMOS process & 108.0 & 135.0 \\ ON Semiconductor LA72914V & FM modulator and demodulator & 165.0 & 200.0 \\ New Japan Radio Co. NJM2519A & FM Modulator for VHF Band & 76.5 & 95.1 \\ RDA Micoelectronics RDA5820 & single-chip broadcast FM, CMOS process & 63.4 & 74.3 \\ Atmel U4065B & FM Receiver & 296.0 & 376.0 \\ Philips TDA1596T & FM Demodulator & 170.0 & 221.0 \\ Philips TDA7088T & FM receiver circuit for battery supply & 15.6 & 19.8 \\ Silicon Labs Si4702/03-C19 & Broadcast FM radio tuner for portable applications & 165.0 & 181.5 \\ \hline  & **Average** & 132.4 & 162.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Power consumption of FM chips. The power consumption of the digital transmission is very difficult to estimate due to the great dependence of the implementation and hardware performance. Nevertheless, in the literature, there exist high-level power consumption models, which can be used to analyze the energy efficiency of the considered system. The most popular and general model assumes that the power dissipation in a chip can be modeled as the sum of a static term and a dynamic term [20]:  
\[P_{\text{totD}}^{\text{QAM}}=P_{\text{CD}}^{\text{QAM}}+P_{\text{PA}}+2P_{ \text{ADC}}+2P_{\text{DAC}}+P_{\text{COMP}}, \tag{8}\]  
where \(P_{\text{CD}}^{\text{QAM}}\) is the power consumed by the transmitter and receiver active components such as mixers, filters, oscillators, modulator and demodulator, \(P_{\text{ADC}}\), \(P_{\text{DAC}}\) describe the powers consumption of the analog to digital converter (ADC) and DAC, respectively. Most importantly, the two-channel converters are assumed, so that event though 3 DACs and 3 ADCs are visible in Figure 3, the power consumption of each DAC/ADC is multiplied by 2 in Equation (8). The last term, \(P_{\text{COMP}}\), determines the power consumption of the baseband signal processing including encoding, decoding, symbol mapping, demapping, channel estimation and correction, etc.). The powers consumed by the ADC and DAC have been extracted from \(P_{\text{CD}}^{\text{QAM}}\) because they depend on the sample rate being a changeable parameter in our system. Based on datasheets of the ADC and DAC produced by Analog Devices, the power consumption model has been proposed. Form our analysis, it turns out that the consumed power mainly depends on the number of channels, the device architecture and the sample rate \(R_{\text{samp}}\) of the ADC and DAC and not on the number of bits as in the power consumption models in [14; 16; 18].