# Flexible, Brain-Inspired Communication in Massive Wireless Networks
## 2 System Model
### Analog Communication Power Consumption  
The high energy efficiency of a human brain results from the fact that inside each neuron, information incoming from synapses is integrated and processed in a simple, analog manner, thus avoiding additional energy-intensive processing. For our communication model, let us consider the well-known frequency modulation (FM) and analyze it from the energy-efficiency perspective. The block diagram of the considered FM system is presented in Figure 2. For modulating signal \(x_{\text{m}}\left(t\right)\) and carrier wave \(x_{\text{c}}\left(t\right)=A_{\text{c}}\cos\left(2\pi f_{\text{c}}t\right)\) (where \(f_{\text{c}}\) is the carrier's base frequency, and \(A_{\text{c}}\) is the carrier's amplitude), the modulated signal has the following form [15]:  
\[x_{\text{FM}}\left(t\right)=A_{\text{c}}\cos\left(2\pi f_{\text{c}}t+2\pi \Delta f\int_{0}^{t}x_{\text{m}}\left(\tau\right)d\tau\right), \tag{1}\]  
where \(\Delta f\) is the frequency deviation. The Carson's rule defines the bandwidth wherein about 98% of the power of a frequency-modulated signal lies:  
\[B_{\text{sigA}}=2\left(\Delta f+f_{\text{m}}\right), \tag{2}\]  
where \(f_{\text{m}}\) is the highest frequency component of \(x_{\text{m}}\left(t\right)\).  
In order to analyze the energy efficiency of the considered analog transmission, it is necessary to estimate the total power consumed, which results from the structure of the transmitter and receiver. For our transmitter and receiver model presented in Figure 2, the total power consumption can be calculated as:  
\[P_{\text{totA}}=P_{\text{PA}}+P_{\text{C}}+P_{\text{FMmod}}+P_{\text{FMdemod}}, \tag{3}\]  
where \(P_{\text{PA}}\) is the power consumed by the power amplifier, while \(P_{\text{C}}\) is the power required to run the circuit components such as oscillators, mixers, filters, radio and intermediate frequency amplifiers (RFA, IFA). Moreover, the powers consumed by the FM modulator and demodulator are denoted as: \(P_{\text{FMmod}}\), \(P_{\text{FMdemod}}\). The direct FM modulation can be implemented using a Voltage-Controlled Oscillator (VCO). In [16], the power consumption model of VCO based on a resonant circuit is presented. Based on Equation (7) in [16], it can be observed that the power consumption of VCO is independent on dynamically changing transmission parameters and the authors assumed the constant value. In the case of demodulation of FM signals, which can be realized by the Phase Locked Loop  
Figure 1: The general block diagram of the considered system.  
Figure 2: The transmitter and receiver block diagram of analog transmission schemes.  
(PLL), the situation is similar. In [16; 17], the authors proposed the PLL power consumption model, where the power consumption of PLL takes the constant value. Based on the power consumption models described in [3; 14; 16; 18], \(P_{\text{C}}\) can be modeled as the constant value as well, while the power consumption of PA class B as [19]:  
\[P_{\text{PA}}=\frac{4}{\pi}\sqrt{P_{\text{TX}}\cdot PAR\cdot P_{\text{T}}\left(t \right)}, \tag{4}\]  
where \(P_{\text{TX}}\) is the average transmission power, \(PAR\) determines Peak to Average Power Ratio while \(P_{\text{T}}\left(t\right)\) is the transmission power at time \(t\). Thus, the power consumption model from Equation (3) can be simplified to:  
\[P_{\text{totA}}=P_{\text{PA}}+P_{\text{CA}}, \tag{5}\]  
where \(P_{\text{CA}}=P_{\text{C}}+P_{\text{FMmod}}+P_{\text{FMdemod}}\). The power consumption model presented above is relatively simple but indeed realistic and based on models from literature. Moreover, in Table 1, the power consumption values of the FM chips are given. It can be observed that the consumed power highly depends on hardware implementation and applications, and the presented model can be easily scaled.