## 4 Energy Consumption Model and Power Control
### Power Control  
Different powers should be selected based on the channel variance and the SNR requirement of the node. The clustering protocol itself divides the nodes into two different kinds: member nodes and CH nodes. Relative to a member node, a CH node plays an important role in data communication. The power of a CH node should be a compromise between spatial multiplexing and correct receiving probability because an excessive amount of power guarantees spatial coverage but wastes a considerable amount of energy and interferes with other cluster sets, whereas an insufficient amount of power makes the receiver unable to meet the requirement of a correct receiving rate, which leads to message retransmission and wasting of bandwidth resources and energy. This section describes the node transmission power mechanism of each stage under the PEAFC-CL protocol and the requirement for transmission power under wireless channel fluctuations. The receiving power of the receiving node and the number of decibels of transmission loss can typically be measured: \(P_{L}(dB)=P_{T}(dB)-P_{R}(dB)\), where \(P_{T}\) and \(P_{R}\) refer to transmitting power and receiving power, respectively; \(P_{R}\) can also be acquired from the RSSI value of the physical layer of the node components. When various communication equipment and application scenes are adopted in practice, the transmission loss obtained is also different. Through modeling analysis, \(P_{R}\) is mainly determined logically by considering the distance between links, the antenna gain and the additional loss in a scene. In this paper, it is supposed that the channel characteristics conform to Gaussian distribution characteristics and that all communication losses are as shown in Equation (2). Then, the logarithmic value of \(PL\) is \(P_{L}(dB)=10\text{log}_{10}PL+X_{\sigma}\). Two concepts will be defined here to better regulate the transmission power of a node in different periods:  
Figure 5: Block diagram of the transmission system. **Definition 3**. : _Transmission range: this satisfies the effective data transmission under the pre-set quality of service (QoS) in the transmission range; its minimum transmission power is \(P_{\rm Rmin}\) (i.e., the aforementioned receiving power threshold \(P_{\rm th}\))._  
**Definition 4**. : _Carrier sensing range: a node within the carrier sensing range can sense the communications of a node but may not satisfy the data transmission needs under the pre-set QoS; its minimum transmission power is \(P_{\rm Smin}\), and typically \(P_{R\rm min}/P_{\rm Smin}>1\)._  
When the receiving power of a node is \(P_{R}<P_{\rm Smin}\), the node can neither sense data packet transmission nor transmit data; when \(P_{\rm Smin}<P_{R}<P_{R\rm min}\), the node can sense data transmission but cannot calculate the path loss; thus, the information that the node sent cannot be read; when \(P_{R}>P_{R\rm min}\), the node can try to read the data transmitted by the sending end and calculate the path loss between links. Now, we set \(p_{ep}=10^{-2}\), _i.e._, the data packet transmission error rate is not higher than 0.01; then:  
\[p_{ep}=\sum_{i=t+1}^{z}\left( \begin{array}{c}z\\ i\end{array} \right)p_{eb}^{i}(1-p_{eb})^{z-i} \tag{14}\]  
where \(z\) is the length of the data packet and \(p_{eb}\) refers to the bit error rate. Supposing that the BPSK debugging mode is adopted for the signal,  
\[P_{e,BPSK}=Q\left(\sqrt{\frac{2E_{b}}{N_{0}}R_{c}}\right) \tag{15}\]  
where \(R_{c}\) is the coding rate, \(N_{0}\) is the one-sided power spectral density of the additive white Gaussian noise (AWGN), and \(E_{b}\) is the received energy per information bit. \(\gamma_{SNR}\) is the signal-to-noise ratio (SNR) at the receiver input, \(\gamma_{SNR}=P_{R}/P_{N}=(E_{b}\cdot R_{b})/(N_{0}\cdot W)\), and \(W\) refers to the noise bandwidth, viz., the number of bits transmitted per unit time.