# Sustainable Power Consumption for Variance-Based Integration Model in Cellular 6G-IoT System
## 3 System Model  
Considering a sustained 6G-cellular-IoT network as exposed in Figure 1, in which a BS built with \(M\) antennas interacts with \(Q\) multi-modal IoT User Equipment items (UEs) built with each \(N\) antenna. It functions in Time-Division-Duplex (TDD) mode. Throughout the initial part of a time period, the BS holds as a powerful beacon for charging IoT UEs via energy BF. IoT UEs carry out computation and communication in the second half of the time slot using the uplink energy that has been captured. In particular, the signals from IoT devices serve two purposes: one is to aggregate data based on the signals of several devices, and the other is to transmit information based on the signal of a single device. As a result, the first signal is referred to as a calculation signal, while the second signal is referred to as a communication signal. IoT devices should have adequate energy to simultaneously realize precise processing and effective communication. However, energy supply for a large IoT is not an easy operation. Frequent battery replacement for widespread IoT is impractical due to the significant human cost and environmental strain. Therefore, using the WPT method to provide one-to-many charging by taking advantage of the wireless broadcast channel's open nature is absorbing. The energy harvested at the \(qth\) UE [1] could be modeled as in Equation (1). \[e_{q}=\frac{U}{2}\phi_{q}\Big{\|}C_{q}^{G}\xi\Big{\|}^{2} \tag{1}\]  
In Equation (1), \(C_{q}\in C^{M\times N}\) refers to the MIMO channel matrix from the \(qth\) UE to BS that remains constant in a time interval; however, it independently weakens over the time interval. \(U\) refers to the length of a time period, \(\phi_{q}\) refers to the efficiency of energy transfer and \(g\in C^{M\times 1}\) refers to the energy beam broadcasted by the BS. Figure 1: The architecture of the 6G-IoT network. With no generality losses, it is presumed that the \(qth\) UE recorded data of \(R\) heterogeneous parameters to be calculated and \(L\) heterogeneous parameters to be communicated that produce a vector for computation symbol \(d_{q}=\left[d_{q,1},\ldots d_{q,R}\right]^{U}\) and a vector for communication symbol \(S^{\prime}_{q}=\left[S^{\prime}_{q,1},\ldots S^{\prime}_{q,L}\right]^{U}\), in which \(d_{q,r}\) and \(S^{\prime}_{q,L}\) refer to the estimated values of the \(rth\) computational constraint and the \(jth\) communication constraint at the \(qth\) UE, respectively. Notice that for computation, the BS engaged itself in calculating the \(rth\) targeted operation utilizing Air Comp as in Equation (2). \[k_{r}=g_{r}\left(\sum\limits_{q=1}^{Q}f_{q,r}\big{(}d_{q,r}\big{)}\right),\ r=1,2\ldots R \tag{2}\]  
In Equation (2), \(k_{r}\) refers to perfect computation output, \(f_{q,r}(. )\) and \(g_{r}(. )\) stand for the pre-processing operation at the \(qth\) IoT UEs and the post-processing operation at the BS, respectively. Every IoT device in the network is uniformly distributed and integrated with a single RRU. Consider that every deployed RRU communicates the data with the integrated IoT devices. The activated RRUs are moderately stable to enable possible execution in IoT networks. The power amplifiers and RRU power consumption create the major part of the complete power consumption in the 6G-IoT network. The overall summation of power consumption includes transmit power, fixed power consumption (\(P_{FIX}\)) and circuit power consumption (\(P_{\text{C}}\)) from the activated RRUs. Accordingly, the total power consumption is  
\[ \begin{split} P_{T}&=P_{FIX}+P_{t}+P_{\text{C}}\\ P_{T}&=P_{FIX}+\sum\limits_{n=1}^{N}\sum\limits_{k=1 }^{K}\frac{1}{\eta_{e}}p_{n,k}+p_{s}\sum\limits_{n=1}^{N}L\end{split}