# Sustainable Power Consumption for Variance-Based Integration Model in Cellular 6G-IoT System
## 3 System Model
### Model of Variance-Based Integration of 6G Cellular IoT  
In this section, a variance-based algorithm is proposed to realize an effective integration of ECC in 6G cellular IoT. Despite sharing the same RF carrier, the communication and computation signals have different performance metrics. Each IoT UE's communication signal should be isolated from the mixed signal at the BS for communication. Thus, the received quality of the communication signal, or SINR, should be high. The signals from various IoT UEs are combined at the BS for computation. Consequently, the calculated result ought to have a low MSE. In general, the integration of ECC is a multiple-objective optimization problem. Here, we formulate it as the minimization of MSE for computation while satisfying the SINR requirement of communication with the harvested energy. Figure 2 shows the system block illustration of signal uplink transmission, which is developed in the VIM6G-IoT model. As shown in Figure 2, each IoT UE first performs beamforming on the computation signals and the communication signals to be transmitted, respectively. In addition, the signals from IoT systems 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 a communication signal. Every IoT UE initially accomplishes BF on the communication signals and computation signals that will be transmitted. Then, in the baseband-processing system, the two types of signals are superimposed, and the signal is then coded and transmitted to BS over the uplink channel using the identical front end of RF. The BS first acquires the computation result directly through simultaneous data transfer, which is made feasible by air computation, and then makes use of a computation receiver to retrieve the desired function signal. The BS, on the other hand, uses communication receivers to decode each UE communication signal. The problem could be modeled as the following SDP issue as specified in Equation (4). In Equation (4), \(V_{q}\), \(W_{q,ij}\) and \(O\) refer to transmit beams, and \(\sigma_{n}^{2}\) refers to variance. For ease of study and with no generality losses, the communication signals and computation signals are assumed as Gaussian-distributed with the unit term \(E\Big{\{}S_{q}S_{q}^{C}\Big{\}}=I\). Moreover, \(Z\) refers to receive beams that are formulated in Equation (5). Here, LACO is deployed for resolving the optimization issues of finding optimal \((V,W,O)\) by fixing the fitness as shown in Equation (4). \((. )^{G}\) denotes conjugate transpose. Equation (4) shows the proposed variance integration including two forms--arithmetic means and geometric mean--thereby influencing the addition of all individual summations, and giving the central tendency of the series of observations. \[Obj=\underset{V_{q},W_{q,ij},O}{\text{\emph{min}}}\sum_{q=1}^{Q}Z^{G}G_{q}V_{ q}-I_{O}^{2}+\sqrt{\frac{Z^{G}G_{q}V_{q}-I^{2}-\overline{Z^{G}G_{q}V_{q}-I}}{Q-1}}+ \sqrt{\frac{Z^{G}G_{q}V_{q}-I^{2}-\overline{Z^{G}G_{q}V_{q}-I}}{Q-1}}+P_{T} \tag{4}\]  
\[Z=\left(\sigma_{n}^{2}I+\sum_{q=1}^{Q}G_{q}\Xi_{q}G_{q}^{G}\right)^{-1}\sum_{q =1}^{Q}G_{q}V_{q} \tag{5}\]  
\[\Xi_{q}=V_{q}V_{q}^{G}+\sum_{j=1}^{L}w_{q,ij}w_{q,j}^{G} \tag{6}\]  
\[W_{q,j}=w_{q,j}w_{q,j}^{G} \tag{7}\]  
A detailed methodology for integrating ECC with 6G cellular IoT has been developed in this research. A joint beamforming design algorithm was proposed from the perspective of minimizing the computation error while ensuring the Signal-to-Interference-plus-Noise-Ratio (SINR) requirements of communication signals in order to realize accurate computation and effective communication with the harvested energy at a large number  
Figure 2: System block illustration of signal uplink transmission for developed VIM6G-IoT model. of IoT UEs.