Sustainable Power Consumption for Variance-Based Integration Model in Cellular 6G-IoT System

Abstract

With the emergence of the 5G network, the count of analysis papers associated with the 6G Internet of Things (IoT) has rapidly increased due to the rising attention of researchers in next-generation technology, 6G networks and IoT techniques. Owing to this, grasping the overall research topics and directions is a complex task. To mutually address the significant issues of 6G cellular IoT, i.e., information transmission, data aggregation and power supply, we proposed a variance-based integrating model for the 6G-IoT approach that considers energy, communication and computation (ECC). Initially, the base station (BS) charges huge IoT devices concurrently utilizing WPT in the downlink. After that, IoT devices gather the energy to perform the communication task and the computation task in the uplink in a similar spectrum. Also, the model integrates the optimization of transmit beams via the Improved Ant Colony Optimization (IACO) model to balance the system performance, power consumption and computational complexity. Further, this study exploited activated Remote Radio Units (RRUs) to improve the network performance and energy efficiency in the downlink model. The simulation outcomes evaluate the performance of the proposed work over the conventional models concerning error analysis. From the results, the MSE value in the IACO work is much lower, around 0.011, while the compared schemes achieved comparatively higher MSE values.

1. Introduction

Recent advancements in smart device technology and wireless communication have encouraged the proliferation of IoT with ubiquitous computing and sensing abilities to connect millions of objects to the Internet [1,2,3]. The IoT is becoming a crucial component of the future Internet and is receiving a lot of interest from both academics and businesses owing to its enormous potential to provide consumer services in all facets of contemporary life [4,5,6]. Enterprise technology supported by 6G will change how businesses handle information, communicate, make decisions and train staff. This new technology will lead to fascinating and novel use cases, significant social changes, and new difficulties. Through fully automated and intelligent remote managing systems, the IoT facilitates easy interactions and automated management among heterogeneous devices without the need for human intervention. This has the power to transform industries and benefit society significantly [7,8,9]. Mobile applications from the first to the fifth generation have already been suggested and commercially implemented as an enabler for enabling IoT networks and apps [10,11,12]. However, 5G cannot fully fulfill the evolving technological requirements, such as independent, highly dynamic, ultra-wide scale and fully intellectual services, due to the unknown number of connected devices and the quick growth of IoT networks [13,14,15]. Additionally, while 5G networks have the ability to support a variety of IoE-based services, they are unable to fully satisfy the needs of emerging smart applications. To overcome the significant shortcomings in the current 5G networks, there is a growing demand for imagining the 6G wireless communication technologies. Additionally, the inclusion of AI in 6G will offer solutions for extremely difficult issues pertaining to network optimization. Additionally, researchers are looking into new technologies like THz and quantum communications to enhance the future 6G networks. The potential of 5G wireless systems is anticipated to be exceeded by the rapid rise of automatic IoT networks [16,17,18]. Additionally, new IoT applications and services like flying cars and remote robotic surgery require improvements to the present 5G systems to enhance the quality of IoT delivering services and business operations [19,20,21].

Research on 6G wireless networks and the associated technical advances has lately received significant attention from both academia and industry, helping the advancement of the IoT and beyond [22,23,24]. Because of its improved features over the prior network decades, like ultra-low latency communication, ultrahigh throughput, satellite-based client services and massive and automatic networks, 6G is anticipated to offer a completely new service quality and improve users’ experiences in current IoT systems [25,26,27]. In the areas of IoT data detection, device connectivity, wireless connectivity and 6G network, these levels of capability will be exceptional and will hasten the appliances and deployment of a 6G-oriented IoT network. Due to the enormous potential of 6G IoT, a lot of work has been put into this potential field of study [9] concerning clustering techniques [6] and optimization strategy [4] to enhance the overall network features, including coverage, capacity and mobility managing; however, the models need more improvisation towards the improvement of 6G networks as a major downlink traffic overload will result. The 6G networks are designed to improve performance by offering ultra-low latency (ms) and peak data speeds of roughly 1 Tbps [28,29]. Additionally, by using THz frequencies and spatial multiplexing, the 6G networks are designed to increase bandwidth by 1000 times over the 5G networks. Through the efficient implementation of underwater and satellite communication networks, the 6G networks would also offer worldwide coverage. Furthermore, the IoT device observes the subchannel in an opportunistic way while being allocated to one RRU. Assume that the centralized Baseband Unit (BU) receives signals from the IoT device and transmits them to the RRUs via a relay mechanism.

The Ubiquitous Mobile Ultra BroadBand (uMUB), Ultrahigh Speed with Low Latency Communications (uHSLLC), and Ultrahigh Data Density (uHDD) are three further innovative classifications for 6G networks [30,31]. The significant contributions that were reported in the literature have exploited the benefits of the 6G IoT. Few of the contributions have worked on enhancing the security features of the system, but the limitations still persist. The literature still lags with computational overhead and communication overhead, when the security layers such as anomaly detection are incorporated into the application system. The literature works follow a linear error model that often lags in precise data communication, and also the convex-optimization-assisted updating model does not consider the nonlinear environment when there is increased mobile users. To tackle these issues, the model needs to consider the variance of information. The enormous human cost and environmental burden make it unaffordable for huge IoT to change batteries frequently. Here, a few states of the models such as, for example, zero-forcing beamforming (ZFBF), uniform-forcing beamforming, Joint Beam forming Design Algorithm (JBDA), Artificial Neural Network (ANN) and K-nearest Neighbors (KNN) are employed in the literature and compared in the result analysis. As a result, using the wireless power transfer (WPT) technique to implement one-to-many charging by taking advantage of the wireless broadcast channel’s open nature is intriguing. Energy beamforming has been added to increase the effectiveness of WPT over fading channels. In reality, information transmission, data aggregation, and energy supply are all interconnected. They compete on the same wire with fewer resources for improving performance. With scarce wireless resources, performance must be enhanced overall. To improve the efficiency of the system, the proposed model is used. In this regard, this paper follows a model with the following research contributions:

• A variance-based integration scheme is proposed for a 6G-IoT system by considering constraints like energy, computation, consumption and communication, separately.
• Here, the base station (BS) simultaneously charges numerous large IoT devices via WPT in the downlink. Then, in the uplink, IoT devices gathered the energy to carry out the communication task and the processing task in a same spectrum. In order to balance system performance, power consumption and computational complexity, the model is then integrated using IACO.
• At last, the IACO algorithm deals with the subproblem for optimization of transmit beams. The two subproblems are assigning a user to a beam and resources to beams.

The paper is organized as follows: The studies in the literature are outlined in Section 2. The system model and the process of the proposed VIM6G IOT is described in Section 3. Section 4 presented an analysis of the results. Finally, the conclusion is given in Section 5.

2. Literature Review

The number of analytic papers related to the 6G IoT has significantly expanded since the advent of the 5G network as a result of academics’ growing interest in 6G networks and IoT. Therefore, this section presents a complete review of existing papers based on the 6G-IoT system.

2.1. Related Works

A framework combining ECC was created in 2020 by Qi et al. [1]. First, Wireless Power Transfer (WPT) in the downlink is used by the base station (BS) to simultaneously charge a large number of IoT devices. IoT devices use the energy they have captured to carry out processing and communiqué in uplink at a similar frequency. They proposed a hybrid BF design method for the BS and IoT to enhance the overall efficiency of Energy, Computation and Communication (ECC). At last, the results of the simulation confirmed the success of the suggested algorithm in 6G IoT. Energy, communication and computation models have been integrated into a framework, where the error model remains linear. The IoT applications are accommodated with nonlinear data and transmission rate and so a linear error model cannot determine the precise data-communication framework. To enhance precise data communication and the respective energy consumption, variance of information has to be incorporated into the model.

A process-oriented approach to developing communications and Mobile-Edge-Computing (MEC) networks in a time-division way was put forward by Liu et al. [2] in 2022. In this approach, a non-convex latency-reduction issue is developed and large-scale Channel State Information (CSI) is employed to differentiate the complicated propagation surroundings at a reasonable cost. The estimated problem is then given, and it can be divided into smaller problems. Then, sequentially, these problems are resolved. The simulation outcomes proved the suggested process-oriented scheme’s advantage over competing methods. The researchers adopted successive convex optimization to handle the latency issues in mobile-edge-computing environments. The successive convex optimization uses an updating model based on weighted error, which does not consider a nonlinear environment when the mobile users are increasing exponentially.

Nazar et al. [3] detected malicious activity on Software-Defined-Network (SDN) switches in 2021 that resulted in network disruption. The suggested method relies on signatures and can identify malfunctioning switches that discard and switch packets because of their malicious intent rather than a broken link. Every assault has a signature, and these attacks may be recognized by their distinct behaviors and predetermined signatures. The demonstration of anomaly detection and an assessment of the network’s performance were carried out. The experimental findings highlight the recognition method that can identify assaults, accomplish a high detection rate with a low FPR and outline potential future work, as well as the efficacy of the suggested work. Even though anomaly detection in 6G IoT has been effectively handled, communication and computation overheads are considered to a limited extent. The usage anomaly detection increases the communication-link establishments and computational burden, though it is unavoidable.

Based on the distribution efficiency of existing agricultural-goods logistics distribution methods, Li and Xiao [4] improved and optimized the logistics mode in 2021. Through the use of Genetic Algorithms (GAs) and MATLAB, the logistics cost and client satisfaction are evaluated and assessed under the logistics mode. GA computation shows that the logistics of agricultural goods with the best common distribution method have a big impact on things like oil consumption and damage costs. Similar to [3], the researchers adopted the 6G IoT for e-commerce applications for which vehicle routing was carried out with the aid of data-mining algorithms. This is because of the efficient communication-link establishments between the users. However, the genetic algorithm was adopted for selecting the user path, which requires advanced optimization algorithms to handle the large scale of users. Since the number of users is increasing, the usage of small-scale algorithms remains a bottleneck in handling the large solution space.

A unique hierarchical 6G-IoT system with UAVs in the air and Intelligent Reflecting Surfaces (IRSs) was created in 2021 by Qi et al. [5]. The system uses free-ride BackCom to convey data. IRS boosts the energy via beam forming, increasing BackCom’s range and effectiveness. Based on the results of our simulations, it is clear that our method outperforms conventional approaches in terms of overall system performance. The key focus of this research remains on the precise transmission and reception of data, while energy efficiency has also been considered. Since the adopted methodology is for UAV networks, link establishments and computational complexity play key roles. This necessitates joint performance consideration against the existing proposal.

Lyu and He (2021) [6] aimed to incorporate sophisticated technology in the field of drama. A data-mining clustering technique is used to assess theatre language using the IOT AI. Through the use of relevant data-mining techniques and their analysis, the traditional K-means algorithm and the enhanced K-means algorithm were compared. The texts were examined using the Latent Dirichlet Allocation (LDA) topic-clustering model. The findings imply that the enhanced algorithm was more trustworthy and effective in data processing and clustering, which demonstrates the enhancement of the enhanced K-means algorithm. Unlike [3,4], the usage of 6G IoT for drama language art worked on data-handling issues to reduce the computation overhead. However, energy and communication overheads have not been considered in the clustering model. Moreover, K-means clustering has a drawback in its dependency on initial centroids.

The relevant feedback technique was merged with the conventional image-data-mining technique depending upon the KNN algorithm and was then optimized by Ye and Su [7] in 2021. This would further enhance the conventional systems and increase the intellect of image-data-mining technology. For extracting image shape features, the negative-feedback K-Nearest-Neighbor (K-NN) method is the most accurate one. Thus, the best accuracy for image-feature extraction reached 99.3% when utilizing the improved KNN method. The usage of the KNN algorithm in connection with 6G IoT incurs computational complexity because the unknown input to KNN has to be processed with the knowledge library at every instant. Since the degree of unknown input increases with the number of users, the computing complexity shall increase further.

To examine the use of smart technology in the 6G-IoT communiqué environment, Xu [8] developed a human-behavior-identification technique for wearable devices in 2021. Data-mining technology is deployed to evaluate and process the IoT information, and trials are used to develop the classifier model. Second, an ANN is used to create a model for recognizing human behavior, and the BP technique was used to learn the parameters of the ANN to enhance behavior identification. The classifier and the ANN-based model for recognizing human behavior are then evaluated. The methodology established a robust application of 6G IoT under wearable technology, but the energy constraints, communication and computation overhead remain unaddressed. When wearable technology has become a limelight application of 6G IoT, the trade-off between energy, communication and computation overheads needs to be addressed extensively.

Libing Wu et al. [32] suggested an application-centric framework and built a finer-grained offloading scheme based on application partitioning. Here, we depicted application partitioning via directed acyclic graphs (DAGs) and used vehicles and MEC servers as offload nodes. In addition, the offloading scheme took the total execution time and throughput of the application as optimization goals. As bandwidth increases, the partitioning approach can transfer some subtasks to other devices for execution in order to reduce computational overhead. Thus, when communication bottlenecks occur, an increase in bandwidth can undoubtedly improve throughput performance. In order to achieve the shortest total execution time in the partitioning approach, most subtasks are allocated to local devices for execution. In this case, as the CCR value increases, this may result in an increase in the total execution time, while the throughput decreases.

Rui Zhang et al. [33] suggested the MPTO-MT algorithm to address the task-offloading problem at different periods. Specifically, the algorithm first determines whether the task can be offloaded in time at a certain period according to the number of candidates offloading nodes of the task in this period. Secondly, the algorithm selects the offloading node and the task-transmission method. In order to select the appropriate offloading node and transmission method, we introduce the service utility and propose three heuristics of selecting the offloading node. Finally, the algorithm updates the resource information of nodes at the next period based on the utilization and release of node resources at the period, and the service time of the nodes. In order to balance the overall service time and transmission costs, the MPTO-MT algorithm uses WiFi as the transmission method for some tasks. However, the MPTO-MT algorithm has a higher task-completion rate than the RtDS algorithm, which reflects that the MPTO-MT algorithm may have more tasks that are not completed in time.

Arash Heidari et al. [34] suggested the D2-QDPO3 method, a novel offloading method based on learning for IoT edge systems. The Markov Decision Process (MDP) and Deep Learning (DL) are used in this work to solve the dynamic online/offline IoT-edge offloading scenario. The D2-QDPO3 method employs the IoT object to develop an appropriate privacy-aware offloading strategy at a much quicker speed by utilizing the additional information about the EH process. With the use of edge computing, the D2-QDPO3 technique significantly improves high processing and is handled effectively compared to conventional online DL algorithms. One likely explanation is that the computing jobs becomes harder as the number of cells rises, which puts a greater burden on the controllers. Additionally, the agent wants to offload duties rather than carry them out locally to conserve energy. This increases D2-QDPO3’s operational time.

James Adu Ansere et al. [35] suggested a novel low-complexity joint resource algorithm named Joint Energy-Efficient Resource Allocation (JEERA) to maximize the energy efficiency of the radio sub-system. The main computational task was distributed into various subproblems, which were solved optimally by exploiting Lagrangian decomposition and the Kuhn–Munkres (KM) algorithm to enhance system performance and energy efficiency in dynamic large-scale IoT systems. The JEERA algorithm fully utilizes the available resource allocation at a sufficiently low threshold and therefore avoids multi-user interference. The JEERA algorithm achieves better energy-efficiency performance than the baseline algorithm. However, the complexity of the proposed JEERA algorithm used in the second and third iterations is efficiently evaluated and it was demonstrated that the proposed algorithm has polynomial complexity.

Roseline Oluwaseun Ogundokun et al. [36] suggested a novel Non-Orthogonal Multiple-Access-Enabled Mobile Edge Computing (NOMA-enabled MEC) in 6G Communications. We summarized the significant aspects and technologies used by the many publications featured in the survey and gave a comprehensive overview of NOMA-enabled MEC. It achieves superior spectral efficiency by serving multiple users simultaneously with the same frequency resource and mitigating interference through SIC. It increases the number of simultaneously served users, thus supporting massive connectivity. NOMA-based MEC technologies have a lot of benefits, yet they also have many shortcomings, such as short battery life, high energy consumption, unfair workload offloading and resource allocation, restrictive latency constraints and security issues.

Mohamed Amine Ouamri et al. [37] suggested a Multi-Agent Deep Q-Network (MADQN) to optimize the EE and throughput resource-allocation framework. Firstly, we introduce a nonlinear EH model for SWIPT to include the underlying harvest circuit. We then formulate EE and total throughput in a mmWave scenario while ensuring the minimum QoS requirements for all users according to the environment. Multiple constraints, such as path-loss model, UAV height, distance and minimum transmission rate are employed to describe our mathematical problem. The proposed MADQN algorithm converges to highly satisfactory results compared to the other approaches. This is because our algorithm handles interference perfectly. Our results also indicated that the EE is affected by the number of D2D pairs to be deployed in the coverage area, as well as the maximum altitude variation.

Daljeet Singh et al. [38] suggested a generalized approach to the performance analysis of relay-aided communication systems for 5G-and-beyond scenarios. We formulate an outage probability expression that is valid for all fading scenarios, irrespective of the nature or complexity of the fading PDF. The relationship between the outage performance and cumulative distribution function (CDF) of the signal-to-noise ratio (SNR) is exploited to derive the expression. We observed that increasing η from 0.5 to 1 while keeping other parameters constant improved the performance of the suggested system because as η approached 1, the fading approached the Rayleigh fading scenario. Additionally, the performance of the suggested system was also affected by changes in the fading parameter.

Daljeet Singh et al. [39] suggested an RF-wireless-power-transfer-enabled dual-hop relay system for generalized fading scenarios which are not limited to only a single family of fading distribution. A closed-form expression is derived for the outage probability of the decode and forward as well as amplify and forward systems valid for all fading scenarios. The current system has a lot of applications in scenarios where the relay and/or destination node has the availability of a proportion of the required energy and only desires some additional energy to be transferred using WPT. The optimum design parameters for the system are also calculated, which act as the upper limit for setting the design parameters while constructing a practical system.

2.2. Overall Analysis

Specifically, the signals from IoT devices serve two purposes: the first is data aggregation based on signals from several devices, and the second is information transmission based on signals from a single device. IoT devices should have adequate energy to concurrently realize precise computing and effective communication. Energy supply for a large IoT, however, is not an easy operation. The enormous human cost and environmental burden make it unaffordable for huge IoT to change batteries frequently. It is therefore enticing to use the WPT to achieve one-to-many charging by taking advantage of the wireless broadcast channel’s open nature. In actuality, information transmission, data aggregation and energy supply are all interrelated. The existing method involves more processing and offers less accurate localization. In those challenging circumstances, the wireless signal-based approaches might be less limited, which would improve sensing precision. By using variance-based integration, all of the aforementioned issues have been resolved. An energy, communication and computation (ECC)-based variance-based integrating model for the 6G-IoT method is suggested in order to increase overall performance with constrained wireless resources.

2.3. Research Gaps

The large-scale installation of small networks for the improvement of overall network features, including coverage, capacity and mobility management, is the main cause for concern for 6G networks since it will result in a major downlink traffic overload. Because of the reduced access time and traffic offloading provided by proactive caching, these restrictions will be circumvented, thereby improving user experience. Additionally, comprehensive research is needed to clarify the combined optimization of different aspects, together with proactive caching, interference management, smartly coded strategies and scheduling methods that are crucial for the 6G networks, to allow for the widespread implementation of the 6G networks. Because of its self-optimization and automation capabilities, 6G networks need improvement with the deployment of massive volumes of data, DL protocols and big-data analytics. Also, energy supply and communication, and data aggregation need to be considered in the near future [10].

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).

$$e_q=\frac{U}{2}{\vartheta }_q{‖G_q^{G}g‖}^2$$

(1)

In Equation (1), $G_q\in C^{M\times N}$ 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, ${\vartheta }_q$ refers to the efficiency of energy transfer and $g\in C^{M\times 1}$ refers to the energy beam broadcasted by the BS.

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 $d_q={\left[d_{q,1},\dots d_{q,R}\right]}^U$ and a vector for communication symbol $S{’}_q={\left[S{’}_{q,1},\dots S{’}_{q,L}\right]}^U$, in which $d_{q,r}$ and $S{’}_{q,L}$ 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).

$$k_r=g_r\left({\displaystyle \sum _{q=1}^Q{f}_{q,r}\left(d_{q,r}\right)}\right),\hspace{0.17em}\hspace{0.17em}r=1,2\dots R$$

(2)

In Equation (2), $k_r$ refers to perfect computation output, $f_{q,r}\left(.\right)$ and $g_r\left(.\right)$ 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 ($P_C$) from the activated RRUs. Accordingly, the total power consumption is

$$\begin{gathered} P_T=P_{FIX}+P_t+P_C \\ {P}_T=P_{FIX}+{\displaystyle \sum }_{n=1}^N{\displaystyle \sum }_{k=1}^K\frac{1}{{\eta }_e}{p}_{n,k}+p_s{\displaystyle \sum }_{n=1}^{N}L \end{gathered}$$

(3)

where $P_C=p_s{\displaystyle \sum _{n=1}^N}L$ refers the power consumption of the circuit; $p_s$ denotes the cost of power for serving the organized RRUs, $L$ symbolizes the large-scale organized RRUs; ${\eta }_e$ signifies the efficiency of power amplifier ${\eta }_e\in \left\{0,1\right\}$; $P_t={\displaystyle \sum _{n=1}^N}{\displaystyle \sum _{k=1}^K}\frac{1}{{\eta }_e}{p}_{n,k}$ refers to a transmission of power.

3.1. 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), $V_q$, $W_{q,j}$ 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 ${\rm E}\left\{S_q{S}_q^G\right\}=I$. Moreover, ${\rm Z}$ refers to receive beams that are formulated in Equation (5). Here, IACO is deployed for resolving the optimization issues of finding optimal $\left(V,W,O\right)$ by fixing the fitness as shown in Equation (4). ${\left(.\right)}^G$ 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.

$$Obj=\underset{V_q,W_{q,j},O}{min}{{\displaystyle \sum }}_{q=1}^Q{{\rm Z}}^G{G}_q{V}_q-I_O^2+\sqrt{\frac{{{\rm Z}}^G{G}_q{V}_q-I^2-\overline{{{\rm Z}}^G{G}_q{V}_q-I}}{Q-1}}+\sqrt{\frac{{{\rm Z}}^G{G}_q{V}_q-I^2-\overline{{{\rm Z}}^G{G}_q{V}_q-I}}{Q-1}}+P_T$$

(4)

$${\rm Z}={\left({\sigma }_n^{2}I+{\displaystyle \sum _{q=1}^Q{G}_q{\mathrm{\Xi }}_q{G}_q^G}\right)}^{-1}{\displaystyle \sum _{q=1}^Q{G}_q{V}_q}$$

(5)

$${\mathrm{\Xi }}_q=V_q{V}_q^G+{\displaystyle \sum _{j=1}^L{w}_{q,j}{w}_{q,j}^G}$$

(6)

$$W_{q,j}=w_{q,j}{w}_{q,j}^G$$

(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 of IoT UEs. It was discovered that the suggested method performed better than baseline approaches and was able to integrate ECC successfully.

3.2. Improved ACO for 6G-IoT Error Minimization

ACO has issues with delayed convergence and poor search performance while looking for the best path. To address this issue, punishment and reward coefficients are included in the Ant-Colony-Optimization (ACO) pheromone-update equation. An ant will instantly “reward” the current path in accordance with the punishment and reward coefficient when it discovers the best path while traveling. In other words, the pheromone is increased by the equivalent value, increasing the pheromone concentration along the path. The punishment and reward coefficient is used to “punish” the current path if it is longer than the previous path.

To reduce the pheromone concentration along the altered path, deduct the relevant pheromone value. The longest path and hence the worst solution is discovered during the whole search phase of the present ant through correlation. Punish it severely by deducting the greater value of the worst path pheromone in accordance with the punishment and reward coefficient. By doing this, the impact on the ants’ decision-making process is reduced. Employ ${\tau }_{ij}^{bf}\left(t\right)$ for the pheromone level prior to the update and employ ${\tau }_{ij}^{ud}\left(t+1\right)$ for the pheromone level following the update. The pheromone would be adjusted in accordance with Equation (8) throughout every searching process of an ant [40].

$${\tau }_{ij}^{ud}\left(t+1\right)=\left\{\begin{array}{l}{\tau }_{ij}^{bf}\left(t\right)+\frac{\omega \xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}\hspace{0.17em}\min imum\\ {\tau }_{ij}^{bf}\left(t\right)-\frac{\omega \xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}<J_{last}\\ {\tau }_{ij}^{bf}\left(t\right)-\frac{{\omega }^2\xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}\max imum\end{array}\right.$$

(8)

In Equation (7), $\omega$ refers to the adaptive reward coefficient, and is evaluated as $\omega =\frac{J_{last}}{J_{cr}}\times \frac{J^{\max }}{J_{cr}}\times \frac{J^{\min }}{J_{cr}}$ and $\xi$ refers to the load coefficient initiated by the model that is a predetermined constant. $J_{cr}$ refers to the entire length of the present path and $J_{last}$ refers to the entire length of the final path. If the optimal path takes place, $\frac{\omega \xi }{J_{cr}}$ is summed to the present pheromone level as a reward. If a comparatively poor path arises, the present pheromone level is deducted from $\frac{\omega \xi }{J_{cr}}$ as a penalty. If the worst path happens, the present pheromone level minus $\frac{{\omega }^2\xi }{J_{cr}}$ is considered as a harsh punishment. Additionally, the rational setting of the volatility coefficient $\rho$ would affect the searching capability and computation efficiency of the model with respect to discovering the optimal allocation plan. By varying the value of $\rho$ dynamically, the pheromone size could be adaptively adjusted. As a result, it could efficiently fortify the earlier searching capability of the scheme and improve the variety of solutions. And with the increase in the iteration count, the probability is improved, ensuring the overall performance of the scheme. The adjusting approach of $\rho$ is shown in Equation (9).

$$\rho \left(t\right)=\left\{\begin{array}{l}{\rho }_{\min },\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\rho }_b\left(t\right)<{\rho }_{\min }\hspace{0.17em}\hspace{0.17em}\\ {\rho }_b\left(t\right),\hspace{0.17em}\hspace{0.17em}{\rho }_{\min }\le {\rho }_b\left(t\right)\le {\rho }_{\max }\hspace{0.17em}\\ {\rho }_{\max },\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\rho }_b\left(t\right)\ge {\rho }_{\max }\hspace{0.17em}\end{array}\right.$$

(9)

$${\rho }_b\left(t\right)=1-\ln \left(t\right)/\ln \left(t+a\right)$$

(10)

In Equation (10), $a$ refers to a constant, and the dimension of $\rho$ is restricted to $\left[{\rho }_{\min },{\rho }_{\max }\hspace{0.17em}\right]$. This prevents the $\rho$ value from being too huge or too small, resulting in slow efficiency of solution or weak searching abilities, to ensure the overall algorithm performance [32].

The key challenges for the ACO algorithms are premature convergence and poor utilization. This research introduces an Improved Ant Colony Optimization (IACO) for addressing nonlinear problems by examining the peculiarities of the network topology. IACO uses a swarm of ants to seek for the promising path node by node along a single direction, and taboo lists are established at the crucial activity nodes. Therefore, IACO efficiently improves the convergence rate to balance the system performance, power consumption and computational complexity. The pseudo-code of the IACO algorithm is presented in Algorithm 1.

Algorithm 1: IACO Algorithm

Input: $\left(V,W,O\right)$

Output: $V^{*},W^{*},O^{*}$

Initializing algorithm constraints, count of ants $\mathrm{{\rm K}}$

While do

For each ant do

While do

Compute the probability according to ${\tau }_{ij}^{ud}\left(t+1\right)=\left\{\begin{array}{l}{\tau }_{ij}^{bf}\left(t\right)+\frac{\omega \xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}\hspace{0.17em}\min imum\\ {\tau }_{ij}^{bf}\left(t\right)-\frac{\omega \xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}<J_{last}\\ {\tau }_{ij}^{bf}\left(t\right)-\frac{{\omega }^2\xi }{J_{cr}},\hspace{0.17em}\hspace{0.17em}{J}_{cr}\max imum\end{array}\right.$

If the ant is moved to a new node, update its path pheromone and modify the tabu list

When the ant discovers a possible path, trace the total length of the path

End While

Evaluate the fitness using $P_T=P_{FIX}+{\displaystyle \sum _{n=1}^N}{\displaystyle \sum _{k=1}^K}\frac{1}{{\eta }_e}{p}_{n,k}+p_s{\displaystyle \sum _{n=1}^N}L$

Pheromone is updated using $W_{q,j}=w_{q,j}{w}_{q,j}^G$ with $\omega$, adaptive reward coefficient

Randomly choose the ant position again

End for

End While

For termination, set the maximum number of iterations (maxTimes) and total number of ant groups. In every iteration, the ant groups are simultaneously initialized, mapped and updated. Iterate repeatedly until the maximum iterations are reached to stop the algorithm. To balance system performance and computational complexity, the system incorporates transmit beam optimization using the Improved-Ant-Colony-Optimization (IACO) model. The results of the simulation comparing the performance of the proposed work to the traditional models in terms of error analysis are discussed in the following section.

4. Results and Discussion

The performance of the developed VIM6G-IoT model was computed and established against a fixed MMSE scheme whose receivers are only related to the channels, a zero-forcing beamforming (ZFBF) scheme whose transmitters are designed based on the zero-forcing principle and a uniform-forcing beamforming (UFBF) scheme. In particular, conventional IACO [32] is also compared.

The mathematical formulas of the undertaken performance measures, Mean Squared Error ($MSE$), Mean Absolute Error ($MAE$), Mean Absolute Log Error ($MALE$) and Mean Absolute Percentage Error ($MAPE$), are stated in Equations (11)–(14).

$MSE$: $MSE$ measures how much error is present in statistical models. Between the observed and projected values, it evaluates the average squared difference. The $MSE$ is equal to 0 when a model is error-free.

$$MS{E}_{\left(z^{\prime },z\right)}=\frac{1}{n}\sum _{i=1}^n\left(z_i^{’}-z_i\right)$$

(11)

$MAE$: The absolute inaccuracy of the measurement refers to the size of the discrepancy between each measurement and the quantity’s actual value.

$$MA{E}_{\left(z^{\prime },z\right)}=\frac{1}{n}\sum _{i=1}^n\left|z_i^{’}-z_i\right|$$

(12)

$MALE$: Instead of utilising “raw” or percentage mistakes to measure forecast errors, it uses the Log Error ($LE$). To do this, metrics based on the $LE$ must be used to measure model performance.

$$MALE=MEAN \left(\left|LE\right|\right)=\frac{1}{n}\sum _{i=1}^n\left|log\left(\frac{z_i}{{\widehat{z}}_i}\right)\right|$$

(13)

$MAPE$: This is a relative error metric that compares forecast accuracy of models while using relative errors to prevent positive and negative mistakes from cancelling one another out.

$$MAPE=\frac{1}{n}\sum _{i=1}^n\left|\frac{z_i-{\widehat{z}}_i}{z_i}\right|$$

(14)

where $n$ represents number of samples, $z_i^{\prime }$ refers to the predicted value and $z_i$ refers to the measured value.

4.1. Simulation Setup

The implemented VIM6G-IoT model using Improved Ant Colony Optimization (IACO) was executed in MATLAB 2021b, Version 9.11 on a computer running 64-bit Windows 11 and equipped with an Intel Core i7-4702MQ 2.20 GHz processor and 16 GB of RAM. The simulation constraints of the developed VIM6G-IoT model are shown in

Table 1. Simulation Constraints.

Constraints	Values
Number of BS antennas	$N$ = 32, 34, 40, −50, −40, −30, −20, 64, 66 and 80
IoT UEs	$Q$ = 32; $N$ = 2; $R$ = 1; $L$ = 1
Energy-conversion efficiency	${\vartheta }_q$ = ${\vartheta }_0$ = 0.5
Cell radius	$Ra$ = 500 m
Minimal needed SINR threshold	0.1 dB
Noise power	${\sigma }_n^2$ = −50 dBm

.

Table 2. Key settings and parameters for baseline models.

Constraints	Values
Learning rate	0.2
Batch size	90
Maximum iterations	150
Evaporation rate	0.05
Population size	100

provides the key settings and parameters present in the baseline models.

4.2. Error Analysis

The error metrics such as Mean Squared Error (MSE), Mean Absolute Error (MAE), MALE and Mean Absolute Percentage Error (MAPE) are considered for computing the error of the developed VIM6G-IoT model. “The MSE or Mean Squared Deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors, that is, the average squared difference between the estimated values and the actual value. MAE is simply, as the name suggests, the mean of the absolute errors. The absolute error is the absolute value of the difference between the forecasted value and the actual value. MAE tells us how big of an error we can expect from the forecast on average. The MAPE is the sum of the individual absolute forecast errors, divided by the actual values for each period. It is an accuracy measure based on the relative percentage of errors. The closer the MAPE value is to zero, the better the predictions”. The MSE of IACO work is 0.011, while ZFBF, Fixed Minimum MSE (MMSE), Uniform-Forcing Beam forming (UFBF), Joint Beam forming Design Algorithm (JBDA), ACO and IACO-C obtained relatively high errors of 0.021, 0.028, 0.015, 0.012, 0.023 and 0.052. The MAE of IACO work is 0.086, while ZFBF, Fixed MMSE, UFBF, JBDA, ACO, ANN, KNN and IACO-C obtained relatively high errors of 0.091, 0.093, 0.093, 0.090, 0.084, 0.079, 0.076 and 0.074. This lower error attainment is due to the proposed variance-based integration scheme for the 6G-IoT system. Here, ECC evaluation is done with the proposed variance-based integration with arithmetic-mean and geometric-mean specifications. Moreover, the proposed IACO algorithm deals with the sub-problem for optimization of transmit beams that also ensure the attainment of minimal MSE. The MAPE of IACO work is 0.249, while ZFBF, Fixed MMSE, UFBF, JBDA, ACO, ANN, KNN and IACO-C obtained relatively high errors of 0.346, 0.287, 0.301, 0.354, 0.412, 0.0058, 0.0054 and 0.321. For all errors (MSE, MAE, MALE and MAPE), the adopted IACO model for VIM6G IoT acquired fewer error values over the extant ZFBF, Fixed MMSE, UFBF, JBDA, ACO, ANN, KNN and IACO-C models. 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. Hence, 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. Thus, the computation’s output ought to have a low MSE. The error analysis using the proposed IACO with other models for VIM6G IoT is tabulated in

Table 3. Error analysis using IACO over other models for VIM6G IoT.

	ZFBF	Fixed MMSE	UFBF	JBDA	ACO	IACO-C	IACO	ANN	KNN
MSE	0.021	0.028	0.015	0.012	0.023	0.052	0.011	0.037	0.044
MAE	0.091	0.093	0.093	0.090	0.084	0.074	0.086	0.079	0.076
MALE	0.009	0.005	0.006	0.006	0.006	0.005	0.005	0.005	0.005
MAPE	0.346	0.287	0.301	0.354	0.412	0.321	0.249	0.366	0.343
Throughput (Kbps)	10.236	9.625	9.124	9.351	12.301	12.945	13.601	9.358	9.847
Latency (s)	23.1	22.3	23.9	21.9	13.7	13.4	12.7	20.3	20.6

. Further, Table 3 provides the information about the throughput and latency analysis for various models.

4.3. Analysis of Varying BS Antenna Count

The analysis of varying BS antenna counts for varied values for VIM6G IoT such as 32, 34, 40, −50, −40, −30, −20, 64, 66 and 80 are discussed in this section. The NCE is analyzed for a varied range of SNRs such as 0.0, 2.5, 5.0, 7.5, 10.0, 12.5, 15.0 and 17.5. The analysis of varying BS antenna counts for varied values such as 32, 34 and 40 is shown in Figure 3. The analysis of varying BS antenna counts for varied values such as −50, −40, −30 and −20 is shown in Figure 4. The analysis on varying BS antenna counts for varied values such as 64, 66 and 80 is shown in Figure 5. For N = 32, when SNR = 17.5, the NCE of IACO work is less than 0.000, while NCE of ZFBF is 0.110, NCE of Fixed MMSE is 0.050, NCE of UFBF is 0.060 and NCE of JBDA is 0.055. These outcomes are similar to SNR = 2.5, 5.0, 7.5, 10.0, 12.5, 15.0 and 17.5. At initial values of SNR, the NCE is high for ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C as well as IACO. Gradually, the NCE drops down and when SNR = 2.5, the values came to a stable range until SNR = 17.5. When N = 40, the NCE of ZFBF is higher over Fixed MMSE, UFBF, JBDA, ACO and IACO-C. The JBDA model has a higher NCE next to ZFBF. Fixed MMSE has a higher NCE than UFBF and IACO. For N = −50, when SNR = 15.0, the NCE of IACO work is 0.055, while the NCE of ZFBF is 0.180, the NCE of Fixed MMSE is 0.120, the NCE of UFBF is 0.110 and the NCE of JBDA is 0.070. These outcomes are similar to SNR = 2.5, 5.0, 7.5, 10.0, 12.5, 15.0 and 17.5. At initial values of SNR, the NCE is high for ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C as well as IACO works. Gradually, the NCE drops down and when SNR = 2.5, the values come to a stable range until SNR = 17.5. Likewise, for N = 80, the NCE of ZFBF is 0.07, the NCE of Fixed MMSE is 0.05, the NCE of UFBF is 0.045 and the NCE of JBDA is 0.055. Thus, for all varying counts of BS, the NCE of IACO is less than ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C. Given that more power is utilized to improve the communication signal quality and less power is used for lower computation distortion, it can be seen that the normalized computation error increases when the minimum SINR is increases. Moreover, when the number of BS antennas rises, the computation error lowers. This is so that the overall performance can be enhanced by obtaining greater array gains. This lower NCE is owing to the adopted variance-based integration model. Here, ECC evaluation is carried out with the proposed variance-based integration with arithmetic-mean and geometric-mean specifications. Moreover, the proposed IACO algorithm deals with the sub-problem for optimization of transmit beams that also ensure the attainment of minimal MSE.

4.4. Analysis of Power Consumption

Figure 6 demonstrates the average power consumption set in contradiction of $P_{max}$ in assessing 20 IoT devices at 10 iterations for ZFBF, Fixed MMSE, UFBF, JBDA, ANN, KNN, ACO, IACO-C and IACO. In $P_{max}\le 30$ dBm, it detected that IACO needs extra power at $L\le 35$ compared to existing methods, since it requires additional activated RRUs to confirm the provided data rate. The IACO method steadily rises to persistent power consumption whenever the $P_{max}$ expands.

Once extra RRUs are installed, power consumption starts to rise that subsequently decreases the energy efficiency of the network. Therefore, the proposed IACO activates lesser RRUs to confirm QoS requirements with minimized power consumption. $L$ executes equally with proposed IACO, which needs additional power to manage larger complex optimization issues. At the end, energizing additional RRUs for the IACO not only enhances the transmit power considerably but also increases energy efficiency. Figure 6 clearly shows that the proposed IACO accomplishes better results in energy-efficiency optimization when compared with existing methods.

4.5. Convergence Analysis

The convergence analysis is presented in Figure 7. The graph is plotted for the iteration-vs-cost function. The iteration value ranges among 0 to 25. The proposed model exhibits the minimum value for ACO and IACO-C. Thus, the superiority of the proposed model is proved over other existing models.

Figure 7 clearly shows that convergence analysis of proposed IACO is much better when compared to existing models. This study presented a variance-based integrating model for the 6G-IoT approach that takes Energy, Communication and Computation (ECC) into account in order to jointly handle the important concerns of 6G cellular IoT, namely information transfer, data aggregation and energy supply. In the beginning, the base station (BS) simultaneously charges numerous large IoT devices using WPT in the downlink. Then, using the energy that was collected, IoT devices carried out communication and computation tasks in the uplink in a similar spectrum. To balance system performance and computational complexity, the model also incorporates transmit-beam optimization using the Improved-Ant-Colony-Optimization (IACO) model. The results of the simulation compare the performance of the suggested work to the traditional models in terms of error analysis. The MSE of the IACO task was 0.011 according to the analysis, whereas ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C achieved comparatively high errors of 0.021, 0.028, 0.015 and 0.012. Although ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C generated comparatively large errors of 0.091, 0.093, 0.093 and 0.090, the MAE of the IACO task was 0.086. Here in this research, the complexity analysis is computed in terms of time. The required time for completing the entire simulation is up to 3 min (nearly 180 s). The analysis clearly shows IACO performs with better stability; however, when working with an extensive amount of data, it has some issues with convergence speed and accuracy.

4.6. Comparative Analysis

Here in this section, the proposed IACO is evaluated with existing methods such as D2-QDPO3 [34] and JEERA [35].

Table 4. Comparative Analysis.

Performance	D2-QDPO3 [34]	JEERA [35]	Proposed IACO
EE (Mbit/Joule)	11.2	4.8	14.3
Throughput (Kbps/Hz/J)	-	10	13.6
Latency (s)	19.1	-	12.7
Power Consumption (dBm)	-	48	34
Average Response Time (ms)	-	147	98

shows an analysis of proposed and existing methods in terms of Energy Efficiency (EE), Throughput, Latency, Power Consumption and Average Response Time.

Table 4 clearly shows that the proposed IACO outperforms the existing methods by achieving better results in EE (14.3 Mbit/Joule), Throughput (13.6 Kbps/Hz/J), Latency (12.7 s), Power Consumption (34 dBm) and Average Response Time (98 ms). The existing D2-QDPO3 [34] obtained the results of EE of 11.2 Mbit/Joule and Latency of 19.1 s. The existing JEERA [35] obtained the results of EE of 4.8 Mbit/Joule, Throughput of 10 Kbps/Hz/J, Power Consumption of 48 dBm and Average Response Time of 147 ms.

5. Conclusions

This study introduced a variance-based integrating model for the 6G-IoT approach that considered ECC. Initially, the BS charged huge IoT devices concurrently utilizing WPT in the downlink. After that, IoT devices with the gathered energy performed the communication task and the computation task in the uplink in a similar spectrum. To develop the overall ECC performance, a JBDA model was proposed for IoT devices and BS. From the results, for N = 32, when SNR = 17.5, the NCE of IACO work was less than 0.000, while the NCE of ZFBF was 0.110, the NCE of Fixed MMSE was 0.050, the NCE of UFBF was 0.060 and the NCE of JBDA was 0.055. Gradually, the NCE dropped down and when SNR = 2.5, the values came to a stable range until SNR = 17.5. The MSE of IACO work was 0.011, while ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C obtained relatively high errors of 0.021, 0.028, 0.015 and 0.012. The MAE of IACO work was 0.086, while ZFBF, Fixed MMSE, UFBF, JBDA, ACO and IACO-C obtained relatively high errors of 0.091, 0.093, 0.093 and 0.090. The numerical findings demonstrate that the proposed IACO optimizes energy efficiency and reduces the power consumption by deploying only a subset of the activated RRUs in the integrated IoT models to enhance the energy efficiency. In the future, this research will be further extended by analyzing other optimization algorithms to consider the accuracy and other convergence factors.