Intelligent Network Solution for Improved Efficiency in 6G-Enabled Expanded IoT Network

Abstract

The fast-moving world relies on intelligent connected networks to support the numerous applications of the expanded Internet-of-Things (IoT). The evolving communication requirements of this connected world require a new sixth generation (6G) radio to enable intelligent interaction with the massive number of connected objects. The energy management of billions of connected devices supporting massive Internet-of-Things (IoT) applications is the main challenge. These IoT devices and connected nodes are energy limited, and hence, energy-aware solutions are needed to enable seamless information flow between these communicating nodes. This paper presents an intelligent network solution for improved energy efficiency in a 6G-enabled expanded IoT network. A cell-free massive multiple input multiple output (mMIMO) technology is utilized for maximum energy efficiency with optimum network resource allocation. A practical power consumption model is proposed for the designed network topology which contains all the power components related to data transmission and circuit power. The proposed scheme aims to achieve maximum energy efficiency by the optimal allocation of pilot reuse factor and access point (AP) density for a given number of antennas at each AP and number of users. It is observed that the maximum energy efficiency of 5.2362 Mbit/Joule is achieved at the AP density of 29 and pilot reuse factor of 4 with PMMSE receive combining. In the end, the role of energy efficiency and area throughput tradeoff on the system performance is also evaluated, which suggests that both the energy efficiency and area throughput can be jointly increased until maximum energy efficiency is reached at a point.

1. Introduction

1.1. Need and Motivation

The explosive surge in the number of connected devices, sensor nodes, IoT devices and the huge volumes of generated data traffic has revolutionalized the wireless communication technology. To provide support to the ever-growing data demands of these IoT networks, wireless communication systems are advancing at a rapid pace. High communication capacity, network reliability, reduced latency and reduced network congestion are needed by these massive IoT networks to enable various IoT applications including smart transportation, smart healthcare, smart agriculture, smart industry and smart cities [1,2]. The fifth generation (5G) networks whose deployment is under way aim to provide gigahertz connectivity to the users. However, the need for higher frequency, high data rates, and reduced latency to realize the applications of holographic communication, telemedicine and self-driving cars has shifted the research focus toward 6G [3,4]. There will be a revolution in the IoT devices and services in the road to 6G. It is expected that the number of connected devices will reach 50 billion by the year 2030 [5]. The huge data demands of these proliferating connected devices in the massive IoT networks will lead to a huge energy crisis. The battery-operated devices will soon run out of energy to meet the data-sharing demands of future massive IoT networks. Thus, there is a need to look for energy-efficient designs for 6G massive IoT networks to be implemented in an intelligent way so as to enhance the system performance [6,7,8].

1.2. Promising Technologies

The 6G-enabled massive IoT networks aim for higher data rates but with reduced power consumption. Achieving higher data rates with minimum energy consumption is a challenging task. A promising solution to achieve high data rates is the network densification that exploits spatial reuse to enable mobile throughput growth [9]. The network performance is degraded by reducing the network density below a threshold [10]. Another key technology used in 5G communication networks for achieving 10 times higher rates than conventional systems is the massive multiple input multiple output (mMIMO) [11]. Tens of hundreds of antenna elements are deployed at the base station to serve the user nodes. This system is limited by the increased power consumption of the radio frequency (RF) chains associated with the antennas [12,13]. A promising alternative is to deploy a large number of access points in a given coverage area to serve a large user base.The transmission of signals coherently through multiple APs led to increased received power with the same transmit power [14]. This approach is known as a cell-free approach, as there are no autonomous cells which are capable of resolving the interference issues of the conventional systems. This is similar to operating the antennas distributed over a given area in a network MIMO manner [15,16]. In the 6G IoT networks, the cell-free mMIMO has gained popularity, as the joint coherent transmission and reception through distributed APs result in a higher signal-to-noise ratio (SNR). It is possible to obtain better data rates through the user-centric approach of cell-free mMIMO in which a group of users are served by APs in contrast to serving all the users [17,18]. Another approach is the network-centric approach, where the network is divided into clusters with a few APs in each cluster [19].

1.3. Related Work

The cell-free systems can combine the benefits of low overlead, improved path loss and enhanced diversity [20]. The performance of cell-free mMIMO systems for these properties is evaluated for single antenna systems in [21] and multiple antenna systems in [22,23,24]. The average spectral efficiency achieved by $95\%$ of the users in the cell-free system increases by five times as compared to conventional cellular systems [25]. This can be increased further by having multiple antennas at each user and AP. The literature contains papers that evaluate the signal processing in cell-free networks. The use of modified conjugate beamforming eliminates the self-interference in cell-free networks [26]. The role of pilot assignment and different receive combining schemes on network performance are highlighted in [27,28]. The dynamic clustering based on cooperating APs is exploited in cell-free networks with channel estimation [29] and precoding [30]. The coverage probability is evaluated in [31], considering poisson point process (PPP) distribution for AP locations. The comparison of different receivers—namely, large scale fading decoding (LSFD) receivers and a matched filter reciever—is carried out in [32] for a cell-free network.

Concerning the high energy consumption of 6G massive IoT networks, there are many works that studied the energy efficiency (EE) of massive MIMO systems [33,34,35]. The EE of uplink cellular mMIMO system is evaluated in [33] with distributed base stations (BSs), while [35] considers a multi-slope model for the same network topology. As compared to a cellular mMIMO system, the energy efficiency in a cell-free mMIMO system can be improved by ten times [36,37]. The concept of energy harvesting is utilized in [38] for 6G Internet-of-Everything (IoE) networks where the cell-free approach offers energy self sustainability. Ref. [39] aims to achieve maximum energy efficiency in a large-scale cell-free system utilizing an iterative approach. The proposed approach has reduced computational complexity and run time. Ref. [40] uses a transmit power control algorithm for energy efficiency maximization based on the location and configuration of APs and UEs. The number of APs and UEs along with the propagation channels between them are also considered in the proposed framework. Ref. [41] uses the approach of uniform quantization to obtain improved performance in a cell-free massive MIMO system. The optimum spectral and energy efficiency can be obtained by exploiting the step size of the quantizer. Ref. [42] reduces the power consumption in the downlink of a cell-free network to achieve optimum energy efficiency through efficient load balancing. Ref. [43] utilizes a user-centric cell-free apprach for EE optimization at millimeter-wave frequencies. The use of optimum power allocation schemes for the improved performance of cell-free mMIMO systems is explained in [44]. Aiming for reduced computation time and enhanced performance, [45] proposes two power allocation algorithms for a cell-free mMIMO system. The power consumption is reduced in [42] by allocating optimal transmit powers to the active APs based on the traffic load. Ref. [46] investigates the performance of the cell-free mMIMO system taking into account imperfect channel state information (CSI) and fronthaul quantization. Ref. [47] offers an AI-based solution for the problem of offloading policy and network resource allocation in a 6G-enabled massive IoT network. Refs. [48,49] considers the downlink of a cell-free mMIMO system and aims to achieve maximum average spectral efficiency and energy efficiency based on stochastic geometry.

In this paper, an energy-efficient design for a 6G-enabled massive IoT network is proposed based on the cell-free approach. The massive number of connected devices is supported by the APs distributed in the coverage area. The proposed network design is evaluated for average spectral efficiency, area throughput, total power consumed and energy efficiency.

1.4. Contributions and Outcomes

The huge volumes of data traffic generated from the massive number of connected IoT devices have put a huge burden on the communication capabilities of massive IoT networks. With the increase in communication capacity, the energy requirements also increases. The 6G massive IoT networks suffer from the main challenge of energy crisis owing to the battery-powered IoT devices. To overcome this challenge, this paper proposes an energy-efficient design for a massive IoT network with reduced power consumption. The novel contributions of the paper are as follows:

• An energy-aware network design is proposed based on a cell-free approach where a large number of connected devices are served by a large number of APs deployed in a given coverage area.
• A power consumption model for the proposed network strategy is defined, and all the power components related to data transmission, circuitry associated with the front-end RF transceiver chains, signal processing, site-cooling and backhaul are computed for the considered design model.
• Using the proposed power consumption model, the energy efficiency analysis is carried out for different receive combining schemes and the dependency on various other parameters such as pilot reuse ratio and AP density is elaborated.
• The proposed system is also evaluated for average spectral efficiency, area throughput and total power consumed.
• In the end, the impact of tradeoff between energy efficiency and area throughput on the system performance is evaluated.

Table 1. Summary of Notations.

Notation	Description
K	Number of users
N	Number of APs
M	Number of antennas at each AP
B	System bandwidth
$\alpha$	Path loss exponent
$T_c$	Length of coherence block
$B_c$	Coherence bandwidth
${\tau }_c$	Number of samples in a coherence block
${\tau }_{tr}$	Length of training signals
${\tau }_{ul}$	Length of uplink payload data
${\tau }_{dl}$	Length of downlink payload data
$\xi$	Uplink payload fraction
$\psi$	A set of ${\tau }_{tr}$ pilot sequences
f	Pilot reuse factor
${\widehat{s}}_k$	Signal estimates in the uplink
$n_n^{tr}$	Additive white Gaussian noise
$d_{kn}$	Distance between user node k and AP n
$h_{kn}$	Channel vector between user node k and AP n
${\widehat{h}}_{kn}$	Estimates of channel vector between user node k and AP n
$\lambda$	Access points density
${\rho }_{tr}$	Average pilot transmit power
${\rho }_k$	Average data transmit power of uesr k
$R_{kn}$	Spatial correlation matrix
${\varphi }_{tn}$	Correlation matrix of the received signal
$C_{kn}$	Error correlation matrix
$v_k$	Receive combiner vector
$v_k^{MR}$	Maximal ratio receive combiner vector
$v_k^{PMMSE}$	PMMSE receive combiner vector
$v_k^{PRZF}$	Partial zero-forcing receive combiner vector

lists the summary of notations used throughout the paper.

2. System Model

Consider a network model where a large number of access points (APs) are deployed in a given coverage area with no cell boundaries. A large number of user nodes are uniformly distributed in the network. User nodes are randomly selected from the large user base to be served by the APs. A deployment scenario of a cell-free mMIMO empowered 6G network is shown in Figure 1, demonstrating the respective use cases. To accomplish the vision of a connected world, a large number of access points are serving the large number of users to support application areas such as smart schools, smart vehicles, smart factories and smart cities. Suppose there are N APs and K number of users. The APs are equipped with M antennas, while all the users are single-antenna users. It is assumed that the APs are distributed in a given coverage area of size S in (km²) according to the homogenous poisson point process (H-PPP). The number of APs per square kilometer of the coverage area is a poisson random variable with mean $E\left[N\right]=\lambda .S$ where $\lambda$ is the AP density. The APs are connected to the central processing unit (CPU) via a perfect fronthaul network. The channel between the kth user and nth AP denoted by $h_{kn}$ is given as

$$h_{kn}={\beta }_{kn}^{1/2}{g}_{kn},n=1,2\cdots N,k=1,2\cdots \cdots K$$

(1)

where ${\beta }_{kn}$ and $g_{kn}$ are the path loss and small-scale fading coefficients between the kth user and nth AP. The path loss is described as ${\beta }_{kn}=min(1,d_{kn}^{\alpha })$ with a value of path loss exponent $\alpha$ greater than zero, and $d_{kn}$ represents the distance between the kth user and nth AP. The distances $d_{kn}$ are independent and follow uniform distribution. The proposed system model considers correlated Rayleigh fading channel $h_{kn}$ between user k and AP n and is given as

$$h_{kn}\sim \mathcal{N}\left(0_{M,}{R}_{kn}\right),$$

(2)

$R_{kn}$ is the spatial correlation matrix between user k and AP n with the collective matrix given by $R_k=diag\left(R_{k1},\cdots \cdots R_{kN}\right)$. This paper considers a block fading model in which a time-varying channel is divided into coherence blocks. The channel remains independent and frequency flat in each coherence block of duration of $T_c$ s, bandwidth $B_c$ Hz and number of samples ${\tau }_c=B_c{T}_c$. Time division duplex (TDD) protocol is employed with an uplink training phase of ${\tau }_{tr}$ samples, uplink data phase of ${\tau }_{ul}$ samples and downlink data phase of ${\tau }_{dl}$ samples. It is assumed that the pilots are randomly allocated to the user nodes. Thus, ${\tau }_c={\tau }_{tr}+{\tau }_{ul}+{\tau }_{dl}$ where ${\tau }_{tr}=K/f$ with $f\ge 1$ being the pilot reuse factor and ${\tau }_{ul}=\xi ({\tau }_c-{\tau }_{tr})$ with $\xi \le 1$ being the fraction of uplink payload transmission.

2.1. Uplink Training Phase

In this phase, known training signals are transmitted from all the users to all the APs. To ensure that the pilot transmission of one user does not interfere with the pilot transmissions of other users, a set of ${\tau }_{tr}$ pilot sequences are used, which are mutually orthogonal. Let $\psi =\left\{{\psi }_1,{\psi }_2\cdots {\psi }_{{\tau }_{tr}}\right\}$ denote a set of ${\tau }_{tr}$ pilot sequences such that ${∥{\psi }_k∥}^2={\tau }_{tr}$ for $k\in 1,2,\cdots \cdots {\tau }_{tr}$. The pilot signals transmitted by all the users are received by the $n^{th}$ AP and are given by $y_n^{tr}\in {\mathbb{C}}^{M\times {\tau }_{tr}}$

$$y_n^{tr}=\sum _{k=1}^K\sqrt{{\tau }_{tr}{\rho }_{tr}}{h}_{kn}{\psi }_k^H+{\mathbf{n}}_n^{tr}$$

(3)

where ${\mathbf{n}}_n^{tr}\in {\mathbf{C}}^{M\times {\tau }_{tr}}$ is the additive white gaussian noise with $\mathcal{N}\left(0,{\sigma }^{2I_M}\right)$ and ${\rho }_{tr}$ is the average pilot transmit power. The channel between user k and AP n is estimated using the minimum mean square error (MMSE) estimation method as

$${\widehat{h}}_{kn}=\sqrt{{\rho }_k{\tau }_{tr}}{R}_{kn}{\left(\sum _{k=1}^K{\rho }_{tr}{\tau }_{tr}{R}_{kn}+{\sigma }^2{I}_M\right)}^{-1}{y}_n^{tr}$$

(4)

Here, ${\rho }_k$ is the average data transmit power of user k, the correlation matrix of received signal is ${\varphi }_n^{tr}=E\left\{y_n^{tr}{\left(y_n^{tr}\right)}^H\right\}={\sum }_{k=1}^K{\rho }_k{\tau }_{tr}{R}_{kn}+{\sigma }^{2I_M}$, ${\tilde{h}}_{kn}=h_{kn}-{\widehat{h}}_{kn}$ and $C_{kn}=E\left\{{\tilde{h}}_{kn}{{\tilde{h}}_{kn}}^H\right\}=R_{kn}-{\rho }_k{\tau }_{tr}{R}_{kn}{{\varphi }_n^{tr}}^{-1}{R}_{kn}$ is the error correlation matrix.

2.2. Uplink Payload Data Transmission

After the acquisition of channel state information from the uplink pilots, the users transmit the data signals to the APs in this phase. The data signals received by the APs are used to compute the signal estimates by applying receive combining schemes. Suppose $v_{kn}{G}_{kn}$ defines the effective receive combining vector and $y_n\in {\mathbb{C}}^{MN}$ represents the signal received at the $n^{th}$ AP; then, the signal estimates can be obtained as

$${\widehat{s}}_{kn}=v_{kn}^H{G}_{kn}{y}_n$$

(5)

where $G_k=diag\left(G_{k1},\cdots \cdots G_{kN}\right)$ and $v_k={\left[v_{k1}^T,\cdots \cdots v_{kN}^T\right]}^T\in {\mathbb{C}}^{MN}$.

Depending upon the available CSI at the AP, different receive combiners can be used for obtaining the signal estimates.

Maximal-ratio combining (MR)

$$v_k^{MR}=G_k{\widehat{h}}_k$$

(6)

Partial minimum mean square error combining (PMMSE)

$$v_k^{PMMSE}={\rho }_k{\left(\sum _{i=1}^N{\rho }_i{G}_k{\widehat{h}}_i{\widehat{h}}_i^H{G}_k+Z_i+{\sigma }^2{I}_{NM}\right)}^{-1}{G}_k{\widehat{h}}_k$$

(7)

with $Z_i={\sum }_{i=1}^N{\rho }_i{G}_k{C}_i{G}_k$ being the combined spatial correlation matrix and $C_i$ being the error correlation matrix of the channel ${\widehat{h}}_i$.

Partial regularized zero forcing combining (PRZF)

$$v_k^{PRZF}={\rho }_k{\left(\sum _{i=1}^N{\rho }_i{G}_k{\widehat{h}}_i{\widehat{h}}_i^H{G}_k+{\sigma }^2{I}_{NM}\right)}^{-1}{G}_k{\widehat{h}}_k$$

(8)

The average spectral efficiency can be obtained using the signal-to-interference-plus-noise ratio as follows

$${SINR}_k=\frac{{\rho }_k{\left|v_k^H{G}_k{\widehat{h}}_k\right|}^2}{{\sum }_{i=1,i\ne k}^K{\rho }_i{\left|v_k^H{G}_k{\widehat{h}}_k\right|}^2+v_k^H{G}_k{v}_k+{\sigma }^2{∥G_k{v}_k∥}^2}$$

(9)

and

$${SE}_k=\frac{{\tau }_{ul}}{{\tau }_c}{log}_2\left(1+{SINR}_k\right)$$

(10)

The area spectral efficiency (ASE) defined in bits/s/Hz/km² is given by

$$ASE=K^{{}^{\prime }}·SE$$

(11)

with $K^{\prime }$ being the number of users per area.

3. Power Consumption Model and Energy Efficiency Analysis

A power consumption model is proposed in this section to carry out the energy-efficiency analysis of the proposed network design. The area spectral efficiency calculated in the previous section is utilized to evaluate the area throughput of the system, which also depends on network bandwidth B. It defines the number of bits of information transmitted per second per square kilometer, which is the product of bandwidth and area spectral efficiency. The energy efficiency of the system is another important parameter that defines the system performance. It is defined as the number of bits of information transmitted reliably per unit of energy.

$$EE=\frac{B\left(Hz\right).ASE(bit/s/Hz/k{m}^2)}{AreaPowerConsumption(W/k{m}^2)}$$

(12)

$$EE=\frac{AreaThroughput(bit/s/k{m}^2)}{AreaPowerConsumption(W/k{m}^2)}$$

(13)

Power Consumption Model

For the considered system model, the power consumption model is proposed here which takes into account both the transmission power and the circuit power associated with the circuit components of the model. The area power consumption is expressed as

$$APC=\lambda \left({\epsilon }^{-1}{P}_{tx}+P_{cir}\right)$$

(14)

$P_{tx}$ is the transmit power consumption which contains power usage for uplink pilot transmission and data payload transmission [48].

$$P_{tx}=K\frac{K/f{\rho }_{tr}+{\tau }_{ul}{\rho }_{ul}}{{\tau }_c}$$

(15)

In each coherence block, each user transmits pilot signals for the fraction $\frac{{\tau }_{tr}}{{\tau }_c}$ with power ${\rho }_{tr}$ and data signals for the fraction $\frac{{\tau }_{ul}}{{\tau }_c}$ with power ${\rho }_{ul}$, respectively. $\epsilon$ is the efficiency of the power amplifier while $P_{cir}$ is the circuit power dissipation involved in a variety of operations such as cooling, signal processing, backhaul signaling and power supply. This is not a fixed constant but varies with the circuitry associated with each antenna element to contribute to the total system power consumption.

$$P_{cir}=P_{fix}+P_{tc}+P_{ce}+P_{sp}+P_{c-bc}$$

(16)

where these power terms account for the power consumption of different circuit parts. $P_{fix}$ is the fixed power consumption owing to control signaling and site-cooling and traffic independent backhaul power. $P_{tc}$ is the power consumed by the RF front ends of the transceiver chains. $P_{ce}$ is the power consumed in the channel estimation process. $P_{sp}$ accounts for power consumed in signal processing operations while $P_{c-bc}$ is the power consumed for coding and traffic dependent backhaul.

$$P_{tc}=N{P}_{ap}+P_{lo}+K{P}_{ue}$$

(17)

Here, $P_{ap}$ and $P_{ue}$ are the powers of each AP antenna and user antenna, which depends on the system parameters such as the number of APs and number of users. $P_{lo}$ corresponds to the power of the local oscillator at the AP.

$$P_{c-bc}=B.ASE(P_{cd}+P_{dec}+P_{bt})$$

(18)

This involves the power for coding, decoding and backhaul traffic. The power required for the MMSE channel estimation requires $KN({\tau }_{tr}+1)$ operations with $L_{AP}$ being the computational efficiency of AP as given below.

$$P_{ce}=\frac{3B}{L_{AP}{\tau }_c}KN\left(\frac{K}{f}+1\right)$$

(19)

The power consumed by the signal processing can be expressed as the sum of power required for the reception of data payload and the power consumed for the receive combiner computation.

$$P_{sp}=P_{sp,r}+P_{sp,c}$$

(20)

$$P_{sp,r}=\frac{3B}{L_{AP}{\tau }_c}KN\xi ({\tau }_c-{\tau }_{tr})$$

(21)

$$P_{sp,c}=\frac{BK}{7L_{AP}{\tau }_c}$$

(22)

4. Results and Discussion

A wireless communication model considered in the paper is simulated for performance evaluation here in this section. MATLAB is used to obtain the simulation results for which the simulation setup considers 100 setups each with ${10}^5$ realizations. The range of access points density, that is, the number of access points distributed in the given area of 1 sq km varies between 10 and 100. The simulation setup considers a list of simulation parameters as tabulated in

Table 2. Important parameters considered in the simulation setup.

Parameters	Value	Parameters	Value
K	10	M	20
$\lambda$	10–100	$f_p$	1–10
$t_c$	200	${\rho }_k$	100 mW
B	20 MHz	${\sigma }^2$	$-94$ dBm
$T_c$	1 ms	$\xi$	$1/3$
$B_c$	100 KHz	$P_{FX}$	5 W
$\alpha$	4	$P_{CD}$	$0.01$ W/(Gbit/s)
$\epsilon$	$0.5$	$P_{DEC}$	$0.08$ W/(Gbit/s)
${\rho }_{tr}$	100 mW	$P_{LO}$	$0.1$ W
$P_{AP}$	$0.2$ W	$P_{UE}$	$0.1$ W
$L_{AP}$	750 Gflops/W	$P_{BC}$	$0.025$ W/(Gbit/s)

.

The system performance is evaluated in the uplink using the different receive combiners explained in Section 2 where the MMSE channel estimation technique is used to obtain the channel coefficients between the APs and the communication nodes. The pilot signals of different lengths are used in the uplink to obtain the channel estimates.

Figure 2 gives the variation of average spectral efficiency of the proposed model as a function of AP density. Deploying more APs in a given geographical area led to increased average spectral efficiency. The maximum spectral efficiency of 12.776 bit/s/Hz is obtained with PMMSE combiner with 100 APs. PMMSE combiner outperforms both PRZF and MR combiners in evaluating the spectral efficiency performance of the system. Another important parameter is the area throughput, which defines the number of bits of information transmitted per second per square kilometer. It is plotted against varying pilot reuse factors in Figure 3. The area throughput reaches its maximum value of 3.6813 Gbit/s/km² at a pilot reuse factor of 4. It is depicted that as the pilot reuse factor increases, the area throughput also increases, which reaches the maximum value at a certain point, and then, it saturates as the pilot reuse factor is further increased. This is because the further increase in pilot reuse factor reduces the number of data signals in a coherence block.

The power consumption model presented in Section 3 is simulated, and all the power components are computed. Figure 4 shows the total power consumed by the proposed network design, and the different power terms are plotted. The effective transmit power consumption stands at 37.7 dBm. The circuit power consumption includes 16.06 dBm for the process of channel estimation and 11.64 dBm for coding and decoding. The power consumed by the linear signal processing is −20.29 dBm and backhaul traffic is 6.13 dBm. The processing independent power consumption stands at 44.17 dBm.

Using the proposed power consumption model and the evaluated area throughput, the system energy efficiency is calculated. To validate the numerical analysis done in Section 2 and Section 3, Figure 5 shows the energy efficiency of the proposed network design as a function of AP density. The energy efficiency increases with the increase in AP density until it reaches maximum value at a particular point; after, that the value saturates. The performance of PMMSE, PRZF and MR suggests that the optimal value of energy efficiency in all the three schemes is obtained at the same AP density. With PMMSE, the EE achieved is 5.2362 Mbit/Joule with 29 APs deployed in a given coverage area, while MR combining provides 3.0404 Mbit/Joule at the same AP density. The PRZF method improves the optimal EE by $40.7\%$ over the MR scheme with the same AP deployment. The optimal EEs for the three schemes are shown in Figure 6. To show the variation of energy efficiency with the average area throughput, EE is plotted against the area throughput in Figure 7. It is clear from the figure that the energy efficiency and area throughput can be jointly increased until maximum EE is reached at a point. After that point, increasing the area throughput will lead to a decrease in energy efficiency. At the area throughput of 2.2603 Gbit/s/km², the maximum EE of 5.0595 Mbit/Joule is achieved with PMMSE combiner. The PRZF method reduces the maximum EE by $22.3\%$ to achieve the same area throughput.

5. Conclusions

The energy overhead due to the increasing number of battery-limited devices is the main challenge in 6G-enabled expanded IoT networks. To support IoT applications involving huge information flow between the connected devices, these massive IoT networks need to have high communication capacity and reduced energy consumption. This calls for energy-efficient design for these IoT networks. In this paper, a cell-free approach is used to propose an energy-efficient network design where a large number of connected devices are supported by a large number of APs deployed in the given coverage area. To carry out the energy efficiency analysis of the proposed design model, a power consumption model is proposed which considers both the power required for data transmission and the circuit power. The investigation of energy efficiency reveals that the optimum EE of 5.2362 Mbit/Joule is achieved with an AP density of 29 and pilot reuse factor of 4 with PMMSE combiner. The system performance evaluation suggests an increase of average spectral efficiency with AP density for all the three receive combiners: namely, PMMSE, PRZF and MR. The maximum spectral efficiency of 12.776 bit/s/Hz is obtained with PMMSE combiner with 100 APs. Furthermore, it is observed from the energy efficiency and area throughput relation that both the energy efficiency and area throughput can be jointly increased until maximum EE is reached at a point. At the area throughput of 2.2603 Gbit/s/km², the maximum EE of 5.0595 Mbit/Joule is achieved with PMMSE combiner.