Energy Efficiency and Throughput Maximization Using Millimeter Waves–Microwaves HetNets

Abstract

The deployment of millimeter waves can fulfil the stringent requirements of high bandwidth and high energy efficiency in fifth generation (5G) networks. Still, millimeter waves communication is challenging because it requires line of sight (LOS). The heterogeneous network (HetNet) of millimeter waves and microwaves solves this problem. This paper proposes a millimeter -microwaves heterogeneous HetNet deployed in an indoor factory (InF). In InF, the manufacturing and production are performed inside big and small halls. We consider non standalone dual-mode base stations (DMBS) working on millimeter waves and microwaves. We analyze the network in terms of throughput and energy efficiency (EE). We formulate mixed-integer-non-linear-programming (MINLP) to maximize the throughput and EE of the network. The formulated problem is a complex optimization problem and hard to solve with exhaustive search. We propose a novel outer approximation algorithm (OAA) to solve this problem, and the proposed algorithm OAA achieves optimal solution at β = 10⁻³. At this β, the average throughput value obtained is approximately 50 Mbps, whereas the value of EE is 4.4 Mbits/J. We also compare the performance of OAA with the mesh-adaptive-direct-search-algorithm (NOMAD), and the experimental results verify that OAA outperforms NOMAD in terms of throughput and EE maximization. We also compare the performance of OAA with particle swarm optimization (PSO), genetic algorithm (GA), and many others optimization algorithms. Experimental results verify that OAA outperforms all other algorithms.

1. Introduction

The past few years have shown that millimeter-wave deployment can fulfil the spectrum shortage requirement for 5G [1]. The mm-wave has an unlicensed band of 60 GHz [2]. It opens the door for future correspondence utilizing channel transfer speed past 1 GHz [3], and this is the motivation behind 5G research committees and working groups effectively contributing huge research endeavors towards utilizing the mm-waves in cellular networks [4].

The mm-waves communication requires LOS, and the availability of LOS is one of the biggest challenges for mm-wave communication. These waves face the challenge of interference due to attenuation at shorter distances due to shorter ranges. However, reducing the interference effect due to attenuation at shorter distances improves transmission quality. An outdoor propagation environment produces rich multi-paths at 28 GHz. These multi-paths can be utilized to receive signal power, particularly in the case of non-line of sight (NLOS) [5]. Intelligent antennas with directional beamforming improve the propagation [6].

The mm-waves have so many advantages such as broad bandwidth, high data rate, and low latency to fulfil the requirements of future 5G networks, but mm-wave communication is highly challenging. The reason behind this is the requirement of the LOS, and to overcome this challenge in an indoor factory (InF), the mm-wave–µ wave HetNet is used. To deploy these HetNets, parameters such as throughput, EE, latency, and reliability must be considered. The greenhouse effect is caused by the emission of carbon dioxides (CO₂) from factories due to energy consumption. An increase in energy consumption increases the operational expenditure (OPEX) of the network. The other reasons for the rise in energy consumption are high data rates and dense deployment of base stations. These concerns have highlighted the need for energy-efficient resource allocation strategies for HetNets, reducing energy consumption while high-quality service standards are met.

This paper considers the InF scenario with mm-wave–µ wave HetNet. The primary objective is to increase the throughput and EE of this mm-wave–µ wave HetNet. The use of µ wave will improve EE and network throughput and be an appropriate solution to problems such as line of sight in mm-wave communication.

The following is the paper organization: Section 1 describes the introduction. Section 2 explains the work associated with the paper and its contributions. In Section 3, a system model is defined with problem solving and algorithm description. Section 4 illustrates the experimental results. Finally, Section 5 summarizes the entire work in the conclusion.

2. Related Work

Ansari et al. illustrated a scheme based on control database separation architecture (CDSA) which comprised a control base station (CBS) overlaying on database base station (DBS) [7]. They formulated an optimization problem having multiple objectives to improve energy and spectral efficiency. In Reference [8], the writers demonstrated the use of a recurrent neural network (RNN) and support vector machine (SVM) for resource allocation. In Reference [9], the authors assigned power in HetNets by using a convolutional neural network (CNN) which demands 6.76% of central processing unit (CPU) runtime. Similarly, the authors in [10], used CNN for the security analysis of the Internet-of-Things (IoT) enabled network and achieved 20% gain in precision. Chergui et al. proposed SVM based framework for semi-blind decoupling of uplink and downlink in sub-6 GHz band [11]. This method achieved an accuracy of 95%.

In Reference [12], the authors used Q-learning to minimize latency in mm-wave–µ waves HetNets. However, their model is limited to overhead beam preparation, which enhances the risk of failure. The writers of [13] suggested traditional infrastructure and medium access control (MAC) layer convergence for ultra-reliability and low latency of HetNet. However, this system fails to perform well in MIMO situations. In Reference [14], the authors propose a framework to enhance the throughput in the mm-wave communication network. This framework is based on game theory and is valid for short-range communication only. In Reference [15], the authors used extreme gradient boosting (XGBoost) to improve the handovers success rate in HetNets. This technique had the drawback of service degradation during handovers. In Reference [16], Okamoto et al. proposed an online learning-based adaptive regularization of weight vectors (AROW) algorithm to find the throughput of HetNets. This scheme was only applicable to networks with throughput limited to 1 Gbit/s.

In Reference [17], game theory maximized data rate and energy utilization in HetNets. The network did not work well beyond a certain specified distance outside the same radius; the interference signal plus the noise ratio (SINR) decreased, which reduced efficiency. In Reference [18], a joint resource allocation algorithm (JRAA) and a greedy algorithm were put forward to maximize data rate in HetNets. The suggested framework utilized E-band and V-band, and the LTE band for resource allocation. In Reference [19], SVM based user allocation algorithm and alternating direction method of multipliers (ADMM) were recommended to make HetNets ultra-reliable with low latency. Both these algorithms were low complexity phase heuristic solutions. The network efficiency decayed with a sudden increase in the number of users. In Reference [20], exhaustive search and greedy zero-forcing dirty paper algorithms were utilized to maximize throughput in HetNets. However, this technique was only applicable to the selection of multi-users in MMIMO orthogonal frequency division multiple access (OFDMA) networks. An efficient method to improve the EE of mm-wave–µ wave HetNet is proposed [21]. In this method, constraints such as interruption, power, and network rate are considered. The problem was solved by using the matching game approach.

Likewise, an algorithm was demonstrated in [22] to create mm-wave–µ wave HetNet more effectively when considering power limitations, interruption, and LOS. However, this method was better suited to massive MIMO. Similarly, in Reference [23], the DBMBOLA algorithm was proposed to maximize the EE in mm-wave–µ wave HetNet. The shortcomings of QoS were considered in this strategy. In Reference [24], the energy-efficient power allocation (EEPA) algorithm was proposed for EE in an mm-wave network. This algorithm was based on enhanced non-orthogonal multiple access (E-NOMA). The major drawback of this algorithm was that it did not apply to HetNets. In Reference [25], the authors enhanced the performance of HetNets considering the restrictions of path loss, power use, and LOS. The suggested algorithm is applied to the dense implementation of the mm-wave self-backhauls network. The authors in [26] demonstrated a signal-to-interference ratio-based algorithm to optimize throughput in an mm-wave network termed heuristic interference mitigation (HIM) algorithm. Similarly, in Reference [27], a heuristic algorithm (HUA) was proposed to increase the coverage and capacity of mm-wave–µ wave HetNet. QoS constraints were considered in this scheme, but mm-wave propagation problems such as path loss, rain fading, and LOS were ignored. Furthermore, the advantage of using a bag of features (BoF) to train classifiers such as SVM is illustrated in [28].

Mesodiakaki et al. in Reference [29] proposed the heuristic algorithm to maximize the EE and spectral efficiency of the mm-wave small cell network. However, the authors only focused on the small cell. Similarly, in Reference [30], the authors proposed a low complexity algorithm for the resource allocation in 5G HetNets. The proposed algorithm achieved optimal performance for the 3GPP scenarios. However, no existing studies have considered an InF scenario in which several robots, machines, and humans communicate with each other inside a small or big hall.

Table 1. Summary of the existing mm-wave resource allocation techniques.

Ref. No.	Het Nets	mm- Waves	InF	Objective	Constraints	Sample Approach	Limitations
[11]	🗷	🗹	🗷	Maximum reliability and low latency	LOS, path loss	Semi blind decoupling approach	Low accuracy with NLOS
[12]	🗹	🗷	🗷	Resource allocation	QoS, CSI, QoE, LOS	Q-learning	Increased probability of outage due to beam overhead training
[13]	🗹	🗷	🗷	Ultra-Reliable Low latency	Radio interference	Reinforcement learning- Q-learning	Applicable in C-plane and U-plane
[14]	🗷	🗹	🗷	Throughput maximization	Beamwidth of transmitter and receiver, power	Scheduling algorithm	Network throughput decreased with increase in transmission beamwidth
[15]	🗷	🗹	🗷	Throughput maximization	Beamwidth, power	Matching theory	Short range mm-wave scenarios
[16]	🗹	🗷	🗷	Throughput estimation	Online learning	AROW algorithm	Applicable for throughput less than 1Gbps
[17]	🗹	🗷	🗷	Data rate and energy utilization	Power, interference	Game theory	Worked within specified radius
[18]	🗹	🗷	🗷	Data-rate maximization	Power exclusive pairing, minimum rate	Joint resource allocation algorithm and greedy algorithm	Used E-band, V-band, and LTE band for resource allocation
[20]	🗹	🗷	🗷	Throughput maximization	Power, resource selection	Exhaustive search and greedy zero forcing dirty paper	Multiuser selection in MIMO-OFDMA
[21]	🗹	🗷	🗷	EE maximization	Power, interference, network rate	Matching theory and matching game theory	Applicable to small cells only
[22]	🗹	🗷	🗷	EE maximization	Power, interference, QoS	ARA algorithm	Based on massive MIMO
[23]	🗹	🗷	🗷	EE maximization	Interference, power, LOS	DBMBOLA algorithm	Two tier massive MIMO HetNet with wireless backhaul
[24]	🗷	🗹	🗷	EE maximization	Power, interference, QoS	EEPA algorithm	Based on E-NOMA
[25]	🗷	🗹	🗷	Throughput maximization	LOS, interference, path loss	RAMA algorithm	Based on dense deployment of mm-wave-SBH
[26]	🗹	🗷	🗷	Throughput maximization	LOS, interference, path loss, power	HIM algorithm	Based on SIR
[27]	🗹	🗷	🗷	Coverage and capacity maximization	Interference, QoS	HUA algorithm	Lack of mm-wave propagation probabilities
[29]	🗷	🗹	🗷	EE and SE maximization	Power, SINR, traffic	Heuristic algorithm	Only focused on small cell network
[30]	🗹	🗷	🗷	User association	Power, LOS	Backhaul routing algorithm	Computationally complex approach
This paper	🗹	🗹	🗹	EE and throughput maximization	Power, rate, LOS	OAA	Applicable to InF having dual mode base stations

shows the existing mm-wave resource allocation techniques.

After analyzing Table 1, we conclude that there is little work on millimeter-wave–µ wave HetNets in the literature. Still, the authors have not proposed an optimal solution that jointly maximizes EE and network throughput in the InF scenario. In InF, the deployment of HetNets is quite challenging, as several robots and machines are communicating with each other simultaneously. We formulate an MINLP problem and propose a novel algorithm to optimize throughput and EE. We have used a plethora of algorithms such as firefly algorithm (FA) [31], cuckoo search (CS) [32], PSO [33], artificial bee colony (ABC) [34], teaching learning-based optimization (TLBO) [35], social group optimization (SGO) [36], basic open-source non-linear mixed integer programming (BOMIN) [37], genetic algorithm (GA) [38], and exhaustive search (ES) to compare and validate the results of the proposed algorithm.

Contribution

Analyzing the literature, we conclude that no maximization method considers the joint optimization of EE and throughput using mm-wave–µ wave HetNets in InF scenario. Our main contributions are summarized below:

• A mathematical formulation of a model for throughput and EE maximization.
• A solution to the formulated problem using OAA.
• Extensive evaluation of results for validation of our method.
• Comparison of the proposed algorithm with existing state-of-the-art algorithms.

3. System Model and Problem Formulation

3.1. Scenario of Indoor Factory

This article considers an InF scenario, as illustrated in Figure 1. All the base stations deployed in the design are dual mode. When there is LOS, these base stations work on millimeter waves. However, when there is NLOS, these base stations shift to µ waves.

3.2. Indoor Factory (InF)

An InF is a smart factory based on the industrial internet of things (IIoT 4.0). The factory considered in this article has two types of halls in it. One type is a big hall, while the other is a small hall. The details about area and base station deployment in both arenas are described in

Table 2. Abbreviations used for indoor factory scenario.

Abbreviation	Description
InF	Indoor factory
InF-SL	Indoor factory with sparse clutter and low base station height
InF-SH	Indoor factory with sparse clutter and high base station height
InF-DL	Indoor factory with dense clutter and low base station height
InF-DH	Indoor factory with dense clutter and high base station height
DMBS	Dual mode base station
UE	User

:

3.2.1. Big Hall of Indoor Factory

According to 3GPP Release 16 [39], the total area inhabited by one big hall of InF is 300 by 150 m². Each big gallery contains eighteen base stations. All the base stations are 50 m apart, and their height is 1.5 m and 8 m for InF-DL and InF-SH, respectively. The distribution of DMBS in the hall is illustrated in Figure 2.

3.2.2. Small Hall of Indoor Factory

According to 3GPP Release 16 [39], the total area inhabited by one small hall of InF is 120 by 60 m². Each big gallery contains eighteen base stations. All the base stations are 50 m apart, and their height is 1.5 m and 8 m for InF-DL and InF-SH. The deployment of DMBS within the hall is illustrated in Figure 2. The height of the rooms having DMBS varies from five meters to ten meters. 3GPP Release 16 provides assessment factors for the InF.

3.2.3. LOS and NLOS Path Loss

Equation (2) calculates the path loss of LOS, while path loss of NLOS in InF-SL, InF-DL, InF-SH, and InF-DH can be calculated by using Equations (4), (6), (8), and (10), respectively [39]. In these equations, d_3D is the distance between user (UE) and DMBS, and Equation (1) calculates d_3D, f_c is the central frequency normalized by 1 GHz [40].

$$d_{3D}=\sqrt{{\left(d_{2D}\right)}^2+{\left(h_{BS}-h_{UT}\right)}^2},$$

(1)

$${\mathrm{PL}}_{\mathrm{LOS}}=31.84+21.50 {\log }_{10}\left(d_{3D}\right)+19.00 {\log }_{10}\left(f_c\right)$$

(2)

$$\mathrm{InF-SL}:\mathrm{PL}=33.00+25.50 {\log }_{10}\left(d_{3D}\right)+20.00 {\log }_{10}\left(f_c\right)$$

(3)

$${\mathrm{PL}}_{\mathrm{NLOS}}=\max \left(\mathrm{PL},{\mathrm{PL}}_{\mathrm{LOS}}\right)$$

(4)

$$\mathrm{InF-DL}:\mathrm{PL}=18.60+35.70 {\log }_{10}\left(d_{3D}\right)+20.00 {\log }_{10}\left(f_c\right)$$

(5)

$${\mathrm{PL}}_{\mathrm{NLOS}}=\max \left(\mathrm{PL},{\mathrm{PL}}_{\mathrm{LOS}},{\mathrm{PL}}_{\mathrm{InF-SL}}\right)$$

(6)

$$\mathrm{InF-SH}:\mathrm{PL}=32.40+23.00 {\log }_{10}\left(d_{3D}\right)+20.00 {\log }_{10}\left(f_c\right)$$

(7)

$${\mathrm{PL}}_{\mathrm{NLOS}}=\max \left(\mathrm{PL},{\mathrm{PL}}_{\mathrm{LOS}}\right)$$

(8)

$$\mathrm{InF-DH}:\mathrm{PL}=33.63+21.90 {\log }_{10}\left(d_{3D}\right)+20.00 {\log }_{10}\left(f_c\right)$$

(9)

$${\mathrm{PL}}_{\mathrm{NLOS}}=\max \left(\mathrm{PL},{\mathrm{PL}}_{\mathrm{LOS}}\right)$$

(10)

3.2.4. Mathematical Model

In this article, an mm-waves–µ waves HetNet is considered. This network has M links between UEs and DMBS. The time slot is shown in Figure 3. This time has two portions, including one for the alignment and the second for the data transmission.

3.2.5. Overhead of Alignment

Let T_p represents the pilot transmission time. The sector-level beamwidth for transmitter and receiver is represented by ${\psi }_i^t$ and ${\psi }_i^r$, respectively, whereas beam-level beamwidth for transmission and reception is denoted by ${\phi }_i^t$ and ${\phi }_i^r$, respectively. Consequently, the overall duration for the alignment in a sector is given by Equation (11).

$${\tau }_i\left({\phi }_i^t,{\phi }_i^r\right)=\lceil \frac{{\psi }_i^t}{{\phi }_i^t}\rceil \lceil \frac{{\psi }_i^t}{{\phi }_i^t}\rceil T_P$$

(11)

where $\lceil .\rceil$ denotes ceiling function. This function returns the smallest integer. The connection between transmitter and receiver is formed when the optimal directions are calculated after this data transmission begins. After the alignment process, any pair of DMBS and UE starts data communication. We derive continuous approximation τ_i by dumping the noncontinuous ceiling function. The latter cannot exceed the overall time T and can be excluded from the lower limit on possible bandwidth (12).

$${\phi }_i^t{\phi }_i^r\ge \frac{T_P}{T}{\psi }_i^t{\psi }_i^r$$

(12)

Even though alignment happens within beamwidths at the sector level, we have ${\phi }_i^t\le {\psi }_i^t$ and ${\phi }_i^r\le {\psi }_i^r$. The transmission between DMBS and UEs is shown in Figure 4.

3.2.6. The Effective Rate of Transmission

Let the channel gain be denoted by g_c(i,j) for DBMS_i and UE_j.

Table 3. Description of symbols.

Symbol	Description	Symbol	Description
${\phi }^t$	Beam level beamwidth of a transmitter	${\phi }^r$	Beam level beamwidth of the receiver
${\psi }^t$	Sector beamwidth of a transmitter	${\psi }^r$	Sector level beamwidth of the receiver
$T_P$	Pilot transmission time	$T$	Total transmission time
$\tau$	Alignment time	$g^t$	Gain of transmitter
$g^r$	Gain of receiver	$g^c$	Channel gain
$p_i$	Power of the ith base station	$Ef$	Error frame
$d_i$	Data rate of the ith link	$N$	Noise
${\theta }^t$	Transmission angle	${\theta }^r$	Reception angle
$E$	Energy	$r$	Network rate
$M$	Maximum number of links	-	-

gives the summary of symbols used in a mathematical model. The transmitter and corresponding receiver gain can be determined by Equations (13) and (14) respectively.

$$g_{i,j}^t\left({\theta }_{i,j}^t,{\phi }_i^t\right)=\{\begin{array}{c}\frac{2\pi -\left(2\pi -{\phi }_i^t\right)z}{{\phi }_i^t}, if \left|{\theta }_{i,j}^t\right|\le \frac{{\phi }_i^t}{2}\\ z, otherwise\end{array}$$

(13)

$$g_{i,j}^r\left({\theta }_{i,j}^r,{\phi }_i^r\right)=\{\begin{array}{c}\frac{2\pi -\left(2\pi -{\phi }_i^r\right)z}{{\phi }_i^r}, if \left|{\theta }_{i,j}^r\right|\le \frac{{\phi }_i^r}{2}\\ z, otherwise\end{array}$$

(14)

In Equations (13) and (14), z is $0<z\ll 1$. Considering transmission and reception gain, SINR can be evaluated by Equation (15).

$$SIN{R}_i=\frac{p_i{g}_{i,i}^t{g}_{i,i}^c{g}_{i,i}^r}{{{\displaystyle \sum }}_{k=1, k\ne i}^M{p}_i{g}_{k,i}^t{g}_{k,i}^c{g}_{k,i}^r+n}$$

(15)

Then the network rate can be evaluated by (16) by using (15).

$$R_i=\left(1-\frac{{\tau }_i}{T}\right){\log }_2\left(1+SIN{R}_i\right)$$

(16)

Here, $R_i$ signifies the ith link rate in the network, T represents the total transmission time, ${\tau }_i$ represents the time needed for the orientation of the ith link, while $SIN{R}_i$ signifies the signal to noise and interference ratio of the corresponding ith link.

3.2.7. The Energy Efficiency (EE) of Network

The ith link EE is determined by Equation (17) [41].

$$E{E}_i=\frac{d_i}{p_i}$$

(17)

In Equation (17), E_i represents energy. d_i shows data rate of the ith link, and p_i denotes the power of the ith DBMS.

3.3. Objectives and Constraints

3.3.1. Objectives

The aim of our study is to increase the throughput as well as EE of the HetNet deployed in the InF.

3.3.2. First Objective

This objective is related to the maximum throughput in mm-waves–µ wave HetNets. This is mathematically described using Equation (18).

$$\underset{{\phi }^t,{\phi }^r,p,r}{\max }F1={\displaystyle \sum }_{i=1}^M{R}_i$$

(18)

$$\mathrm{s}.\mathrm{t}. \begin{array}{cc}{\phi }_i^t\le {\psi }_i^t,& 1\le i\le M\end{array}$$

(18a)

$$\begin{array}{cc}{\phi }_i^r\le {\psi }_i^r,& 1\le i\le M\end{array}$$

(18b)

$$\begin{array}{cc}0\le p_i\le p^{max},& 1\le i\le M\end{array}$$

(18c)

$$\begin{array}{cc}{r}_i\ge r^{max},& 1\le i\le M\end{array}$$

(18d)

$$\begin{array}{cc}SIN{R}_i\ge SIN{R}^{max},& 1\le i\le M\end{array}$$

(18e)

$$\begin{array}{cc}{\phi }_i^t{\phi }_i^r\ge \frac{T_P}{T}{\psi }_i^t{\psi }_i^r,& 1\le i\le M\end{array}$$

(18f)

3.3.3. Second Objective

The corresponding second objective of this work is to maximize EE in mm-waves–µ wave HetNets. This is mathematically described in Equation (19).

$$\underset{{\phi }^t,{\phi }^r,p,r}{\max }F2={\displaystyle \sum }_{i=1}^{M}E{E}_i$$

(19)

$$\mathrm{s}.\mathrm{t}. \begin{array}{cc}{\phi }_i^t\le {\psi }_i^t,& 1\le i\le M\end{array}$$

(19a)

$$\begin{array}{cc}{\phi }_i^r\le {\psi }_i^r,& 1\le i\le M\end{array}$$

(19b)

$$\begin{array}{cc}0\le p_i\le p^{max},& 1\le i\le M\end{array}$$

(19c)

$$\begin{array}{cc}{r}_i\ge r^{max},& 1\le i\le M\end{array}$$

(19d)

$$\begin{array}{cc}SIN{R}_i\ge SIN{R}^{max},& 1\le i\le M\end{array}$$

(19e)

$$\begin{array}{cc}{\phi }_i^t{\phi }_i^r\ge \frac{T_P}{T}{\psi }_i^t{\psi }_i^r,& 1\le i\le M\end{array}$$

(19f)

3.3.4. Constraints

• According to Equations (18a) and (19a), for any ith transmitter, the sector level beamwidth must be greater than or equal to the beam level beamwidth.
• According to Equations (18b) and (19b), for any ith receiver, the sector level beamwidth must be greater than or equal to the beam level beamwidth.
• According to Equations (18c) and (19c), the maximum power level is always more significant than the power of any ith link.
• According to the fourth constraints Equations (18d) and (19d), the rate of the ith link should be greater than the minimum rate for communication for successful communication.
• According to the fifth constraint Equations (18e) and (19e), the SINR of the ith link should be higher than or equal to the minimum level of SINR.
• The last constraint Equations (18f) and (19f) rationalize the corresponding lower bounds on the accessible bandwidth.

4. Proposed Algorithm

The performance analysis of throughput and EE in mm-wave–µ wave HetNet using OAA and heuristic algorithms is carried out in this section. At first, the algorithm is described, then modeled mathematically using (18) and (19), and correspondingly optimized utilizing OAA.

4.1. Outer Approximation Algorithm (OAA)

The problems in (18) and (19) are MINLP. These problems are very hard to solve due to their complexity, and exhaustive search achieves optimal solutions to these problems. However, it becomes complex when M increases. Therefore, we suggest an outer approximation algorithm (OAA) to resolve this problem. Figure 5 shows the flowchart of the OAA algorithm. Algorithm 1 explains the pseudo-code of OAA.

Algorithm 1: Outer Approximation Algorithm

$m\leftarrow 1$ $Intialize \gamma$ $\beta \leftarrow {10}^{-3}$ $Convergence\leftarrow FALSE$ $while Convergence==FALSE do$ $|\begin{array}{c}{\alpha }^m\leftarrow \{\begin{array}{c}\underset{\alpha }{\min }-f\left(\gamma ,\alpha \right)\\ s.t. \psi \left(\gamma ,\alpha \right) \le 0;\end{array}\\ Upper Bound \leftarrow f\left({\gamma }^m,{\alpha }^{\ast }\right)\\ \left({\gamma }^{\ast },{\alpha }^{\ast },{\sigma }^{\ast }\right) \leftarrow \{\begin{array}{c}\underset{\gamma ,\sigma ,\alpha }{\min }\sigma \\ subject to\\ \sigma \ge -\delta \left({\gamma }^m,{\alpha }^m\right)\\ -\nabla f\left({\gamma }^m,{\alpha }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ 0\end{array}\right)\\ {\psi }_{C1-C6}\left({\gamma }^m,{\alpha }^M\right)\\ -{\nabla }_{{\psi }_{C1-C6}}\left({\gamma }^m,{\alpha }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ 0\end{array}\right)\le 0\end{array}\\ Lower Bound\leftarrow \sigma \\ if Upper Bound-Lower Bound \le \beta then\\ |Convergence\leftarrow TRUE\\ end\\ else\\ |\begin{array}{c}m \leftarrow m+1\\ {\gamma }^k \leftarrow {\gamma }^{\ast }\end{array}\\ end\end{array}$ End

Explanation of the Algorithm

Let f be the corresponding objective, ${\psi }_{C1-C6}$ signify constraints from C1 to C6 in Equations (18) and (19), α = {P_{DBMS using mm Waves}, P_{DBMS using Waves}} and γ = x ∪ α. (19) fulfil the following propositions.

• The objective function f and ${\psi }_{C1-C6}$ are convex in α for a specified value of γ because α is nonempty, convex, and compact.
• Continuous differentiation of objective function f and ${\psi }_{C1-C6}$ must be possible.
• By fixing the value of γ, the solution of every non-linear continuous sub-problem qualifies the constraints.
• After solving γ, the appropriate solution NLP problem is obtained.

These assumptions convert Equations (18) and (19) into unique problems. OAA provides the solution to these master problems. The separation of objective function f and the constrained constraints of convex directs to external measurements. The OAA utilizes high limits and low-frequency sequences to fulfil proposals, as indicated above, for corresponding mixed problems. OAA achieves optimal value when β converges. A problem that does not match the line has a higher sequence. The main problem can be written as

$$\{\begin{array}{c}\underset{\alpha }{\min }-f\left(\gamma ,\alpha \right)\\ s.t. \psi \left(\gamma ,\alpha \right)\le 0;\end{array}$$

(20)

The solution to (20) is ${\alpha }^m$, and it is used for the master problem. The upper bounds can be obtained from the primary concern, while the lower bounds can be achieved by solving the master problem. The first solution α is used to drive the master problem. The solution to the master problem presents a new set of variables ${\gamma }^{m+1}$. As the iteration progresses, the upper and lower limits come together. The algorithm terminates when both boundaries are close such that their difference is less than β. The master problem can be extracted in two steps. Initially, an issue that has been created in a total space γ is labelled as:

$$\{\begin{array}{c}\underset{\gamma }{\min } \underset{\alpha }{\min }-f\left({\gamma }^m,\alpha \right)\\ s.t. \psi \left({\gamma }^m,\alpha \right)\le 0;\end{array}$$

(21)

The above problem is expressed as

$$\underset{\gamma }{\min }-\theta \left(\gamma \right)$$

(22)

here

$$\{\begin{array}{c}\theta \left(\gamma \right)=\underset{\alpha }{\min }-f\left({\gamma }^m,\alpha \right)\\ s.t. \psi \left({\gamma }^m,\alpha \right)\le 0;\end{array}$$

(23)

The projection of the problem in (18) and (19) using discrete variable γ is expressed as a problem (22). The outer approximation can be made by applying linearization in the second step. Therefore, the solution to the projection problem is:

$$\{\begin{array}{c}\underset{\gamma }{\min } \underset{\alpha }{\min }-f\left({\alpha }^m,{\gamma }^m\right)-\nabla f\left({\alpha }^m,{\gamma }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ \gamma -{\gamma }^m\end{array}\right)\\ s.t.-\psi \left({\alpha }^m,{\gamma }^m\right)-\nabla \psi \left({\alpha }^m,{\gamma }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ \gamma -{\gamma }^m\end{array}\right)\end{array}$$

(24)

With the introduction of new variables, the optimization problem can be expressed as:

$$\begin{array}{c}\underset{\gamma ,\alpha ,\sigma }{\mathrm{minimum}} \sigma \\ s.t.:\{\begin{array}{c}\sigma \ge -f\left({\alpha }^m,{\gamma }^m\right)-\nabla f\left({\alpha }^m,{\gamma }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ \gamma -{\gamma }^m\end{array}\right)\\ -\psi \left({\alpha }^m,{\gamma }^m\right)-\nabla \psi \left({\alpha }^m,{\gamma }^m\right)\left(\begin{array}{c}\alpha -{\alpha }^m\\ \gamma -{\gamma }^m\end{array}\right)\le 0\end{array}\end{array}$$

(25)

The above master problem provides lower bounds. The projection of the issues in (18) and (19) is the problem formulated in (25). The problem is a linear mixed-integer programming problem (MILP), and the iterative method solves it. The following section explains the results obtained by the simulation of the proposed algorithm.

5. Results and Experiments

The system model is simulated in MATLAB 2021Ra using the OPTI toolbox. The experimental results obtained from the simulations are shown in this section, and the outcomes also explain the usefulness and the convergence of the corresponding algorithm. The experimental results of the proposed algorithm are also compared with the state-of-the-art algorithms. The performance analysis of the network is calculated in terms of throughput, EE, link rate, and channel efficiency.

Simulation Parameters

The values of the different parameters employed to simulate the system model are demonstrated in

Table 4. Simulation parameters of each base station.

Parameter	Value
DBMS power, p	25 Watts
Minimum users	2
Maximum users	50
UE increment	2
TP	20 µ seconds
T	65,535 µ seconds

. The simulation parameters of the other algorithms are illustrated in Appendix A 

Table A1. Simulation parameters of the other algorithms.

Algorithm	Parameters	Values
NOMAD	DBMS power, p	25 Watts
	Minimum users	2
	Maximum users	50
	UE increment	2
	TP	20 µ seconds
	T	65,535 µ seconds
FA	DBMS power	25 Watts
	Minimum rate	1 kbps
	TP	20 µ seconds
	T	65,535 µ seconds
CS	DBMS power	25 Watts
	Minimum rate	1 kbps
	TP	20 µ seconds
	T	65,535 µ seconds
	Bandwidth	180 kHz
PSO	DBMS power	25 Watts
	Minimum rate	1 kbps
	Maximum users	50
	Minimum users	2
	TP	20 µ seconds
	T	65,535 µ seconds
	Bandwidth	180 kHz
ABC	DBMS power	25 Watts
	Minimum rate	1 kbps
	TP	20 µ seconds
	T	65,535 µ seconds
TLBO	DBMS power	25 Watts
	Minimum rate	1 kbps
	Pilot time	30 µ seconds
	Bandwidth	180 kHz
SGO	DBMS power, p	25 Watts
	Minimum users	2
	Maximum users	50
	UE increment	2
	TP	20 µ seconds
	T	65,535 µ seconds
BOMIN	DBMS power, p	25 Watts
	Minimum users	2
	Maximum users	50
	UE increment	2
	TP	50 µ seconds
	T	65,535 µ seconds
GA	DBMS power	25 Watts
	Minimum rate	1 kbps
	Pilot time	40 µ seconds
	Bandwidth	180 kHz

.

We have used two algorithms, namely OAA and NOMAD [38], to increase the throughput and corresponding EE. Figure 6 demonstrates the throughput using OAA. Additionally, it reveals that it increases with the corresponding number of UEs. Likewise, Figure 7 shows the EE using the OAA. It indicates that the output converges as UEs rise. By increasing the UEs, average EE increases. When the number of users is 18, the average EE of the network is 4.5 Mbits/J; it remains approximately 4.5 Mbits/J until the number of users reaches 46. After 46 users, the interference dominates, and the EE decreases. This is due to the congestion of the UEs in the hall, as for the successful operation the hall should have less than 60% density according to 3GPP InF scenario.

Figure 8 shows the distribution of users on mm-waves and µ waves when the OAA algorithm is applied. Initially, when the total number of users is two, then one user is on mm-waves while the other is on µ waves. With the increment in users, the distribution does not remain symmetrical; µ waves users become more significant, such as when the number of users is 34, and mm-waves users are 20 while µ waves users are 14. The procedure for selecting a particular mode depends on several factors. For the selection of mm-wave mode, the sparse density should be less than 40%, and there should be enough possibility to have LOS for a more significant duration while the sparse density is greater than 40% for microwave mode.

We have also calculated the variations in the link rates by changing SINR. Figure 9 shows the plot between SINR in decibels (dB) and link rate (Mbps) and the link rate of mm-wave link is better than µ wave link. When SINR is 40 dB, the link rate of mm-wave link approaches 60 Mbps while the link rate of µ wave link approaches 42 Mbps which is relatively low compared to mm-wave link.

We have evaluated the performance of the proposed algorithm in the case of LOS, NLOS and HetNet scenarios. Figure 10 illustrates the relationship between the average throughput of the network and the number of users for the LOS, NLOS, and HetNet scenarios. From the plot, the optimal performance from the proposed HetNet scheme using the OAA algorithm.

Similarly, we have calculated the relationship between energy efficiency and the number of users for the LOS, NLOS, and HetNets scenario using the OAA algorithm. Figure 11 shows the plot of energy efficiency against the number of users for all three designs. When there is LOS, the communication is very smooth and maximum throughput is achieved using mm-wave. However, when there is NLOS, and microwaves are used then the performance of the network is relatively worse than the proposed HetNet which shows optimal performance and works in both LOS and NLOS scenarios.

We also compare the performance of the proposed algorithm OAA and other existing algorithms regarding EE and throughput of the network. Figure 12 illustrates the average EE of the system when all the algorithms are applied. The plot curves show that all other algorithms converge slowly, and the maximum average EE achieved by the GA algorithm is more petite than OAA, i.e., approximately 4.2 Mbits/J. In contrast to all these algorithms, the OAA has a better convergence rate, and it provides a better average EE of the network, i.e., 4.5 Mbits/J. These observations from Figure 12 show that OAA is better than existing optimization algorithms.

We also compare the performance of both algorithms regarding the throughput of the network, as shown in Figure 13. When the total users are two, the network throughput with the OAA algorithm is 12 Mbps, while GA is 10 Mbps. Throughput varies directly with the entire users, but the network’s throughput with OAA remains better than NOMAD when users are approaching the upper limit, i.e., 50. The average throughput of the network is 50 Mbps with OAA and 48 Mbps with GA.

After all of the experiments, we find that the performance of the OAA is better than algorithms. Finally, we have calculated the relationship between throughput and channel efficiency of the network using the OAA algorithm. Figure 14 shows the plot between channel efficiency and throughput in LOS and NLOS.

We have also compared the optimal solution of the proposed algorithm with the other algorithms in terms of EE and throughput.

Table 5. Comparison of the optimal solution of proposed algorithm with the existing algorithms.

Algorithm	Optimal EE (MbJ−1)	Gain in the EE	Optimal Throughput (Mbps)	Gain in the Throughput
OAA	4.50	7.4%	50.00	4.34%
NOMAD	4.10		46.93
FA	3.46		39.52
CS	3.67		41.99
PSO	3.59		41.61
ABC	3.80		43.47
TLBO	3.71		42.48
SGO	3.75		42.98
BOMIN	4.01		45.94
GA	4.19		47.92

highlights the optimal solution of all the algorithms.

We have also evaluated the runtime complexity of the proposed algorithm with other existing algorithms and summarized in

Table 6. Comparison of the runtime complexity of the proposed algorithm with others.

Algorithm	Runtime Complexity (GPU)	Difference	Overall Gain	Runtime Complexity (CPU)	Difference	Overall Gain
OAA	0.8 s	0s	47.06%	46 s	0 s	45.10%
NOMAD	4 s	3.2 s		224 s	178 s
FA	3 s	2.2 s		168 s	122 s
CS	6 s	5.2 s		336 s	290 s
PSO	2.5 s	1.7 s		90 s	44 s
ABC	1.7 s	0.9 s		102 s	56 s
TLBO	5 s	4.2 s		280 s	234 s
SGO	9 s	8.2 s		504 s	458 s
BOMIN	11 s	10.2 s		616 s	570 s
GA	4 s	3.2 s		224 s	178 s
ES	30 s	29.2 s		1680 s	1634 s

. All the runtime complexities are evaluated on the CPU core i5 (Intel, Chandler, AZ, USA) and GPU Tesla K80 (NVIDIA, Santa Clara, CA, USA).

6. Conclusions

We have analyzed the problem of throughput and corresponding energy efficiency in mm-wave–µ waves HetNets. We studied the problem of the concave fractional system. We suggest OAA resolves the issue. The proposed algorithm varies sequentially and gives good results within β = 10⁻³. The performance of the β-optimal solution obtained by the OAA method is indicated by different system parameters such as the number of users and network input. EE improves as the total users increase and become more stable as we grow UEs again. The average throughput increases with the increase in the number of users, and with the rise in users, more users switch to µ wave links. The optimal throughput obtained by the proposed algorithm is 50 Mbps, while the optimal energy efficiency achieved by the proposed algorithm is 4.5 Mbits/J. The proposed algorithm applies to millimeter-waves microwaves heterogeneous networks within the defined area, as in the case of the indoor factory. In future, we will extend this to metropolitan area networks. We will also use more robust artificial intelligence and machine learning algorithms to make the network perform well in different environments rather than focusing on the only indoor factory.