**1. Introduction**

Intelligent systems, whether biological or artificial, require the ability to make decisions under uncertainty using the available evidence. Several computational models exhibit some of the required functionality to handle uncertainty. These computational models in Artificial Intelligent (AI) and Machine Learning are judged by two main criteria: ease of creation and effectiveness in decision making. For example, Neural Networks (NNs) which represent complex input/output relations using combinations of simple nonlinear processing elements, are a familiar tool in AI and computational neuroscience. Alternatively, probabilistic networks (also called Bayesian Networks) are a more explicit representation of a domain through modelling the joint probability distribution (the probability of all possible outcomes in a domain). This paper provides a short summary of the previous methods in Intelligent Data Analysis (IDA) in disease progression, decision making and probabilistic modelling of patients. It then describes some existing key methods that can be updated or combined to model multiple diabetes complications in the presence of unmeasured factors. There is considerable research on predicting diabetes, especially Type 2 Diabetes Mellitus (T2DM), complications. Nevertheless, the previous research of the author is discussed in order to address these issues. In particular, these previously proposed methods have contributed to the diabetes literature by explaining unknown risk factors and identifying temporal phenotypes employing hybrid methods (including descriptive and predictive). These suggested methodology includes rule-based methods for an explanation of patient subgroups and a probabilistic framework for modelling data explicitly.

disease that guide predictions or decisions. This is because clinicians expect to understand AI diagnoses to be able to make decisions. There is a great deal of debate over the importance of explanation in AI models inferred from health data. In particular, there is a balance that needs to be made between the accuracy of complex deep models such as convolutional neural networks (in predictive strategy) and the transparency of models (in descriptive strategy) that aims to model data in

*Predicting Type 2 Diabetes Complications and Personalising Patient Using Artificial…*

A combination of explainable and deep strategies rather than either one of them alone would have a better prognostic value. Furthermore, in order to obtain a more accurate and explainable prediction of progression, the predictive models need to be personalised based on how an individual patient matches historical data by identi-

Understanding the pattern of complications associated with the disease has been used significantly in the clinical domain [6]. It provides an insight into the prediction and relative prevention of the associated complications which are expected to occur in a patient follow-up [7]. It generally can lead to less suffering time for patients while saving time and cost to healthcare. However, that is highly dependent on the stage of disease along with the prior occurring complications, which is associated with time-series analysis. In time-series analysis, every disease risk factor and complication is determined by various features in previous patient visits (time interval). At every medical visit, all diabetic patients have a unique profile of symptoms and complications that change over time, regardless of the phase of the disease. This non-stationary characteristic of clinical data collected as part of the monitoring of T2DM creates a difficult context for effective forecasting [8]. Clinical data needs to be considered as time-series data in order to provide a description of the progression of a disease over time. Nevertheless, dealing with time-series patient records is known to be a major issue in the prognosis of comorbidities [9], particularly when time-series data is imbalanced and contains few examples of patients without comorbidities that are common to all patients. In Type 2 Diabetes, for example, once patients are diagnosed with T2DM, half of them show signs of complications [10]. Unfortunately, these life-threatening complications remain undiagnosed for a long time because of the hidden patterns of their associated risk factors [11]. If T2DM is not appropriately managed, the development of serious complications, such as neuropathy, retinopathy, and hypertension lead to disability, premature mortality and financial cost [12]. The prediction process is complex due to the interactions between these complications and other features, as well as between complications themselves. More importantly, each patient has a unique profile of complication occurrence and the status of T2DM risk factors during a patients time-series is subject to change, as their levels may rise and fall over time. Early diagnosis and prevention techniques are needed to reduce the associated mortality and morbidity caused by T2DM complications [13]. Although there are various methodologies for T2DM prediction, for example, risk-prediction equation and Markov models [14], studies that enable early predictions of diabetes using predictive models are limited [15]. The risk-prediction equations suffer from uncertainty as well as performing only one-step-ahead predictions, while Markov models are limited to a small number of discrete risk factors. Other existing literature on investigating the prognosis of T2DM complications [16, 17] focuses particularly on logistic regression and Naive Bayes. Such studies are unsatisfactory for modelling the complex T2DM complications/risk factors. Logistic regression does

a more human way such as expert systems.

*DOI: http://dx.doi.org/10.5772/intechopen.94228*

**3. Probabilistic model for time-series analysis**

fying patient subgroups.

**199**


*6.2.2 Kirsch's response expectancy theory*

Proposes that subjects have generalized response expectancy in a hypnotic situation and follow the hypnotists's instructions and experience involuntary behaviors attributable to external causes (the hypnotist). Two social factors associated with response to hypnosis: rapport ("therapeutic alliance," "resonance," and "harmony,") and social context are taken in account.


Preface

Infections are immune-mediated illnesses that can range from mild to serious. In recent years, new pathogens have appeared, such as the COVID-19 virus, which caused a worldwide pandemic. Due to the appearance of new and serious pathogens, the human immune response is continually being tested.

Phagocytosis is one of the main mechanisms in innate immune defense and the first process to respond to pathogens. It is also one of the initiating branches of an adaptive immune response. In the immune system, the cells that are capable of phagocytosis are called "professional phagocytes." These include neutrophils, macrophages, monocytes, dendritic cells, and eosinophils. In these cells, the phagosome is the organelle formed by phagocytosis of material. It then moves toward the centrosome of the phagocyte and is fused with lysosomes, forming a phagolysosome and leading to degradation. Progressively, the phagolysosome is acidified, activating degradative enzymes and killing all pathogens.

This book discusses the main aspects of phagocytosis and related cells in the human immune response. It also examines the molecular mechanisms involved in infections and related pathogens, providing a comprehensive review of infectious diseases and their pathophysiology, diagnosis, management, and treatment.

As educators, we are frequently faced with probing questions from students who are confused by the paradoxical functions of the immune system. We think this book can help students to understand the molecular pathways of phagocytosis. Thus, it is a useful resource not only for undergraduate and graduate students but also for immunology specialists and clinicians.


*Article* **Resource Allocation in Uplink NOMA-IoT Based UAV for URLLC Applications**

**Rana Karem 1,2,\*, Mehaseb Ahmed 1 and Fatma Newagy 2**

**Abstract:** One of the main targets of future 5G cellular networks is enlarging the Internet of Things (IoT) devices' connectivity while facing the challenging requirements of the available bandwidth, power and the restricted delay limits. Unmanned aerial vehicles (UAVs) have been recently used as aerial base stations (BSs) to empower the line of sight (LoS), throughput and coverage of wireless networks. Moreover, non-orthogonal multiple access (NOMA) has become a bright multiple access technology. In this paper, NOMA is combined with UAV for establishing a high-capacity IoT uplink multi-application network, where the resource allocation problem is formulated with the objective of maximizing the system throughput while minimizing the delay of IoT applications. Moreover, power allocation was investigated to achieve fairness between users. The results show the superiority of the proposed algorithm, which achieves 31.8% delay improvement, 99.7% reliability increase and 50.8% fairness enhancement when compared to the maximum channel quality indicator (max CQI) algorithm in addition to preserving the system sum rate, spectral efficiency and complexity. Consequently, the proposed algorithm can be efficiently used in ultra-reliable low-latency communication (URLLC).

**Keywords:** internet of things; non-orthogonal multiple access; resource allocation; ultra reliable low latency communication; unmanned aerial vehicles; uplink transmission

## **1. Introduction**

Due to their mobility and flexibility, unmanned aerial vehicles (UAVs)—also called drones—have become popular and have a wide range of applications. These applications include—though are not confined to—monitoring the environment, fertilizing and dusting crops, searching for mines, police monitoring, and operations of rescue. UAVs have received great attention thanks to its lower cost, high mobility, wide coverage and ease of deployment and flexibility [1]. These applications are not restricted to industrial and civilian fields only, but can also be extended to military applications [2].

In the near future, UAVs will be highly deployed in many applications in wireless networks, especially 5G networks, to serve ultra-reliable low-latency communication (URLLC) [3]. UAVs can present either in a single-UAV or multi-UAV system [4]. UAVs can be utilized as airborne base stations and flying relays to provide LoS connections to improve the coverage and power consumption for IoT devices. The recent era will witness billions of connections of Internet of Things (IoT) devices that will be served simultaneously [5]. Smart mobiles, vehicles, home appliances, and sensors are examples of these IoT devices [6].

The fifth generation (5G) network is intended to provide coverage for high-density devices with various applications of diverse quality of service (QoS) requirements [7]. Non-orthogonal multiple access (NOMA) is a promising multiple access technology which can face the challenging requirements of high throughput and low latency accompanied

**Citation:** Karem, R.; Ahmed, M.; Newagy, F. Resource Allocation in Uplink NOMA-IoT Based UAV for URLLC Applications. *Sensors* **2022**, *22*, 1566. https://doi.org/10.3390/ s22041566

Academic Editor: Margot Deruyck

Received: 9 January 2022 Accepted: 15 February 2022 Published: 17 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

with the traffic of IoT devices. The basic concept of NOMA lies in the ability of NOMA to serve numerous users simultaneously over the same resource block (RB) to increase the spectrum efficiency [8]. However, due to simultaneous transmission, interference occurs between users sharing the same RB, so that successive interference cancellation (SIC) is used to detect the signal [9]. The exploitation of UAVs combined with NOMA is used to support the required massive connections of IoT devices and also provide long transmission range for IoT devices with limited transmission power capabilities. UAVs can easily overpass the IoT nodes, collect the information data and then transmit them to the data center or the other IoT devices [4]. IoT is accommodating numerous various applications with extremely precise performance requirements. Delay is one of the essential key metrics and one of the biggest challenges facing IoT applications [10]. In this paper, the UAV as a base station was exploited with NOMA to support URLLC IoT network with devices of different applications; each application has its own traffic parameters and delay requirements. A resource and power allocation scheme was proposed to manage the different QoS requirements for each application in uplink networks achieving high spectral efficiency, fairness and data rate as well as improving the delay and reliability.

The main contributions of this research are listed as follows:

#### **2. Related Works**

This section presents the state-of-the-art in resources scheduling in uplink 5G networks, UAV communication, and NOMA-based URLLC systems. Resource allocation and scheduling techniques in uplink 5G networks have been studied in many research papers presented in this literature. In [8], the authors proposed two resource allocation algorithms; the first one is the local rate maximization (LRM) in which the subcarrier is allocated to the user which gives the maximum rate on the chosen subcarrier. The second approach is global objective maximization (GOM) in which the allocated subcarrier is that which achieves maximum increase in the objective function.

A weighted sum rate maximization problem is modeled in [11], then a subcarrier allocation scheme which is based on iterative water-filling (IWF) algorithm is introduced. Its main idea is to initially begin with all devices allocated to all subchannels then remove the subchannel-device pair which gives the worst gain and power; repeatedly doing so until it meets the constraint that *L* devices are allocated to each subchannel [11]. The authors in [12] came up with a many-to-many matching model, where each subchannel forms a preference list based on the system throughput and each user creates its own preference list based on the received power. Iterative addition or substitution processes for the users

to the subchannels are performed; for the purpose of enhancing the system performance until there is no more enhancement [12]. Reference [13] shows a two-sided matching and swapping technique, where firstly, each device forms its preference list based on channel gain and data rate, then each subchannel receives requests from the demanding devices and chooses the *L* devices with the highest energy efficiency. Then swapping operations are performed if and only if it is accompanied by an enhancement in energy efficiency [13]. UAV cellular networks were investigated with 5G technologies in [14,15] considering the channel model but the resource allocation problem was not inspected. In [16], backscatter communication technology, which is based on reflecting the incident wireless signals for the purpose of data collection, is investigated. The mobility of UAVs is exploited for maximizing the energy efficiency while optimizing the backscatter devices allocation and UAV trajectory [16]. The authors in [17] proposed NOMA scheme with index modulation to reduce the effect of contention, interference and collision in grant-free access. However, the system throughput was not considered. The authors in [18] used resource slicing and presented two user clustering mechanisms to meet the delay constraints of time stringent applications in uplink NOMA. NOMA technology is used in [19] and the resources are classified into shared and private. If the transmission and delay requirements of users cannot be achieved by the shared resources, then the private resources can be used [19]. Unlike the studies, the proposed algorithm is the first to consider the restricted delay limits of the IoT devices in addition to throughput maximization which makes the proposed algorithm suitable for URLLC applications.

The following sections in the rest of the paper are organized as follows. In Section 3, the system model is illustrated for the uplink of IoT devices served by UAV using NOMA access technique. Section 4 shows the problem formulation with the purpose of delay minimization and maximizing the network sum rate. Section 5 demonstrates the delay-rate optimization scheduling algorithm and the fairness optimization power allocation algorithm. Section 6 shows the performance evaluation of the proposed algorithm through the simulation results. Finally, the conclusion of the presented work is discussed in Section 7.

#### **3. System Model**

As shown in Figure 1, a UAV-assisted IoT network is considered where the UAV serves as an aerial base station, all IoT devices are served by a UAV that covers a cell with radius *Rc*. The UAV is located at 3D coordinates (*xUAV*, *yUAV*, *hUAV*); assume that (*xUAV* = 0, *yUAV* = 0, *hUAV*); i.e., the UAV is at the center of the cell with altitude *hUAV*; such that (*hmin* ≤ *hUAV* ≤ *hmax*) where *hmin* and *hmax* are the minimum and maximum allowable heights of the UAV. Assume that there are *N* ground IoT devices; each device is equipped with a single antenna. These devices are distributed randomly in the cell covered by the UAV; each device is located at (*xi* , *yi* ) where *i* = {1, 2, . . . , *N*}. Each IoT device has a packet arrival rate *λi* and transmits minimum rate *Ri* with delay limit *Di* . Each IoT device has a transmitted power *Pi* (*Pmin,i* ≤ *Pi* ≤ *Pmax,i*) where *Pmin,i* and *Pmax,i* are the minimum and maximum transmitted power of IoT device *i* respectively. Path loss between IoT device *i* to the UAV expresses the large-scale fading component which is given by

$$PL\_i = \frac{A}{1 + ae^{-b\ (\theta\_i - a)}} + B\_{i\prime} \tag{1}$$

$$A = \eta\_{\text{LOS}} - \eta\_{\text{NLOS}}.\tag{2}$$

$$B\_i = 20\log\_{10}(d\_i) + 20\log\_{10}\left(\frac{4\pi f\_c}{c}\right) + \eta\_{NLOS\_{\prime}}\tag{3}$$

where *fc* is the carrier frequency, *c* is the light speed, *ηLOS*, *ηNLOS*, *a*, *b* are constants related to the propagation environment either urban, suburban, dense urban or high-rise urban environments. Considering air to ground (A2G) communication between the UAV and the ground IoT devices, thus, each device can have line of sight (*LoS*) view or non-line of sight (*NLoS*) view with respect to the aerial base station with certain probability. *NLoS* occurs when the propagation path is partially or fully obscured by physical obstacles. The *LoS* probability or *NLoS* probability are highly dependent on the device location, environment and the elevation angle between the device and the UAV, as illustrated in Figure 1. *PrLoSi* , *PrNLoSi* are the probabilities of IoT device *i* having *LoS* link or having non-line of sight (*NLoS*) link respectively between the UAV and IoT device, which could be calculated as [20] environment and the elevation angle between the device and the UAV, as illustrated in Figure 1. ௌ , ேௌ are the probabilities of IoT device *i* having *LoS* link or having nonline of sight (*NLoS*) link respectively between the UAV and IoT device, which could be calculated as [20]

and the ground IoT devices, thus, each device can have line of sight (*LoS*) view or nonline of sight (*NLoS*) view with respect to the aerial base station with certain probability. *NLoS* occurs when the propagation path is partially or fully obscured by physical obstacles. The *LoS* probability or *NLoS* probability are highly dependent on the device location,

*Sensors* **2022**, *22*, x FOR PEER REVIEW 4 of 17

$$\text{Time} = \text{conv number} + \text{new} + \text{volume} \times \text{volume} \times \text{acceleration} \times \text{(25)}$$

$$Pr\_{LoS\_i} = \frac{1}{1 + a \exp(-b[\theta\_i - a])} \text{ \,\, \text{(4)}$$

$$\text{Pr}\_{\text{NLoS}\_l} = 1 - \text{Pr}\_{\text{LoS}\_l} \tag{5}$$

where *θi* is the elevation angle (measured in "degree") between IoT device *i* and the *UAV* as illustrated in Figure 1; it can be calculated as as illustrated in Figure 1; it can be calculated as ℎ

$$\theta\_i = \frac{180}{\pi} \sin^{-1} \left(\frac{h\_{LAV}}{d\_i}\right) \tag{6}$$

*di* is the distance between the IoT device *i* at (*xi* , *yi* ) and the *UAV* located at (*xUAV*, *yUAV*, *hUAV*) is *(*, *,*ℎ*)* is

$$d\_i = \sqrt{(\mathbf{x}\_{ULV} - \mathbf{x}\_i)^2 + (y\_{ULV} - y\_i)^2 + (h\_{ULV})^2} \tag{7}$$

**Figure 1.** Illustration of the elevation angle in case of static UAV [21]. **Figure 1.** Illustration of the elevation angle in case of static UAV [21].

The *UAV* uses the NOMA access technique to communicate with the IoT devices. Assume that the total bandwidth allocated to the *UAV* is *B*, which is divided equally into *K* orthogonal subcarriers. Let *bk,i*(*t*) is the subcarriers assignment index, where *bk,i*(*t*) = 1 means that subcarrier *k* is allocated to device *i*, otherwise *bk,i*(*t*) = 0. There are maximum *L* IoT devices allowed to be scheduled over a single subcarrier at the same time and each IoT device gets exactly one subcarrier for simplicity. IoT devices can give preferences for the resource blocks, and their preferences are considered based on their channel quality indicator (CQI) [22] which depends on the channel quality between the *UAV* and IoT devices. The signal to noise plus interference ratio (SNIR) of IoT device *i* on subcarrier *k* is The *UAV* uses the NOMA access technique to communicate with the IoT devices. Assume that the total bandwidth allocated to the *UAV* is *B*, which is divided equally into *K* orthogonal subcarriers. Let *bk,i*(*t*) is the subcarriers assignment index, where *bk,i*(*t*) = 1 means that subcarrier *k* is allocated to device *i*, otherwise *bk,i*(*t*) = 0. There are maximum *L* IoT devices allowed to be scheduled over a single subcarrier at the same time and each IoT device gets exactly one subcarrier for simplicity. IoT devices can give preferences for the resource blocks, and their preferences are considered based on their channel quality indicator (CQI) [22] which depends on the channel quality between the *UAV* and IoT devices. The signal to noise plus interference ratio (SNIR) of IoT device *i* on subcarrier *k* is modeled as

$$\Gamma\_{k,i}(t) = \frac{b\_{k,i}(t)p\_{k,i}(t) \left| \mathbf{g}\_{k,i}(t) \right|^2}{\sum\_{f=1,\ |\mathcal{R}\_{k,f}(t)|^2 < |\mathcal{R}\_{k,i}(t)|^2} b\_{k,f}(t) p\_{k,f}(t) \left| \mathbf{g}\_{k,f}(t) \right|^2 + \sigma^2},\tag{8}$$

సభ,ቚೖ,()ቚమ ಬቚೖ,()ቚమ ,() is the channel gain between the *UAV* and IoT device *i* on subcarrier *k*. ,() *gk*,*i*(*t*) is the channel gain between the *UAV* and IoT device *i* on subcarrier *k*. *gk*,*i*(*t*) which is invariant in one time slot but varies over different time slots, can be modeled as:

$$\mathbf{g}\_{k,i}(\mathbf{t}) = \sqrt{PL\_{k,i}} h\_{k,i}(\mathbf{t}) \,\tag{9}$$

modeled as

where *hk*,*i*(*t*) is the small scale fading of complex Gaussian distribution given by *hk*,*i*(*t*)∼ *CN*(0,*σ* 2 ). URLLC uses short packets to ensure low latency transmission, so Shannon capacity, which acts as the upper bound in terms of data rate, can no longer be applied. Consequently, the user data rate at finite blocklength transmission [23] is given by pacity, which acts as the upper bound in terms of data rate, can no longer be applied. Consequently, the user data rate at finite blocklength transmission [23] is given by ,() = logଶ ቀ1+,()ቁ − ඨ, ିଵ() (10)

where ℎ,() is the small scale fading of complex Gaussian distribution given by ℎ,()

*CN(0,*ଶ). URLLC uses short packets to ensure low latency transmission, so Shannon ca-

$$R\_{k,l}(t) = \log\_2(1 + \Gamma\_{k,l}(t)) - \sqrt{\frac{V\_{k,l}}{m}} \ Q^{-1}(\varepsilon) \tag{10}$$

,() = ඥ,ℎ,()*,* (9)

∼

(14)

where, the decoding error probability *ε* [24] is given by = ൭ln 2ට ቀlogଶ(1+) −

The sum rate can be calculated as

*Sensors* **2022**, *22*, x FOR PEER REVIEW 5 of 17

$$
\varepsilon = Q \left( \ln 2 \sqrt{\frac{m}{V}} \left( \log\_2 \left( 1 + \Gamma \right) - \frac{D}{m} \right) \right),
\tag{11}
$$

$$
\text{Such that the O function and } V \text{ are defined accordingly as}
$$

Such that the *Q* function and *V* are defined respectively as √2 න ି௧మ ଶ ௫ (12)

$$Q(\mathbf{x}) = \frac{1}{\sqrt{2\pi}} \int\_{\mathbf{x}}^{\infty} e^{\frac{-\overline{x}^2}{2}} \, dt \tag{12}$$

ቁ൱, (11)

$$V\_{k,i} = 1 - \left(1 + \Gamma\_{k,i}\right)^{-2} \tag{13}$$

where *D* states the packet size, and *m* represents the blocklength of the channel. The sum rate can be calculated as ௦௨ = ,(), ே ୀଵ

ୀଵ

$$R\_{sum} = \sum\_{k=1}^{K} \sum\_{i=1}^{N} R\_{k,i}(t),\tag{14}$$

Assume that packet arrival of the IoT device *i* follows a Poisson process with the average arrival rate as *λi* packets per second. The average service rate of the same IoT device is assumed to be *µi* packets per second. Both *λi* and *µi* are statistically identical and independent distributed. The queuing system model of the IoT device is shown in Figure 2. Then, the average delay *dav*,*i* , which is based on the *M/M/1* queuing model [25], can be given by the following formula: device is assumed to be *μi* packets per second. Both and *μi* are statistically identical and independent distributed. The queuing system model of the IoT device is shown in Figure 2. Then, the average delay ௩,, which is based on the *M/M/1* queuing model [25], can be given by the following formula: ௩, = ௩, − (15)

$$d\_{av,i} = \frac{S\_i}{R\_{av,i} - S\_l \lambda\_i} \tag{15}$$

where *Si* and *Rav*,*i* are the packet size and the average rate of IoT device *i* respectively.

**Figure 2.** Queuing system model of the IoT device [26]. **Figure 2.** Queuing system model of the IoT device [26].

௩, can be given as the rate of device *i* averaged over time as follows: *Rav*,*i* can be given as the rate of device *i* averaged over time as follows:

$$R\_{av,i} = \frac{1}{T} \sum\_{t=1}^{T\_{slots}} \sum\_{k=1}^{K} R\_{k,i}(t) b\_{k,i}(t) \,\prime \tag{16}$$

where ௦௧௦ represents the total number of time slots. where *Tslots* represents the total number of time slots.

#### **4. Problem Formulation**

The main objective is to maximize the sum data rate of all users while achieving minimum device delay through selecting the assignment index *bk*,*i* at every time slot. Hence, the resource allocation problem is formulated with data rate maximization objective function as follows:

$$\underset{\{b\_{k,i}(t)\}}{\text{Max}} \sum\_{k=1}^{K} \sum\_{i=1}^{N} \mathbb{R}\_{k,i}(t) \tag{17}$$

$$\text{s.t.} \,\text{C1}: \sum\_{k=1}^{K} b\_{k,i}(t)\mathbb{R}\_{k,i}(t) \ge \text{R}\_{\text{min},i} \tag{18}$$

$$\text{C2}: \sum\_{k=1}^{K} b\_{k,i}(t) p\_{k,i}(t) \le P\_{\text{max}} \tag{19}$$

$$\mathcal{C} \mathbf{3} \colon b\_{k,i}(t) \in \{0, 1\} \tag{20}$$

$$\text{C4} : \sum\_{k=1}^{K} b\_{k,i}(t) p\_{k,i}(t) \ge 0 \tag{21}$$

$$\text{C5}: \sum\_{i=1}^{N} b\_{k,i}(t) \le L \tag{22}$$

$$\mathbb{C}\mathfrak{G}: d\_{av,i} < D\_i \tag{23}$$

$$\text{C7}: h\_{\text{min}} < h\_{\text{ULAV}} < h\_{\text{max}} \tag{24}$$

where *Pmax* is the maximum available transmission power of the IoT device. *C*1 is the minimum required data rate for all users to ensure QoS. *C*2 means that any IoT device transmit power cannot exceed *Pmax*. *C*3 and *C*4 are the constraints of the assignment matrix *bk,i* and power *pk,i*. *C*5 mentions that one subcarrier cannot be allocated to more than *L* users at the same time. *C*6 is the delay constraint, states that the average delay of the device *i* (*dav*,*i* ) should not exceed the delay limit requirement *Di* . *C*7 is the UAV height constraint between the minimum and maximum allowable altitudes.

The optimization problem is non-convex due to the coupled variables *bk*,*i* and *pk*,*i* in (20) and (21). Hence, the proposed algorithm uses a linear weighted utility function to overcome the complexity of the optimization problem (17).

#### **5. Proposed Algorithm**

The optimization problem is non-convex due to the coupled variables *bk*,*i* and *pk*,*i* in (20) and (21). To find a simplified solution, the proposed scheduler in this section exploits the convexity property of the sub-problems [27] for the main non-convex problem (17). In addition, the proposed algorithm makes use of the resource element structure in NOMA which takes one subcarrier in frequency and one time symbol known as transmission time interval (TTI) [28], as demonstrated in Figure 3. Hence, the proposed algorithm operates in two domains, as illustrated in Figure 4. The first is delay minimization to guarantee the delay requirement of each IoT device which is performed by a time domain packet scheduler (TDPS). The second domain is rate maximization to increase the spectral efficiency and maximize the system sum rate which is performed by a frequency domain packet scheduler (FDPS).

*Sensors* **2022**, *22*, x FOR PEER REVIEW 7 of 17

**Figure 3.** General NOMA resource allocation. **Figure 3.** General NOMA resource allocation. **Figure 3.** General NOMA resource allocation.

**Figure 4.** Illustration of the proposed scheduler. **Figure 4.** Illustration of the proposed scheduler. **Figure 4.** Illustration of the proposed scheduler.

The optimum height of the UAV should be calculated to solve constraint C7. The optimal UAV elevation angle ௧௨ was derived for each environment in [29] to cover a circular cell of certain radius in A2G communication independent of the multiple access technique used .Thus, according to [30]; the values of ௧௨ given by (25) for UAV placement corresponding to each environment either suburban, urban, dense urban or high-rise urban environments are illustrated in Table 1. Thus, the optimum UAV altitude The optimum height of the UAV should be calculated to solve constraint C7. The optimal UAV elevation angle ௧௨ was derived for each environment in [29] to cover a circular cell of certain radius in A2G communication independent of the multiple access technique used .Thus, according to [30]; the values of ௧௨ given by (25) for UAV placement corresponding to each environment either suburban, urban, dense urban or The optimum height of the UAV should be calculated to solve constraint C7. The optimal UAV elevation angle *θoptimum* was derived for each environment in [29] to cover a circular cell of certain radius in A2G communication independent of the multiple access technique used. Thus, according to [30]; the values of *θoptimum* given by (25) for UAV placement corresponding to each environment either suburban, urban, dense urban or high-rise urban environments are illustrated in Table 1. Thus, the optimum UAV altitude *hoptimum* to cover a cell of radius *Rc* can be given by

$$\theta\_{\text{optimum}} = \tan^{-1} \left( \frac{h\_{\text{optimum}}}{R\_{\text{c}}} \right) \tag{25}$$

ℎ௧௨

൰ (25)

**Table 1.** Values of optimal elevation angle of each environment.

௧௨ = ିଵ ൬

#### High-rise urban 75.52° Urban 42.44° *5.1. Time Domain Packet Scheduling (TDPS)*

*5.1. Time Domain Packet Scheduling (TDPS)*

*5.1. Time Domain Packet Scheduling (TDPS)*  Dense urban 54.62° High-rise urban 75.52° The main function of TDPS is to select a certain number of IoT devices to be scheduled in the next TTI; this process should guarantee that there are no devices exceed their

The main function of TDPS is to select a certain number of IoT devices to be scheduled in the next TTI; this process should guarantee that there are no devices exceed their

uled in the next TTI; this process should guarantee that there are no devices exceed their maximum delay limits by minimizing the average delay. Hence, the optimization problem

for time domain scheduling can be formulated using (15) as

for time domain scheduling can be formulated using (15) as

maximum delay limits by minimizing the average delay. Hence, the optimization problem for time domain scheduling can be formulated using (15) as

$$\min d\_{av,i} = \frac{\mathbb{S}\_i}{R\_{av,i} - \mathbb{S}\_i \lambda\_i} \,\,\,\tag{26}$$

The device selection criteria in TDPS is based on a weighted delay metric which is essentially needed to prioritize the devices requests. The metric function is based on delay [31] to satisfy the delay constraint C6. The UAV uses the information in the BSR to compute the metric function for each requesting device. This metric aims to order the IoT devices requests to control the TDPS decision. The metric considers average delay and buffer status reports [32] as follows:

$$M\_{\rm i} = \alpha\_{\rm j} \, w\_{\rm i,j} d\_{a\rm v,i} \tag{27}$$

where *αj* states the priority of each traffic group, where the TDPS categorizes stations according to their delay limits into *j* groups, and *wi*,*j* is the traffic weight of user *i* in traffic class *j*, this weight can be calculated as

$$w\_{i,j} = \frac{q\_{i,j}}{bl},\tag{28}$$

where *qi*,*j* is the queue size of user *i* in traffic group *j*, and *bl* is the buffer length to avoid buffer overflow of the IoT device.

After grouping and calculating metric for the IoT devices that send scheduling requests. The TDPS selects maximum *Nmax* = *KL* devices to be scheduled in the next TTI, since there are *L* devices can be scheduled over the same resource block according to constraint C5 (22). Consider *N\_sel* to be the number of chosen IoT devices to be scheduled. The rejected users send scheduling requests in the next TTI.

#### *5.2. Frequency Domain Packet Scheduling (FDPS)*

The main purpose of FDPS is allocating resources for IoT devices based on channel conditions (CQI) to increase spectral efficiency [32]. FDPS allocates resources to the IoT devices chosen by TDPS. Thus, the optimization problem of FDPS could be formulated as

$$\underset{\{b\_{k,l}(t)\}}{\text{Max}} \sum\_{k=1}^{K} \sum\_{l=1}^{N\_{-}} \text{s}\_{k,l}(t) \tag{29}$$

$$\text{s.t.} \,\text{C1}: \sum\_{k=1}^{K} b\_{k,l}(t) R\_{k,l}(t) \; \ge \, R\_{\text{min},l} \tag{30}$$

*C*3 : *bk*,*l*(*t*) ∈ {0, 1} (31)

$$\text{C5}: \sum\_{l=1}^{N\_{\text{sle}}} b\_{k,l}(t) \le L \tag{32}$$

In the proposed algorithm in FDPS each of the selected users prioritizes the RBs, where each IoT device sorts the RBs in descending order of CQI. The CQI value is an indication for the channel quality of each user on each subchannel. CQI value ranges from 0 to 15. The higher the value, the better the channel quality and vice versa. The CQI value is determined according to the estimated value of SINR [33]. Therefore, a preference matrix is formed containing the CQI values of all users on all RBs such that *CQIi*,*k* is the CQI value of user *i* on RB *k*; where the rows correspond to the IoT devices and the columns are related to the RBs. Each IoT device's preferences (CQI values) are listed in a row in this matrix; such that a higher CQI value indicates that the IoT device prefers this RB.

A weighted preference matrix is then formed which is based on the weighted metrics (27) computed in TDPS and the preferences determined in FDPS, and can be given by

*fobj* = *Diag*(*M*1*xN*\_*sel* ) *CQIN*\_*sel xK* (33)

where *M*1*xN*\_*sel* is a row vector of the metrics of the selected devices and *CQIN*\_*sel xK* is the preference matrix which contains the CQI values of the selected devices on all RBs. Hence, the problem in (29) can be easily modified to

$$\underset{\{b\_{k,l}(t)\}}{\text{Max}} - \text{Diag}\left(M\_{1\text{xN}\_{\text{sl}}}\right) \\ \mathbb{C}Q I\_{N\_{\text{sl}}\ge \text{K}} b\_{k,l}(t) \tag{34}$$

$$s.t \text{ C3}: b\_{k,l}(t) \in \{0, 1\} \tag{35}$$

$$\text{C5}: \sum\_{l=1}^{N\_\text{-sel}} b\_{k,l}(t) \le L \tag{36}$$

The problem in (34) can be solved using binary integer programming which is used to solve the constrained problem to maximize *fobj* The algorithm (Algorithm 1) to find the optimum allocation matrix is listed in detail as shown in the pseudo code.

In the Joint Delay-Rate Optimization Scheduler, the UAV receives scheduling requests in every TTI. In TDPS, the UAV classifies the requests to groups according to the application. Then, the metric function is computed for all requesting devices using (27). The scheduler selects *N\_sel* devices with the highest metrics. Then, in FDPS, the RBs allocated to each IoT device are chosen with the objective to maximize the weighted preference matrix in (33).

#### *5.3. Power Allocation Algorithm*

The Uplink power allocation scheme is used to ensure fair data rates between users sharing the same RB [34]. Consider two users share the same RB, if *gk*,*n* > *gk*, *f* then according to (8) the SNIR of near and far users respectively are given as

$$\Gamma\_{k,n}(t) = \frac{p\_{k,n}(t) \left| g\_{k,n}(t) \right|^2}{p\_{k,f}(t) \left| g\_{k,f}(t) \right|^2 + \sigma^2} \tag{37}$$

$$\Gamma\_{k,f}(t) = \frac{p\_{k,f}(t) \left| \mathcal{g}\_{k,f}(t) \right|^2}{\sigma^2},\tag{38}$$

Assuming that the UAV will decode the signal of the nearest user first then decode the signal of the far user using SIC. To achieve fair data rates for both users, then,

$$\frac{p\_{k,n}(t)|\mathcal{g}\_{k,n}(t)|^2}{p\_{k,f}(t)\left|\mathcal{g}\_{k,f}(t)\right|^2+\sigma^2} \xrightarrow{p\_{k,f}(t)\left|\mathcal{g}\_{k,f}(t)\right|^2} \tag{39}$$

Let *gk*,*n*(*t*) 2 = *gN* as the gain of the near user and *gk*, *f*(*t*) 2 = *gF* as the gain of the far user. Thus, the power allocation coefficients *aN* and *aF* of the near and the far users respectively can be derived as

$$\frac{a\_N P\_{\max} g\_N}{a\_F P g\_F + \sigma^2} = \frac{a\_F P\_{\max} g\_F}{\sigma^2} \,\,\,\,\tag{40}$$

Let *ρ* = *Pmax*/*σ* 2 , then divide both sides by *σ* 2

$$\frac{a\_N \rho g\_N}{a\_F \rho g\_F + 1} = \frac{a\_F \rho g\_F}{1},\tag{41}$$

$$(g\_F^2 \rho^2 a\_F^2 + (g\_F + g\_N)\rho a\_F - \rho g\_N = 0\tag{42}$$

$$a\_F = \frac{-(\mathcal{g}\_N + \mathcal{g}\_F) \pm \sqrt{(\mathcal{g}\_N + \mathcal{g}\_F)^2 + 4\rho \mathcal{g}\_F^2 \mathcal{g}\_N}}{2\mathcal{g}\_F^2 \rho} \tag{43}$$

where 0 < *aN* < 0.5 because *aF* > *aN* and *aN* + *aF* = 1.

#### **6. Simulation Results**

In this section, simulation is introduced to evaluate the proposed algorithm performance. Consider a single UAV covering a cell of radius *Rc* = 1 km; assuming a suburban environment. An aerial UAV is centered and placed at the optimum height of the cell according to the values in Table 1. Consider IoT devices (N = 300) randomly deployed in the cell, IoT devices are supporting different applications, assuming there are 4 groups of IoT devices each has its unique traffic parameters. The maximum transmit power of each IoT device is 27 dBm and the minimum transmit power is 20 dBm. Unless stated, it is assumed that the system total available bandwidth B = 1.4 MHz consisting of 6 RBs. The noise power density *σ* 2 = −174 dBm/Hz. The main simulation parameters are summarized in Table 2.

To verify the efficiency of the proposed scheduler; the proposed algorithm is compared with the maximum CQI scheduling algorithm. According to [35], the best CQI algorithm shows its superiority in the achieved sum rate and spectral efficiency. The idea of the best CQI is based on scheduling the *N\_sel* nodes which have the maximum CQI regardless of any other parameters.

*Sensors* **2022**, *22*, x FOR PEER REVIEW 11 of 17

**Table 2.** Simulation parameters. ௫ IoT device maximum power 500 mW–27 dBm

Figure 5 shows the percentage of IoT devices that exceeds the delay limit, and as clearly seen the proposed algorithm outperforms the maximum CQI and the gap increases with the time, until it reaches a certain point at which the percentage of devices exceeding the delay limit saturates in both algorithms. This is due to its receiving large requests and scheduling *N\_sel* nodes only in each TTI while rejecting the rest of nodes. The percentage of devices exceeding the delay tolerance saturates in the proposed algorithm to nearly 30% but around 44% in maximum CQI. The proposed algorithm gives priority to the nodes of the maximum buffer and least delay tolerance, resulting in 31.8% delay improvement. with the time, until it reaches a certain point at which the percentage of devices exceeding the delay limit saturates in both algorithms. This is due to its receiving large requests and scheduling *N\_sel* nodes only in each TTI while rejecting the rest of nodes. The percentage of devices exceeding the delay tolerance saturates in the proposed algorithm to nearly 30% but around 44% in maximum CQI. The proposed algorithm gives priority to the nodes of the maximum buffer and least delay tolerance, resulting in 31.8% delay improvement.

clearly seen the proposed algorithm outperforms the maximum CQI and the gap increases

**Figure 5.** Percentage of devices exceeding the application delay limit at each time slot. **Figure 5.** Percentage of devices exceeding the application delay limit at each time slot.

To evaluate the fairness of the proposed algorithm; the formula of Jain's fairness index in [8] is used, which is given by To evaluate the fairness of the proposed algorithm; the formula of Jain's fairness index in [8] is used, which is given by

where represents the rate of user *k* and *K* is the total number of users. The fairness index values are confined between 0 and 1 such that the maximum value is achieved when the users have equal data rates. As obviously seen in Figure 6, the proposed algorithm is

$$\text{Jain's failures index} = \frac{\left(\sum\_{k=1}^{K} R\_k\right)^2}{K \sum\_{k=1}^{K} R\_k^2} \tag{44}$$

(44)

sulting in 50.8% fairness enhancement at 300 users.

where *Rk* represents the rate of user *k* and *K* is the total number of users. The fairness index values are confined between 0 and 1 such that the maximum value is achieved when the users have equal data rates. As obviously seen in Figure 6, the proposed algorithm is significantly fairer than the best CQI, since scheduling is performed sequentially from all groups, in addition to the fair power allocation algorithm used unlike the best CQI; resulting in 50.8% fairness enhancement at 300 users. *Sensors* **2022**, *22*, x FOR PEER REVIEW 12 of 17 *Sensors* **2022**, *22*, x FOR PEER REVIEW 12 of 17

**Figure 6.** Fairness index versus number of users. **Figure 6.** Fairness index versus number of users. **Figure 6.** Fairness index versus number of users.

In Figure 7, the relationship between the transmitted power of the IoT devices and the sum rate is shown. As expected, the sum rate of the maximum CQI is greater than the proposed algorithm by only 1.6%; therefore, they still have a very close performance. By increasing the IoT device's maximum power, the sum rate is nearly the same and does not change; this is due to the slight increase in the device's maximum power that it does not affect the sum rate. In Figure 7, the relationship between the transmitted power of the IoT devices and the sum rate is shown. As expected, the sum rate of the maximum CQI is greater than the proposed algorithm by only 1.6%; therefore, they still have a very close performance. By increasing the IoT device's maximum power, the sum rate is nearly the same and does not change; this is due to the slight increase in the device's maximum power that it does not affect the sum rate. In Figure 7, the relationship between the transmitted power of the IoT devices and the sum rate is shown. As expected, the sum rate of the maximum CQI is greater than the proposed algorithm by only 1.6%; therefore, they still have a very close performance. By increasing the IoT device's maximum power, the sum rate is nearly the same and does not change; this is due to the slight increase in the device's maximum power that it does not affect the sum rate.

and 25 resource blocks. They achieved nearly the same performance, which proves the superiority of the proposed algorithm. As the number of users increases, the sum rate increases to a certain saturation point after which the sum rate is almost constant due to

and 25 resource blocks. They achieved nearly the same performance, which proves the superiority of the proposed algorithm. As the number of users increases, the sum rate increases to a certain saturation point after which the sum rate is almost constant due to

Figure 8 shows a comparison between the proposed algorithm and the best CQI in

**Figure 7.** Sum rate versus the power of the IoT devices. **Figure 7.** Sum rate versus the power of the IoT devices. **Figure 7.** Sum rate versus the power of the IoT devices.

Figure 8 shows a comparison between the proposed algorithm and the best CQI in the achieved sum rate versus the number of users at different bandwidths; in case of 6, 10 and 25 resource blocks. They achieved nearly the same performance, which proves the superiority of the proposed algorithm. As the number of users increases, the sum rate increases to a certain saturation point after which the sum rate is almost constant due to scheduling the maximum number of users *Nmax* in every TTI achieving almost the same sum rate. It can be noticed that the sum rate in case of 25 RBs outperforms that in case of 6 RBs and 10 RBs, while it is the least in the case of 6 RBs. It is observed that the saturation point is shifted to the right as the number of RBs increases, meaning that as the number of RBs increases, the sum rate saturates at larger number of users. *Sensors* **2022**, *22*, x FOR PEER REVIEW 13 of 17 scheduling the maximum number of users *Nmax* in every TTI achieving almost the same sum rate. It can be noticed that the sum rate in case of 25 RBs outperforms that in case of 6 RBs and 10 RBs, while it is the least in the case of 6 RBs. It is observed that the saturation point is shifted to the right as the number of RBs increases, meaning that as the number of RBs increases, the sum rate saturates at larger number of users.

**Figure 8.** Sum rate versus number of users. **Figure 8.** Sum rate versus number of users.

Figure 9 shows the achieved sum rate versus the bandwidth (number of RBs) with maximum 2 users allocated to the resource block. The spectral efficiency of the proposed algorithm is almost closer to that of the maximum CQI, which verifies the efficiency of the proposed algorithm in terms of spectral efficiency. Figure 9 shows the achieved sum rate versus the bandwidth (number of RBs) with maximum 2 users allocated to the resource block. The spectral efficiency of the proposed algorithm is almost closer to that of the maximum CQI, which verifies the efficiency of the proposed algorithm in terms of spectral efficiency.

The results obtained in Figures 7–9, show the excellence of the proposed algorithm in terms of spectral efficiency and sum rate. This is because the proposed algorithm cannot exceed the best CQI which represents the upper bound in throughput and spectral efficiency. However, the proposed algorithm records a very close performance. The results obtained in Figures 7–9, show the excellence of the proposed algorithm in terms of spectral efficiency and sum rate. This is because the proposed algorithm cannot exceed the best CQI which represents the upper bound in throughput and spectral efficiency. However, the proposed algorithm records a very close performance.

Figure 10 shows the spectral efficiency versus the maximum power of the IoT devices comparing the performance of both the proposed resource allocation algorithm and the best CQI once using the proposed power allocation and once using distance-based power allocation. As can be clearly seen, the proposed power allocation outperforms the distance=based power allocation. Moreover, as expected, the maximum CQI is superior in terms of spectral efficiency which is on average 41.2 bps/Hz followed by the proposed algorithm which achieves very close performance, nearly 40.5 bps/Hz and about 1.69% decrease only.

To evaluate the reliability of the algorithms, the relationship between the packet size and probability of decoding error is shown in Figure 11. As expected, as the packet size increases, the probability of error increases in both algorithms. However, the probability of error *ε* in the proposed algorithm is significantly lower than that of the max CQI, where at

*Sensors* **2022**, *22*, x FOR PEER REVIEW 13 of 17

of RBs increases, the sum rate saturates at larger number of users.

scheduling the maximum number of users *Nmax* in every TTI achieving almost the same sum rate. It can be noticed that the sum rate in case of 25 RBs outperforms that in case of 6 RBs and 10 RBs, while it is the least in the case of 6 RBs. It is observed that the saturation point is shifted to the right as the number of RBs increases, meaning that as the number

packet size = 1000 bits, *ε* is about 8.5 × 10−11 and 4.2 × 10−8 in the proposed algorithm and the max CQI respectively, resulting in nearly 99.7% performance improvement. exceed the best CQI which represents the upper bound in throughput and spectral efficiency. However, the proposed algorithm records a very close performance.

Figure 9 shows the achieved sum rate versus the bandwidth (number of RBs) with maximum 2 users allocated to the resource block. The spectral efficiency of the proposed algorithm is almost closer to that of the maximum CQI, which verifies the efficiency of the

The results obtained in Figures 7–9, show the excellence of the proposed algorithm in terms of spectral efficiency and sum rate. This is because the proposed algorithm cannot

**Figure 9.** Sum rate versus the number of RBs. decrease only.

**Figure 8.** Sum rate versus number of users.

proposed algorithm in terms of spectral efficiency.

To evaluate the reliability of the algorithms, the relationship between the packet size and probability of decoding error is shown in Figure 11. As expected, as the packet size increases, the probability of error increases in both algorithms. However, the probability of error in the proposed algorithm is significantly lower than that of the max CQI, where at packet size = 1000 bits, is about 8.5 ∗ 10ିଵଵ and 4.2 ∗ 10ି଼ in the proposed algorithm and the max CQI respectively, resulting in nearly 99.7% performance improve-

**Figure 10.** Spectral efficiency versus the power of the IoT devices. **Figure 10.** Spectral efficiency versus the power of the IoT devices.

ment.

**Figure 11.** Decoding error probability versus the packet size. **Figure 11.** Decoding error probability versus the packet size.

The computational complexity of both the proposed algorithm and the best CQI is () which means that they have linear complexity in the number of users and number of RBs. However, in [36], resource allocation for uplink multi carrier NOMA is developed using graph theory with complexity (ଷ). The shortest processing time (SPT) strategy is presented in [37] for uplink NOMA with complexity (ଶ). Thus, the proposed algorithm has a worthy complexity improvement. The computational complexity of both the proposed algorithm and the best CQI is *O*(*KN*) which means that they have linear complexity in the number of users and number of RBs. However, in [36], resource allocation for uplink multi carrier NOMA is developed using graph theory with complexity *O KN*3 . The shortest processing time (SPT) strategy is presented in [37] for uplink NOMA with complexity *O N*2 . Thus, the proposed algorithm has a worthy complexity improvement.

#### **7. Conclusions**

**7. Conclusions**  In this paper, an uplink NOMA resource allocation algorithm is proposed for a UAV-IoT-based communication network serving a large number of IoT devices of different applications. The optimization problem is formulated under constraints with the objective to maximize the data rate and minimize the delay. The scheduler works in time domain to optimize the delay, and in frequency domain to optimize the data rate. The power allocation is used to ensure fair data rates between users allocated the same RB. The simulation results show that the proposed algorithm significantly enhances the system fairness, delay and reliability, in addition to achieving a spectral efficiency and sum rate that In this paper, an uplink NOMA resource allocation algorithm is proposed for a UAV-IoT-based communication network serving a large number of IoT devices of different applications. The optimization problem is formulated under constraints with the objective to maximize the data rate and minimize the delay. The scheduler works in time domain to optimize the delay, and in frequency domain to optimize the data rate. The power allocation is used to ensure fair data rates between users allocated the same RB. The simulation results show that the proposed algorithm significantly enhances the system fairness, delay and reliability, in addition to achieving a spectral efficiency and sum rate that are nearly closer to the system upper bound.

**Author Contributions:** Conceptualization, R.K., M.A. and F.N.; methodology, R.K. and M.A.; software, R.K.; validation, R.K., M.A. and F.N.; formal analysis, R.K. ; writing—original draft preparation, R.K.; writing—review and editing, R.K. and M.A.; visualization, M.A.; supervision, M.A. and **Author Contributions:** Conceptualization, R.K., M.A. and F.N.; methodology, R.K. and M.A.; software, R.K.; validation, R.K., M.A. and F.N.; formal analysis, R.K.; writing—original draft preparation, R.K.; writing—review and editing, R.K. and M.A.; visualization, M.A.; supervision, M.A. and F.N. All authors have read and agreed to the published version of the manuscript.

F.N.; All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding.

**Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.

are nearly closer to the system upper bound.

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable.

**Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


**Acknowledgements**

This work was supported by the Robotics and Cybernetics Group at the *Centre for Automation and Robotics (CAR) UPM-CSIC*, and funded under the project *ROBOCITY 2030* sponsored by the Community of Madrid (S-0505/DPI/000235) and The project *ROTOS (MultiRobot Systems for Protection of large outdoor infrastructures)* sponsored by the Ministry of Science And Innovation of Spain (DPI2010-17998)


**2. Methods**

#### **2.1 Animals and diets**

Female pregnant *Wistar* rats weighing 200-250 g were obtained from the colony of Department of Nutrition of the Federal University of Pernambuco. Twenty-four hours after the birth of the entire mothers´ nestling, born on the same day, were contained in a large group and randomly each litter was culled to six males and two female pups. The litters

Among the various organic systems, the nervous system plays the main role in controlling several physiological processes. During development, this system presents a rapid growth spurt period or a vulnerable period which corresponds to the highest rate of cellular migration and differentiation, neurogenesis, synaptogenesis, myelinization and maturation of neurotransmitter pathways. Depending on the animal species, this critical period of intense neural development occurs at different time points early in life (Dobbing, 1968). In human, for example, it occurs during the last trimester of gestation until the second year of life, while in rats it corresponds the lactation period. During this period, the nutrition is one of the essential environmental factors to a normal development because it provides

The classical studies about malnutrition show that nutritional deficiency in macro or micronutrients has deleterious effects on the brain (Winick & Rosso, 1969). In rats, malnutrition induces functional and developmental failures, as well as reduction in brain size (Morgane et al., 1992;1993). In children, malnutrition showed influence both short and long term problems of cognition and behavior (Grantham-McGregor & Baker-Henningham,

Essential fatty acids are important constituents of structural lipids in nervous membranes cell and signaling molecules, as such, are involved in many brain functions. Around 30–40% of the total phospholipids in these structures are docosahexaenoic acid molecules (Young et al., 2000), which appear to be specifically concentrated in membranes surrounding synapses (Carlson, 2001). Changes in the quantity and quality of the dietary fatty acids are often

At the cellular level, an -linolenic deficient diet can induce less complex patterns of dendritic branching (Wainwright, 2002), smaller neurite growth in hippocampal neurons (Calderon & Kim 2004) and reduced neuronal soma size in some brain regions (Ahmad et al., 2002). Modification in the fatty acid composition of rat brain cell membranes of neurons, astrocytes, oligodendrocytes, and of subcellular fractions, such as myelin and synaptosomes, are also induced by a diet with reduced levels of n-3 fatty acids (Bourre et al., 1984). It has been shown that essential fatty acids imbalance as well as specific fatty acid deficiencies in the maternal diet can affect the neuromotor development of pups, including the ability to respond to environmental stimulation (Lamptey & Walker, 1976; Wainwright, 2002;

Fats and oils as they exist in nature must be processed before they are suitable for human consumption (González et al., 2007). On the other hand, only a few studies have described the effects of the ingestion of trans fatty acids early in life on the rat brain development. In this study we investigated the replacement of soybean oil in the diet by partially hydrogenated vegetable oil, rich in trans fatty acids, from the beginning of gestation

Female pregnant *Wistar* rats weighing 200-250 g were obtained from the colony of Department of Nutrition of the Federal University of Pernambuco. Twenty-four hours after the birth of the entire mothers´ nestling, born on the same day, were contained in a large group and randomly each litter was culled to six males and two female pups. The litters

nutrients without them the neurodevelopment would be impaired (Walker, 2005).

associated with developmental and functional alterations in the nervous system.

**1.2 The role of lipids on the development of nervous system**

2005; Benton, 2008).

Anselmo et al., 2006).

**2. Methods**

**2.1 Animals and diets**

through lactation on reflex ontogeny.

were also randomly assigned to isocaloric diets containing as lipid source 7% soybean oil (control group-C; n=32) or 7% of hydrogenated vegetal fat (experimental group-E; n=39), since gestation until weaning (21 days old). Both diets (table 1) were formulated based on recommendations of the American Institute of Nutrition-AIN-93 (Reeves et al., 1993). The animals were kept on a 12:12-h light –dark photoperiod at 24o C temperature during the whole period. The animals were maintained according to recommendations from the National Institute of Health (USA) and approved by the Ethics Committee for Use Animal, Federal University of Pernambuco (CEUA, protocol.23076.020339/2010-24). After delivery, from P1 until 21d, the pups were weighted at 1, 7, 14 and 21days of age. Indicators of somatic maturation and reflex ontogeny were studied daily from P1 to P21 between 07:00 am and 09:00 am. Daily it was observed the occurrence of the reflex responses, being considered the consolidation day to be the first one, of a series of three consecutive days where the reply was verified. For each reflex it was established a maximum observation time of 10s according to the experimental model established by Smart & Dobbing (1971).

Table 1. Composition of the diets. Vitamin mixture (Rhoster Ind.Com. LTDA. SP. Brazil) containing (m%): folic acid (20); niacin (300); biotin (2); calcium pantothenate 160; pyridoxine 70; riboflavin 60; thiamine chloride 60; vitamin B12 0.25; vitamin K1 7.5. Additionally containing (UI%): vitamin A 40.000; vitamin D3 10.000; vitamin E 750. 2 Mineral mixture (Rhoster Ind. Com. LTDA. SP. Brazil) containing (m%): CaHP04 (38); K2HP04 (24); CaCO3 (18.1); NaF (0.1); NaCl(7.0); MgO (2.0); MgS04 7H20 (9.0); FeS04 7H20 (0.7); ZnS04 H20 (0.5); MnSO+ H20 (0.5); CuS04 5H20 (0.1); Al2 (S04)3K2S04 24H20 (0.02); Na2SeO3 5H20 (0.001); KCl (0.008).

#### **2.2 Indicators of somatic maturation**

The following indicators of somatic maturation, as illustrated in figure 1, were analyzed in order to study whether the replacement of soybean oil by vegetable hydrogenated fat in the diet influenced the development of physical features of the rat pups.

#### **2.3 Indicators of reflex ontogeny**

The following indicators of the reflex ontogeny investigated at the present study are described and illustrated below (figure 2):

*Palmar Grasp (PG)-* This reflex is present at birth and consists of a dorso flexion of the digits ('grasping') in response to the stimulation of the hand-palm with a small metallic stick. The

Lipids, Nutrition and Development 101

expected response is the disappearance of the palmar grasping response, as the organism

*Righting (R)-* The newborn is placed on its back on a flat surface and the expected mature response is to turn over on the ventral surface, resting in the normal position with the four

*Vibrissa Placing (VP)-* The pup is held by the tail, with the head facing the edge of a table and the vibrissae just touching the vertical surface of the table. The expected response is to lift

*Cliff Avoidance (CA) -* The newborn is placed on the edge of a 'cliff' (for instance, on the edge of a table), with the forepaws and face just over the edge. The expected response is to move

*Negative Geotaxis (NG)-* The pup is placed on an inclined ramp (45º slope) with its head pointing to the ground. The expected mature response is to turn around and crawl up the

*Free-Fall Righting (FFR)-* The pup is held with the back downwards 35cm above a cotton pad

*Auditory Startle Response (ASR)-* The newborn is exposed suddenly to a loud, sharp noise. The expected response is a prompt extension of the head and the limbs, followed by

The body weight was analyzed by Student's t-test. Results are presented as means±standard error of the mean (SEM). Differences were significant when p< 0.05. Results of the somatic maturation and reflex ontogeny were evaluated by Mann-Whitney test. Results are

The figure 3 shows that pups fed an experimental diet did not exhibited significant differences in the body weight at the 1st, 7th, 14th and 21th day, during the lactation period when compared to the controls. (C = 6.7 g ± 0.12; 16.3 g ± 0.49; 29.6 g ± 1.18; 46.4 g ±1.52; E =

The effect of the experimental diet on somatic development is shown in Figure 4, where the results are expressed in median (min. – max.) and compared with the control group. There was no difference between the number of days for ear unfolding, eye opening and the eruptions of superior and inferior incisors. However, the opening of the external auditory canal was significantly delayed in the experimental group as compared to the control (C: 12-

As can be seen in Figure 5, the development of the early reflexes which appear in the first postnatal week such as righting, cliff avoidance and vibrissa placing did not differ between control and experimental pups. In the second postnatal week, the negative geotaxis was the only reflex which was delayed in the experimental group when compared to the control (C:

and dropped. The expected response is to turn in mid-air to land on its four paws.

expressed as median interquartile. Statistical significance was set at p < 0.05.

the head and to extend the fore legs in direction of the table.

away from the cliff, to avoid dropping.

withdrawal of the limbs and a crouching posture.

6.6 g ± 0.11; 16.5 g ± 0.22; 30.3 g ± 0.48; 47 g ± 0.86).

**3.2 Indicators of somatic maturation**

**3.3 Indicators of reflex ontogeny**

matures.

slope.

feet on the ground.

**2.4 Statistical analysis**

**3. Results**

**3.1 Body weight**

1; E: 14-2.5; p<0.05).

11-3; E: 9-1.5).

Fig. 1. Indicators of somatic maturation. A) Eruption of the Upper Incisors (EUI) and Eruption of the Lower Incisors (ELI); B) Ear Unfolding (EU); C) Eye Opening (EO); D) Auditory Conduit Opening (ACO).

Fig. 2. The figure represents the indicators of reflex ontogeny observed during lactation period.

Fig. 1. Indicators of somatic maturation. A) Eruption of the Upper Incisors (EUI) and Eruption of the Lower Incisors (ELI); B) Ear Unfolding (EU); C) Eye Opening (EO); D)

Fig. 2. The figure represents the indicators of reflex ontogeny observed during lactation

Auditory Conduit Opening (ACO).

period.

expected response is the disappearance of the palmar grasping response, as the organism matures.

*Righting (R)-* The newborn is placed on its back on a flat surface and the expected mature response is to turn over on the ventral surface, resting in the normal position with the four feet on the ground.

*Vibrissa Placing (VP)-* The pup is held by the tail, with the head facing the edge of a table and the vibrissae just touching the vertical surface of the table. The expected response is to lift the head and to extend the fore legs in direction of the table.

*Cliff Avoidance (CA) -* The newborn is placed on the edge of a 'cliff' (for instance, on the edge of a table), with the forepaws and face just over the edge. The expected response is to move away from the cliff, to avoid dropping.

*Negative Geotaxis (NG)-* The pup is placed on an inclined ramp (45º slope) with its head pointing to the ground. The expected mature response is to turn around and crawl up the slope.

*Free-Fall Righting (FFR)-* The pup is held with the back downwards 35cm above a cotton pad and dropped. The expected response is to turn in mid-air to land on its four paws.

*Auditory Startle Response (ASR)-* The newborn is exposed suddenly to a loud, sharp noise. The expected response is a prompt extension of the head and the limbs, followed by withdrawal of the limbs and a crouching posture.

#### **2.4 Statistical analysis**

The body weight was analyzed by Student's t-test. Results are presented as means±standard error of the mean (SEM). Differences were significant when p< 0.05. Results of the somatic maturation and reflex ontogeny were evaluated by Mann-Whitney test. Results are expressed as median interquartile. Statistical significance was set at p < 0.05.


**7. Conclusion**

**Figure 2.** Various shapes of gold nanoparticle.

20 Advanced Technology for Delivering Therapeutics

(610 nm), and Maple Red-Orange (620nm).

Quantum dots are tiny semiconductor crystals of luminescent nanocrystals with rich surface chemistry and unique optical properties with the size of 1–10 nm made up of compounds from group II to VI and III to V, for example, Ag, Cd, Hg, Ln, P, Pb, Se, Te, Zn, and so on. QDs have distinctive characteristics such as size-tunable light emission, improved signal brightness, resistance against photobleaching, and simultaneous excitation of multiple fluorescence

Depending on their size by laser, the quantum dots glow brightly in different colors, such as Adirondack Green (520nm), Blue (514 nm), Greenish blue (544 nm), Green (559 nm), Yellowish green (571 nm), Yellow (577 nm), Yellowish orange (581 nm), Fort Orange (600nm), Orange

QDs are nearly spherical semiconductor particles with core-shell structure. Colloidal core/shell QDs, such as CdSe/ZnS, CdSe/CdS/ZnS, CdTe/CdSe, and InP/ZnS, are commonly synthesized for biomedical applications, whereas CdSe/ZnS, CdTe/ZnS, and CdSe/CdS/ZnS have been

**Core** is made up of CdSe, which is a semiconductor material. Core is surrounded by shell which is made up of ZnS for improving its optical properties and cap encapsulates the double layer quantum dots by different materials like silica which helps in improving solubility in

Quantum dots are made up of three parts, that is, core, shell, and cap.

aqueous buffers. Structure of quantum dot is shown in **Figure 3**.

**6.3. Quantum dots**

colors.

commonly used.

Recently nanotechnology-based gene delivery is one of the most attractive therapeutic methods for treatment of various diseases. In drug delivery, size and distribution of particles are critical parameters to target specific organs and tissues. Proteins (derived from their secondary structure) are suitable materials for drug/gene carriers due to their precise molecular sizes. An ideal nanoparticle formulation for a drug or gene carrier system can achieve long circulation time, low immunogenicity, good biocompatibility, and selective targeting.

Gene delivery involves viral and non-viral vectors. Viral vectors are having low loading capacity, large-scale manufacturing, quality control cost, and safety factor such as immunogenicity and potential oncogenicity. From the stability and safety concern, non-viral vectors have more efficiently passing the gene transfection through the biological barriers compared to viral vectors. Organic, inorganic, and various hybrid materials are used for the preparation of nanoparticles. Among these, polymeric nanoparticles have great therapeutic application due to its wide range of sizes and varieties and can be used in sustained and targeted gene delivery for long periods. Biopolymers used for the preparation of nonviral vectors possess several favorable characteristics, such as high biocompatibility, low toxicity, good biodegradability, and abundant renewable sources, which can be used for efficiency delivery of drug/ gene to the target site.

Choosing a suitable design of nanoparticle structure can increase gene transfection efficiency to overcome extracellular and intracellular transfection barriers: the blood stream, the cellular membrane, endosomes, and the nuclear membrane. Nanoparticle in gene delivery depends upon the nature of the polymer charge and its chain length. Furthermore, modifications in the nanoparticle by introducing ligands onto the surface can enhance localization and retention in specific target tissue, local delivery of agents to a large volume of tissues for better clinical application. However, biopolymer-based nanoparticle will become a tool in near future for the precisely targeted delivery of drugs and genes in many therapeutic fields, but toxicological issues and degradation products of nanoparticles are need to be considered before being applied into humans.


**5. Experimental results**

The DTC strategy were implemented using a Texas Instruments DSP TMS320F2812 platform. The system consists of a three-phase voltage source inverter with insulated-gate bipolar transistors (IGBTs) and the three-phase induction motor parameters are shown in the appendix. The stator voltage commands are modulated by using symmetrical space vector PWM, with switching frequency equal to 2.5 kHz. The DC bus voltage of the inverter is 226 V. The stator voltages and currents are sampled in the frequency of 2.5 kHz. A conventional PI regulators generates a torque reference by using the speed error. The flux and torque estimation, and the flux and torque PIs regulators and speed controller have the same sampling frequency of 2.5 kHz. The encoder resolution is 1500 pulses per revolution. The algorithm of the DTC strategy was programmed on the Event Manager 1 of the Texas Instruments DSP TMS320F2812 platform and its flowchart is presented in Figure 11 and the schematic of implemention is presented in Figure 12.

**Figure 12.** Schematic of implemention.

motor speed operation at 2 Hz and 6 Hz.

measurements of currents, voltages and parameters variations.

Five no-load induction motor tests were made. The first one was the response to a torque step of 12.2 Nm which is shown in Figure 13. It can be seen the satisfactory response of torque although it has oscillation. This oscillation occurs due to the natural lack of accuracy in the

335

Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

Figure 14 shows when the speed varies from 6.28 rad/s to 18.85 rad/s in 200 ms. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions although the gains of PI are designed for induction

In the third test the speed varies in forward and reversal operation and the result are presented in Figures 15(a) and 15(b). The speed changes from 13 rad/s to -13 rad/s in 1 s and the gains of PI regulator are not changed during the test. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions and the PI regulator was designed for induction motor speed operation at 4.15 Hz. The small

Figure 16 presents the speed response when the speed varies from 6.28 rad/s to -6.28 rad/s. The result confirms the satisfactory performance of the PI regulator again due to the fact that

error occurs due the natural lack of accuracy in the measurement of the speed.

**Figure 11.** The flowchart of the DSP program.

**Figure 12.** Schematic of implemention.

10 Will-be-set-by-IN-TECH

The DTC strategy were implemented using a Texas Instruments DSP TMS320F2812 platform. The system consists of a three-phase voltage source inverter with insulated-gate bipolar transistors (IGBTs) and the three-phase induction motor parameters are shown in the appendix. The stator voltage commands are modulated by using symmetrical space vector PWM, with switching frequency equal to 2.5 kHz. The DC bus voltage of the inverter is 226 V. The stator voltages and currents are sampled in the frequency of 2.5 kHz. A conventional PI regulators generates a torque reference by using the speed error. The flux and torque estimation, and the flux and torque PIs regulators and speed controller have the same sampling frequency of 2.5 kHz. The encoder resolution is 1500 pulses per revolution. The algorithm of the DTC strategy was programmed on the Event Manager 1 of the Texas Instruments DSP TMS320F2812 platform and its flowchart is presented in Figure 11 and the

**5. Experimental results**

schematic of implemention is presented in Figure 12.

**Figure 11.** The flowchart of the DSP program.

Five no-load induction motor tests were made. The first one was the response to a torque step of 12.2 Nm which is shown in Figure 13. It can be seen the satisfactory response of torque although it has oscillation. This oscillation occurs due to the natural lack of accuracy in the measurements of currents, voltages and parameters variations.

Figure 14 shows when the speed varies from 6.28 rad/s to 18.85 rad/s in 200 ms. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions although the gains of PI are designed for induction motor speed operation at 2 Hz and 6 Hz.

In the third test the speed varies in forward and reversal operation and the result are presented in Figures 15(a) and 15(b). The speed changes from 13 rad/s to -13 rad/s in 1 s and the gains of PI regulator are not changed during the test. This result confirms the satisfactory performance of the controller due to the fact that the the speed reaches the reference in several conditions and the PI regulator was designed for induction motor speed operation at 4.15 Hz. The small error occurs due the natural lack of accuracy in the measurement of the speed.

Figure 16 presents the speed response when the speed varies from 6.28 rad/s to -6.28 rad/s. The result confirms the satisfactory performance of the PI regulator again due to the fact that

(a) Speed reversal operation (12.57 rad/s.div).

337

Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

(b) Speed forward and reversal (13 rad/s.div).

**Figure 15.** Speed forward and reversal operation and *a* phase current (10 A/div)

**Figure 16.** Speed response to step operation (12.57 rad/s.div) and *a* phase current (10 A/div).

**Figure 13.** Responses to step torque operation (9 Nm/div).

**Figure 14.** Speed forward and reversal operation (15.7 ras/s.div) and *a* phase current (10 A/div).

the speed reaches the reference value and the gains of PI are designed for induction motor speed operation at 2 Hz.

In load test the speed reference was 36.6 rad/s and a load torque of 11.25N.m was applied to the motor. In this test a dc generator is coupled to the rotor of induction motor. So the generated voltage of the DC generator is conected to the load with variable resistance. The test is shown in Figure 17 and the steady state error is 4.5%.

336 Induction Motors – Modelling and Control Tuning PI Regulators for Three-Phase Induction Motor Space Vector Modulation Direct Torque Control Using Complex Transfer Function Concept 13 337 Tuning PI Regulators for Three-Phase Induction Motor Space Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

12 Will-be-set-by-IN-TECH

**Figure 14.** Speed forward and reversal operation (15.7 ras/s.div) and *a* phase current (10 A/div).

test is shown in Figure 17 and the steady state error is 4.5%.

the speed reaches the reference value and the gains of PI are designed for induction motor

In load test the speed reference was 36.6 rad/s and a load torque of 11.25N.m was applied to the motor. In this test a dc generator is coupled to the rotor of induction motor. So the generated voltage of the DC generator is conected to the load with variable resistance. The

**Figure 13.** Responses to step torque operation (9 Nm/div).

speed operation at 2 Hz.

(b) Speed forward and reversal (13 rad/s.div).

**Figure 15.** Speed forward and reversal operation and *a* phase current (10 A/div)

**Figure 16.** Speed response to step operation (12.57 rad/s.div) and *a* phase current (10 A/div).

**Author details**

**7. References**

39(5): 217–220.

*Engineering Society* .

*Trans. Power Electronics* 3(4): 420–429.

graphs, *IEEE Trans. Ind. Electron.* 42: 263–271.

*IEEE Trans. Ind. Applications* 40: 1388–1397.

The Netherlands: Elsevier.

*Applications* 43(6): 1639–1649.

16(6): 846–851.

Alfeu J. Sguarezi Filho

*Universidade Federal do ABC, Brazil*

José Luis Azcue and Ernesto Ruppert

*School of Electrical and Computer Engineering, University of Campinas, Brazil*

using complex vectors, *IEEE Trans. Ind. Applicat.* 32: 817–825.

motor direct torque control, *Sba Controle e Automação* 20(2).

of stator flux, *Electric Power Systems Research* 78: 1712–1718.

complex transfer functions, *IEEE Trans. Ind. Electron.* 42: 263–271.

[1] Blaschke, F. [1977]. The principle of field orientation control as applied to the new transvector closed loop control system for rotating machines, *Siemens Review*

Tuning PI Regulators for Three-Phase Induction Motor Space

Vector Modulation Direct Torque Control Using Complex Transfer Function Concept

339

[2] Briz, F., degener, M. W. & Lorenz, R. D. [2000]. Analysis and design of current regulators

[3] Buja, G. & Kazmierkowski, M. [2004]. Direct torque control of pwm inverter-fed ac

[4] Cad, M. M. & de Aguiar, M. L. [2000]. The concept of complex transfer functions applied to the modeling of induction motors, *IEEE Winter Meeting 2000 of the IEEE Power*

[5] Casadei, D., Serra, G. & Tani, A. [2001]. Steady-state and transient performance evaluation of a dtc scheme in the low speed range, *IEEE Trans. on Power Electronics*

[6] Depenbrock, M. [1988]. Direct self-control(dsc) of inverter-fed induction machine, *IEEE*

[7] Filho, A. J. S. & Filho, E. R. [2008]. The complex controller applied to the induction motor control, *IEEE Applied Power Electronics Conference and Exposition - APEC* pp. 1791–1795. [8] Filho, A. J. S. & Filho, E. R. [2009]. The complex controller for three-phase induction

[9] Gataric, S. & Garrigan, N. R. [1999]. Modeling and design of three-phase systems using

[10] Holtz, J. [1995]. The representation of ac machine dynamics by complex signal flow

[11] Holtz, J., Quan, J., Pontt, J., Rodríguez, J., newman, P. & Miranda, H. [2004]. Design of fast and robust current regulators for high-power drives based on complex state variables,

[12] Kenny, B. H. & Lorenz, R. D. [2001]. Stator and rotor flux based deadbeat direct torque control ofinduction machines, *IEEE Industry Applications Conference* 1: 133–139. [13] Kovács, P. K. & Rácz, E. [1984]. *Transient Phenomena in Electrical Machines*, Amsterdam,

[14] Kumsuwana, Y., Premrudeepreechacharna, S. & Toliyat, H. A. [2008]. Modified direct torque control method for induction motor drives based on amplitude and angle control

[15] Lee, K.-B., Blaabjerg, F. & Yoon, T.-W. [2007]. Speed-sensorless dtc-svm for matrix converter drives with simple nonlinearity compensation, *IEEE Transactions on Industry*

motors - a survey, *Industrial Electronics, IEEE Transactions on* 51(4): 744–757.

**Figure 17.** Load test (18,3 rad/s.div) and *a* phase current (20 A/div).


*2.4. Data Analysis*

Descriptive data are presented, including range and mean ± SD as appropriate. An unpaired *t*-test on the excursions (ΔT ◦C = threshold temperature–skin temperature) was used to compare the data collected with wired and wireless systems in cats and horses. Friedman's test was used to compare baseline data with NT after opioid treatment as the data are not normally distributed due to "capping" of the peak TT by the cut-off (GraphPad Prism v8). *p* < 0.05 was regarded as significant.


**2.2 CD96**

CD96 is a member of the immunoglobulin superfamily, a transmembrane glycoprotein, and a T-cell surface-specific receptor 6. By using blood samples from 55 patients with AML, Du et al. found that CD96 (>10%)-enriched patients showed a poor response to chemotherapy [20]. Of note, CD96 was proved to be an efficient identical marker of LSCs in CD34+ CD38<sup>−</sup> groups.


2.2.2. Performance Analysis

According to the above analysis, it is easy to obtain the directivity function of the passive two-hydrophone algorithm based on FDA technology:

$$R(\theta) = \left| \frac{\sin(\pi M \Delta f \frac{d \sin \theta}{c})}{M \sin(\pi \Delta f \frac{d \sin \theta}{c})} \right|. \tag{14}$$

The azimuth resolution, based on half the width of the main lobe, is defined as in Equation (14):

$$\theta\_{\mathcal{I}} = \arcsin(\frac{c}{N\Delta f d}).\tag{15}$$

In order not to obtain a grating lobe, the scanning angle θ needs to satisfy sin(θ) ≤ *c* 2Δ*f d* . In general, the scanning angle is −90◦ to 90◦, so when frequency domain sampling is performed on the signal, the frequency interval Δ*f* ≤ *c* 2*d* should be satisfied.

According to the beamforming of Equation (13), the output SNR is:

$$SNR\_{out} = 10\log\frac{\sum\_{m=1}^{M} \left| X\_1(f\_m) \right|^2}{\sum\_{m=1}^{M} A\_{f\_m} Z\_N(f\_m)}.\tag{16}$$

It can be seen from Equation (16) that the less related the ambient noise between the frequencies, the higher the output SNR.


**1. Introduction**

Bone quality depends on the structural and material properties of the bone. By increased mortality and healthcare costs due to bone fractures, bone fragility becomes a major health concern [1]. In order to assess bone fragility, the integration of quantity, quality, and turnover of bone factors is necessary. The BMD, quantified using the clinical imaging technique called X-ray radiography, namely, the dual-energy X-ray absorptiometry (DXA), is one of the most important bone factors reflecting the quality of bone in terms of quantity to assess bone fracture risk in osteoporotic patients [2]. Osteoporosis is a biochemical problem characterized by a decrease in bone mass, a deterioration and an alteration of bone tissue microarchitecture, which increases the risk of fractures. Old bone fracture, oxidative stress, age, and menopause are among the main causes of osteoporosis. Giving its various causes, osteoporosis could affect any gender at any age. For women and men, for example, osteoporosis is associated with aging and more specifically, for women, with hormonal deficiency caused by menopause [3]. Meanwhile for children, BMD loss is generally related to diseases' or treatments' use.

A wide variety of diseases and treatments containing toxic agents for bone cause or contribute to osteoporosis development [4]. In this chapter, we will discuss the diseases and treatments inducing BMD abnormal loss or gain and report different studies' findings concerning diseases and treatment association with osteoporosis. Our work would be subdivided into three main parts: (i) BMD generalities; (ii) osteoporosis in women, men, and children; and (iii) diseases and clinical interventions to limit osteoporosis development.


**Acknowledgements**

M. S. G. Tsuzuki is partially supported by CNPq (process 311.195/2019-9). A. K. Sato is supported by FUSP/Petrobras.

## **Author details**

Marcos S.G. Tsuzuki1 \*†, Ahmad Barari2†, André K. Sato1†, Rogrio Y. Takimoto1† and Tomoki Saka3†

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Introductory Chapter: Optimization Problems in Engineering DOI: http://dx.doi.org/10.5772/intechopen.103719*


**1. Introduction**

Solder alloys are widely used bonding materials in electronics industry. The reliability con‐ cerns for solder interconnections, which provide both mechanical and electronic connec‐ tions, are rising with the increasing use of highly integrated components in portable electronic products [1-6]. As shown in Fig. 1, a typical ball grid array (BGA) component board usually consists of a silicone die, molding compound, solder interconnections, and printed wiring board (PWB). In service, all products are subjected to thermal cycles as a re‐ sult of temperature changes due to component internal heat dissipation or ambient tempera‐ ture changes. The existence of coefficient of thermal expansion (CTE) mismatches between dissimilar materials (about 16 ppm/°C for PWB and 2.5 ppm/°C for Si die [7]) is the source of deformation and thermomechanical stress in the solder interconnection, which leads to the cracking of the interconnections and failures of the electronic devices.

© 2013 Li et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Since failure of solder interconnections is a typical failure mode in many electronic devices, the reliability and life time prediction of solder interconnections become crucial. Various re‐ liability test and computer-aided simulations have been carried out to study the solder inter‐ connection reliability [8-17]. With the experimental and simulation results, a number of lifetime prediction models have been established and they can be classified into two main categories: strain-based and energy-based. For instance, the Engelmaier model is based on the total shear strain range, the Coffin-Manson model on the plastic strain, and the Dar‐ veaux model on the energy density [18-20]. However, microstructural changes in the bulk solder have not yet been included in any of the popular prediction models. Especially the microstructural changes associated with recrystallization and grain growth are of impor‐ tance because they can significantly affect the mechanical properties and can cause recrystal‐ lization induced failure of solder interconnections [21-26]. A new approach for lifetime prediction needs to be developed that takes into account the microstructural changes. In or‐ der to achieve this, the first step is to quantitatively study the recrystallization and grain growth occurring in solder interconnections.

In this chapter, the current understanding of the microstructural changes in solder intercon‐ nections is introduced, followed by a brief review of the Monte Carlo simulations of grain growth and recrystallization. Then, a new algorithm for predicting dynamic recrystallization in solder interconnections during thermal cycling tests is presented.

**Figure 2.** The as-solidified microstructure of a SnAgCu solder interconnection; (a) optical bright field image, (b) cross-

Simulation of Dynamic Recrystallization in Solder Interconnections during Thermal Cycling

http://dx.doi.org/10.5772/53820

93

For decades, the industry has used recrystallization to control microstructures, and static re‐ crystallization of structural metals after deformation is probably the best understood recrys‐ tallization process [22]. On the other hand, dynamic recrystallization during cyclic deformation, which occurs in solder interconnections, has received much less attention and is still poorly understood. This is because the related microstructural events are highly com‐ plex from the microstructural point of view. The major understanding of this subject is brief‐

Thermal cycling tests with extreme temperatures in the range of about -40 °C to +125 °C are usually carried out to assess the reliability of electronic devices [35, 36]. During thermal cy‐ cling, the solder interconnections are under cyclic loading conditions. The induced thermo‐ mechanical stresses are often higher than the yield strength of the material, which leads to plastic deformation. A fraction of the energy associated with the plastic deformation of sol‐ der interconnections is stored in the metal, mainly in the form of dislocations. The stored en‐ ergy is subsequently released during restoration, which can be divided into three main processes: recovery, primary recrystallization and grain growth. Recovery and recrystalliza‐ tion are two competing processes, which are driven by the increased internal energy of the deformed solder. Recovery decreases the driving force for recrystallization and thus hinders the initiation of recrystallization. In high stacking fault energy metals such as Sn, the release of stored energy takes place so effectively by recovery that recrystallization will not practi‐ cally take place [22, 23]. Studies have shown that after a single deformation static recrystalli‐ zation rarely occurs in Sn-rich solders [37]. However, under dynamic loading conditions such as in thermal cycling tests, recrystallization often takes place in the high stress concen‐

Experimental observations indicate that the microstructure of solder interconnections may change significantly during thermal cycling tests. The as-solidified microstructure can trans‐

**2.2. Recovery and recrystallization of Sn-rich solder interconnections**

polarized light image.

ly summarized as follows.

tration regions of solder interconnections [28, 38, 39].


**1. Introduction**

With an amorphous atomic structure, metallic glasses (MGs) (also called amorphous alloys) own some unique features compared to the conventional metal alloys, which make them versatile materials [1–7]. For example, MGs commonly show very high strength [8, 9], and thus they are very promising materials for fabrication of aircraft frames. High hardness and excellent resistance to wear make them potential candidates for contact applications such as phone's shell. The high elasticity makes them suitable for applications as golf clubs or spring [10]. High-strength, low elastic modulus, and good corrosion resistance make MGs promising applications as biomedical materials [2]. Although great progress has been achieved for MGs in the past decades, their practical applications as structural and functional materials are greatly impeded due to three main problems [1, 11], that is, dimensional limit, poor tension plasticity, and hard-to-machining and shaping.

As the formation of amorphous structure requires a high cooling rate, the size of MGs is greatly limited. Although some MGs with relatively good glass forming ability (GFA) are developed recently, the size of MG sample is quite small compared to that of conventional metal alloys. Currently, some new methods such as laser additive manufacturing are employed to produce MGs [12–15], which are promising to solve the problem of dimensional limit. However, additional issues such as crystallization and crack appear, which require further investigation.

For applications as structural materials, tensile plasticity is necessary. However, most MGs exhibit brittle fracture under tensile stress due to the fast propagation of single or very few shear bands [16, 17]. Therefore, improving the tensile plasticity of MGs is a very significant topic for their practical applications. Recently, some methods such as introduction of secondary phase into the glass matrix (i.e., fabrication of metallic glass matrix composites (MGMC)) [18–20], mechanical pre-deformation [21], surface modification [22–25] are proposed to tune the tensile plasticity of MGs, achieving some progress. However, the foundational mechanism

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and physical nature for plastic deformation and improvement of the plasticity of MGs are still not very clear. Further investigation by advanced experiments and simulations is required.

[6] Inoue A, Nishiyama N. New bulk metallic glasses for applications as magnetic-sensing,

Introductory Chapter: Properties and Processing of Metallic Glasses

http://dx.doi.org/10.5772/intechopen.78665

5

[7] Inoue A, Takeuchi A. Recent development and applications of bulk glassy alloys. Inter

[8] Amiya K, Inoue A. Fe-(Cr,Mo)-(C,B)-Tm bulk metallic glasses with high strength and

[9] Amiya K, Urata A, Nishiyama N, Inoue A. Fe-B-Si-Nb bulk metallic glasses with high strength above 4000 MPa and distinct plastic elongation. Materials Transactions. 2004;

[11] Hofmann DC, Suh JY, Wiest A, Duan G, Lind ML, Demetriou MD, Johnson WL.Designing metallic glass matrix composites with high toughness and tensile ductility. Nature.

[12] Shen YY, Li YQ, Chen C, Tsai HL. 3D printing of large, complex metallic glass structures.

[13] Yang C, Zhang C, Xing W, Liu L. 3D printing of Zr-based bulk metallic glasses with complex geometries and enhanced catalytic properties. Intermetallics. 2018;**94**:22-28 [14] Li N, Zhang JJ, Xing W, Ouyang D, Liu L. 3D printing of Fe-based bulk metallic glass composites with combined high strength and fracture toughness. Materials and Design.

[15] Ouyang D, Li N, Xing W, Zhang JJ, Liu L. 3D printing of crack-free high strength Zr-based bulk metallic glass composite by selective laser melting. Intermetallics. 2017;**90**:128-134

[16] Sun BA, Wang WH. The fracture of bulk metallic glasses. Progress in Materials Science.

[17] Xu J, Ramamurty U, Ma E. The fracture toughness of bulk metallic glasses. JOM. 2010;

[18] Ning ZL, Liang WZ, Zhang MX, Li ZZ, Sun HC, Liu AL, Sun JF. High tensile plasticity and strength of a CuZr-based bulk metallic glass composite. Materials and Design.

[19] Hays CC, Kim CP, Johnson WL. Microstructure controlled shear band pattern formation and enhanced plasticity of bulk metallic glasses containing in situ formed ductile phase

[20] Qiao JW, Jia HL, Liaw PK. Metallic glass matrix composites. Materials Science and

[21] Gu J, Song M, Ni S, Liao XZ, Guo SF. Improving the plasticity of bulk metallic glasses via pre-compression below the yield stress. Materials Science and Engineering A.

dendrite dispersions. Physical Review Letters. 2000;**84**:2901-2904

chemical, and structural materials. MRS Bulletin. 2007;**32**:651-658

high glass-forming ability. Materials Transactions. 2006;**47**:1615-1618

[10] Telford M. The case for bulk metallic glass. Materials Today. 2004;**7**:36-43

national Journal of Applied Glass Science. 2010;**1**:273-295

**45**:1214-1218

2008;**451**:1085-10U3

2018;**143**:285-296

2015;**74**:211-307

2016;**90**:145-150

2014;**602**:68-76

Engineering Reports. 2016;**100**:1-69

**62**:10-18

Materials and Design. 2017;**117**:213-222

For practical applications of MGs, shaping them into parts is the first step. Due to the superplasticity within the supercooled liquid region (SCLR), thermoplastic forming provides a unique method for processing MGs, which has been widely employed and investigated [4, 26, 27]. However, the flexibility of this method is quite low, and this method also requires expensive molds. Furthermore, it may be only suitable for MGs with large SCLR; otherwise, crystallization may occur. Apart from thermoplastic forming, conventional machining such as diamond cutting [28–32], and non-conventional machinings such as micro-electrical discharge machining (micro-EDM) and laser irradiation [33–36] are also attempted for processing MGs. Some progress is achieved by these methods but also challenges remain [29, 36, 37]. Further investigations on these processing methods as well as developing new methods are required.