*6.1.1 Methods*

In the first years of the emergence of 3D printing, conventional methods of this technique such as fused deposition modeling (FDM), stereolithography (SLA), and selective laser sintering (SLS) were used to print tissue engineering structures. Although these methods provided unique capabilities compared to the traditional scaffold construction methods, however, as time passed and the disadvantages of these methods became clear, such as the inability to load cells and bioactive molecules, the inadequate resolution, and the impossibility of using a wide range of materials led researchers to develop 3D bio-printing technology. In recent years, the use of 3D bio-printing technology has accelerated. This method is divided into three main types: inkjet-based bioprinting, extrusion-based bioprinting, and laser-assisted bioprinting [136–139]. Inkjet-based bioprinting includes the deposition of bio-ink droplets onto a substrate. Although this method can print a cell-laden scaffold at a high speed, the number of biomaterials that can be used in an inkjet printer is limited, due to the rapid gelation time requirement. The extrusion-based bioprinting method is extruding high cell density laden bio-inks to create scaffold structures. It is the most easiest and popular 3D bio-printing method. In laser-assisted bioprinting, the bioinks are printed using the laser in a nozzle-free manner with higher resolution. The laser heats the determined points and deposits the cells in the exact place [140].

### *6.1.2 Bone model optimizing*

As mentioned before, the 3D bio-printing can create personalized complex structures. The computer modeling of the 3D bio-printing structures has two main steps. The first step is data acquisition using computed tomography (CT) or magnetic resonance imaging (MRI) and the second step is image processing and model generation [141]. The 3D models should be predictable and shows controllable shape change. Therefore, the 3D model design should be optimized by considering chemical composition, volume fraction, and structural features such as pore size, pore shape, pore distributions, and mechanical properties [142]. The finite element analysis can be used to calculate the mechanical properties of the designed structures and predict the results, theoretically. Liang et al. [143] demonstrated the tetragonal structures showed better mechanics than the tetragonal, hexagonal, and wheel-like designed structures for bone replacements using finite element analysis and an electromechanical universal testing system. The combination of state-of-the-art optimization

techniques with computer models can provide a basis for predicting scaffold behavior and optimizing the designed scaffolds for bone regeneration, especially for large bone defect regeneration [144].


**4. Conclusions**

The study successfully functionalized the algal material with tetramethylethylenediamine, and the FTIR spectrum provided evidence of its functional groups capable of binding metal ions. Adsorption of the three metals was best at lower pH values (4.2–6.8). Beyond these values, the adsorption decreased considerably. The rate of adsorption was very fast as more that 90% of the metals were removed from the solution within 30 min. The adsorption of copper fitted into the Langmuir adsorption isotherm with *R*2 values of 0.974 and 0.512 for the unmodified and modified sorbents, respectively, indicating a monolayer-binding mechanism. Cadmium and lead fitted into the Freundlich adsorption mechanism (R2 values were Cd modified = 0.993, unmodified = 0.251, Pb modified = 0.906, unmodified = 0.929). The adsorption of lead and cadmium was by Ho's pseudo-second-order kinetics confirming a multi-site interaction, whereas copper followed the pseudo-first-order kinetics, evidence of single-site adsorption. The adsorption by the algal material did not improve upon modification since natural ligands were replaced with ethylenediamine which has a lower stability constant for the metal analytes but minimized leaching of dissolved organic matter. In general the study has shown that the algal material can be used for as an effective sorbent for removal of lead, cadmium and copper from contaminated wastewater at low pH values.


*2.5. Phylogenetic Analysis of PPR Proteins*

A total of 422 PPR protein sequences from watermelon and 44 typical PPR proteins from Arabidopsis, which utilized were in a previous study [3], were used to build a phylogenetic evolutionary tree. The translated sequences of the whole coding regions of PPR proteins were aligned using the MUSCLE method. The tree was constructed using the neighbor-joining (NJ) method with MEGA X software [37] and bootstrap analysis of 1000 replicates.

### *2.6. Expression Pattern of ClaPPR Genes in Watermelon*

To study the expression patterns of *ClaPPR* genes in 97103 watermelon, the transcriptome RNA-seq data (BioProject: SRP012849) from the cucurbit expression atlas (http://cucurbitgenomics.org/rnaseq/ home) were used [38]. These RNA-seq data contained data on fruit flesh (FF) and fruit rind (FR) at four stages (10, 18, 26, and 34 days after pollination (DAP)) during the development of the watermelon cultivar 97103. Furthermore, to examine the contribution and regulatory roles of *ClaPPR* genes, which are involved in fruit ripening, among different flesh-colored watermelons, the comparative watermelon transcript data (BioProject: PRJNA338036), containing five different fruit ripening stages (10, 18, 26, 34, and 42 DAP) of a pale yellow-flesh cultivated watermelon ('COS') and red-flesh cultivated watermelon ('LSW-177'), were used. DEG (differentially expressed gene) values for corresponding *ClaPPR* were obtained using the list of *ClaPPR* accession numbers. The obtained DEG values were log2 base transformed. The visualization of expression in heatmap and hierarchical clustering was investigated using Cluster 3.0 and TreeView software [39].

### *2.7. Identification of Single Nucleotide Polymorphisms (SNPs) for ClaPPR Genes and Match Rate Analysis with Flesh Color*

Single-nucleotide polymorphisms (SNPs) for *ClaPPR* genes in different flesh-colored (red, yellow, and orange) watermelons were identified from the whole genome resequencing (WGRS) data (Bioproject: PRJNA516776) of our recent study [29]. The SNP variant calling procedure was carried out according to our recent study [29] in which the reads of different flesh-colored watermelons from WGRS were mapped on to the watermelon 97103 reference genome. From this SNP variant calling, we searched for the SNPs that were specific to either of the flesh types such as red, yellow, and orange in the SNP subset matrix by identifying protein-coding *ClaPPR* genes bearing SNPs that were 1) monomorphic among a chosen flesh color-type, 2) monomorphic among other unchosen flesh color-types, and 3) polymorphic

between a chosen and an unchosen flesh color-types. Then, the sequences of selected *ClaPPR* SNP variants were converted into CAPS markers using SNP2CAPS software [40] and simultaneously, primers were designed using Primer3Plus software (http://www.bioinformatics.nl/primer3plus). To validate CAPS markers, genomic DNA extraction, PCR assays, restriction digestion of PCR amplicons, and match rate analyses were carried out according to a previous study [29].


**1. Introduction**

The cancer is one of the most dreaded and threatening diseases in the world, causing more than 6 million deaths a year [1]. Colon cancer is recognized as the third most common cancer worldwide with high morbidity and mortality, and the fourth common cause of death [2]. Various cytotoxic drugs are used for the treatment of colorectal cancer like 5-Fluorouracil, Oxaliplatin and Cisplatin drugs are their hydrophobic nature and their susceptibility to develop drug resistance [3, 4].

In these current work great efforts for the discovery and development of nanoformulation based on natural products on *in vitro* HCT 116 cell lines study. Here gallic acid isolated from amla fruit (*Emblica officinalis*) and quercetin isolated from peels of pomegranate fruit (*Punica granatum*). Gallic acid is a naturally available phenolic compound present in amla fruit which is water insoluble and one of the major constituent of amla which might contribute to the health effects [5, 6]. Gallic acid exerts an anticarcinogenic activity, antiproliferative and antiapoptotic activities against pancreatic cancer cells [7–9]. Flavonoids are a group of naturally occurring class of plant secondary metabolites having polyphenolic

structure in addition quercetin has anti-tumor properties, anti-inflammatory**,** anti-proliferative, anti-angiogenic [10–15].

There have been particular efforts to evaluate the therapeutic role of these active constituents present in plants rather than using whole extracts. The fundamental method of reasoning behind these systems contributes greatly to enhance the targeting delivery and bioavailability of phenolic and flavonoid remarkable formulation development can be made by preparation of nanotechnology products. The eco-friendly synthesis of gallic acid and quercetin loaded chitosan nanoparticles (CS nanoparticles) through green route from plant extracts have renowned a wide range of application in the field of modern science, due to increased drug efficacy and less toxicity in the nanosized mediated drug delivery model. At the same time, the use of gallic acid and quercetin in pharmaceutical formulations is limited due to its poor water solubility, poor bioavailability and instability in physiological medium [16, 17].

Lack of site specificity is one of the major reasons for the drug in reaching the target site in therapeutic concentrations in colorectal cancer [18]. Chitosan (CS), as the only naturally occurring positive charge polysaccharide, has remarkable properties including high bioavailability, super biodegradability, high biocompatibility, non-toxicity etc., On the other hand it causes sustained release of the drug from the particle in the tumor environment [19]. The main rationale behind using these types of polymers is their ability to prevent drug degradation in the gastric environment in the stomach and their ability to release the drug after entering the distal ileum [20]. Poloxamer 407 is a hydrophilic nontoxic copolymer used for its stabilizing properties and incorporation of hydrophobic drugs capability to increase the solubility of biomolecules [21]. Here combined biomolecules synergistic activity of nanotechnology approach has been developed to improve the bioavailability as to entrap these natural biomolecules into biodegradable polymeric CS nanoparticles [22].

The system of glyceryl monooleate (GMO)/chitosan is a surface-modified nanoparticulate system consisting of GMO as a lipid portion and chitosan as a coating polymer to target colonic area with poloxamer 407 as a stabilizer. Therefore, the purpose of this study was to formulate CS nanoparticles of where quercetin isolated from peels of pomegranate fruit and gallic acid isolated from amla fruit as a model hydrophobic biomolecules followed by lyophilization using probe sonicator and High Pressure Homogenization (HPH) method. CS nanoparticles prepared and optimized using Quality by design approach by using central composite factorial design. Optimized formulation further characterized for different parameters as particle size, zeta potential, FT-IR and. Release kinetic studies performed using method for conventional nanoparticle release behavior assessment.

In this study, we systematically analyzed the *In vitro* anti-cancer potential of the gallic acid and quercetin loaded chitosan nanoparticles synergy approach for combined active biomolecules and compared to their activity to combined extracts on HCT 116 human colon cancer cell lines and the mechanism of action of CS nanoparticles in regulating the growth of CRC cells. The human HCT116 cell line by MTT (3-(4,5-dimethyl-2-tiazolyl)-2,5-diphenyl-2-tetrazolium bromide) assay was exposed to cytotoxicity of polyherbal extracts, chitosan nanoparticles and cisplatin (Standard) and activity is dependent up to the concentration of 6.25- 100ug/mL for 24 h followed by MTT cellular assays [23]. To determine the potential anti-cancer effect of, we synthesized CS nanoparticles using gallic acid and quercetin biomolecules, which is a phenolic and flavonoid predominantly found in amla fruit and peels of pomegranate fruit. HCT116 cells exposed to gallic acid and quercetin for 24 h exhibited significant loss of cell viability and proliferation in a dose-dependent manner.

**257**

*Colon Available Bioactive Compounds Exhibits Anticancer Effect on* In-Vitro *Model…*

The IC50 of polyherbal extract, chitosan nanoparticles and standard cisplatin after 48 h treatment it was found to be 60.32 and 36.17 and 8.915 ug/ml respectively. The obtained result inferred that the synthesized CS nanoparticles demonstrated shows more effective antiproliferative potential on HCT-116cell lines with IC50 value of 36.17 ug/ml than polyherbal extract 60.32 ug/ml were discussed briefly in this

Poloxamer 407 from BASF, Chitosan 90% dda obtained from CIFT Cochin, GMO

from Mohini organics, standard gallic acid and quercetin purchased from Loba Chemie., 10% fetal bovine serum (Invitrogen Life Technologies USA). RPMI 1640 and McCoy's 5A medium (Fisher Scientific, Waltham, USA). All the solvents and chemicals used were procured from Himedia Laboratories, Research Lab. Mumbai.

The sample of different parts of plant of amla and pomegranate was collected from Kolhapur district and was authenticated by Dr. Madhukar Bachulkar, Principal, Arts and Science College Peth Vadagaon Kolhapur. The voucher herbarium (PSP-1 and 2) has been deposited in the department of Pharmacognosy Bharati Vidyapeeth College of Pharmacy, Kolhapur. Amla fruit and peels of pomegranate fruit were collected in season (Feb-March), were dried under shade for

In order to extract Flavonoid and phenolics from plants with a high degree of accuracy, various solvents of differing polarities were tried as chloroform, ethanol and ethyl acetate. The dried powder of amla fruit and peels of pomegranate powder extracted with 800 ml in various solvents for 6 hours separately. All extracts were filtered and evaporated to dryness under reduced pressure at 60 °C by a rotary evaporator and to determine percentage yield for all three different solvents [24].

Phytochemical analysis was carried out to detect the presence of primary and secondary metabolites were used to identify the biomolecules present in the plant extract [25]. The phytochemical tests carried out for amla and peels of pomegranate extract include alkaloids, glycosides, saponins, tannins, triterpenoids, steroid,

Phenolic compounds are important plant constituents with redox properties responsible for antioxidant activity. Folin–Ciocalteu's method (FC) is a colorimetric

*DOI: http://dx.doi.org/10.5772/intechopen.96632*

manuscript.

**2.1 Materials**

**2.2 Plant material**

10–15 days in air.

**2.3 Soxhlet extraction method**

**2.4 Phytochemical screening**

flavonoids and carbohydrate [26].

*<IP_ADDRESS> Determination of total phenolic content for amla extract*

*2.4.1 Qualitative test*

*2.4.2 Quantitative tests*

**2. Materials and methods**

*Colon Available Bioactive Compounds Exhibits Anticancer Effect on* In-Vitro *Model… DOI: http://dx.doi.org/10.5772/intechopen.96632*

The IC50 of polyherbal extract, chitosan nanoparticles and standard cisplatin after 48 h treatment it was found to be 60.32 and 36.17 and 8.915 ug/ml respectively. The obtained result inferred that the synthesized CS nanoparticles demonstrated shows more effective antiproliferative potential on HCT-116cell lines with IC50 value of 36.17 ug/ml than polyherbal extract 60.32 ug/ml were discussed briefly in this manuscript.


**1. Introduction**

The fast penetration of information and communication technology (ICT) into our lives and society is causing how, when, and where we work and study. School-aged children nowadays

© 2015 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.

spend their free time immersed in a media-rich, ubiquitous, always-connected world where most of the time they usually play computer games. For two decades, scientists were trying to figure out why are computer games so motivating and why children spend so much time playing them [1]. The results of research were three features: challenge, fantasy, and curiosity. The same three features are also very important aspects in learning. Challenge helps us to stay motivated to achieve our goal, fantasy helps us to better imagine how things should work, and curiosity drives us to figure out things that we did not know.

Educators around the world in the last 50 years try to incorporate ICT and computers into the education system. Four threads have been identified [2]. The first thread, computer-assisted instruction (CAI) and lately intelligent tutoring systems (ITS), has promised a new way of how learners would learn but never gained much attention. Second thread, computer science and computer programming, is gaining momentum lately as few countries are bringing them as obligatory subjects in school curriculum. The third thread is cognitive development and problem solving skills, which are getting much of attention as problem solving is one of the key competencies for 21st century citizen. The fourth thread is Internet use for gathering information and as a tool for improving problem solving skills. Perhaps the greatest potential for ICT in education is the improvement of traditional teaching with the inclusion of different tools in the classrooms.

The next generation of jobs will be characterized by increased technology use, extensive problem solving, and complex communication [3]. These are the skills that go beyond typical reading, writing, and arithmetic of years past. It is not only what students need to learn that is shifting but also how and when they learn. Students of today are growing up with laptops, tablets, cell phones, and video call, and they expect to use this technology in their daily interactions [4].

One area of significant promise in this regard is a movement toward the use of educational computer games as learning tools in schools [5]. We will tackle this area in subsequent sections.

This chapter is structured as follows, we first categorize computer and educational games, and then we introduce the computer game *Angry Birds* and describe how *Angry Birds* can be used in physics curriculum. Next we explain which computer programs and how to use them with *Angry Birds* in the classroom. We conclude this chapter with the survey on how teachers would use *Angry Birds* in classrooms.


**1. Introduction**

Self-enforcing agreements—those for that no party has any incentive to break given that all others comply—should be carried out even if they are not binding in a formal sense. This is in fact the defining characteristic of the standard Nash equilibrium concept, and thus, one of the common justifications for this concept is that if players are allowed to communicate before playing a game, they could hardly reasonably agree on an outcome not satisfying this criterion. Recall that a Nash equilibrium constitutes for each player a set of strategies and beliefs (about other players' strategies), such that the strategies are the best responses to beliefs and the beliefs are correct (see e.g., Osborne 2004 [1]). We assume that there is no recourse to court-enforceable contracting, or equivalently that any such interactions have already taken place. Unfortunately, while intuitively pleasing, this justification for the use of a Nash equilibrium has been characterized by a shortage of formal models.

On a related, but distinctly different track of reasoning, it is natural to wonder why agents would ever agree on an inefficient outcome, assuming that they had the chance to talk in the first place. In other words, why would players agree ahead of time to an inefficient outcome of a game if there were another potential outcome, also an equilibrium, that gave strictly greater payoffs to all of them? Once again, the challenge has lied in constructing a realistic, but necessarily simplified, formal model of the agents' communication process. Among other problems, this inefficient result appears to be incompatible with the arguments outlined above, in which Nash equilibria in general are justified.

This type of preplay communication is often called *cheap talk* , which may be roughly defined as nonbinding, nonpayoff relevant, preplay communication. Although cheap talk has indeed received attention as a potential solution to these questions surrounding the equilibrium concept, in practice, it has been mostly used in the study of signaling games, in repeated environments (often in connection with learning), and in certain applied settings. These are of course all important applications, but these leave the original ambiguities unresolved. This paper, then, returns to the goal of constructing a

more comprehensive model of pure cheap talk and explores its relationship with equilibria and equilibrium selection.

This paper develops a model of cheap talk that involves an unlimited communication session, called a *conversation* , before the play of a standard game begins. Players announce in advance what actions they plan to take in the upcoming game, and taken together, these announcements form one possible prediction of what they may actually do. On the other hand, there is also a common prior forecast, given exogenously, of what each player will do; this forecast is updated as the conversation proceeds. An announcement is defined to be credible only if it is close to the best response to one or the other of these two predictions about the rest of the players. Otherwise, an announcement has no external justification, so it is deemed unbelievable and disregarded. The conversation continues indefinitely in this manner, possibly, but not inexorably toward some limit. Realistically, it will rarely if ever go on for very long (although, for complicated games, it may take some time), since if it is going to converge, it will do so rapidly. However, it is important not to have an artificial limit imposed externally, just as long finitely repeated games behave very differently than infinitely repeated games.

The paper's first main result is that if the conversation converges toward a limit, then this limit must be a Nash equilibrium of the underlying action game in which payoffs are determined.1 Conversely, any Nash Equilibrium forms a possible limit of the conversation. This result can be interpreted as saying that meaningful communication before a game can only lead to Nash outcomes. Since the cheap talk is the initial interaction between the players, we assume that they cannot be sure of the strategies that their opponents will follow in the communication stage. Any strategy in this phase that is weakly dominated by another is clearly not optimal; anything else is potentially the preferred choice and is therefore, given the lack of information, one possible optimal choice.2 The paper's second result then states that optimal pregame play in the conversation stage leads to an efficient outcome and that any efficient final outcome is a possible result of such a strategic conversation.3 This can be interpreted as saying that rational, or thoughtful, speech leads to efficiency. This completes the connection between cheap talk (as modeled here, i.e., in an environment where rationality and utilities are common knowledge), Nash equilibria, and Pareto optimality. The first result applies to all games (at least those with a Nash equilibrium), while the second result only has bite in games with multiple equilibria.

The conclusion derived from the second main result contrasts with previous "babbling" results, in which it is impossible to select among the set of Nash equilibria because all pregame communication is ignored. The main reason for the difference is that those previous studies looked for equilibria of the extended communication game as a whole—for instance, by assuming that the full strategies of all players are known. This allows equilibrium strategies in which no value is placed even on seemingly mutually informative communication, whereas the model below presupposes the impossibility of ignoring beneficial interchange. Thus, the present paper takes a more primitive view of pregame strategies, especially since in part it is attempting to justify the equilibrium concept in the first place. Naturally, although the model does not impose beliefs about the cheap talk stage, it still must make some assumption about beliefs held upon entering the action game. Another approach that will destroy the babbling equilibria is to assume an arbitrarily small, but positive cost to sending messages—this is a restriction on the environment rather than on the structure of equilibrium or on belief formation. While this limitation is plausible in reality, it is, strictly speaking, no longer a model of cheap talk, even if the total sum spent on sending messages is always lower than the game's smallest payoff differential.

The paper proceeds as follows. Section 2 provides a brief survey of some of the relevant literature. In Section 3, some motivation is given for the specific assumptions made in this conversational model

1 The limit is an *ε*-Nash equilibrium.

2 This is discussed in further detail in Section 3.

3 The notion of efficiency used here is *stable efficiency*, a concept that is equivalent to Pareto efficiency in generic two person games.

of cheap talk. Section 4 lays out the formal model, stating and proving the paper's two main results. Several examples are detailed in Section 5 in order to illustrate both the cheap talk process and the implications of the theorems. Finally, Section 6 concludes the paper by summarizing the model and discussing some possible extensions of its implications.


**2.3 Natural history**

Disease progression can be slow, with overlapping intermittent events, or it can be a fulminant course, with rapid neurologic decline [10]. It has been reported that symptomatic progression is observed for five years, and delay in the rap initiation may have catastrophic consequences [10].


*4.1. Representative Constitutive Relationship Equation for Each Region*

The constitutive relationship equations for a total of 23 dredged clay specimens from three regions and six groups were obtained through back analysis and the results of the centrifugal experiments. The equation of the power function is shown on a log–log scale and is the deduced representative equation for each of the six groups. The units of the constitutive equation are kPa of effective stress and m/day of permeability coefficient.

The Busan-L marine clay (Busan marine clays with low liquid limit) with a liquid limit in the 40–60% range in the Busan region dredged clay was analyzed using six specimens (bs-a, b, c, d, e, f). A constitutive relationship equation for the six specimens is shown in Figure 10 of the log–log scale. The representative constitutive relationship equation (bs-L-clay) of Busan-L marine clay can be expressed as e = 3.1σ 0−0.19 and k = 9 × 10−6 *e* 5.5 (A = 3.1, B = −0.19, C = 9 × 10−6 , D = 5.5) using the arithmetic mean on the log–log plot, as shown in Figure 10. The representative constitutive relationship equations of Busan-L marine clay had the coefficient of determination of 0.87 on void ratio–effective stress and 0.84 on void ratio–permeability. The Busan-H marine clay had a high liquid limit (LL = 60–80%) and was analyzed using four specimens (bs-g~k), as shown in Figure 11. The representative constitutive relationship equations of Busan-H clay (bs-H-clay) can be expressed as e = 4.3σ 0−0.20 and k = 6 × 10−6 *e* 4.5, and had the coefficient of determination of 0.97 on void ratio–effective stress and 0.88 on void ratio–permeability.

**Figure 10.** Constitutive relationship of Busan L marine clay (bs-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 11.** Constitutive relationship of Busan H marine clay (bs-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The Gwangyang-L marine clay with LL = 40–60% and the representative constitutive equation (gy-L-clay) of e = 2.9σ 0−0.18 and k = 9 × 10−6 *e* 6.0 was analyzed using five specimens (gy-a~e), as shown in Figure 12. The equations of gy-L-clay had the coefficient of determination of 0.95 on void ratio–effective stress and 0.86 on void ratio–permeability. The Gwangyang-H marine clay with a high liquid limit of 60–80% and the representative constitutive equation (gy-H-clay) of e = 3.9σ 0−0.20 and k = 8 × 10−6 *e* 4.5 was analyzed using four specimens (gy-f~j), as shown in Figure 13. The equations of gy-H-clay had the coefficient of determination of 0.88 on the e-σ 0 relationship and 0.77 on the e-k relationship.

**Figure 12.** Constitutive relationship of Gwangyang L marine clay (gy-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 13.** Constitutive relationship of Gwangyang H marine clay (gy-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The Incheon-L marine clay with LL = 20–30% and the representative constitutive equation (ic-L-clay) of e = 1.7σ 0−0.15 and k = 1 × 10−4 *e* 5.5 was analyzed using ic-b and ic-c specimens, as shown in Figure 14. The equations of ic-L-clay had the coefficient of determination of 0.98 on the e-σ 0 relationship and 0.92 on the e-k relationship. The representative constitutive equation (ic-H-clay) of the Incheon-H marine clay was e = 2.2σ 0−0.17 and k = 5 × 10−5 *e* 5.5, which was deduced from the ic-c and ic-d specimens, as shown in Figure 15. The equations of ic-H-clay had the coefficient of determination of 0.85 on the e-σ 0 relationship and 0.94 on the e-k relationship.

**Figure 14.** Constitutive relationship of Incheon L marine clay (ic-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 15.** Constitutive relationship of Incheon H marine clay (ic-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The representative constitutive relationship equations for each region are summarized in Table 3.

**Table 3.** Representative constitutive relationship equation.


**5. Conclusions**

Opinions on the cytotoxicity, carcinogenic, and genotoxic potential of hydroxymethylfurfural vary, while certain minerals and toxic metals are known to be deleterious if consumed in large quantities. However, the concentrations of such metals vary depending on the food type used. Infant foods and formulae contained varying amounts of HMF and metals, thus, the total daily intake of these contaminants is a ffected by individual feeding patterns. Notably, a high HMF content was observed in prune-based infant foods. On the other hand, with regard to the metal contents, it was observed that infant foods contained Mn, Zn, Fe, Cu, and Cr, while infant formulae contained Zn, Fe, Cu, Mn, and Cr in decreasing order. There was a low presence of Ni and negligible quantities of Hg. Infants are within a vulnerable age group and have a restricted diet compared to other age groups, therefore, it is recommended that foods are monitored to ensure safe use. The setting up of limits with respect to this vulnerable group should be considered through further studies, using a greater diversification of samples that are subjected under varying conditions.

**Author Contributions:** Conceptualization, writing—review, editing and supervision: E.A.; methodology and investigation: C.V.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors acknowledge Adrian Bugeja-Douglas for technical support.

**Conflicts of Interest:** The authors declare no conflict of interest.


**About the Editors**

#### **Ivet Ferrer**

Dr. Ivet Ferrer is a full professor at the Department of Civil and Environmental Engineering of the Universitat Politecnica de Catalunya·BarcelonaTech. Currently, she leads the Research Group ` of Environmental Engineering and Microbiology (GEMMA-UPC). Her main area of research is the optimization of biomass anaerobic digestion by applying pretreatments and co-digestion. She has also addressed the implementation and assessment of low-tech digesters for rural areas. Her research is now focused on the recovery of resources from waste streams, including high-value bioproducts and biogas.

#### **Cigdem Eskicioglu**

Dr. Cigdem Eskicioglu is a full professor and NSERC/Metro Vancouver Senior Industrial Research Chair in the area of Resource Recovery from Wastewater in the School of Engineering at University of British Columbia (UBC)'s Okanagan Campus. She is also the founder/leader of the Bioreactor Technology Group (BTG), which focuses on advanced wastewater treatment processes for more efficient contaminant removal, energy conservation and production, resource recovery and mitigation of trace contaminants of emerging concern.

#### **Georgia Antonopoulou**

Dr. Antonopoulou Georgia is a senior research associate in the Institute of Chemical Engineering Sciences (ICE-HT) of the Foundation for Research and Technology (FORTH), in Greece. She is a chemical engineer and completed her PhD and MSc at the Department of Chemical Engineer of Patras University. Her research interests focus on waste and wastewater treatment via biological processes, anaerobic digestion and fermentation, bioreactor design, pretreatment of lignocellulosic biomass and modeling of microbial processes.

#### **Audrey Battimelli**

Dr. Audrey Battimelli is a research engineer at the LBE, Laboratory of Environmental Biotechnology INRAE, of the French National Research Institute for Agriculture, Food and the Environment. She is in charge of Bio2E Platform and specialises in application bioprocesses and physico-chemical pretreatments in collaborative work with professionals.


**2. System model**

Throughout this chapter we denote the set of natural, real, and complex numbers by N, R, and C, respectively. Note that the set of natural numbers does not include the element zero. Furthermore, we use the subset F*N* ⊆ N which is defined as F*N* := {1, . . . , *N*} for any given natural number *N*. The mathematical operations |*z*| and |**z**| denote the absolute value of a real or complex-valued number *z* and the Euclidian length of a real or complex vector **z**, respectively.

Distributed *target object* classification can be formally modeled by a multiple hypotheses testing problem with hypotheses *Hk*∀*k* ∈ F*K* for a specified number *K* ∈ N of different objects. We assume that all objects have the same size, shape, alignment, and position. They only differ in material and are classified by their complex-valued reflection coefficients *rk* ∈ C, which are ordered in a strictly increasing manner 0 ≤ |*r*1| < ··· < |*rK*| ≤ 1. Therefore the reflection coefficients are the only recognition features in this work. Generally, this assumption is not realistic, but, this case describes an ideal scenario for increasing the classification probability by performing a power allocation and is not really suitable for analyzing the problems of manifoldness.

166 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 3 167 Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

**Figure 1.** System model of the distributed wireless sensor network.

2 Will-be-set-by-IN-TECH

problems. Therefore, we employ an information theoretic approaches [3], which help to solve the power allocation problem with a lower mathematical complexity. This approach yields a simple however suboptimal analytical solution for the power allocation problem. Furthermore, the proposed technique enables the consideration of object detection and classification at the same time. This is a further advantage of this method, which enables the usage of the same allocation algorithm in both cases. Hence a sensor network, which is used to classify target objects, can also be used to detect the absence or the presence of a target object with equal system settings. Therefore we only describe the case of object classification,

The origin of research on distributed detection has been the attempt to fuse signals of different radar devices [10]. Currently, distributed detection is usually discussed in the context of wireless sensor networks, where the sensor unit of the nodes might be based on radar technology [7, 9, 14]. Other applications for UWB radar systems, which require or benefit from the detection and classification capabilities, are for example localization and tracking [6] or through-wall surveillance [4]. The physical layer design for an integrated UWB radar network that utilizes OFDM technology was analyzed in [11]. In [2] the case of object detection is considered, where for the problem of power allocation an approach based on the maximization of the Kullback-Leibler distance is used. In a recent publication [1] another approach is discussed, where the bit-error probability of data communication is used in order

to allocate the transmission power and to increase the overall detection probability.

with an interpretation of the achieved system performance.

**2. System model**

respectively.

manifoldness.

This chapter is divided into the following three sections except the introduction. First, the system model of the wireless network including sensor nodes and the fusion center is described. Here, all system parameters and assumptions with detailed mathematical formulations are introduced. Furthermore, the global classification rule in the fusion center as well as the local decision rules in the nodes are motivated. In the second section, we present a novel approach for power allocation in order to increase the overall classification probability, following which, the solution of this optimization approach is briefly discussed. The last section shows some results and demonstrates the feasibility of object classification by using the proposed power allocation method in UWB signaling systems. This chapter concludes

Throughout this chapter we denote the set of natural, real, and complex numbers by N, R, and C, respectively. Note that the set of natural numbers does not include the element zero. Furthermore, we use the subset F*N* ⊆ N which is defined as F*N* := {1, . . . , *N*} for any given natural number *N*. The mathematical operations |*z*| and |**z**| denote the absolute value of a real or complex-valued number *z* and the Euclidian length of a real or complex vector **z**,

Distributed *target object* classification can be formally modeled by a multiple hypotheses testing problem with hypotheses *Hk*∀*k* ∈ F*K* for a specified number *K* ∈ N of different objects. We assume that all objects have the same size, shape, alignment, and position. They only differ in material and are classified by their complex-valued reflection coefficients *rk* ∈ C, which are ordered in a strictly increasing manner 0 ≤ |*r*1| < ··· < |*rK*| ≤ 1. Therefore the reflection coefficients are the only recognition features in this work. Generally, this assumption is not realistic, but, this case describes an ideal scenario for increasing the classification probability by performing a power allocation and is not really suitable for analyzing the problems of

which also includes the case of object detection, in the following sections.

At any instance of time, a network of *N* ∈ N independent and spatially distributed sensors, as shown in Figure 1, obtains random observations *X*1,..., *XN* ∈ R. In the case of energy classification, *Xn* models the received signal at the receiver of the *n*th sensor. If a target object is present, then the received energy is a part of the radiated energy of the same sensor, which is reflected from the object's surface and is weighted by its reflection coefficient. We refer to this communication channel, between the sensors and the target object, as the *first* communication link and denote all dedicated parameters by the superscript *R*. The random observations *X*1,..., *XN* are assumed to be conditionally independent for each of the underlying hypotheses, i.e., the joint conditional probability density function of all the observations factorizes according to

$$f^{\mathbb{R}}(\mathbf{X} \mid H\_k) := \prod\_{n=1}^{N} f\_n^{\mathbb{R}}(\mathbf{X}\_n \mid H\_k)\_{\prime} \,\forall k \in \mathbb{F}\_{K\prime} \tag{1}$$

where *X* denotes the sequence of random variables *X*1,..., *XN*. In general, the observations are not identically distributed because the sensor nodes have different distances *dR n* from the target object and their radiated powers *PR n* are also different. Therefore, the signal-to-noise ratio (SNR) varies between the sensor nodes. Due to the distributed nature of the problem, the *n*th sensor *Sn* performs independent measurements and processes its respective observation *Xn* by generating a local decision *Un* := *θn*(*Xn*)∀*n* ∈ F*N*, which depends only on its own observation and not on the observations of other sensor nodes. After deciding locally, each sensor transmits its decision to a fusion center located at a remote location. The communication between the sensor node and the fusion center is determined by the corresponding distance *dC n* as well as by the transmission power *PC n* of the same sensor node. We refer to this communication channel, between the sensor nodes and the fusion center, as the *second* communication link and denote all dedicated parameters by the superscript *C*. Furthermore, we assume that both communication channels are non-fading channels and that all data transmissions are affected only by additive white Gaussian noise (AWGN). We disregard time delays within all transmissions and assume synchronized data communication. We use two distinct pulse-shift patterns for each sensor node in order to distinguish its first and second communication link from the communication links of other sensor nodes as described in [13]. Each pattern has to be suitably chosen in order to suppress inter-user interference at each receiver. Hence the *N* received signals at the fusion center are uncorrelated and are assumed to be conditionally independent for each of the underlying hypotheses. These received random signals correspond to the local decisions *U*1,..., *UN* and

#### 4 Will-be-set-by-IN-TECH 168 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 5

are mapped to **X**˜ 1,..., **X**˜ *N* ∈ R*K*. Their joint conditional probability density function factorizes according to

$$f^{\mathbb{C}}(\tilde{\mathbf{X}} \mid H\_k) := \prod\_{n=1}^{N} f\_n^{\mathbb{C}}(\tilde{\mathbf{X}}\_n \mid H\_k), \,\forall k \in \mathbb{F}\_{K'} \tag{2}$$

*w*(*t*)

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

*w*(−*t*)

Prob(**x**˜ ∈ R*k*, *Hk*), (8)

Power Allocation Procedure for Wireless Sensor Networks

, which are shifted pulses on the time axis.

*n* of this stream is variable in order to adjust

*n* is also variable. In order to increase the available

*n* (*t*) and *hR*

*n* (*t*). Their transfer

169

*n* will be reflected from

*sR n* (*t*)

*sC n* (*t*)

*xn*(*t*)

Receiver

**2.3. Ultra-wide bandwidth sensor nodes**

*n* (*t*).

to the fusion center. The transmission power *PC*

data symbol. Its transmission power *PR*

*n* (*t*) and *sR*

symbols by Dirac delta functions *δ*

data symbols *sC*

The symbol stream *sC*

The symbol stream *sR*

amplifier.

Transmitter

*hR n* (*t*)

*hC n* (*t*)

*hR n* (−*t*)

**Figure 2.** System model of the *n*th sensor node with circulator and antenna.

According to [5], the expected value of correct classification is given by

*Pc* :=

different approach for the optimization, which is described in Section 3.3.

transmission power and to enable distributed power allocation.

distinctive time-shift pattern after passing through the blocks *hC*

When this superposition is transmitted, a part of the radiated signal *sR*

functions are based on time-hopping sequences [13].

order to avoid the intersymbol interferences.

*K* ∑ *k*=1

which in general cannot be analytically evaluated. Therefore, the previous formula cannot be used to optimize the allocation of the total power analytically. Consequently, we choose a

In Figure 2 the system model of the considered impulse-radio UWB (IR-UWB) sensor nodes with pulse position modulation (PPM) is shown. The transmitter generates two streams of

the fusion center, which are generated by the algorithm defined in (3). We describe the data

Their alignment is determined by the modulation index Δ. We assume that the product *K*Δ is much smaller than the symbol duration. Thus *K* different data symbols can be transmitted

power range at every sensor node, time-division multiple-access (TDMA) method is used to separate both streams into different time slots and to periodically share the same power

In order to eliminate collisions due to multiple access, each user stream is assigned to a

After superposition of both streams, a monocyclic pulse shape filter *w*(*t*) limits the bandwidth of the signal. This filter has to fulfill the Nyquist intersymbol interference (ISI) criterion in

the target surface back to the antenna. The received signal will pass through the matched-filter

*t* − [*un*(*i*) − 1]Δ

*n* is used to transmit the local decisions *un*(*i*) ∈ F*K* at the time index *i* to

*n* establishes the radiation to the target object and uses always the same

where **X**˜ denotes the sequence of random vectors **X**˜ 1,..., **X**˜ *N*. In general, these observations are – similar to the observations *X*1,..., *XN* – not identically distributed, because of variation in distances *dC n* as well as that of the radiated powers *PC n* . Unlike the local decision rules, the global decision rule *U*0 := *θ*0(**X**˜ 1,..., **X**˜ *N*) depends on all observations in order to increase the overall classification probability.

All described assumptions are necessary in order to obtain an ideal framework suited for analyzing the power allocation problem without studying problems of different classification methods in specific systems and their settings.

### **2.1. Local classification rules**

The local decision and classification rules *θn* are mappings of the kind *θn* : R → F*K*, ∀*n* ∈ F*N*. In this work, hard-decision rules are used for performing local classification given by

$$\theta\_{\mathbb{H}}(\mathbf{X}\_{\mathbb{H}} = \mathbf{x}\_{\mathbb{H}}) = k\_{\prime} \text{ if } \tau\_{n,k} < \mathbf{x}\_{n} \le \tau\_{n,k+1}, \ k \in \mathbb{F}\_{K\prime} \,\forall n \in \mathbb{F}\_{N\prime} \tag{3}$$

where the thresholds *τn*,*k* ∈ R are suitably chosen. The thresholds must be calculated separately for every sensor node in order to perform optimal classification. They depend on the prior probabilities of the hypotheses. Their values can be calculated by a suboptimal approach which is described in Section 3.1. In this way, every sensor node has a local probability of correct decision given by

$$\text{Prob}(\mathcal{U}\_{\mathbb{N}} = k \mid H\_k) = \text{Prob}(\tau\_{n,k} < X\_n \le \tau\_{n,k+1} \mid H\_k), \forall k \in \mathbb{F}\_{K'} \forall n \in \mathbb{F}\_N \tag{4}$$

and a local probability of false decision given by

$$\text{Prob}(\mathcal{U}\_{\mathbb{N}} \neq k \mid H\_k) = 1 - \text{Prob}(\mathcal{U}\_{\mathbb{N}} = k \mid H\_k)\_{\prime} \,\forall k \in \mathbb{F}\_{K \prime} \,\forall n \in \mathbb{F}\_N. \tag{5}$$

### **2.2. Fusion of local decisions and the global classification rule**

The local decisions *U*1,..., *UN* at the sensor nodes are conditionally independent due to uncorrelated and independent noisy communication channels. By applying the Bayesian-hypotheses-test criterion the optimal fusion rule at the fusion center is given by

$$\mathcal{U}\_0 = \theta\_0(\breve{\mathbf{X}} = \breve{\mathbf{x}}) = \operatorname\*{argmax}\_{k \in \mathbb{F}\_K} \left( \pi\_k f^{\mathbb{C}}(\breve{\mathbf{x}} \mid H\_k) \right), \tag{6}$$

where *πk* := Prob(*Hk*) with ∑*K k*=1 *πk* = 1 denotes the prior probability of hypothesis *Hk*. We use this formula to classify the target object. However, in order to optimize the allocation of the total power to the sensor nodes, we have to consider the overall classification probability. Therefore, we consider *K* pairwise disjoint regions R1,..., R*K* with

$$\mathcal{R}\_k \coloneqq \left\{ \tilde{\mathbf{x}} \in \mathbb{R}^{K \times N} \mid \pi\_k f^{\mathsf{C}}(\tilde{\mathbf{x}} \mid H\_k) \ge \pi\_l f^{\mathsf{C}}(\tilde{\mathbf{x}} \mid H\_l), \forall l \in \mathbb{F}\_{\mathbf{X}}, l \ne k \right\}, \forall k \in \mathbb{F}\_{\mathbf{X}}.\tag{7}$$

168 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 5 169 Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

**Figure 2.** System model of the *n*th sensor node with circulator and antenna.

According to [5], the expected value of correct classification is given by

$$P\_{\mathcal{L}} := \sum\_{k=1}^{K} \text{Prob}(\mathbf{\tilde{x}} \in \mathcal{R}\_k, H\_k)\_{\prime} \tag{8}$$

which in general cannot be analytically evaluated. Therefore, the previous formula cannot be used to optimize the allocation of the total power analytically. Consequently, we choose a different approach for the optimization, which is described in Section 3.3.

### **2.3. Ultra-wide bandwidth sensor nodes**

4 Will-be-set-by-IN-TECH

are mapped to **X**˜ 1,..., **X**˜ *N* ∈ R*K*. Their joint conditional probability density function factorizes

where **X**˜ denotes the sequence of random vectors **X**˜ 1,..., **X**˜ *N*. In general, these observations are – similar to the observations *X*1,..., *XN* – not identically distributed, because of variation

global decision rule *U*0 := *θ*0(**X**˜ 1,..., **X**˜ *N*) depends on all observations in order to increase the

All described assumptions are necessary in order to obtain an ideal framework suited for analyzing the power allocation problem without studying problems of different classification

The local decision and classification rules *θn* are mappings of the kind *θn* : R → F*K*, ∀*n* ∈ F*N*.

where the thresholds *τn*,*k* ∈ R are suitably chosen. The thresholds must be calculated separately for every sensor node in order to perform optimal classification. They depend on the prior probabilities of the hypotheses. Their values can be calculated by a suboptimal approach which is described in Section 3.1. In this way, every sensor node has a local

The local decisions *U*1,..., *UN* at the sensor nodes are conditionally independent due to uncorrelated and independent noisy communication channels. By applying the Bayesian-hypotheses-test criterion the optimal fusion rule at the fusion center is given by

*k*∈F*K*

use this formula to classify the target object. However, in order to optimize the allocation of the total power to the sensor nodes, we have to consider the overall classification probability.

**x**˜ ∈ R*K*×*N* | *πk f C*(**x**˜ | *Hk*) ≥ *πl f C*(**x**˜ | *Hl*), ∀*l* ∈ F*K*, *l* �= *k*

*πk f C*(**x**˜ | *Hk*)

*k*=1 *πk* = 1 denotes the prior probability of hypothesis *Hk*. We

, (6)

, ∀*k* ∈ F*K*. (7)

*θn*(*Xn* = *xn*) = *k*, if *τn*,*k* < *xn* ≤ *τn*,*k*+1, *k* ∈ F*K*, ∀*n* ∈ F*N*, (3)

Prob(*Un* = *k* | *Hk*) = Prob(*τn*,*k* < *Xn* ≤ *τn*,*k*+1 | *Hk*), ∀*k* ∈ F*K*, ∀*n* ∈ F*N* (4)

Prob(*Un* �= *k* | *Hk*) = 1 − Prob(*Un* = *k* | *Hk*), ∀*k* ∈ F*K*, ∀*n* ∈ F*N*. (5)

In this work, hard-decision rules are used for performing local classification given by

*n* (**X**˜ *n* | *Hk*), ∀*k* ∈ F*K*, (2)

*n* . Unlike the local decision rules, the

*N* ∏*n*=1 *f C*

*f C*(**X**˜ | *Hk*) :=

*n* as well as that of the radiated powers *PC*

according to

in distances *dC*

overall classification probability.

**2.1. Local classification rules**

probability of correct decision given by

where *πk* := Prob(*Hk*) with ∑*K*

R*k* :=

and a local probability of false decision given by

**2.2. Fusion of local decisions and the global classification rule**

Therefore, we consider *K* pairwise disjoint regions R1,..., R*K* with

*U*0 = *θ*0(**X**˜ = **x**˜) = argmax

methods in specific systems and their settings.

In Figure 2 the system model of the considered impulse-radio UWB (IR-UWB) sensor nodes with pulse position modulation (PPM) is shown. The transmitter generates two streams of data symbols *sC n* (*t*) and *sR n* (*t*).

The symbol stream *sC n* is used to transmit the local decisions *un*(*i*) ∈ F*K* at the time index *i* to the fusion center, which are generated by the algorithm defined in (3). We describe the data symbols by Dirac delta functions *δ t* − [*un*(*i*) − 1]Δ , which are shifted pulses on the time axis. Their alignment is determined by the modulation index Δ. We assume that the product *K*Δ is much smaller than the symbol duration. Thus *K* different data symbols can be transmitted to the fusion center. The transmission power *PC n* of this stream is variable in order to adjust transmission power and to enable distributed power allocation.

The symbol stream *sR n* establishes the radiation to the target object and uses always the same data symbol. Its transmission power *PR n* is also variable. In order to increase the available power range at every sensor node, time-division multiple-access (TDMA) method is used to separate both streams into different time slots and to periodically share the same power amplifier.

In order to eliminate collisions due to multiple access, each user stream is assigned to a distinctive time-shift pattern after passing through the blocks *hC n* (*t*) and *hR n* (*t*). Their transfer functions are based on time-hopping sequences [13].

After superposition of both streams, a monocyclic pulse shape filter *w*(*t*) limits the bandwidth of the signal. This filter has to fulfill the Nyquist intersymbol interference (ISI) criterion in order to avoid the intersymbol interferences.

When this superposition is transmitted, a part of the radiated signal *sR n* will be reflected from the target surface back to the antenna. The received signal will pass through the matched-filter

#### 6 Will-be-set-by-IN-TECH 170 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 7

*w*(−*t*) and will be decoded from its time-hopping sequence by *hR n* (−*t*). The additive noise signal *bR n* (*t*) will pass as well through both filters at the receiver. We denote the corresponding noise power by *P*noise. If all receiver components are linear, then we can describe the received power by

$$\tilde{P}\_{n|k}^{R} := P\_n^{R} \frac{{a\_n^R} {|r\_k|}^2}{g^2 (2d\_n^R)'} \,\forall k \in \mathbb{F}\_{K'} \,\forall n \in \mathbb{F}\_{N'} \tag{9}$$

*hC* 1 (−*t*)

*hC* 2 (−*t*)

1

*w*(−*t*)

of the received signal has the expected value of

the same power for all kinds of transmitted data symbols.

*γC n* := *PC n P*noise · *αC n g*2(*dC*

*π*˜ *n*,*l*|*k* (2*πP*noise)*K*/2 exp

where the operator **z**T denotes the transpose of any vector **z**.

information theory and is described in the next section.

which is conditionally distributed according to

*K* ∑ *l*=1

**X**˜ *n* | *Un* = *l*

*P*˜*C n* := *PC*

**m***n*|*l* := E

sensor node is given by

The additive noise signal *bC*

*f C*

*n* (**X**˜ *n* | *Hk*) :=

The power *P*˜*C*

it by

**Figure 3.** System model of the fusion center.

*hC N*(−*t*)

 = *PC n αC n g*2(*dC*

1

In case of additive zero-mean noise and due to the assumptions of *w*(*t*), each vector sample

which depends on the transmitted symbol *Un* = *l*. Thus the received power from the *n*th

where we assume that the path loss function is the same as for the first communication link.

spectral density at the fusion center is the same as at the sensor nodes. Due to similarity in architecture of the fusion center and the sensor nodes, the noise power in each dimension of each stream is equal to *P*noise. Because of the whiteness of noise, the interferences are uncorrelated in each dimension of each stream. Therefore the noise covariance matrix is

Similar to (10) we define an observed SNR for each data stream at the fusion center and denote

Due to the Gaussian distribution of noise, each vector sample is a Gaussian random vector,

Because of the convex superposition of multivariate Gaussian distributions, it is difficult to use (16) with the properties of (2) to optimize the distributed power allocation. Bounds, such as the Bhattacharyya bound [8], are also difficult to use due to multidimensional nature of (2) and (16). Therefore we propose an applicable technique which is motivated by concepts of

−(**x**˜ *n*−**m***n*|*l*)T(**x**˜ *n*−**m***n*|*l*) 2*P*noise

determined by the product *P*noise · **I***K*. Here **I***K* denotes the identity matrix of size *K*.

*n* is independent of the underlying hypothesis because the data stream *sC*

*n* (*t*) will also pass through all the filters. We assume that the noise

*n αC n g*2(*dC* 1

1

**x**˜1(*t*) **v**(−*t*)

Power Allocation Procedure for Wireless Sensor Networks

*K*

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

**x**˜2(*t*) **v**(−*t*)

*K*

**x**˜ *N*(*t*) **v**(−*t*)

*n* ) · **e***l*, ∀*l* ∈ F*K*, ∀*n* ∈ F*N*, (13)

*n* ), ∀*n* ∈ F*N*, (14)

*n* ), ∀*n* ∈ F*N*. (15)

, ∀*k* ∈ F*K*, ∀*n* ∈ F*N*, (16)

*n* has

171

*K*

where the transmitted power is weighted by the product of the factors *αR n* > 0, |*rk*| 2 , and *g*−2(2*dR n* ). The factor *αR n* includes the radar cross section, the influence of the antenna, the impacts of the filters, and all additional attenuation of the transmitted power. Due to the reflection coefficient *rk* of the target object the received power depends on the underlying hypothesis. The path loss function *g* depends on the assumed multipath propagation channel and is usually an increasing function of the distance between transmitter and receiver. Here, the factor of two in the distance results from that back and forth transmission between the transceiver and the object. The ratio of *P*˜*R n*|*k* and *P*noise is the observed conditional SNR at the receiver and is given by

$$\gamma\_{n|k}^{\mathbb{R}} := \frac{P\_n^{\mathbb{R}}}{\mathbb{P}\_{\text{noise}}} \cdot \frac{a\_n^{\mathbb{R}} |r\_k|^2}{\mathcal{S}^2(\mathbb{Z}d\_n^{\mathbb{R}})'} \, \forall k \in \mathbb{F}\_{K}, \forall n \in \mathbb{F}\_N. \tag{10}$$

Due to the Gaussian distribution of the noise, each sample is also a Gaussian random variable, which is conditionally distributed according to

$$f\_n^{\mathbb{R}}(X\_{\mathbb{R}} = x\_{\mathbb{R}} \mid H\_k) := \frac{1}{\sqrt{2\pi P\_{\text{noise}}}} \exp\left(-\frac{\left(x\_{\mathbb{R}} - \sqrt{P\_{\text{noise}}}\right)^2}{2P\_{\text{noise}}}\right), \forall k \in \mathbb{F}\_K, \forall n \in \mathbb{F}\_N. \tag{11}$$

The local decision probabilities Prob(*Un* = *l* | *Hk*), see (4) and (5), can be computed by solving the integral

$$\begin{split} \pi\_{n,l|k} := \text{Prob}(\mathcal{U}\_{\mathbb{N}} = l \mid H\_k) &= \int\_{\tau\_{nl}}^{\tau\_{nl,l+1}} f\_n^R(\mathbf{x}\_n \mid H\_k) \, \mathbf{dx}\_n \\ &= \frac{1}{2} \left[ \text{erf} \left( \frac{\sqrt{\mathcal{P}\_{\boldsymbol{s}|k}^R} - \tau\_{\boldsymbol{s}l}}{\sqrt{2P\_{\text{noise}}}} \right) + \text{erf} \left( \frac{\tau\_{\boldsymbol{s},l+1} - \sqrt{P\_{\text{s}|k}^R}}{\sqrt{2P\_{\text{noise}}}} \right) \right] \end{split} \tag{12}$$

for all *k*, *l* ∈ F*K* and for all *n* ∈ F*N*. Here, the mapping erf(*z*) denotes the error function of *z*.

### **2.4. Fusion center**

After radiation of the stream *sC n* by the sensor node *Sn*, the signal is attenuated depending on the distance and it reaches the antenna at the fusion center as depicted in Figure 3. The received signal is matched-filtered and decoded from its time-hopping sequence. Then a data splitter **v**(*t*) is used to split the received signal into a *K*-dimensional vector space. This is necessary in order to retain the Euclidian distances between all transmitted symbols and achieve a higher classification probability. This filter is mathematically implemented as ∑*K k*=1 **e***k δ t* − (*k* − 1)Δ , where **e***k* is the standard basis vector of the *K*-dimensional space that points in the *k*th direction. Therefore the received signals **X**˜ 1,..., **X**˜ *N* ∈ R*K* are *K*-dimensional vectors. This new approach extends the method given by [13].

Power Allocation Procedure for Wireless Sensor Networks

170 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 7 171 with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

**Figure 3.** System model of the fusion center.

6 Will-be-set-by-IN-TECH

impacts of the filters, and all additional attenuation of the transmitted power. Due to the reflection coefficient *rk* of the target object the received power depends on the underlying hypothesis. The path loss function *g* depends on the assumed multipath propagation channel and is usually an increasing function of the distance between transmitter and receiver. Here, the factor of two in the distance results from that back and forth transmission between the

> *n* |*rk* | 2 *g*2(2*dR*

> > exp − *xn*− *P*˜*R n*|*k* 2

> > > *τ n*,*l*+1

*τn*,*l*

for all *k*, *l* ∈ F*K* and for all *n* ∈ F*N*. Here, the mapping erf(*z*) denotes the error function of *z*.

on the distance and it reaches the antenna at the fusion center as depicted in Figure 3. The received signal is matched-filtered and decoded from its time-hopping sequence. Then a data splitter **v**(*t*) is used to split the received signal into a *K*-dimensional vector space. This is necessary in order to retain the Euclidian distances between all transmitted symbols and achieve a higher classification probability. This filter is mathematically implemented as

points in the *k*th direction. Therefore the received signals **X**˜ 1,..., **X**˜ *N* ∈ R*K* are *K*-dimensional

= 1 2 erf *P*˜*R n*|*k*−*τn*,*l* √2*P*noise

Due to the Gaussian distribution of the noise, each sample is also a Gaussian random variable,

The local decision probabilities Prob(*Un* = *l* | *Hk*), see (4) and (5), can be computed by solving

*f R*

2*P*noise

*n* (*xn* | *Hk*) d*xn*

 + erf

*n* by the sensor node *Sn*, the signal is attenuated depending

, where **e***k* is the standard basis vector of the *K*-dimensional space that

*n* (*t*) will pass as well through both filters at the receiver. We denote the corresponding noise power by *P*noise. If all receiver components are linear, then we can describe the received

*n* (−*t*). The additive noise

*n* > 0, |*rk*|

2 , and

*n* ), ∀*k* ∈ F*K*, ∀*n* ∈ F*N*, (9)

*n*|*k* and *P*noise is the observed conditional SNR at the

*n* ), ∀*k* ∈ F*K*, ∀*n* ∈ F*N*. (10)

*τn*,*l*+1− *P*˜*R n*|*k* √2*P*noise

, ∀*k* ∈ F*K*, ∀*n* ∈ F*N*. (11)

(12)

*n* includes the radar cross section, the influence of the antenna, the

*w*(−*t*) and will be decoded from its time-hopping sequence by *hR*

*n αR n* |*rk* | 2 *g*2(2*dR*

where the transmitted power is weighted by the product of the factors *αR*

*P*˜*R n*|*k* := *PR*

signal *bR*

power by

*g*−2(2*dR*

*n* ). The factor *αR*

receiver and is given by

*f R*

the integral

**2.4. Fusion center**

∑*K k*=1 **e***k δ*

After radiation of the stream *sC*

*t* − (*k* − 1)Δ

vectors. This new approach extends the method given by [13].

transceiver and the object. The ratio of *P*˜*R*

*γR*

*π*˜ *n*,*l*|*k* := Prob(*Un* = *l* | *Hk*) =

which is conditionally distributed according to

*n* (*Xn* = *xn* | *Hk*) := √

*n*|*k* := *PR n P*noise · *αR*

> 1 2*πP*noise

In case of additive zero-mean noise and due to the assumptions of *w*(*t*), each vector sample of the received signal has the expected value of

$$\mathbf{m}\_{n|l} := \mathbb{E}\{\breve{\mathbf{X}}\_n \mid \mathcal{U}\_{\hbar} = l\} = \sqrt{P\_n^{\mathbb{C}} \frac{a\_n^{\mathbb{C}}}{\mathcal{g}^2(d\_n^{\mathbb{C}})}} \cdot \mathbf{e}\_{l\prime} \,\forall l \in \mathbb{F}\_{\mathcal{K}\prime} \,\forall n \in \mathbb{F}\_{N\prime} \tag{13}$$

which depends on the transmitted symbol *Un* = *l*. Thus the received power from the *n*th sensor node is given by

$$\vec{P}\_n^{\mathbb{C}} := P\_n^{\mathbb{C}} \frac{a\_n^{\mathbb{C}}}{g^2(d\_n^{\mathbb{C}})'} , \forall n \in \mathbb{F}\_{N'} \tag{14}$$

where we assume that the path loss function is the same as for the first communication link. The power *P*˜*C n* is independent of the underlying hypothesis because the data stream *sC n* has the same power for all kinds of transmitted data symbols.

The additive noise signal *bC n* (*t*) will also pass through all the filters. We assume that the noise spectral density at the fusion center is the same as at the sensor nodes. Due to similarity in architecture of the fusion center and the sensor nodes, the noise power in each dimension of each stream is equal to *P*noise. Because of the whiteness of noise, the interferences are uncorrelated in each dimension of each stream. Therefore the noise covariance matrix is determined by the product *P*noise · **I***K*. Here **I***K* denotes the identity matrix of size *K*.

Similar to (10) we define an observed SNR for each data stream at the fusion center and denote it by

$$
\gamma\_n^{\mathbb{C}} := \frac{P\_n^{\mathbb{C}}}{P\_{\text{noise}}} \cdot \frac{a\_n^{\mathbb{C}}}{g^2(d\_n^{\mathbb{C}})'} \quad \forall n \in \mathbb{F}\_N. \tag{15}
$$

Due to the Gaussian distribution of noise, each vector sample is a Gaussian random vector, which is conditionally distributed according to

$$f\_{\rm II}^{\rm C}(\tilde{\mathbf{X}}\_{\rm II} \mid H\_{\rm k}) := \sum\_{l=1}^{K} \frac{\boldsymbol{\pi}\_{\rm u, l \parallel k}}{(2\pi P\_{\rm noise})^{K/2}} \exp\left(-\frac{(\mathbf{\hat{x}}\_{\rm n} - \mathbf{m}\_{\rm u \parallel l})^{\rm T} (\mathbf{\hat{x}}\_{\rm n} - \mathbf{m}\_{\rm ul})}{2P\_{\rm noise}}\right), \forall k \in \mathbb{F}\_{K}, \forall n \in \mathbb{F}\_{N\prime} \tag{16}$$

where the operator **z**T denotes the transpose of any vector **z**.

Because of the convex superposition of multivariate Gaussian distributions, it is difficult to use (16) with the properties of (2) to optimize the distributed power allocation. Bounds, such as the Bhattacharyya bound [8], are also difficult to use due to multidimensional nature of (2) and (16). Therefore we propose an applicable technique which is motivated by concepts of information theory and is described in the next section.

8 Will-be-set-by-IN-TECH 172 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 9

### **3. Allocating power to the radar and to the communication task**

In this section, we motivate and present an approach to suboptimally allocate transmission power to the radar and to the communication task. The objective is to maximize the overall classification probability, given a limited total transmission power *P*tot that can be arbitrarily allocated to the radar task as well as to the communication task. A direct solution to this problem does not exist, since no analytical expression for the overall classification probability (8) is available. Instead, we independently maximize the mutual information of both communication channels to increase the information flow and in order to determine the power allocation. The motivation for this approach is the separation of the power allocation problem from the object classification procedure. Because in this case the data communication does not affect the classification of the target object.

the limited total transmission power *P*tot is an upper bound for the sum

*PR n* Radar sensing

case in which all sensor nodes have the same power limitation *P*max with *P*tot

equal to its highest possible limitation given by *P*max, recalculate *PC*

procedure described in the next section. In a case, where the power *PC*

of unallocated sensor nodes in order to decrease the computation complexity.

+ *PC*

Total transmission power of one sensor for a single observation

By using this restriction, we present the power allocation procedure in the next section. But,

In real applications the transmission power of each sensor node is also limited. Consider the

the power regulation, which is described in the next section, wants to allocate a higher power

will be regulated higher than *P*max, we can reverse the roles of both transmission powers and repeat this reallocation method until no more sensor nodes are left which exceed their power limitation. Therefore, the described limitation of the total transmission power is the generalized case which includes the limitation of the transmission power of each sensor node. Note that this procedure is applicable for individual power constraints per node as well. Furthermore, note that in each iteration more than one node can be discarded from the list

For the maximization of the information flow we set the mutual information of both communication channels equal. This leads to the same symbol error probabilities on both sides for low SNR values. For each sensor node an upper bound for the mutual information

has to be computed in order to find the relationship between the powers for all *n* ∈ F*N*. After

√*K* 1 + *x* ≈ 1 + *x*

In the next step, we increase the overall information flow by maximization of the cumulative mutual information subject to the given total power of the sensor network. Then the

(|*rK*|−|*r*1|)2

of its first and second link can simply be calculated. The identity of obtained bounds

*n* ) = *K* 2 log

*n* (|*rK*|−|*r*1|)2 4*P*noise*g*2(2*dR*

> *g*2(*dC n* ) *g*2(2*dR n* ) *K K*−1

*n* = *P*max, discard this *n*th sensor node from the list of unallocated sensor nodes, decrease

*n* of the *n*th sensor node than its limitation, then we set the transmission power *PR*

*n* (*P*max) recursively to the remaining sensor nodes by the same

1 + *PC n αC n* (*K*−1) *P*noise*g*2(*dC*

*n* )*K*2

*K* (22)

4 , ∀*n* ∈ F*N*. (23)

*n* Data communication ≤ *P*tot . (20)

*N* ≤ *P*max < *P*tot. If

*n* which is given in terms

*n* instead of *PR*

*n* (*P*max), and reallocate the remaining

Power Allocation Procedure for Wireless Sensor Networks

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

*n*

173

*n* > *PC n*

(21)

*N* ∑ *n*=1

to *PR*

of *PR*

*n* > *PC*

total power *P*tot − *P*max − *PC*

we will have a look at some special cases previously.

the given total transmission power *P*tot by *P*max + *PC*

**3.3. Mutual information-based power allocation**

1 + *PR n αR*

for any small values of *x* we obtain the analytical relationship

*n* · *αR n αC n*

1 2 log

calculation and usage of the simple approximation

*PC n* = *PR*

Note that this theoretical concept is not realistic. However, we apply this concept as a heuristical method in this work.

### **3.1. Threshold calculation**

For the optimization of the thresholds in Section 2.1, in order to increase the overall classification probability, the analytic evaluation of (8) is needed. Due to the fact that this explicit form for the overall classification probability is unknown and due to the separation of the data communication from the classification task we propose the following simple approach to calculate the thresholds.

We increase the probability of correct decision of each sensor node independently to achieve suboptimal values for the thresholds. Thus, the overall classification probability should be increased as well. According to equations (4) and (12) the local probability of correct decision, which has to be maximized, is given by

$$\sum\_{k=1}^{K} \text{Prob}(H\_k) \text{Prob}(\mathcal{U}\_{\mathbb{R}} = k \mid H\_k) = \sum\_{k=1}^{K} \frac{\pi\_k}{2} \left[ \text{erf} \left( \frac{\sqrt{\mathcal{P}\_{\text{vjk}}^{\mathbb{R}}} - \tau\_{\text{vk}}}{\sqrt{2\mathcal{P}\_{\text{noise}}}} \right) + \text{erf} \left( \frac{\tau\_{\text{v},k+1} - \sqrt{\mathcal{P}\_{\text{v},\text{k}}^{\mathbb{R}}}}{\sqrt{2\mathcal{P}\_{\text{noise}}}} \right) \right]. \tag{17}$$

Its solution can be found explicitly by using differential calculus. The corresponding result is identical to the one obtained by using the Bayesian-hypotheses-test criterion. It is given by

$$
\tau\_{n,k} = \begin{cases}
\inf(\mathbb{I}\_{n,k}) & \text{if} \quad \mathbb{I}\_{n,k} \neq \{\}, \ k \in \mathbb{F}\_{K'} \\
\tau\_{n,k+1} & \text{if} \quad \mathbb{I}\_{n,k} = \{\}, \ k \in \mathbb{F}\_{K'} \\
\infty & \text{if} \quad k = K+1,
\end{cases} \tag{18}
$$

for all *n* ∈ F*N*, where the function inf(I*n*,*k*) is the infimum of the interval I*n*,*k* that is defined by

$$\mathbb{L}\_{n,k} \coloneqq \left\{ \mathbf{x} \in \mathbb{R} \mid \pi\_k f\_{\mathbf{n}}^{\mathbb{R}}(\mathbf{x} \mid H\_{\mathbf{k}}) > \pi\_l f\_{\mathbf{n}}^{\mathbb{R}}(\mathbf{x} \mid H\_{\mathbf{l}}), \forall l \in \mathbb{F}\_{K}, l \neq k \right\}, \forall k \in \mathbb{F}\_{K}, \forall n \in \mathbb{F}\_{N}. \tag{19}$$

### **3.2. Limitation of transmission power**

We assume that both the radar and the communication signal use the same bandwidth and are uncorrelated to each other, due to separation of the sensing task and the communication task into different time slots (see Section 2.3). In this case and for each new classification process, the limited total transmission power *P*tot is an upper bound for the sum

8 Will-be-set-by-IN-TECH

In this section, we motivate and present an approach to suboptimally allocate transmission power to the radar and to the communication task. The objective is to maximize the overall classification probability, given a limited total transmission power *P*tot that can be arbitrarily allocated to the radar task as well as to the communication task. A direct solution to this problem does not exist, since no analytical expression for the overall classification probability (8) is available. Instead, we independently maximize the mutual information of both communication channels to increase the information flow and in order to determine the power allocation. The motivation for this approach is the separation of the power allocation problem from the object classification procedure. Because in this case the data communication

Note that this theoretical concept is not realistic. However, we apply this concept as a

For the optimization of the thresholds in Section 2.1, in order to increase the overall classification probability, the analytic evaluation of (8) is needed. Due to the fact that this explicit form for the overall classification probability is unknown and due to the separation of the data communication from the classification task we propose the following simple

We increase the probability of correct decision of each sensor node independently to achieve suboptimal values for the thresholds. Thus, the overall classification probability should be increased as well. According to equations (4) and (12) the local probability of correct decision,

Its solution can be found explicitly by using differential calculus. The corresponding result is identical to the one obtained by using the Bayesian-hypotheses-test criterion. It is given by

∞ if *k* = *K* + 1,

for all *n* ∈ F*N*, where the function inf(I*n*,*k*) is the infimum of the interval I*n*,*k* that is defined

We assume that both the radar and the communication signal use the same bandwidth and are uncorrelated to each other, due to separation of the sensing task and the communication task into different time slots (see Section 2.3). In this case and for each new classification process,

inf(I*n*,*k*) if I*n*,*k* �= {}, *k* ∈ F*K*, *τn*,*k*+1 if I*n*,*k* = {}, *k* ∈ F*K*,

*n* (*x* | *Hl*), ∀*l* ∈ F*K*, *l* �= *k*

� + erf

�

�*τn*,*k*+1− � *P*˜*R n*|*k* √2*P*noise

��

, ∀*k* ∈ F*K*, ∀*n* ∈ F*N*. (19)

. (17)

(18)

*K* ∑ *k*=1 *πk* 2 � erf �� *P*˜*R n*|*k*−*τn*,*k* √2*P*noise

**3. Allocating power to the radar and to the communication task**

does not affect the classification of the target object.

heuristical method in this work.

**3.1. Threshold calculation**

approach to calculate the thresholds.

which has to be maximized, is given by

*x* ∈ R | *πk f R*

**3.2. Limitation of transmission power**

Prob(*Hk*) Prob(*Un* = *k* | *Hk*) =

*τn*,*k* =

⎧ ⎪⎨

⎪⎩

*n* (*x* | *Hk*) > *πl f R*

*K* ∑ *k*=1

by

I*n*,*k* := �

$$\sum\_{n=1}^{N} \underbrace{\mathbf{P}\_n^R}\_{\mathbf{Radar sensing}} + \underbrace{\mathbf{P}\_n^C}\_{\mathbf{Data}\text{ communication}} + \underbrace{\mathbf{P}\_n^C}\_{\mathbf{Data}\text{ communication}} \le \mathbf{P}\_{\text{bot}}\tag{20}$$

Total transmission power of one sensor for a single observation

By using this restriction, we present the power allocation procedure in the next section. But, we will have a look at some special cases previously.

In real applications the transmission power of each sensor node is also limited. Consider the case in which all sensor nodes have the same power limitation *P*max with *P*tot *N* ≤ *P*max < *P*tot. If the power regulation, which is described in the next section, wants to allocate a higher power to *PR n* > *PC n* of the *n*th sensor node than its limitation, then we set the transmission power *PR n* equal to its highest possible limitation given by *P*max, recalculate *PC n* which is given in terms of *PR n* = *P*max, discard this *n*th sensor node from the list of unallocated sensor nodes, decrease the given total transmission power *P*tot by *P*max + *PC n* (*P*max), and reallocate the remaining total power *P*tot − *P*max − *PC n* (*P*max) recursively to the remaining sensor nodes by the same procedure described in the next section. In a case, where the power *PC n* instead of *PR n* > *PC n* will be regulated higher than *P*max, we can reverse the roles of both transmission powers and repeat this reallocation method until no more sensor nodes are left which exceed their power limitation. Therefore, the described limitation of the total transmission power is the generalized case which includes the limitation of the transmission power of each sensor node.

Note that this procedure is applicable for individual power constraints per node as well. Furthermore, note that in each iteration more than one node can be discarded from the list of unallocated sensor nodes in order to decrease the computation complexity.

### **3.3. Mutual information-based power allocation**

For the maximization of the information flow we set the mutual information of both communication channels equal. This leads to the same symbol error probabilities on both sides for low SNR values. For each sensor node an upper bound for the mutual information of its first and second link can simply be calculated. The identity of obtained bounds

$$\frac{1}{2}\log\left[1+\frac{P\_n^R a\_n^R (|r\_K|-|r\_1|)^2}{4P\_{\text{noise}}g^2 (2d\_n^R)}\right] = \frac{K}{2}\log\left[1+\frac{P\_n^C a\_n^C (K-1)}{P\_{\text{noise}}g^2 (d\_n^C)K^2}\right] \tag{21}$$

has to be computed in order to find the relationship between the powers for all *n* ∈ F*N*. After calculation and usage of the simple approximation

$$
\sqrt[5]{1+x} \approx 1 + \frac{x}{\mathbb{Z}} \tag{22}
$$

for any small values of *x* we obtain the analytical relationship

$$P\_n^{\mathbb{C}} = P\_n^{\mathbb{R}} \cdot \frac{a\_n^{\mathbb{R}}}{a\_n^{\mathbb{C}}} \frac{\mathcal{S}^2(d\_n^{\mathbb{C}})}{\mathcal{S}^2(2d\_n^{\mathbb{R}})} \xrightarrow[K - 1]{\mathbb{K}} \frac{(|r\_K| - |r\_1|)^2}{4}, \forall n \in \mathbb{F}\_N. \tag{23}$$

In the next step, we increase the overall information flow by maximization of the cumulative mutual information subject to the given total power of the sensor network. Then the

#### 10 Will-be-set-by-IN-TECH 174 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 11

optimization problem is given by

$$\underset{P\_1^{\mathbb{R}}, \dots, P\_N^{\mathbb{R}}}{\text{maximize}} \quad \sum\_{n=1}^N \frac{1}{2} \log \left[ 1 + \frac{P\_n^{\mathbb{R}} a\_n^{\mathbb{R}} \left( |r\_k| - |r\_1| \right)^2}{4 P\_{\text{noise}} \delta^2 (2d\_n^{\mathbb{R}})} \right] \quad \text{subject to} \quad \sum\_{n=1}^N P\_n^{\mathbb{C}} + P\_n^{\mathbb{R}} \le P\_{\text{tot}}.\tag{24}$$

It has to be considered that the sum of concave functions is also concave and that the arguments of the logarithms are linear functions of the powers. Furthermore, the domain of the feasible set is a closed convex set and, therefore, only one global maximum of the problem exists. This maximum can be explicitly calculated by using the method of Lagrange multipliers which is equivalent to the water-filling power allocation result [3]. The result is given by

$$P\_n^R = P\_{\text{noise}} \frac{g^2 (2d\_n^R)}{a\_n^R} \frac{4}{(|r\_k| - |r\_1|)^2} \cdot \max\left(0, \frac{\lambda}{\beta\_n} - 1\right), \forall n \in \mathbb{F}\_{N\prime} \tag{25}$$

where the factor *βn* is defined by

$$\mathcal{B}\_n := \frac{\varrho^2(2d\_\mu^\mathbb{K})}{a\_n^\mathbb{K}} \frac{4}{(|r\_\mathbb{K}| - |r\_1|)^2} + \frac{\varrho^2(d\_\mu^\mathbb{C})}{a\_n^\mathbb{C}} \underset{\mathbb{K} \to \mathbb{T}}{\mathbb{K}}, \forall n \in \mathbb{F}\_N. \tag{26}$$

For the following equations, we assume that the factors *βn* are ordered in an increasing manner. Then the water-filling level *λ* is a value specified by the inequality

$$\mathcal{B}\_{\tilde{N}} < \lambda \le \frac{1}{\tilde{N}} \left[ \frac{p\_{\text{tot}}}{p\_{\text{noise}}} + \sum\_{n=1}^{\tilde{N}} \beta\_n \right],\tag{27}$$

powers, we use the same solution for high transmission powers, too. If instead another approximation is used, the results are indeed different, but the behavior of solutions remains

In order to calculate the transmission powers (25) and (29) the computation of *βn*, *λ*, and *N*˜

of the target object and are therefore unknown. They can be estimated for example by a tracking algorithm. If these values are also determined, then the equations (25) to (29) can be calculated with little effort, because of simple mathematical operations such as summation and multiplication. The only difficulty is the evaluation of the path loss function *g*, which can include complex mathematical operations. Its complexity depends on the given multipath

However, the computation effort of the equations (25) to (29) is less complex than the evaluation of the classification algorithm such as (6). If one can find simpler algorithms than (6) (see, for example [12]), then the assessment of the calculation effort becomes

In this section we present some numerical results obtained by applying the proposed optimization method from Section 3. We simulate target objects with equal prior probabilities

> *P*noise

The verification of the proposed power allocation between both communication links of a single sensor node is shown in Figure 4. The overall error probability of the classification increases for higher SNR values for the case where the allocated power of one link is reduced by 10% and at the same time the power of the other link is stepped up by this 10%. When we reallocate a power amount of 10% − 30% to both links in an inverse manner, then the classification probability remains almost valid. This result shows that the proposed method allocates the given total power nearly optimal to both communication links, especially for

In Figure 5 another verification of the proposed power allocation is shown, where a network of two sensor nodes is considered. The overall error probability of the classification decreases if we decrease the allocated power of the sensor node, which has the smallest part of the total power, by 10% and allocate this amount of power to the other sensor node. This result shows that the proposed method assigns the given total power suboptimal to the sensor nodes. The curves disperse, because of the approximation (22) which has been used for the equation (23). As shown in Figure 6 the proposed method yields a better classification probability in comparison to a uniform power allocation where a network of ten sensor nodes is considered.

*K* ∀*k* ∈ F*K* in sensor networks with different settings as described in Section 2. In all results, we consider three different kinds of target objects with reflection coefficients chosen as

2 , and |*r*3| = 1. Furthermore, the path loss function is modeled as line-of-sight

, instead of *received* SNRs, is depicted on the

*n* , and *αC*

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

*n* and *dC*

Power Allocation Procedure for Wireless Sensor Networks

*n* are fixed system parameters

*n* depend on the position

175

generally valid. However, this study is not the subject of this work.

is necessary. The parameters *K*, *N*, *P*tot, *P*noise, *rk*, *αR*

important and should be considered in detail.

**4. Numerical results and conclusions**

propagation. The ratio SNR = 10*dB* log *P*tot

which are known to the computation unit. The distances *dR*

**3.4. Computational effort**

channel.

*πk* = 1

|*r*1| = 0, |*r*2| = 1

abscissa of all figures.

higher SNR values.

where the number *N*˜ with 1 ≤ *N*˜ ≤ *N* is a suitably chosen integer value for which the inequality

$$\sum\_{n=1}^{\tilde{N}} \left( \mathcal{J}\_{\tilde{N}} - \mathcal{J}\_n \right) < \frac{P\_{\text{tot}}}{P\_{\text{noise}}} \tag{28}$$

holds. From (23) and (25) the allocated power for the second channel is determined as

$$P\_n^{\mathbb{C}} = P\_{\text{noise}} \frac{\chi^2(d\_n^{\mathbb{C}})}{d\_n^{\mathbb{C}}} \frac{\mathbb{K}}{\mathbb{K} - 1} \cdot \max\left(0, \frac{\lambda}{\beta\_n} - 1\right), \forall n \in \mathbb{F}\_N. \tag{29}$$

This allocation has the following interpretation. The sensor node *Sn* with the lowest *βn* gets the largest part of the total power because its communication channels are possibly the best due to the low distances. Therefore the observation of the target object is less interfered by noise and consequently results in better data communication. Sensor nodes with higher distances get smaller parts of the total power and some of them do not get any power at all. The last ones participate neither in the data communication nor in the classification of the target object. Their information reliability is too poor to be considered for data fusion. More and more sensor nodes will become active by increasing the total power. Then the overall classification probability increases because more correct information is provided by the observations.

Note that we have used the approximation (22) in order to simplify the maximization problem and to find analytical solutions for all equations. Without any approximation the maximization problem yields the *Lambert's trinomial equation*, which still does not have any analytical solutions. Although the above approximation is only valid for low transmission powers, we use the same solution for high transmission powers, too. If instead another approximation is used, the results are indeed different, but the behavior of solutions remains generally valid. However, this study is not the subject of this work.


*Article* **Recovery of Li(Ni0.33Mn0.33Co0.33)O 2 from Lithium-Ion Battery Cathodes: Aspects of Degradation**

#### **Tim Sieber, Jana Ducke, Anja Rietig, Thomas Langner and Jörg Acker \***

Department of Physical Chemistry, Brandenburg Technical University Cottbus-Senftenberg, Universitätsplatz 1, D-01968 Senftenberg, Germany<EMAIL_ADDRESS>(T.S<EMAIL_ADDRESS>(J.D<EMAIL_ADDRESS>(A.R<EMAIL_ADDRESS>(T.L.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +49-3573-85-839

Received: 19 December 2018; Accepted: 7 February 2019; Published: 12 February 2019

**Abstract:** Nickel–manganese–cobalt oxides, with LiNi0.33Mn0.33Co0.33 O2 (NMC) as the most prominent compound, are state-of-the-art cathode materials for lithium-ion batteries in electric vehicles. The growing market for electro mobility has led to a growing global demand for Li, Co, Ni, and Mn, making spent lithium-ion batteries a valuable secondary resource. Going forward, energy- and resource-inefficient pyrometallurgical and hydrometallurgical recycling strategies must be avoided. We presented an approach to recover NMC particles from spent lithium-ion battery cathodes while preserving their chemical and morphological properties, with a minimal use of chemicals. The key task was the separation of the cathode coating layer consisting of NMC, an organic binder, and carbon black, from the Al substrate foil. This can be performed in water under strong agitation to support the slow detachment process. However, the contact of the NMC cathode with water leads to a release of Li+ ions and a fast increase in the pH. Unwanted side reactions may occur as the Al substrate foil starts to dissolve and Al(OH)3 precipitates on the NMC. These side reactions are avoided using pH-adjusted solutions with sufficiently high buffer capacities to separate the coating layer from the Al substrate, without precipitations and without degradation of the NMC particles.

**Keywords:** lithium-ion; nickel–manganese–cobalt oxide (NMC); leaching; recycling; recover; degradation; SEM-EDX; Raman spectroscopy


**4. Conclusions**

This work presents the fabrication and characterization of thin and thick channel AlGaN/GaN HEMTs grown on AlN/sapphire templates. Lateral buffer breakdown voltage assessment of the thin channel reveals a remarkable breakdown field of 5 MV/cm for short contact distances, which is far beyond the theoretical limits of a GaN-based material system. Furthermore, fabricated transistors are fully functional with low leakage current and low on-resistance. The use of a sub-10 nm ultrathin GaN channel may not be a limiting factor for the breakdown mechanism of transistors. Temperature measurements up to 300 ◦C show that the AlN buffer enables increased temperature stability of GaN-based transistors. When combined with a thin channel, the related transistors may deliver lower channel temperatures as compared to devices with thicker channels. Proper passivation and associated processing will allow us to take advantage of the properties offered by AlN-based devices, providing both low resistances and high voltages well above 1 kV.

**Author Contributions:** Device design, fabrication and characterization, I.A., R.K. and F.M., TEM images, C.B., Temperature measurements, J.P., C.M., R.C., Growth, Y.C., Writing-Original Draft Preparation, all co-authors.

**Funding:** This work is supported by the French RENATECH network and the French National grant ANR-17-CE05-00131 within the project called BREAKUP and ANR-11-LABX-0014 representing GaNeX: the "Investissements d'Avenir".

**Conflicts of Interest:** The authors declare no conflict of interest.


Preface

Iron is a vital trace element for humans, as it plays a crucial role in oxygen transport, oxidative metabolism, cellular proliferation, and many catalytic reactions. To be beneficial, the amount of iron in the human body needs to be maintained within the ideal range. Iron metabolism is one of the most complex processes involving many organs and tissues, the interaction of which is critical for iron homeostasis. The bone marrow is the prime iron consumer in the body, being the site for erythropoiesis, while the reticuloendothelial system is responsible for iron recycling through erythrocyte phagocytosis. Among the numerous proteins involved in iron metabolism, hepcidin is a liver-derived peptide hormone, which is the master regulator of iron metabolism. This hormone acts in many target tissues and regulates systemic iron levels through a negative feedback mechanism. Hepcidin synthesis is controlled by several factors such as iron levels, anemia, infection, inflammation, and erythropoietic activity. In addition to systemic control, iron balance mechanisms also exist at the cellular level and include the interaction between iron-regulatory proteins and iron-responsive elements. Genetic and acquired diseases of the tissues involved in iron metabolism cause a dysregulation of the iron cycle. Consequently, iron deficiency or excess can result, both of which have detrimental effects on the organism.

This book contains eight chapters divided into three sections on iron, iron metabolism and iron deficiency and new lines of therapy.

Nowadays, research is increasingly dedicated to the field of iron metabolism, but countless questions remain unanswered. Increased knowledge of the physiology of iron homeostasis facilitates understanding the pathology of iron disorders, such as iron deficiency and iron overload, and leads to improved outcomes.

#### **Marwa Zakaria**

Associate Professor of Pediatrics, Faculty of Medicine, Pediatric Department, Zagazig University, Zagazig, Egypt

#### **Tamer Hassan**

Professor of Pediatrics, Faculty of Medicine, Pediatric Department, Zagazig University, Zagazig, Egypt

Section 1