*Build 3D Abstractions with Wireframes DOI: http://dx.doi.org/10.5772/intechopen.96141*

#### **Figure 4.**

{6,9,86,46,49,126} from [22], *S*8 further add two more images {89,129} to the list, *S*10 includes {8,10,12,88,90,48,50,52,128,130}, and *S*12 further adds images {92,132} to the latter. The resulting 3D line sketches from both sides of the house are aligned by using common lines. This completed sketch is finally aligned to the Ground Truth in order to measure the precision. Note that this experiment takes into account just a the variation of the number of images in the dataset [22]. The results show that the method [2] obtains more usable results for a low number of images, and the results of method [1] are only more adequate than method [2] when the number of images gets close to a dozen. The spatial lines are colored attending to its

*Figure from [2]. Quantitative comparison using the sets S*6 *and S*8*. This figure is better viewed on a screen with a 4x zoom. (a) Sample of the set. (b) and (c) [2] against S*6*, resulting in 175 lines. (d) and (e) Same superposed onto the Ground Truth mesh. (f) Histogram of distances to Ground Truth with [1] method. The maximum distance to be accounted is set to be 0.8, already considered as outlier. (g) Sparse atomic lines returned by [1] method. (h) to (l) [1] against the set S*8*, with 294 segments. (m) and (n) same measurements*

distance to the surface of the Ground Truth mesh.

*for the result by [1]. (o) shows the histogram for this latter result.*

**Figure 3.**

*Applications of Pattern Recognition*

**52**

*Figure from [2]. Quantitative comparison using the sets S*10 *and S*12*. This figure is better viewed on a screen with a 4x zoom. (a), (b) and (c) [2] against S*10*. The obtained 475 lines have been discretized in points. The distance from each point in the cloud to the surface of the Ground Truth mesh is represented in colors. (d) and (e) Same superposed onto the Ground Truth mesh. (f) Histogram of distances to Ground Truth with the [2] method. The maximum distance to be accounted is set to be 0.8, already considered as outlier. (g) Sparse atomic lines returned by the method [1]. It has been aligned with the Ground Truth mesh. (h) to (l) Same for the method [2] against the set S*12*, with 556 segments. (m) and (n) same measurements for the result by [1]. (o) shows the histogram for this latter result.*


**Author details**

Ota Fuchs Institute of Hematology and Blood Transfusion, Prague, Czech Republic

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*2.2. Chemometric Analysis of the EOs from Different C. amblyocarpa Ecospecies*

The chemometric analysis of the EO composition of the present studied *C. amblyocarpa* and other reported ecospecies (Saudi, Iranian, Tunisian, and Emirati) was performed using cluster analysis and PCA (Figure 3). The cluster analysis revealed substantial variations among the studied ecospecies, and we can categorize them into three groups: group I comprising the present Egyptian and Tunisian ecospecies, group II containing Emirati and Iranian ecospecies, and finally the Saudi ecospecies separated alone as group III (Figure 3a). Interestingly, the chemometric analysis revealed that the EO compositions of ecospecies from the nearest countries were similar. This observation reflects the effect of environmental and climatic factors [30,32,33].

However, the present studied *C. amblyocarpa* ecospecies showed a correlation with the caryophyllene oxide, hexahydrofarnesyl acetone, and shyobunol, whereas the Tunisian ecospecies showed a correlation with ethyl 3-methylpentanoate, 7-epi-silphiperfol-5-ene, *α*copaene, and 1,8-cineole (Figure 3b). The Saudi ecospecies was characterized by cis-dihydro carvone, 2-methoxy-4-vinyl phenol, and cubebene heptanal.


*3.2.2. Specification of target product characteristics, product decomposition and variant identification*

To create a product, it is necessary to identify product features, quality level, packaging, etc. [37]. Accuracy and efficiency of product configuration depend on product structure used in product configuration.

Procedural knowledge helps to indicate the target value of configuration baseline which is needed for variant identification.

**Figure 5.** Product configuration data.

products. Customer service department staff should know how the product characteristics needed by the customer are different from the product characteristics offered by the enter-

Product offer preparation needs a product requirement analysis, which includes analyzing product functions, reliability, safety, environment, packaging, transportation, storage, etc. The decision problem solved with the use of QFD-KB for product configuration is how to choose and evaluate the right product from the product portfolio and adopt it to particular customer needs. The knowledge needed to solve this problem could origin from, e.g., experi-

Identification of customer requirements, product characteristics, their correlations and variant comparison were denoted with symbols presented in **Figure 6**, where a QFD scheme uses

Configuration items should be determined according to the given criterion included in, e.g., [38]:

Identification of product characteristics from the customer point of view could be made in

The first stage regarding the category of requirements is related to product functions, which, in the case of toothed gear configuration, include, among others, torque transmission, weight

The second stage regarding the category of requirements includes product environment con-

The third stage regarding category of requirements includes product trade characteristics,

To create a product, it is necessary to identify product features, quality level, packaging, etc. [37]. Accuracy and efficiency of product configuration depend on product structure used in

Procedural knowledge helps to indicate the target value of configuration baseline which is

*3.2.2. Specification of target product characteristics, product decomposition and variant*

a square roof instead of a triangular roof matrix, as it is easier to use in a spreadsheet.

• Influence on functional and physical product characteristics determined by the client

prise and what kind of changes it is possible to implement in the product.

Possible data sources used in product configuration are presented in **Figure 5**.

enced staff, databases, and documentation.

58 Product Lifecycle Management - Terminology and Applications

*3.2.1. Identification of product characteristics*

• Safety of product usage

• Product reliability • Logistic aspects

three stages.

*identification*

product configuration.

needed for variant identification.

• Innovatory character of product and process structure

of material handling and velocity of material handling.

e.g., price, delivery time, warranty, etc.

ditions, e.g., environment temperature, dustiness, humidity, etc.

In the presented approach, decision rules were used to identify product alternatives. The premises in the proposed rules contain variation intervals of product features, where the conclusions include the proposed products (*mzl \** ).

One of the important issues in product configuration is product decomposition, which provides the combination of components which gives a product suitable for a particular client. Product decomposition and functional requirements will help to answer the following question: which physical element(s) is responsible for the fulfillment of a specific functional requirement?

In literature we can find different approaches to product decomposition [39]. The presented method applies decomposition tree (**Figure 7**) [40], in which "and" nodes means that all components go together into product structure and "or" nodes mean that one of component alternatives should be put into product structure were used.

In product decomposition tree, there were distinguished standard components, and this one needs to be redesigned.

> The identified configuration items, like product parts, components or modules should be described with the use of attributes and their values as appropriate specification with func-

> Product decomposition in the product configuration process determines how detailed the product structure is. The presented product structures include alternative configuration

> Comparing product variants identifies the range of product change. The presented rank

*woz* − *pmkzt w* \_\_\_\_\_\_\_\_\_| *pmkzt*

*woz* ⋅ 100 (1)

Configuration of a Customized Product http://dx.doi.org/10.5772/intechopen.79523 61

method applies an evaluation indicator calculated according to the formula (1):

tional and physical characteristics (**Figure 8**).

**Figure 7.** Product decomposition.

items, which were characterized in **Table 1**.

*wkzt* = |*pmkzt*

woz—target level of product characteristic;

w—offered attribute value.

where:

pmkzt

pmkzt

*3.2.3. Variant evaluation: choosing the product to be redesigned*

wkzt—assessment indicator for product k, attribute z and variant t;

**Figure 6.** Product planning QFD matrix.

**Figure 7.** Product decomposition.

where:

—range of change, z∈Z,

needs to be redesigned.

**Figure 6.** Product planning QFD matrix.

pmkz—product characteristics, z∈Z,

—a configuration item, k∈K, Z—a set of product characteristics, K—a set of configuration items.

woz—target value of product characteristics, z∈Z,

60 Product Lifecycle Management - Terminology and Applications

tives should be put into product structure were used.

One of the important issues in product configuration is product decomposition, which provides the combination of components which gives a product suitable for a particular client. Product decomposition and functional requirements will help to answer the following question: which physical element(s) is responsible for the fulfillment of a specific functional requirement?

In literature we can find different approaches to product decomposition [39]. The presented method applies decomposition tree (**Figure 7**) [40], in which "and" nodes means that all components go together into product structure and "or" nodes mean that one of component alterna-

In product decomposition tree, there were distinguished standard components, and this one

*xz*

pmkzt

mk

The identified configuration items, like product parts, components or modules should be described with the use of attributes and their values as appropriate specification with functional and physical characteristics (**Figure 8**).

Product decomposition in the product configuration process determines how detailed the product structure is. The presented product structures include alternative configuration items, which were characterized in **Table 1**.


**1. Introduction**

Over the century, the evolution of electronic devices has been rehabilitated rapidly and day by day. The transistor incorporation led to reducing the feature size of any realistic instruments, and besides that, the efficacy has to be ameliorated for that purpose. The continual advancement of the fabrication methodologies of printed circuit boards makes the transistors significantly small, permitting the huge number of transistors in one plate and lessen the consumption of electric power of the integrated circuit. In the present day, many electronic devices are used in miniature sizes and too much power for any operation. Subsequently, energy

storage devices are required in the same formation used in those new small devices, batteries, and capacitors, which are hindrances to their improvement. The batteries are analysed, which are lower of flexibility, higher weight, and mainly possess huge space in the particular equipment. Generally, the capacitors with low storage capacity with low energy occupy a huge space, mainly electrolytic capacitors, restrained by shape. Moreover, the capacitors need to solder directly to the integrated circuit; their electrical polarity cannot be reversed in electrolytic capacitors. In this scenario, this chapter explores a probable elucidation to the above-said context based on IPMC (ionic polymer-metal composite) systems. These attain capacitive features after dipping in the ionic solution; then, the membrane becomes flexible and lightweight with stored potential, a new kind of flexible capacitor. Furthermore, the flexible IPMC membrane capacitor is malleable and easily used in polarity reversal based on needs. In most cases, the analysis and application of the IPMC polymer matrix entirely focused on the actuator's application [1–5]. This chapter focused on another part of IPMC, i.e., the energy storage application. The different fabrication procedures and corresponding attributes of the polymer system are discussed thoroughly here. Prominent displacements analyse IPMCs within lower density forces. In the mechanical energy harvesting system, IPMCs are investigated using the generated lower electric power values, but irrespective of using significant mechanical pressures, the reverse function is happened as with the piezoelectric type materials [6, 7]. Present-day, electric double-layer capacitors (EDLCs) and lithium-ion batteries are the maxima used energy storage devices on the scale of important commercial use. Every device exhibits definite attribution and applications that need high energy density (Whkg�1 ) for lithium batteries and high power density (Wkg�1 ) of EDLC system [8–11]. Furthermore, few polymers depict several characteristics changes and some benefits in the potential application field in the presence of electrical stimulation; those are called electro-active polymers or EAPs. Those materials are showing response in size and shape by the variation of electrical stimulation. This material is categorised into two depending on the activation mechanism, i.e., ionic and electronic or field-activated [12, 13]. Generally, the electronic grade exhibits a higher energy density of mechanical energy; in comparison, ionic systems potentially employed ion diffusion or transportation consist of the electrolyte-electrode interface. Conductive polymers, ionic polymer gels, and composites of ionic polymer-metal are examples of some ionic EAPs. The electromechanical response of the membrane, showing huge strain at electrical stimulation, is very similar to the biological tissues. The Ionic polymers are introduced in fuel cells application in the 1960s; the features of EAP and the connexion of electromechanical ion-transportation of metal-ionic polymer composites (IPMC) were invented in 1992 by researchers in the United States and Japan [14, 15]. In general, IPMC comprises a membrane of polyelectrolyte, normally Flemion or Nafion covered on all sides with a conductive metal. After that, the counter-ions are neutralised, stabilising the electrical anionic charge of the covalently stable to the pillar of the membrane. The hydrated cations transportation between an IPMC polymer matrix is kept within the voltage applied, and corresponding electrostatic interactions enhance the bending. IPMCs are the working actuator that delineates lower impedance. Moreover, the water-based IPMCs generally dissociate with solvent content when it is subjected to 1.23 Volts higher. IPMCs are corroborated as the smartest prominence materials for larger bending deformation and lighter weight within significantly less applied voltages [16–18]. However, To fabricate chemically coated IPMC membrane, electrodes of metal ions gold, platinum, etc., are distributed through the hydrophilic sections of the polymer matrix and generally decrease the consistent metal atoms of zero-valence. Paddison et al. [19] researched the measurement of hydrated Nafion's permittivity in the

range of broadband frequency. Their outcomes denote that the dielectric constant enhances with incrementing the water content, reduced with frequency increase.


**4. Research contributions and questions**

The contributions of this chapter are the following. First, a new rapid 3D physical modelling technique is proposed, this technique is based on formative manufacturing processes. We named this technique Rapid 3D Wireframing. The technique is expected to be used in early conceptual design phases of the new product development process. Therefore, it modifies the industrial design process but this is not evaluated in this chapter. Second, a TRIZ-based design process is proposed to reduce the complexity of the mechatronic design to print the object (Rapid 3D Wireframing). We have named MDSU this design process. Since the Rapid 3D Wireframing technique is new, so the MDSU design process and the application of TRIZ principles to the design of this kind of mechatronic systems. MDSU stands for Mesh, Unfolding (*Desdoblado*), Separation and Union (MUSU in English). The MDSU approach reduces the degree of freedom necessary in mechatronic systems to automate the process. These four sub-processes belong to TRIZ principles. It is expected that the Rapid 3D Wireframing technique will be automatic; therefore a first prototype will be explained briefly. In this chapter the following research questions are explored: the implementation of MDSU will ease the design process of the mechatronic system; the implementation of MDSU improves the design thinking process and reduce the development time of the mechatronic system; the implementation of the Rapid 3D Wireframing technique improves the work conditions of the designers; the implementation of the Rapid 3D Wireframing technique reduces the designers competencies related to the conceptual design phase; the implementation of Rapid 3D Wireframing improves the new product design process. Through our experiments we will try to answer the previous research questions.


**7.4 Data transfer between CE Process and MIC Process internal metrics items**

*7.4.1 Cultural capital, symbolic and social capital incl. performance dimensions versus MIC Process internal metrics items*

Now, we shall investigate the data transfer between BPFs, the internal metrics of which is represented by linguistic sets denoted as cultural capital {[CULC (i, j)]}, symbolic capital {[SYMC (i, j)]}, social capital {[SOCC (i, j)]}, and performance dimensions {[PEDC (i, j)]}within CE Process items and MIC Process internal metrics items postulated as follows:

$$\{ [\text{IM } (\mathbf{i}, \mathbf{j})] \} = \{ [\text{DEV } (\mathbf{i}, \mathbf{j})], [\text{TOOL } (\mathbf{i}, \mathbf{j})], [\text{HR } (\mathbf{i}, \mathbf{j})] \} \tag{15}$$

$$\{\{\text{IRR}\ (\mathbf{i}, \mathbf{j})\}\} = \{\{\text{INP1}(\mathbf{i}, \mathbf{j})\}, [\text{INP2}(\mathbf{i}, \mathbf{j})], [\text{INP3}(\mathbf{i}, \mathbf{j})]\} \tag{16}$$


Preface

Earthquakes are the major geological hazards, which pose serious threat to the human pop‐ ulation and various infrastructures such as highways, rail routes, and civil structures like dams, buildings, and others.

The idea that earthquakes could occur is frightening people in every area prone to such phe‐ nomena. That is because the effects of earthquakes can be devastating, leaving thousands of people without homes and threatening their lives.

Earthquakes often occur together with other natural disasters such as landslides, volcanoes, and tsunamis. Earthquakes play a role of triggering mechanism of landslides and tsunamis.

Mountainous and coastal areas are the regions mostly affected by earthquakes, but that does not mean that the other areas are safe.

When an earthquake occurs in mountainous and coastal areas, the risks of a landslide grow tremendously. Ground shaking allows water to rapidly infiltrate between ground layers and make these layers slide on one another. Ground shaking also causes widespread rock falls.

Earthquakes cause huge damage in the world and kill many people each year. In order to understand this phenomenon better and eventually protect ourselves from its destructive action, people should be aware of how earthquakes arise and how they act.

Depending on the location and type of human activity, the earthquake effect could be less‐ ened. People should know hazard zones and avoid activities in such areas.

For systematic analysis of earthquake hazards, it is fruitful to use the notion of risk.

Geological risk is a relatively new and not fully explored concept. There are many defini‐ tions of geological risk. And often scientific study or scientific approach to the problem be‐ gins with a presentation of the author's position and the choice of the definition of geological risk for the problem under consideration. One of the most common approaches defines that risk is the expectation of the damage, or risk is the product of the probability of possible hazardous events on the damage produced by it.

It is the responsibility of the local governments to establish rules meant to reduce the effects of eventual earthquakes. Land-use regulations and policies are required in areas that are prone to earthquakes.

Apocalyptic images of earthquakes should make local governments pay more attention to the forecasting of such natural phenomena. It is important for a local government to know which areas are prone to earthquakes and take appropriate measures in order to reduce vul‐ nerability to such hazards.

Vulnerability to earthquakes depends on location, frequency of earthquakes, type of human activity in the area, and other factors.

This book addresses principles, concepts, and paradigms of earthquakes, as well as opera‐ tional terms, materials, tools, techniques, and methods including processes, procedures, and

• equips professionals and others with a formal understanding of earthquake hazards

• clarifies the similarities or differences in fundamental concepts and principles in the

• explains the relevance and application of primary tools and practices in earthquake

• directs geologists, engineers, architects, planners, teachers, students, and others in‐

• captures the wide range of expanding disciplinary activities under a single umbrella

**Dr Svalova Valentina**

Moscow, Russia

Preface XI

Sergeev Institute of Environmental Geoscience Russian Academy of Sciences (IEG RAS)

terested in the earthquake discipline to authoritative and vetted sources

of earthquake hazard, disaster, and risk concept.

implications. This book

and risk topics

discipline

risk study

The effects on people and buildings can be lessened if hazardous areas are avoided or if activities in such areas are restricted or deployed under certain conditions. Local govern‐ ments are responsible for land-use policies and other regulations meant to reduce the risks of living in dangerous places.

Exposure to hazards may be reduced if individuals educate themselves on the past history of these phenomena. Departments of local governments that are responsible for planning and engineering may help a lot with their advice.

People can also benefit from the professional services of engineering geologists, civil engi‐ neers, or geotechnical engineers who are all qualified to evaluate the potential risk of a haz‐ ardous site.

Due to the huge losses that earthquakes imply, their prediction is of maximum importance for all the people living in the area of hazard.

An earthquake is the shaking of the surface of the Earth, resulting from the sudden release of energy in the *Earth's lithosphere* that creates *seismic waves*. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people around and destroy the whole cities.

At the Earth's surface, earthquakes manifest themselves by shaking and sometimes displace‐ ment of the ground. When the *epicenter* of a large earthquake is located offshore, the seabed may be displaced sufficiently to cause a *tsunami*. Earthquakes can also trigger *landslides* and occasionally volcanic activity.

Earthquakes are caused not only by rupture of geological *faults* but also by other events such as volcanic activity, landslides, mine blasts, and *nuclear tests*.

Earthquakes lead to serious disruption of the normal functioning of a society causing wide‐ spread human, material, economic, or environmental losses. A disaster results from the combination of earthquake, conditions of vulnerability, and insufficient capacity or meas‐ ures to reduce the potential negative consequences of risk and exposure.

Millions of human lives are lost due to earthquakes, and property damage has exceeded hun‐ dreds of billions USD. It is not possible to make reliable earthquake forecasts now, but there exist a few successful examples. It is possible to estimate the vulnerability of territories to the possible earthquake hazard, and means are available to develop earthquake resilient societies.

'Earthquake early warning' is the rapid detection of earthquakes in progress and alerting people of the ground shaking that could be hazardous. Application of this technique has demonstrated its usefulness. Developing earthquake scenarios, as what would happen if an earthquake repeats, where it had occurred in the past, is also very effective in developing earthquake resilient societies.

This book addresses the multidisciplinary topic of earthquake hazards and risk, one of the fastest growing, relevant, and applied fields of research and study practiced within the geo‐ sciences and environment.

This book addresses principles, concepts, and paradigms of earthquakes, as well as opera‐ tional terms, materials, tools, techniques, and methods including processes, procedures, and implications.

This book

Vulnerability to earthquakes depends on location, frequency of earthquakes, type of human

The effects on people and buildings can be lessened if hazardous areas are avoided or if activities in such areas are restricted or deployed under certain conditions. Local govern‐ ments are responsible for land-use policies and other regulations meant to reduce the risks

Exposure to hazards may be reduced if individuals educate themselves on the past history of these phenomena. Departments of local governments that are responsible for planning

People can also benefit from the professional services of engineering geologists, civil engi‐ neers, or geotechnical engineers who are all qualified to evaluate the potential risk of a haz‐

Due to the huge losses that earthquakes imply, their prediction is of maximum importance

An earthquake is the shaking of the surface of the Earth, resulting from the sudden release of energy in the *Earth's lithosphere* that creates *seismic waves*. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people

At the Earth's surface, earthquakes manifest themselves by shaking and sometimes displace‐ ment of the ground. When the *epicenter* of a large earthquake is located offshore, the seabed may be displaced sufficiently to cause a *tsunami*. Earthquakes can also trigger *landslides* and

Earthquakes are caused not only by rupture of geological *faults* but also by other events such

Earthquakes lead to serious disruption of the normal functioning of a society causing wide‐ spread human, material, economic, or environmental losses. A disaster results from the combination of earthquake, conditions of vulnerability, and insufficient capacity or meas‐

Millions of human lives are lost due to earthquakes, and property damage has exceeded hun‐ dreds of billions USD. It is not possible to make reliable earthquake forecasts now, but there exist a few successful examples. It is possible to estimate the vulnerability of territories to the possible earthquake hazard, and means are available to develop earthquake resilient societies. 'Earthquake early warning' is the rapid detection of earthquakes in progress and alerting people of the ground shaking that could be hazardous. Application of this technique has demonstrated its usefulness. Developing earthquake scenarios, as what would happen if an earthquake repeats, where it had occurred in the past, is also very effective in developing

This book addresses the multidisciplinary topic of earthquake hazards and risk, one of the fastest growing, relevant, and applied fields of research and study practiced within the geo‐

activity in the area, and other factors.

and engineering may help a lot with their advice.

for all the people living in the area of hazard.

as volcanic activity, landslides, mine blasts, and *nuclear tests*.

ures to reduce the potential negative consequences of risk and exposure.

around and destroy the whole cities.

occasionally volcanic activity.

earthquake resilient societies.

sciences and environment.

of living in dangerous places.

ardous site.

X Preface

**Dr Svalova Valentina**

Sergeev Institute of Environmental Geoscience Russian Academy of Sciences (IEG RAS) Moscow, Russia

**Section 1**

**Earthquake Disasters**

**Section 1**


**Abstract**

In this chapter, the fundamentals of distributed inference problem in wireless sensor networks (WSN) is addressed and the statistical theoretical foundations to several applications is provided. The chapter adopts a statistical signal processing perspective and focusses on distributed version of the binary-hypothesis test for detecting an event as correctly as possible. The fusion center is assumed to be equipped with multiple antennas collecting and processing the information. The inference problem that is solved, primarily concerns the robust detection of a phenomenon of interest (for example, environmental hazard, oil/gas leakage, forest fire). The presence of multiple antennas at both transmit and receive sides resembles a multiple-input-multiple-output (MIMO) system and allows for utilization of array processing techniques providing spectral efficiency, fading mitigation and low energy sensor adoption. The problem is referred to as MIMO decision fusion. Subsequently, both design and evaluation (simulated and experimental) of these fusion approaches is presented for this futuristic WSN set-up.

**Keywords:** MIMO, decision fusion, distributed MAC, statistical CSI, instantaneous CSI, large-scale WSN, environmental characterization, experimental validation

#### **1. Introduction**

This chapter addresses the fundamentals of distributed inference problems in wireless sensor networks (WSNs) and provides statistical theoretical foundations to several applications. It adopts a statistical signal processing perspective and focuses on the distributed version of the binary-hypothesis test for detecting an event as correctly as possible. The reference WSN scenario is described in Section 2 which consists of multiple transmit sensors and an information center equipped with multiple antennas for collecting and processing the information to arrive at a robust decision on an observed phenomenon of interest. The presence of multiple antennas at both transmit and receive side resembles a multiple-input-multiple-output (MIMO) system and the inference problem based on information fusion is referred to as MIMO decision fusion. Consequently, several channel-aware fusion rules guiding MIMO decision fusion (DF) is studied in Section 3. The practical implications of employing MIMO decision fusion for distributed inference in WSN is evaluated through an indoor-to-outdoor measurement campaign detailed in Section 4. Performance of the fusion rules over the measured environment is also compared with that over the simulated set-up in Section 4.

## **2. WSN scenario and system model**

In a WSN, decision fusion (DF) refers to the process of arriving at a final decision on an observed phenomenon by fusing local decisions transmitted by individual sensors on the said occurrence at a decision fusion center (DFC). In traditional WSNs, each sensor is allocated a dedicated orthogonal channel for transmitting their local observations, a communication scenario commonly referred to as parallel access channel (PAC) [1]. Sensor signals are transmitted over the PAC using time, frequency or code division multiple access. Over the recent years, largescale or massive WSNs are being deployed, that involves coexistence of multitude of sensors, and the bandwidth requirement increases linearly with the number of sensors. In such scenarios, all sensors transmit their decisions simultaneously over a multiple access channel (MAC), while suffering from intrinsic interference resulting from superposition of multiple sensor signals in time [2]. To alleviate fusion performance in presence of deep fading, shadowing and interference, a DFC equipped with multiple antennas is proposed in [3]. This choice demands only further complexity on DFC side and does not affect simplicity of sensors implementation. The result is a communication over a "virtual" MIMO channel between the sensors and the DFC, as shown in **Figure 1**.

We also assume that *PD*,*s* ≥*PF*,*s*, i.e. the decision taken by individual sensor always results in a receiver operating characteristics (ROC) higher than the decision threshold *γ*. The system probabilities of false alarm and correct detection is given by,

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

where Λ is the fusion statistics, *γ* is the decision threshold to which Λ is compared to, and *P A*ð Þ j*B* is the probability of event A conditioned on event B.

*bs*,*s*

**y** ¼ **H** ffiffiffi **B**

If the composite channel coefficient between the *s*th sensor and the *n*th receive

after sampling and matched filtering at the DFC, where **y**∈ *N* is the received

Gaussian noise (AWGN) vector, **H** ∈ *N*�*S* is the independent small scale fading matrix, **B**∈ *S*�*S* is the large scale attenuation and shadowing matrix with the *s*th

experienced by the *s*th sensor. Here, N ð Þ *λ*, Σ denotes circular symmetric complex normal distribution with mean vector *λ* and covariance matrix Σ respectively.

If the propagation channel is assumed to be Rician distributed, the fading vector

*Δ P*ð Þ Λ>*γ*jH0 for False Alarm (1)

p *hn*,*s*, the received signal can be expressed as,

*w***I***N*

*Δ* diag *β*1, *β*2, … , *βS* ½ �*T* � � accounting for pathloss and shadowing

ffiffiffiffiffiffiffiffiffiffiffiffi 1 � *κ*2 *s*

**h** *^*

*s* � N *C*ð Þ **0***N*,**I***N* is the non-line-of-sight

ffiffiffiffiffiffiffiffiffiffiffiffi 1 � *κ ^*2 *s*

q

, Δ*s* is the shape factor for the fading distribution. For

is the Rician *K*-factor between *s*th

*:* (6)

q

1 2*π* **h** *^ s* ð2*π* 0

p **x** þ **w** (3)

� � is the additive white

*s* (4)

d*α* (5)

*Δ P*ð Þ Λ>*γ*jH1 for Correct Detection*:* (2)

*PF*0 ¼

*PD*0 ¼

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

antenna at the DFC is denoted by ffiffiffiffiffiffi

signal, **x**∈ *XS* is the transmitted signal, **w** � N *C* **0***N*, *σ*2

**h**Rice

*s* ¼ *κs***u** *ϕs* ð Þþ

*^*

ð2*π* 0 *κ ^ s* d*α* þ

**h**DR *s* ¼ Y 2

*Δ* ffiffiffiffiffiffiffiffi *Ks* 1þ*Ks* q

double-Rayleigh (DR) [7] distributed fading vector, the channel coefficients can be

*j*¼1 **h** *^ s j*

sensor and DFC. A Two Wave with Diffused Power (TWDP) [5, 6] distributed

*2.1.2 Signal model*

diagonal element **B** ¼

*2.1.3 Channel model*

where *κ ^ s* ¼

expressed as,

**193**

at the *s*th sensor can be modeled as,

where **u**ð Þ� is the steering vector, **h**

channel fading vector can be modeled by,

**h**TWDP

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *Ks*½ � 1þΔ*s* cos *α* 1þ*Ks*½ � 1þΔ*s* cos *α*

q

*s* ¼ **u** *ϕs* ð Þ 2*π*

(NLOS) scattered component and *κs* ¼

#### **2.1 System model for MIMO configuration**

#### *2.1.1 Sensing and local decision model*

A WSN consisting of *S* sensors and a DFC equipped with *N* receive antennas is considered for investigation in this section, where the *s*th sensor communicates its local decision, d*s*, about the presence or absence of a target, after being mapped on an On-and-Off Shift Keying (OOK) [4] modulated symbol, *xs* ∈*X* ¼ f g 0, 1 . Irrespective of the scenario and target, d*s* ¼ H*i* maps into *xs* ¼ *i*, *i* ∈f g 0, 1 , where H*i* ¼ *Δ* f g H0, H1 is the set of binary hypotheses with H0*=*H1 representing the absence or presence of a specific target. The sensor decisions are assumed to be transported over a flat fading multiple access distributed (or virtual) MIMO channel with perfect synchronization at the receiver end.

The performance of WSN can be evaluated in terms of the conditional probability mass function (pmf) *P*ð Þ **x**jH*i* . Assuming conditionally independent and identically distributed (iid) decisions, we denote the probability of detection *PD*,*s* ¼ *P*1,*s* ð Þ or *PD* ¼ *P*1 and false alarm *PF*,*s* ¼ *P*0,*s* ð Þ or *PF* ¼ *P*0 at the *s*th sensor.

**Figure 1.** *Virtual MIMO based DF in WSN.*

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

We also assume that *PD*,*s* ≥*PF*,*s*, i.e. the decision taken by individual sensor always results in a receiver operating characteristics (ROC) higher than the decision threshold *γ*. The system probabilities of false alarm and correct detection is given by,

$$P\_{F\_0} \triangleq P(\Lambda > \gamma | \mathcal{H}\_0) \qquad \text{for False Alarm} \tag{1}$$

$$P\_{D\_0} \triangleq P(\Lambda > \gamma | \mathcal{H}\_1) \qquad \text{for Correct detection.} \tag{2}$$

where Λ is the fusion statistics, *γ* is the decision threshold to which Λ is compared to, and *P A*ð Þ j*B* is the probability of event A conditioned on event B.

#### *2.1.2 Signal model*

**2. WSN scenario and system model**

*Wireless Sensor Networks - Design, Deployment and Applications*

the sensors and the DFC, as shown in **Figure 1**.

**2.1 System model for MIMO configuration**

perfect synchronization at the receiver end.

*2.1.1 Sensing and local decision model*

H*i* ¼

**Figure 1.**

**192**

*Virtual MIMO based DF in WSN.*

In a WSN, decision fusion (DF) refers to the process of arriving at a final decision on an observed phenomenon by fusing local decisions transmitted by individual sensors on the said occurrence at a decision fusion center (DFC). In traditional WSNs, each sensor is allocated a dedicated orthogonal channel for transmitting their local observations, a communication scenario commonly referred to as parallel access channel (PAC) [1]. Sensor signals are transmitted over the PAC using time, frequency or code division multiple access. Over the recent years, largescale or massive WSNs are being deployed, that involves coexistence of multitude of sensors, and the bandwidth requirement increases linearly with the number of sensors. In such scenarios, all sensors transmit their decisions simultaneously over a

multiple access channel (MAC), while suffering from intrinsic interference resulting from superposition of multiple sensor signals in time [2]. To alleviate fusion performance in presence of deep fading, shadowing and interference, a DFC equipped with multiple antennas is proposed in [3]. This choice demands only further complexity on DFC side and does not affect simplicity of sensors implementation. The result is a communication over a "virtual" MIMO channel between

A WSN consisting of *S* sensors and a DFC equipped with *N* receive antennas is considered for investigation in this section, where the *s*th sensor communicates its local decision, d*s*, about the presence or absence of a target, after being mapped on

*Δ* f g H0, H1 is the set of binary hypotheses with H0*=*H1 representing the absence or presence of a specific target. The sensor decisions are assumed to be transported over a flat fading multiple access distributed (or virtual) MIMO channel with

The performance of WSN can be evaluated in terms of the conditional proba-

bility mass function (pmf) *P*ð Þ **x**jH*i* . Assuming conditionally independent and identically distributed (iid) decisions, we denote the probability of detection *PD*,*s* ¼ *P*1,*s* ð Þ or *PD* ¼ *P*1 and false alarm *PF*,*s* ¼ *P*0,*s* ð Þ or *PF* ¼ *P*0 at the *s*th sensor.

an On-and-Off Shift Keying (OOK) [4] modulated symbol, *xs* ∈*X* ¼ f g 0, 1 . Irrespective of the scenario and target, d*s* ¼ H*i* maps into *xs* ¼ *i*, *i* ∈f g 0, 1 , where

If the composite channel coefficient between the *s*th sensor and the *n*th receive antenna at the DFC is denoted by ffiffiffiffiffiffi *bs*,*s* p *hn*,*s*, the received signal can be expressed as,

$$\mathbf{y} = \mathbf{H}\sqrt{\mathbf{B}}\mathbf{x} + \mathbf{w} \tag{3}$$

after sampling and matched filtering at the DFC, where **y**∈ *N* is the received signal, **x**∈ *XS* is the transmitted signal, **w** � N *C* **0***N*, *σ*2 *w***I***N* � � is the additive white Gaussian noise (AWGN) vector, **H** ∈ *N*�*S* is the independent small scale fading matrix, **B**∈ *S*�*S* is the large scale attenuation and shadowing matrix with the *s*th diagonal element **B** ¼ *Δ* diag *β*1, *β*2, … , *βS* ½ �*T* � � accounting for pathloss and shadowing experienced by the *s*th sensor. Here, N ð Þ *λ*, Σ denotes circular symmetric complex normal distribution with mean vector *λ* and covariance matrix Σ respectively.

#### *2.1.3 Channel model*

If the propagation channel is assumed to be Rician distributed, the fading vector at the *s*th sensor can be modeled as,

$$\mathbf{h}\_s^{\text{Ricce}} = \kappa\_s \mathbf{u}(\phi\_s) + \sqrt{\mathbf{1} - \kappa\_s^2} \,\breve{\mathbf{h}}\_s \tag{4}$$

where **u**ð Þ� is the steering vector, **h** *^ s* � N *C*ð Þ **0***N*,**I***N* is the non-line-of-sight (NLOS) scattered component and *κs* ¼ *Δ* ffiffiffiffiffiffiffiffi *Ks* 1þ*Ks* q is the Rician *K*-factor between *s*th sensor and DFC. A Two Wave with Diffused Power (TWDP) [5, 6] distributed channel fading vector can be modeled by,

$$\mathbf{h}\_{\varepsilon}^{\text{TWDP}} = \frac{\mathbf{u}(\phi\_{\varepsilon})}{2\pi} \int\_{0}^{2\pi} \bar{\kappa}\_{\varepsilon} \, \mathbf{d}a + \frac{1}{2\pi} \left. \bar{\mathbf{h}}\_{\varepsilon} \right|\_{0}^{2\pi} \sqrt{1 - \bar{\kappa}\_{\varepsilon}^{2}} \, \mathbf{d}a \tag{5}$$

where *κ ^ s* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *Ks*½ � 1þΔ*s* cos *α* 1þ*Ks*½ � 1þΔ*s* cos *α* q , Δ*s* is the shape factor for the fading distribution. For double-Rayleigh (DR) [7] distributed fading vector, the channel coefficients can be expressed as,

$$\mathbf{h}\_{\mathbf{s}}^{\text{DR}} = \prod\_{j=1}^{2} \breve{\mathbf{h}}\_{\mathbf{t}\_{j}}.\tag{6}$$

with *κs* ¼ 0 and no line-of-sight (LOS) components existing between the sensors and the DFC.

The sensors are uniformly deployed with distances from the DFC varying between dmin and dmax, and large scale attenuation of *βs* ¼ *νs* dmin d*s* � �*ηP* where *ηP* is the pathloss exponent and *νs* is a log-normal variable such that 10 log 10ð Þ�N *νs μP*, *σ*2 *P* � � with N ^*λ*, Σ^ � � representing normal distribution with mean vector ^*λ* and covariance matrix Σ^ respectively, d*s* is the distance of the *s*th sensor from the DFC, *μP* and *σP* are the mean and standard deviations in dBm respectively.

#### *2.1.4 Modified system model for non-coherent decision fusion*

Non-coherent decision fusion over MAC using the received-energy test has been investigated in [2, 8]. In such a scenario, if the probability of false alarm for any sensor decision is lower than the probability of detection, the received energy can prove to be optimal for arriving at the right decision about an observed phenomenon at the DFC for mutually independent and identically distributed (i.i.d.) sensor decisions.

In this case, let us consider that a group of sensors transmit their local decisions to the DFC equipped with *N* antennas over a Raleigh faded MAC with channel coefficients of equal mean power, thereby exploiting diversity combining, either in time, frequency, code or in polarization domain. Statistical channel state information (CSI) is assumed at the DFC, i.e. only the pdf of each fading coefficient is available.

Let us denote: *yn* the received signal at the *n*th diversity branch of the DFC after matched filtering and sampling; *hn*,*s* � N 0, *σ*2 *h* � �, the fading coefficient between the *s*th sensor and the *n*th diversity branch of the DFC; *wn* the additive white Gaussian noise at the nth diversity branch of the DFC. The vector model at the DFC is the following:

$$\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{w} \tag{7}$$

Λopt ¼ ln

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

**x**∈ *S*�1

given by,

**195**

where Π^*s* ¼

*Δ x*^*s*þ1

**x**^MMSE ¼ sign **x** þ **C H** ffiffiffi

where **x** ¼ Ef g**x** and **C** ¼

statistics for CV-ML and CV-MMSE rules.

P

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

rules [12], defined by the following test statistics,

ΛMax�Log ¼ min

ΛCV ¼ X *S*

*s*¼1

**B** � � p †

**x**∈*XS*

� min **x**∈*XS*

respectively, all assuming identical sensor performances.

Π^*s* ln *PD*,*s PF*,*s* � �

especially, the Maximum Likelihood (ML) detector [13] to obtain,

**x**^ML ¼ arg min **x**∈*XS*

and the Minimum Mean-Squared Error (MMSE) detector [14] to get,

of the transmit signal vector respectively. The estimated **x**^ from the above two detectors can be incorporated directly in the CV-rule of (12) to obtain the test

**H** ffiffiffi **B** � � p **C H** ffiffiffi

P

**x**∈*XS* exp � **y**�**H** ffiffi

**x**∈*XS* exp � **y**�**H** ffiffi

assuming conditional independence of **y** from H*i*, given *xs*, **H** ∈ *N*�*S* and

to this group are considered for this section to compensate for the asymptotically increasing computational complexity of the optimum rule. These rules are Maximal Ratio Combining (MRC) [10], Equal Gain Combining (EGC) [11] and Max-Log

ΛMRC ∝ ℜ **1***t*

ΛEGC ¼ ℜ *e j*�∠ **H** ffiffi

**y** � **H** ffiffiffi **B** p **x** � � �

> *σ*2 *w*

**y** � **H** ffiffiffi **B** p **x** � � �

> *σ*2 *w*

The other set of fusion rules (Decode-then-Fuse) aims at concluding to a global decision after estimating the transmit signal from the received signal vector. Using Chair-Varshney (CV) rule, the test statistics for which over a noiseless channel is

þ 1 � Π^*s*

2 . Two different detectors are considered under this umbrella,

**y** � **H** ffiffiffi **B** p **x**

**B** � � p †

� � " # (14)

� ��1

þ *σ*2 *w***I***N*

*Δ* ð Þ **x** � **x** ð Þ **x** � **x** † � � are the mean and covariance matrix

� � �

.  Finally, we define the random variable *l*≜*l x*ð Þ¼ P*S s*¼1*xs*, representing the number of active sensors and the set L≜f g 0, … , *S* of possible realizations of *l*. It is worth-mentioning here that it will be more practical to assume an asymmetric model for the statistics of the channel coefficients resulting in scenario-dependent analysis. Therefore, symmetric channel model is considered here to analyze performance with power control possibility depending on the application scenario.

#### **3. MIMO decision fusion**

#### **3.1 Instantaneous CSI**

Two types of fusion rules are considered and compared in this chapter in order to arrive at a reliable choice depending on the communication scenario. One set of rules (Decode-and-Fuse) uses the received signal directly to arrive at a decision on whether a target is present or absent, without taking any information from the transmitted signal into consideration, the optimum (opt) test statistics [9] for which is given by,

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

$$\Lambda\_{\text{opt}} = \ln \left[ \frac{\sum\_{\mathbf{x} \in X^{\mathcal{S}}} \exp \left( - \frac{\left\| \mathbf{y} - \mathbf{H} \sqrt{\mathbf{B}} \mathbf{x} \right\|^{2}}{\sigma\_{w}^{2}} \right) \prod\_{s=1}^{S} P(\mathbf{x}\_{s} | \mathcal{H}\_{1})} \right] \tag{8}$$

$$\left[ \frac{\sum\_{\mathbf{x} \in X^{\mathcal{S}}} \exp \left( - \frac{\left\| \mathbf{y} - \mathbf{H} \sqrt{\mathbf{B}} \mathbf{x} \right\|^{2}}{\sigma\_{w}^{2}} \right) \prod\_{s=1}^{S} P(\mathbf{x}\_{s} | \mathcal{H}\_{0})} \right] \tag{9}$$

assuming conditional independence of **y** from H*i*, given *xs*, **H** ∈ *N*�*S* and **x**∈ *S*�1 . The test statistics for three different sub-optimum fusion rules belonging to this group are considered for this section to compensate for the asymptotically increasing computational complexity of the optimum rule. These rules are Maximal Ratio Combining (MRC) [10], Equal Gain Combining (EGC) [11] and Max-Log rules [12], defined by the following test statistics,

$$\Lambda\_{\rm MRC} \propto \Re \left( \mathbf{1}\_{\rm S}^{t} \left( \mathbf{H} \sqrt{\mathbf{B}} \right)^{\dagger} \mathbf{y} \right) \tag{9}$$

$$
\Lambda\_{\rm EGC} = \Re \left( \left( e^{j \cdot \omega \left( \mathbf{H} \sqrt{\mathbf{B}} \ \mathbf{1}\_{\mathbb{S}} \right)} \right)^{\dagger} \mathbf{y} \right) \tag{10}
$$

$$\begin{split} \Lambda\_{\text{Max-Log}} &= \min\_{\mathbf{x} \in X^{\mathcal{S}}} \left[ \frac{\left||\mathbf{y} - \mathbf{H}\sqrt{\mathbf{B}}\mathbf{x}\right||^{2}}{\sigma\_{w}^{2}} - \sum\_{s=1}^{S} P(\mathbf{x}\_{i}|\mathcal{H}\_{0}) \right] \\ &- \min\_{\mathbf{x} \in X^{\mathcal{S}}} \left[ \frac{\left||\mathbf{y} - \mathbf{H}\sqrt{\mathbf{B}}\mathbf{x}\right||^{2}}{\sigma\_{w}^{2}} - \sum\_{s=1}^{S} P(\mathbf{x}\_{i}|\mathcal{H}\_{1}) \right] \end{split} \tag{11}$$

respectively, all assuming identical sensor performances.

The other set of fusion rules (Decode-then-Fuse) aims at concluding to a global decision after estimating the transmit signal from the received signal vector. Using Chair-Varshney (CV) rule, the test statistics for which over a noiseless channel is given by,

$$\Lambda\_{\rm CV} = \sum\_{s=1}^{S} \left[ \hat{\Pi}\_{\rm t} \ln \left( \frac{P\_{D,\rm s}}{P\_{F,\rm s}} \right) + \left( \mathbf{1} - \hat{\Pi}\_{\rm t} \right) \ln \left( \frac{\mathbf{1} - P\_{D,\rm s}}{\mathbf{1} - P\_{F,\rm s}} \right) \right] \tag{12}$$

where Π^*s* ¼ *Δ x*^*s*þ1 2 . Two different detectors are considered under this umbrella, especially, the Maximum Likelihood (ML) detector [13] to obtain,

$$\hat{\mathbf{x}}\_{\text{ML}} = \underset{\mathbf{x} \in X^{S}}{\text{arg min}} \left\| \mathbf{y} - \mathbf{H} \sqrt{\mathbf{B}} \mathbf{x} \right\|^{2} \tag{13}$$

and the Minimum Mean-Squared Error (MMSE) detector [14] to get,

$$\hat{\mathbf{x}}\_{\text{MMSE}} = \text{sign}\left[\overline{\mathbf{x}} + \mathbf{C} \left(\mathbf{H}\sqrt{\mathbf{B}}\right)^{\dagger} \left(\left(\mathbf{H}\sqrt{\mathbf{B}}\right)\mathbf{C} \left(\mathbf{H}\sqrt{\mathbf{B}}\right)^{\dagger} + \sigma\_w^2 \mathbf{I}\_N\right)^{-1} \left(\mathbf{y} - \mathbf{H}\sqrt{\mathbf{B}}\overline{\mathbf{x}}\right)\right] \tag{14}$$

where **x** ¼ Ef g**x** and **C** ¼ *Δ* ð Þ **x** � **x** ð Þ **x** � **x** † � � are the mean and covariance matrix of the transmit signal vector respectively. The estimated **x**^ from the above two detectors can be incorporated directly in the CV-rule of (12) to obtain the test statistics for CV-ML and CV-MMSE rules.

with *κs* ¼ 0 and no line-of-sight (LOS) components existing between the sensors

d*s* � �*ηP*

� �, the fading coefficient between

**y** ¼ **Hx** þ **w** (7)

� � are the received signal, transmit-

where *ηP* is the

*P* � �

The sensors are uniformly deployed with distances from the DFC varying

pathloss exponent and *νs* is a log-normal variable such that 10 log 10ð Þ�N *νs μP*, *σ*2

with N ^*λ*, Σ^ � � representing normal distribution with mean vector ^*λ* and covariance matrix Σ^ respectively, d*s* is the distance of the *s*th sensor from the DFC, *μP* and *σP*

Non-coherent decision fusion over MAC using the received-energy test has been investigated in [2, 8]. In such a scenario, if the probability of false alarm for any sensor decision is lower than the probability of detection, the received energy can prove to be optimal for arriving at the right decision about an observed phenomenon at the DFC for mutually independent and identically distributed (i.i.d.) sensor

In this case, let us consider that a group of sensors transmit their local decisions

Let us denote: *yn* the received signal at the *n*th diversity branch of the DFC after

*h*

*w***I***N*

*s*¼1*xs*, representing the number of active sensors and the set

to the DFC equipped with *N* antennas over a Raleigh faded MAC with channel coefficients of equal mean power, thereby exploiting diversity combining, either in time, frequency, code or in polarization domain. Statistical channel state information (CSI) is assumed at the DFC, i.e. only the pdf of each fading coefficient is

the *s*th sensor and the *n*th diversity branch of the DFC; *wn* the additive white Gaussian noise at the nth diversity branch of the DFC. The vector model at the DFC

ted signal and the AWGN vectors respectively. Finally, we define the random

L≜f g 0, … , *S* of possible realizations of *l*. It is worth-mentioning here that it will be more practical to assume an asymmetric model for the statistics of the channel coefficients resulting in scenario-dependent analysis. Therefore, symmetric channel model is considered here to analyze performance with power control possibility

Two types of fusion rules are considered and compared in this chapter in order to arrive at a reliable choice depending on the communication scenario. One set of rules (Decode-and-Fuse) uses the received signal directly to arrive at a decision on whether a target is present or absent, without taking any information from the transmitted signal into consideration, the optimum (opt) test statistics [9] for

between dmin and dmax, and large scale attenuation of *βs* ¼ *νs* dmin

are the mean and standard deviations in dBm respectively.

*Wireless Sensor Networks - Design, Deployment and Applications*

*2.1.4 Modified system model for non-coherent decision fusion*

matched filtering and sampling; *hn*,*s* � N 0, *σ*2

where **y**∈ *N*, **x**∈ *XS* and **w** � N *C* **0***N*, *σ*2

depending on the application scenario.

**3. MIMO decision fusion**

**3.1 Instantaneous CSI**

which is given by,

**194**

and the DFC.

decisions.

available.

is the following:

variable *l*≜*l x*ð Þ¼ P*S*

#### **3.2 Statistical CSI**

If statistical CSI [15] is used for DF at the receiver instead of the instantaneous CSI extracted from the sensor signals received at the DFC, the optimal test statistics can be formulated as,

$$\Lambda\_{\text{opt}} \triangleq \ln \left[ \frac{p\left(\mathbf{y} | \mathcal{H}\_1\right)}{p\left(\mathbf{y} | \mathcal{H}\_0\right)} \right] \begin{array}{c} \hat{\mathcal{H}} = \mathcal{H}\_1 \\ > \\ < \\ \hat{\mathcal{H}} = \mathcal{H}\_0 \end{array} \tag{15}$$

of receive antennas at the DFC *N*) virtual MIMO system at 2.53 GHz with 20 MHz bandwidth and subcarrier spacing of around 0.15 MHz. The campaign is conducted with different spatial combinations of half-omnidirectional single transmit antennas representing the sensors, deployed in two different rooms of the Facility of Overthe-Air Research and Testing (FORTE) at Fraunhofer IIS in Ilmenau, Germany (Conference Room, C, located on the 1st floor and Instrumentation Room, I, located on the ground floor) and receive antennas mounted and co-located on an outside tower representing the DFC. The antennas emulating the sensors are deployed at different heights, namely, near the ground and ceiling and at heights of 1meter (m), 1.5 m and 2 m from the ground, sometimes on all 4 walls, sometimes on all 3 walls and sometimes only on 1 wall of each room at a time. The channel measurements are collected over a measurement set-up detailed in **Figure 2** and are

The dimensions of the two rooms selected are 8.45 m by 4.52 m by 2.75 m for the C room and 5.7 m by 3.5 m by 3 m for the I room. These rooms are chosen such that a variety of indoor environments is represented including I room with keyhole effect (no windows) and with no direct LOS communication, C room (smart office) and room cluttered with several noisy electrical and metering equipment (potential scenario for Industry 4.0). In both rooms, measurement set-up is repeated for stationary scenarios and scenarios with people moving around. Due to channel reciprocity conditions, it is assumed that channel estimates can be used for both uplink and downlink.

Large and small scale channel statistics are extracted from the channel impulse response (CIRs) and channel frequency responses (CFRs) recorded in the abovementioned campaign. In order to separate out large scale statistics, average received power and attenuation at each measurement location is calculated by averaging the recorded CIRs at that location. The pathloss exponent is determined from the slope of the best fit line to the logarithm of distances v/s logarithm of average attenuation plot. The probability density function (pdf) of deviation of each value of calculated attenuation from the best-fit line to the log–log plot yields the shadowing distribution. **Figures 3**–**5** demonstrates the log–log attenuation plots for three different measurement scenarios, static environment - Conference (SC), dynamic environment - Conference (DC) and static environment - Instrumentation (SI) rooms respectively, while **Table 1** summarizes the average values for the pathloss exponents (*ηP*) and mean and standard deviation (*μP*, *σP*) of the shadowing distributions

recorded using the MEDAV RUSK - HyE MIMO channel sounder.

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

in all the three above-mentioned measurement scenarios.

**4.2 Environment characterization**

**Figure 2.**

**197**

*Block diagram of measurement set-up.*

where *H*^ is the estimated hypothesis, Λopt is the Log-Likelihood-Ratio (LLR) of the optimal fusion rule and *γ* is the decision threshold to which Λopt is compared to. The threshold can be determined using either the Bayesian approach (i.e. the threshold is detected based on the one that minimizes the probability of error) or the Neyman-Pearson approach [16] (i.e. the threshold is detected based on the one that ensures fixed system false-alarm rate). An explicit expression of the LLR from Eq. (15) is given by,

$$\Lambda\_{\text{opt}} = \ln \left[ \frac{\sum\_{l=0}^{S} \frac{1}{\left(\sigma\_w^2 + \sigma\_h^2\right)^N} \exp\left(-\frac{\left\|\mathbf{y}\right\|^2}{\sigma\_w^2 + \sigma\_h^2}\right) P(l|\mathcal{H}\_1)}{\sum\_{l=0}^{S} \frac{1}{\left(\sigma\_w^2 + \sigma\_h^2\right)^N} \exp\left(-\frac{\left\|\mathbf{y}\right\|^2}{\sigma\_w^2 + \sigma\_h^2}\right) P(l|\mathcal{H}\_0)} \right] \tag{16}$$

where we have exploited the conditional independence of **y** from H*i* (given *l*).

In the case of conditionally (given H*i*) i.i.d. sensor decisions ( *PD*,*s* ð Þ¼ , *PF*,*s* ð Þ *PD*, *PF* , *s* ∈*S*) we have that *l*∣H1 � **B**ð Þ *S*, *PD* and *l*∣H0 � **B**ð Þ *S*, *PF* . Differently, when local sensor decisions are conditionally i.n.i.d. the pmfs *P l*ð Þ jH*i* are represented by the more general Poisson-Binomial distribution with expressions given by,

$$\begin{aligned} P(l|\mathcal{H}\_1) &= \sum\_{\mathbf{x}:\mathbf{x}(l)=l} \prod\_{\iota=1}^{\mathcal{S}} (P\_{D,\iota})^{\mathbf{x}\_{\iota}} \prod\_{u=1}^{\mathcal{S}} (P\_{D,u})^{(1-\mathbf{x}\_u)} \\ P(l|\mathcal{H}\_0) &= \sum\_{\mathbf{x}:\mathbf{x}(l)=l} \prod\_{\iota=1}^{\mathcal{S}} (P\_{F,\iota})^{\mathbf{x}\_{\iota}} \prod\_{u=1}^{\mathcal{S}} (P\_{F,u})^{(1-\mathbf{x}\_u)} \end{aligned} \tag{17}$$

It is to be noted here that calculating the sums in Eq. (17) practically becomes impossible with the increase in the number of sensors *S*. Several alternatives have been proposed across literature to tackle such exhaustive computations, which include fast convolution of individual Bernoulli probability mass functions (pmfs) [17], Discrete Fourier Transform (DFT) [18] based computation and recursionbased iterative approaches.

#### **4. Performance evaluation of MIMO decision fusion**

#### **4.1 Measurement campaigns**

An indoor-to-outdoor measurement campaign has been conducted in [19] for investigating propagation characteristics of an 8 � 8 (number of sensors *S* = number

#### *Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

of receive antennas at the DFC *N*) virtual MIMO system at 2.53 GHz with 20 MHz bandwidth and subcarrier spacing of around 0.15 MHz. The campaign is conducted with different spatial combinations of half-omnidirectional single transmit antennas representing the sensors, deployed in two different rooms of the Facility of Overthe-Air Research and Testing (FORTE) at Fraunhofer IIS in Ilmenau, Germany (Conference Room, C, located on the 1st floor and Instrumentation Room, I, located on the ground floor) and receive antennas mounted and co-located on an outside tower representing the DFC. The antennas emulating the sensors are deployed at different heights, namely, near the ground and ceiling and at heights of 1meter (m), 1.5 m and 2 m from the ground, sometimes on all 4 walls, sometimes on all 3 walls and sometimes only on 1 wall of each room at a time. The channel measurements are collected over a measurement set-up detailed in **Figure 2** and are recorded using the MEDAV RUSK - HyE MIMO channel sounder.

The dimensions of the two rooms selected are 8.45 m by 4.52 m by 2.75 m for the C room and 5.7 m by 3.5 m by 3 m for the I room. These rooms are chosen such that a variety of indoor environments is represented including I room with keyhole effect (no windows) and with no direct LOS communication, C room (smart office) and room cluttered with several noisy electrical and metering equipment (potential scenario for Industry 4.0). In both rooms, measurement set-up is repeated for stationary scenarios and scenarios with people moving around. Due to channel reciprocity conditions, it is assumed that channel estimates can be used for both uplink and downlink.

#### **4.2 Environment characterization**

**3.2 Statistical CSI**

can be formulated as,

Eq. (15) is given by,

given by,

based iterative approaches.

**4.1 Measurement campaigns**

**196**

Λopt ¼ ln

P*S l*¼0

*Wireless Sensor Networks - Design, Deployment and Applications*

*P l*ð Þ¼ jH1

*P l*ð Þ¼ jH0

**4. Performance evaluation of MIMO decision fusion**

P*S l*¼0

In the case of conditionally (given H*i*) i.i.d. sensor decisions

X *x*:*x l*ð Þ¼*l*

X *x*:*x l*ð Þ¼*l*

1 *σ*2 *w*þ*σ*2

1 *σ*2 *w*þ*σ*2

( *PD*,*s* ð Þ¼ , *PF*,*s* ð Þ *PD*, *PF* , *s* ∈*S*) we have that *l*∣H1 � **B**ð Þ *S*, *PD* and *l*∣H0 � **B**ð Þ *S*, *PF* . Differently, when local sensor decisions are conditionally i.n.i.d. the pmfs *P l*ð Þ jH*i* are represented by the more general Poisson-Binomial distribution with expressions

> Y *S*

ð Þ *PD*,*s xs*

ð Þ *PF*,*s xs*

It is to be noted here that calculating the sums in Eq. (17) practically becomes impossible with the increase in the number of sensors *S*. Several alternatives have been proposed across literature to tackle such exhaustive computations, which include fast convolution of individual Bernoulli probability mass functions (pmfs) [17], Discrete Fourier Transform (DFT) [18] based computation and recursion-

An indoor-to-outdoor measurement campaign has been conducted in [19] for investigating propagation characteristics of an 8 � 8 (number of sensors *S* = number

Y *S*

ð Þ *PD*,*u* ð Þ 1�*xu*

ð Þ *PF*,*u* ð Þ 1�*xu*

*u*¼1

Y *S*

*u*¼1

*s*¼1

Y *S*

*s*¼1

*h* ð Þ*N* exp � k k**y** 2

*h* ð Þ*N* exp � k k**y** 2

where we have exploited the conditional independence of **y** from H*i* (given *l*).

*σ*2 *w*þ*σ*2 *h*

� �

*σ*2 *w*þ*σ*2 *h*

� �

*P l*ð Þ jH1

*P l*ð Þ jH0

If statistical CSI [15] is used for DF at the receiver instead of the instantaneous CSI extracted from the sensor signals received at the DFC, the optimal test statistics

> � � *p* **y**jH0 � � " #

where *H*^ is the estimated hypothesis, Λopt is the Log-Likelihood-Ratio (LLR) of the optimal fusion rule and *γ* is the decision threshold to which Λopt is compared to. The threshold can be determined using either the Bayesian approach (i.e. the threshold is detected based on the one that minimizes the probability of error) or the Neyman-Pearson approach [16] (i.e. the threshold is detected based on the one that ensures fixed system false-alarm rate). An explicit expression of the LLR from

H¼H ^ 1 > *γ* < H¼H ^ 0

(15)

(16)

(17)

Λopt ≜ ln *p* **y**jH1

Large and small scale channel statistics are extracted from the channel impulse response (CIRs) and channel frequency responses (CFRs) recorded in the abovementioned campaign. In order to separate out large scale statistics, average received power and attenuation at each measurement location is calculated by averaging the recorded CIRs at that location. The pathloss exponent is determined from the slope of the best fit line to the logarithm of distances v/s logarithm of average attenuation plot. The probability density function (pdf) of deviation of each value of calculated attenuation from the best-fit line to the log–log plot yields the shadowing distribution. **Figures 3**–**5** demonstrates the log–log attenuation plots for three different measurement scenarios, static environment - Conference (SC), dynamic environment - Conference (DC) and static environment - Instrumentation (SI) rooms respectively, while **Table 1** summarizes the average values for the pathloss exponents (*ηP*) and mean and standard deviation (*μP*, *σP*) of the shadowing distributions in all the three above-mentioned measurement scenarios.

**Figure 2.** *Block diagram of measurement set-up.*

**Figure 3.** *Log average attenuation versus log distance for conference - static environment.*

contribute constructively to reflected signal power than in an open indoor environ-

**Scenario** *ηP μP*ð Þ dB *σP*ð Þ dB SC 2.72 1.22 2.4 SI 3.96 1.48 1.89 DC 2.56 1.77 3.6

To analyze the small scale channel statistics, the power delay profile (PDP) of the channel is drawn by averaging the power across all the delay bins for each sensor (**Table 2**). The average delay spread is the first moment and the root mean square (rms) delay spread is the square root of the second central moment of each sensor channel PDP respectively. The fading vector is obtained by concatenating CFRs at all the frequency points experienced over each sensor-DFC channel. The number of frequency points encountered is calculated by dividing the discrete bandwidth of the measured signal with the discrete coherence bandwidth of the sensor-DFC channel. The measurement is also used to deduce additional details like

**Scenario** *K* **Δ** *ξ*e**,**f **A** SC 2.5424 0 0.6511 7.64 SI 1.1217 0 0.5877 3.8158 DC 8.5287 0.6004 0.41 4.5227

ment (C room) stocked with wooden tables and chairs.

*Log average attenuation versus log distance for instrumentation - static environment.*

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

**Figure 5.**

**Table 1.**

**Table 2.**

**199**

*Small scale parameters [19].*

*Large scale parameters.*

**Figure 4.** *Log average attenuation versus log distance for conference - dynamic environment.*

The gamma distribution with mean of �1 � 6 dB and standard deviation of �5 � 5 dB offers a good approximation to the shadowing experienced in the campaign. The pathloss exponent varies between 2 to 4. Higher *ηP* is experienced over a shorter distance direct link between the sensors and the DFC. Lower shadowing is observed in an environment (I room) cluttered with metallic surfaces that

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

**Figure 5.** *Log average attenuation versus log distance for instrumentation - static environment.*

**Table 1.** *Large scale parameters.*

contribute constructively to reflected signal power than in an open indoor environment (C room) stocked with wooden tables and chairs.

To analyze the small scale channel statistics, the power delay profile (PDP) of the channel is drawn by averaging the power across all the delay bins for each sensor (**Table 2**). The average delay spread is the first moment and the root mean square (rms) delay spread is the square root of the second central moment of each sensor channel PDP respectively. The fading vector is obtained by concatenating CFRs at all the frequency points experienced over each sensor-DFC channel. The number of frequency points encountered is calculated by dividing the discrete bandwidth of the measured signal with the discrete coherence bandwidth of the sensor-DFC channel. The measurement is also used to deduce additional details like

**Table 2.** *Small scale parameters [19].*

The gamma distribution with mean of �1 � 6 dB and standard deviation of �5 � 5 dB offers a good approximation to the shadowing experienced in the campaign. The pathloss exponent varies between 2 to 4. Higher *ηP* is experienced over a shorter distance direct link between the sensors and the DFC. Lower shadowing is

observed in an environment (I room) cluttered with metallic surfaces that

*Log average attenuation versus log distance for conference - dynamic environment.*

*Log average attenuation versus log distance for conference - static environment.*

*Wireless Sensor Networks - Design, Deployment and Applications*

**Figure 3.**

**Figure 4.**

**198**

**Figure 6.** *CDF of K-factor for all environments.*

antenna correlation, determined from the correlation coefficients between each pair of fading vectors. The phase information from the complex CIRs is used to compute the steering vector for each transmit antenna.

The distribution of the derived fading vector fits the Rician distribution in most cases, with DR and TWDP distributions fitting the remaining few. **Figure 6** demonstrates the range of *K*-factor values for the Rician and TWDP distribution fitting and **Figure 7** plots the range of Δ values good for the TWDP distribution fitting where Δ-factor arises due to the presence of two strong interfering components and is given by Δ ¼ 2*V*1*V*2 *V*2 1þ*V*2 2 � 0 to 1, with *V*1 and *V*2 are the instantaneous amplitudes of the specular components. **Figures 8** and **9** depicts the range of antenna correlation coefficients and amount-of-fading (AF) values experienced over all the measurement scenarios, respectively. The average values for each of channel parameters, *K*, Δ, correlation coefficients, *ξ*e,f and AF (**A**) obtained after analysis of the measurement data over each measurement scenarios of SC, DC and SI.

A special scenario is observed in case of the I room where the propagation environment can be approximated by DR fading (*K* ¼ 0) distribution. As the I room is devoid of any windows, a rich scattering environment with 'keyhole' effect [20] is experienced with the existence of a waveguide propagation channel.

In the dynamic scenario, two sets of specular multipath components arrive at the receiver, one over the direct LOS link and the other due to reflection from the moving human body, thereby yielding en environment which can be accurately approximated by the TWDP fading distribution with *K* values ranging between 6 and 20 and Δ values varying between 0.1 and 0.9. Large distances between the transmit sensor and the DFC and nearness of most of the scattering surfaces to the sensors has resulted in similar AF values over all the measurement scenarios (refer to **Figure 9**).

summary, both fading and shadowing gets detrimental with the increase in intersensor distances. Separation between the sensors leads to very low coordination between them making the transmit signals vulnerable to noise, interference and fading, while a large number of different shadowing values are encountered resulting in higher shadowing variance and increased shadowing severity. For

*CDF of antenna correlation coefficient for all environments.*

*CDF of* Δ *for the dynamic environment in the conference room.*

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

**Figure 8.**

**201**

**Figure 7.**

Rich scattering and diffraction around the sensors in the windowless I room has resulted in low correlation between the transmitted signals, while a high correlation is observed among the sensor signals in the open environment of the C room. In

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

**Figure 7.** *CDF of* Δ *for the dynamic environment in the conference room.*

**Figure 8.** *CDF of antenna correlation coefficient for all environments.*

summary, both fading and shadowing gets detrimental with the increase in intersensor distances. Separation between the sensors leads to very low coordination between them making the transmit signals vulnerable to noise, interference and fading, while a large number of different shadowing values are encountered resulting in higher shadowing variance and increased shadowing severity. For

antenna correlation, determined from the correlation coefficients between each pair of fading vectors. The phase information from the complex CIRs is used to compute

The distribution of the derived fading vector fits the Rician distribution in most cases, with DR and TWDP distributions fitting the remaining few. **Figure 6** demonstrates the range of *K*-factor values for the Rician and TWDP distribution fitting and **Figure 7** plots the range of Δ values good for the TWDP distribution fitting where Δ-factor arises due to the presence of two strong interfering components and

the specular components. **Figures 8** and **9** depicts the range of antenna correlation coefficients and amount-of-fading (AF) values experienced over all the measurement scenarios, respectively. The average values for each of channel parameters, *K*, Δ, correlation coefficients, *ξ*e,f and AF (**A**) obtained after analysis of the measure-

A special scenario is observed in case of the I room where the propagation environment can be approximated by DR fading (*K* ¼ 0) distribution. As the I room is devoid of any windows, a rich scattering environment with 'keyhole' effect

In the dynamic scenario, two sets of specular multipath components arrive at the

Rich scattering and diffraction around the sensors in the windowless I room has resulted in low correlation between the transmitted signals, while a high correlation is observed among the sensor signals in the open environment of the C room. In

[20] is experienced with the existence of a waveguide propagation channel.

receiver, one over the direct LOS link and the other due to reflection from the moving human body, thereby yielding en environment which can be accurately approximated by the TWDP fading distribution with *K* values ranging between 6 and 20 and Δ values varying between 0.1 and 0.9. Large distances between the transmit sensor and the DFC and nearness of most of the scattering surfaces to the sensors has resulted in similar AF values over all the measurement scenarios (refer

ment data over each measurement scenarios of SC, DC and SI.

� 0 to 1, with *V*1 and *V*2 are the instantaneous amplitudes of

the steering vector for each transmit antenna.

*Wireless Sensor Networks - Design, Deployment and Applications*

is given by Δ ¼ 2*V*1*V*2

**Figure 6.**

to **Figure 9**).

**200**

*V*2 1þ*V*2 2

*CDF of K-factor for all environments.*

over the direct LOS link is recorded to be equal to 40 dB yielding an equivalent

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

• *Impact of large scale channel parameters*: In order to analyze the impact of large scale channel effects, the small scale fading vectors are modeled to be Rayleigh

distributed (**h***n*,*s* � N ð Þ 0, 1 ). From the Decode-and-Fuse group of suboptimum fusion rules, MRC and Max-Log are used for DF over four different communication scenarios; No Shadowing ('Th'; *ηP*, *μP*, *σP* = 1, 0 dB, 0 dB; **h***n*,*s* � N ð Þ 0, 1 ), SC (*ηP*, *μP*, *σP* = 2.72, 1.22 dB, 2.4 dB), DC (*ηP*, *μP*, *σP* = 2.56, 1.77 dB, 3.6 dB), SI (*ηP*, *μP*, *σP* = 1.96, 1.48 dB, 1.89 dB), and the ROC

With increase in shadowing and pathloss, MRC outperforms Max-Log. Depen-

behind its poor performance in presence of rich shadowing. From the second group, CV-ML and CV-MMSE rules are used for DF over the above-mentioned four communication scenarios and the ROC performances are plotted in **Figure 11**. With increase in large scale channel effects, CV-MMSE outperforms CV-ML. The propagation environment has no impact on the performance of CV-ML owing to its dependence only on the SNR which is kept constant for the plots in **Figure 11**. In general, sub-optimum fusion rules perform better over SC scenario than over DC and over DC than over SI. With a strong LOS link existing in case of the SC scenario, it experiences the lowest pathloss. The DC scenario experiences higher pathloss due to penetration losses contributed by the moving human bodies.

• *Impact of small scale channel parameters*: In order to analyze the effect of the small scale channel effects, sub-optimum fusion rules are used for DF over four

*Comparative ROC for the first group of fusion rules for different measured large scale parameters (varying ηP, μP and σP) with S* ¼ 8*, N* ¼ 8 *and Rayleigh distributed fading vector. Results for no shadowing condition,*

*w* is the principle reason

channel SNR of 40 ð Þ¼ � 20 20 dB.

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

performances are plotted in **Figure 10**.

different communication scenarios;

**Figure 10.**

**203**

*denoted by 'Th' are also plotted for comparison.*

dence of Max-Log rule on the noise spectral density *σ*2

**Figure 9.** *CDF of amount of fading (AF) for all environments.*

#### **Table 3.**

*Generalized range of values small scale parameters.*

indoor-to-outdoor virtual MIMO based communication scenario in WSNs, the propagation environment can experience a *K*-factor varying between 0 to 20 and a Δ-value varying between 0.1 to 0.9 in an open-concept smart office or home and in industry-like environments, as compiled in **Table 3**.

#### **4.3 Performance analysis**

The fusion performance of the formulated sub-optimum fusion rules is evaluated in this subsection, where the propagation environment is modeled using the accumulated measurements. Based on the observation in SC, DC and SI experimental scenarios, Ricean, TWDP and DR distributions are used to characterize the propagation channel.

#### *4.3.1 Receiver operating characteristics (ROC)*

For the different fusion rules of Section 3, probability of detection (*PD*0 ) is plotted against probability of false alarm (*PF*0 ) (commonly referred to as the Receiver Operating Characteristics (ROC)) for *S* ¼ 8 and *N* ¼ 8 in presence of a fixed channel SNR of 20 dB. The particular value of 20 dB is chosen for the plots, as the average attenuation **A**ð Þ*i* recorded for any measurement location *i* is approximately around 20 dB across all measurement environments. The measured SNR

*Cross-Layer Inference in WSN: From Methods to Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.93848*

over the direct LOS link is recorded to be equal to 40 dB yielding an equivalent channel SNR of 40 ð Þ¼ � 20 20 dB.

• *Impact of large scale channel parameters*: In order to analyze the impact of large scale channel effects, the small scale fading vectors are modeled to be Rayleigh distributed (**h***n*,*s* � N ð Þ 0, 1 ). From the Decode-and-Fuse group of suboptimum fusion rules, MRC and Max-Log are used for DF over four different communication scenarios; No Shadowing ('Th'; *ηP*, *μP*, *σP* = 1, 0 dB, 0 dB; **h***n*,*s* � N ð Þ 0, 1 ), SC (*ηP*, *μP*, *σP* = 2.72, 1.22 dB, 2.4 dB), DC (*ηP*, *μP*, *σP* = 2.56, 1.77 dB, 3.6 dB), SI (*ηP*, *μP*, *σP* = 1.96, 1.48 dB, 1.89 dB), and the ROC performances are plotted in **Figure 10**.

With increase in shadowing and pathloss, MRC outperforms Max-Log. Dependence of Max-Log rule on the noise spectral density *σ*2 *w* is the principle reason behind its poor performance in presence of rich shadowing. From the second group, CV-ML and CV-MMSE rules are used for DF over the above-mentioned four communication scenarios and the ROC performances are plotted in **Figure 11**. With increase in large scale channel effects, CV-MMSE outperforms CV-ML. The propagation environment has no impact on the performance of CV-ML owing to its dependence only on the SNR which is kept constant for the plots in **Figure 11**. In general, sub-optimum fusion rules perform better over SC scenario than over DC and over DC than over SI. With a strong LOS link existing in case of the SC scenario, it experiences the lowest pathloss. The DC scenario experiences higher pathloss due to penetration losses contributed by the moving human bodies.

• *Impact of small scale channel parameters*: In order to analyze the effect of the small scale channel effects, sub-optimum fusion rules are used for DF over four different communication scenarios;

#### **Figure 10.**

*Comparative ROC for the first group of fusion rules for different measured large scale parameters (varying ηP, μP and σP) with S* ¼ 8*, N* ¼ 8 *and Rayleigh distributed fading vector. Results for no shadowing condition, denoted by 'Th' are also plotted for comparison.*

indoor-to-outdoor virtual MIMO based communication scenario in WSNs, the propagation environment can experience a *K*-factor varying between 0 to 20 and a Δ-value varying between 0.1 to 0.9 in an open-concept smart office or home and in

**Scenario** *K* **Δ** SC 0.5 to 4 — SI 0 — DC 6 to 20 0.1 to 0.9

The fusion performance of the formulated sub-optimum fusion rules is evaluated in this subsection, where the propagation environment is modeled using the accumulated measurements. Based on the observation in SC, DC and SI experimental scenarios, Ricean, TWDP and DR distributions are used to characterize the

For the different fusion rules of Section 3, probability of detection (*PD*0 ) is plotted against probability of false alarm (*PF*0 ) (commonly referred to as the Receiver Operating Characteristics (ROC)) for *S* ¼ 8 and *N* ¼ 8 in presence of a fixed channel SNR of 20 dB. The particular value of 20 dB is chosen for the plots, as the average attenuation **A**ð Þ*i* recorded for any measurement location *i* is approximately around 20 dB across all measurement environments. The measured SNR

industry-like environments, as compiled in **Table 3**.

*Generalized range of values small scale parameters.*

*CDF of amount of fading (AF) for all environments.*

*Wireless Sensor Networks - Design, Deployment and Applications*

*4.3.1 Receiver operating characteristics (ROC)*

**4.3 Performance analysis**

**Table 3.**

**Figure 9.**

propagation channel.

**202**

3.DC scenario with TWDP fading vectors (*ηP*, *μP*, *σP* = 2.56, 1.77 dB, 3.6 dB;

*s* with ½*Ks*, min , *Ks*, max � ¼ ½ � 6, 20 , ½Δ*s*, min , Δ*s*, max � ¼ ½ � 0*:*1, 0*:*9 ),

and the ROC performances are plotted in **Figures 12**–**14** respectively.

*Cross-Layer Inference in WSN: From Methods to Experimental Validation*

4.SI scenario with DR fading vectors (*ηP*, *μP*, *σP* = 1.96, 1.48 dB, 1.89 dB;

If the small scale fading vectors are Rayleigh distributed, EGC performs best and CV-ML performs worst. CV-ML is worst under all considered propagation scenario. Max-Log performs a tad bit better than CV-ML over Rician, TWDP and DR fading channels. If the fading vectors are Rician and TWDP distributed, MRC, EGC and CV-MMSE perform almost equivalently. CV-MMSE however champions over MRC and EGC if the small scale channel effects follow DR distribution. Some analogies between performances under measured environment and simulated (as in [21]) can also be concluded from the results presented in **Figures 10–14**. In both cases ROC performance demonstrates that CV-MMSE performs better than CV-ML rule, CV-MMSE performs close to MRC/EGC rules, while CV-ML exhibits the worst

In **Figures 15** and **16**, we show system probabilities of detection, *PD*0 with two groups of fusion rules as an interpolated function of the number of receive antennas

• *Impact of measurement environment*: If both large and small scale channel parameters are varied, the probability of detection *PD*0 with MRC and CV-MMSE rules saturates with the increase in *N* over the SC scenario, but increases

*Comparative ROC for all fusion rules for the* DC *environment with S* ¼ 8*, N* ¼ 8 *in TWDP fading condition.*

*Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

**h**TWDP

*DOI: http://dx.doi.org/10.5772/intechopen.93848*

*Ks* ¼ 0),

performance.

*4.3.2 PD*0 v/s *N*

**Figure 13.**

**205**

*N* under *PF*0 ≤0*:*01.

#### **Figure 11.**

*Comparative ROC for the second group of fusion rules for different measured large scale parameters (varying ηP, μP and σP) with S* ¼ 8*, N* ¼ 8 *and Rayleigh distributed fading vector. Results for no shadowing condition, denoted by 'Th' are also plotted for comparison.*

#### **Figure 12.**

*Comparative ROC for all fusion rules for the* SC *environment with S* ¼ 8*, N* ¼ 8 *in Rician fading condition. Results for Rayleigh fading-only condition ('Th') are plotted for comparison.*

and the ROC performances are plotted in **Figures 12**–**14** respectively.

If the small scale fading vectors are Rayleigh distributed, EGC performs best and CV-ML performs worst. CV-ML is worst under all considered propagation scenario. Max-Log performs a tad bit better than CV-ML over Rician, TWDP and DR fading channels. If the fading vectors are Rician and TWDP distributed, MRC, EGC and CV-MMSE perform almost equivalently. CV-MMSE however champions over MRC and EGC if the small scale channel effects follow DR distribution. Some analogies between performances under measured environment and simulated (as in [21]) can also be concluded from the results presented in **Figures 10–14**. In both cases ROC performance demonstrates that CV-MMSE performs better than CV-ML rule, CV-MMSE performs close to MRC/EGC rules, while CV-ML exhibits the worst performance.