Nghiên cứu giải pháp đánh giá và đảm bảo tương thích điện từ trường cho các thiết bị vô tuyến điện tử tt tiếng anh

NGUYEN DUC TRUONG

RESEARCH SOLUTIONS TO ASSESS AND ENSURE
ELECTROMAGNETIC COMPATIBILITY FOR
ELECTRONIC RADIO DEVICES

Specialization: Radio and Electronic Physics
Code:

9 44 01 05

SUMMARY OF PHYSICS DOCTORAL THESIS

Hanoi - 2020


This Thesis was completed at:
Academy of Military Science and Technology

Academic Supervisors:
1. Assoc. Prof. Dr Ho Quang Quy
2. Assoc. Prof. Dr Bui Van Sang

Reviewer 1: Assoc. Prof. Dr Nguyen Quang Hung
Reviewer 2: Assoc. Prof. Dr Do Trong Tuan
Reviewer 3: Dr Ta Chi Hieu

This thesis will be defended in front of Doctor Examining E valuating
Committee held at Academy of Military Science and Technology at
…..….., ……………………2020

This thesis can be found at:
- The Library of Academy of Military Science and Technology
- The Vietnam National Library


1
INTRODUCTION
1. The Urgency: Today the EMC (Electromagnetic Compatibility) has
quickly played an important role in of circuit analysis and electronics
engineering. The rapid growth is due to the increasing use of electronic
devices, in addition to which most countries around the world have set
limits on radiation and transmission noise of products, electronic
products. The presence of interference caused by electrical and
electronic equipment can reduce the performance of themselves and
surrounding devices, especially in military equipment such as
submarines and warships, fighter planes, etc., where system space is
very limited, but the number of electrical and electronic devices can be
very large and operate simultaneously. Therefore, ensuring
electromagnetic compatibility (Electromagnetic Compatibility-EMC)
for electronic radio equipment (VTDT) is a very urgent issue. This area
of science needs more attention due to the sharp increase in the number
and scale of electrical and electronic devices. Therefore, I have chosen
the topic "Research solutions to assess and ensure electromagnetic
compatibility for electronic radio devices" with the following objectives
and contents as follows:
2. The objective: Research and complete evaluation solutions, ensuring
EMC when designing and manufacturing radio devices based on
electromagnetic shielding and estimating the distance of functional
blocks; study the EMC influence of the nearest noise source and the
total noise power in the radio system to determine a simple and

appropriate evaluation method.
3. The object: The thesis goes into research, analyzes evaluation
solutions, ensures EMC for blocks in radio equipment, assesses the
impact of the nearest source of interference on radio equipment and
radio systems are currently in common use.
4. The scope: Research on EMC theory, analyze the methods applied
currently in the system and devices VTDT on domestic and foreign
telecom devices, from which proposing complete solutions. New
improvement in both theory and practice. Study of EMC in a specific
telecom system or device VTDT, find out the electromagnetic
relationships and interactions between devices in a system and between
functional blocks in a separate electronic device, simulate research results
by software and draw conclusions.


2
5. Research content: Research solutions to ensure electromagnetic
compatibility for electronic devices VTDT, focusing on electromagnetic
shielding method and distance estimation. The study evaluates the
probability of interrupting the operation of radio systems under the
action of the nearest source of disturbance replacing the effect of total
disturbance power.
6. Research methodology: Research methodology is based on
collecting information, documents, general analysis of scientific works
and articles published in the world and in the country, applying them.
Radio wave theory, electromagnetic field theory, statistical probability
and calculus calculus to build mathematical relationships between
elements and the entire system. Evaluate results using CST and MonteCarlo simulation software on computers and test on hardware.
7. Scientific and practical significance: The remarks and conclusions
of the thesis are given on the basis of mathematical analysis, verified by

experiment and simulation, ensuring reliability, contributing to
perfecting the method of ensuring EMC for telecom equipment VTDT.
The method of electromagnetic shielding and the estimation of the
distance of blocks with recommendations drawn from experiment and
simulation help in the design and manufacture of telecom equipment.
The method of evaluating the probability of interruption of the
operation of the telecom system under the impact of the nearest
interference source replacing the effect of the total interference power
contributes to simplifying the method of ensuring EMC for telecom
equipment. These are two contents with new and scientific significance.
The results of calculation, experiment and verification simulation in the
thesis contribute to perfecting the method of ensuring EMC for telecom
equipment. From these results, it helps design and manufacture of new
telecom devices to achieve and comply with EMC standards, improve
the reliability of the equipment.
8. Structure of the thesis: In addition to the introduction, conclusion,
list of published works of the thesis, references and appendices, the
content of the thesis consists of 3 chapters: Chapter 1. General review
of EMC assessment and assurance solutions for radio devices; Chapter
2. Proposing solutions to ensure EMC when designing electronic
telecommunication equipment; Chapter 3. Proposal solution to assess
the nearest noise source instead of the total noise power.


3
Chapter 1. OVERVIEW OF EMC ASSURANCE AND
ASSESSMENT SOLUTIONS FOR RADIO DEVICES
1.1. Concepts and EMC characteristics of radio equipment
1.1.1. General concept
Electromagnetic compatibility is the ability of a device (electricity,

electronics, radio) to operate stably and to ensure parameters in a
specific electromagnetic environment and not to produce noise that
exceeds the standards specified for other devices [51].
1.1.2. EMC characteristic of radio equipment
When dealing with EMC electromagnetic compatibility issues of
radio equipment, there are many parameters and characteristics of radio
receivers (MT), radio transmitters (MF) and antennas used. used to
evaluate EMC. These characteristics and parameters describe certain
properties of the aforementioned devices, derived from the perspective
of electromagnetic interference and their ability to prevent them.
Specifically, within the scope of the thesis, the following content can be
considered among the characteristics of EMC [4], [5], [51].
1.2. Some solutions to ensure EMC for radio equipment
In order to ensure EMC for radio components, blocks and devices,
many solutions have been implemented and yielded certain results. The
basic methods for limiting or eliminating the effects of interference in
equipment circuits are: needle shielding, earthing, filtering, balancing,
isolation, distribution and orientation of conductors in the space. adjust
the circuit impedance ... [4], [51]. Figures 1.7, 1.8 and 1.9 show
methods for limiting noise in electrical circuits.
1.2.1. Electromagnetic shielding solution
As electronic radio equipment became more complex, the requirement
to reduce the effects of interference became even more necessary. One
of the most commonly used methods applied to blocks or the entire
electronic device is electromagnetic shielding using metal boxes [6].
Electromagnetic shielding is a very useful and common solution to
ensure EMC for all components and devices.

Figure 1.10. The effect of electromagnetic shielding

4
The shielding effect (SE [dB]) of a needle cover can be expressed as
a sum of the reflectances (R [dB]), the absorption (A [dB]) and the
multiple reflections (B [dB]) as follows [48]:
SE [dB] = R [dB] + A [dB] + B [dB]
(1.8)
1.2.2. Distance estimation solution
Another method used is to estimate the distance between components
of an electronic device. This method is based on the principle that when
an electromagnetic wave propagates through space, the signal strength
decreases with distance [47].

Figure 1.12. Distance inverse method

E ( R' )[dB]  E ( R)[dB]  20lg(

R
)
R'

(1.10)

1.2.3. Other solutions
1.3. Models for evaluating the maximum power of noise
1.3.1. Statistical model of maximum power of noise
In mobile phone networks, receivers (MT) and transmitters (MPs) are
often used in two types: mobile stations (MS) and base stations (BS),
forming the basic types of transportation for these two types. In [4]
surveying 4 models, Figure 1.20 is the typical model we choose for

analysis.
MP(MS)
MT(BS)

r
Rc

D
MS

BS
MP(BS)j

MT(MS)j

Figure 1.20. Statistical model


5
1.3.2. Some other evaluation models
1.4. Comments and discussions on EMC solutions for
electronic radio
Electromagnetic compatibility is really interested in countries in the
1970 - 1980 of the 20th century. Since the 1980 year, countries such as
the US, the former Soviet Union, Japan, ... have built EMC standards
when using electromagnetic resources such as frequency spectrum,
electronic components layout density, receiver sensitivity, generator
capacity, ...
Currently, our country has only a few EMC electromagnetic
compatibility measuring rooms at some key agencies such as: Radio

Frequency Department /Ministry of Information and Communications;
National Metrology Institute (VMI)/General Department of Finance,
Administration, Ministry of Science and Technology; Bureau of
Standards - Metrology - Quality/BTTM/BQP. Currently, some
universities such as Hanoi University of Science and Technology, Posts
and Telecommunications Institute, Danang University have a number of
topics related to EMC research such as frequency planning,
electromagnetic radiation disturbance measurement. from elements of
receiver, transmitter, antenna - phide, etc. For example, at the
University of Danang, Dr. Tang Tan Chien has had ministerial-level
researches "Studying to build a grafting model to expand the bandwidth
of TEM cells ”2016 [2]; "Simulation of electromagnetic field
transmission by TLM method" in 2002 [3].
However, it can be affirmed that until now, there are still a lot of
studies on EMC for specific elements, function blocks, electronic
devices and telecommunication system, and there is a lack of domestic
research on solutions, the evaluation model and EMC criteria for
elements, blocks and electronic telecommunication devices can ensure
EMC when designing and manufacturing radio equipment and
networks, especially in the military field.
1.5. The problem of building a solution to assess and ensure
electromagnetic compatibility for radio devices
1.5.1. Set the problem
With the above analysis, the problem posed and solved in the thesis
is: Research, propose solutions to assess and ensure electromagnetic
compatibility for electronic radio devices. Experimental simulation of
computer statistics and hardware testing based on EMC characteristics


6

of electronic devices to analyze, evaluate research results and propose
solutions to ensure EMC.
1.5.2. Research object, scope and limits
With the above posed problem, the thesis identifies the research
object as solutions to ensure EMC of radio devices. Therefore, the
scope of the thesis will focus on the evaluation method, ensuring EMC
for electronic telecommunication equipment. From there, propose
solutions, models to evaluate and ensure EMC for electronic
telecommunication devices according to EMC characteristics based on
the input parameters of the equipment.
1.5.3. Research methodology, content and solution
The problem is solved based on the application of electromagnetic
field theory and wave propagation, statistical probability theory and
calculus calculus to build mathematical relationships, proposing some
solutions in the problem. EMC guaranteed price. Perform verification,
evaluate results by computer simulations and test EMC algorithms on
hardware.
1.6. Conclusion of chapter 1
Based on the findings of the review in chapter 1, some comments can
be drawn as follows:
1. Ensuring EMC electromagnetic compatibility is important for
reliable, proper operation of electrical, electronic and constituent
components. In order for the EMC research content to be effective, it is
necessary to have a firm grasp of the design, function of the device,
element, and sources of impact.
2. Electrical and electronic equipment are diverse in type, structure,
function and increasingly innovative in manufacturing technology, so a
total solution to ensure EMC for all types of equipment is difficult.
Feasibility. Therefore, research works on EMC that are specific to each
specific case are very necessary and topical.

3. For the reasons mentioned above, the research direction of the
thesis is limited to the following contents: electromagnetic shielding for
elements and estimation of distances for blocks in radio equipment,
proposing solutions to ensure EMC when design electronic
telecommunication equipment, propose mathematical model to evaluate
the statistics of electromagnetic interference, in which the nearest noise
source is evaluated instead of the total noise power. These are new
contents to be studied in chapters 2 and 3 of the thesis.


7
Chapter 2. PROPOSED SOLUTIONS TO ENSURE EMC WHEN
DESIGNING RADIO DEVICES
With the EMC research and analysis in chapter 1, the thesis proposes
a solution to ensure EMC when designing electronic radio devices
based on the application of electromagnetic shielding (needle coating)
in combination with method of estimating the distance between blocks,
thereby serving as a basis for building a model to ensure EMC when
designing radio equipment.
2.1. Proposed Solutions
2.1.1. Question
The EMC assurance methods mentioned in section 1.2 each have
their own advantages and disadvantages. The thesis will mention to
ensure EMC for electronic equipment with one or more blocks
available, ie do not interfere with the circuit or block design process.
Therefore, the thesis proposes a solution combining needle coating
method and estimating distance between blocks to improve EMC for
electronic radio equipment.
2.1.2. Implementation model
The problem is carried out with an aluminum-coated first needle box

(the reason for choosing materials in section 2.2.1) is 16 cm x 10 cm x 3
cm, the thickness of the shell is 2 mm. The radiation source is placed
inside the first needle box through a coaxial cable of 50 Ω impedance
and copper wire with a diameter of 0,16 cm to ensure uniform
istribution of electromagnetic radiation inside the box as shown in
Figure 2.1 [31 ]. A second needle-wrapped box measuring 10 cm x 10
cm x 3 cm in aluminum is placed at a distance of d from the first needle
box.

Figure 2.1. Needle-wrapped box model
2.2. Analysis of proposed solutions
2.2.1. Solution coated with needles


8

Figure 2.2. Theoretical shielding effect of aluminum alloy box
With the needle-coated box selected by the author, the thickness of
the needle cover is 2 mm, the material of the needle cover is aluminum
 r = 1 and  r = 0,61 (with frequencies above 500 kHz) [48]. The
shielding effect of the needle coating method calculated according to
(2.1) is shown in Figure 2.2. As can be seen in Figure 2.2, when using
an aluminum alloy cover of 2 mm thickness and considering the
frequency range of CISPR-22 standard from 30 MHz to 1 GHz [43], the
shielding effect is great (more than 1000 dB).
2.2.2. Distance estimation solution
In the far field the emission intensity of the radio waves is assumed to
be inversely proportional to the distance as (2.7):

R

)
R'
R
 L  dB   E R '  dB   E  R   dB   20lg  ' 
R 
E ( R' )[dB]  E ( R)[dB]  20lg(

(2.7)

 

(2.8)

The attenuation efficiency of the distance estimation solution
calculated by the formula (2.8) is shown in Table 2.3.
Table 2.1. Theoretical attenuation of the distance estimation solution
Distance (cm)
3
4
5
6
7

Attenuation L (dB)
3,52
6,02
7,96
9,54
10,88

9
8
9
10
15
20
30
50

12,04
13,06
13,98
17,50
20,00
23,52
27,96

2.2.3. Solution combination
After analyzing the two alternatives, the thesis combines both needlewrapped solutions and estimates the distance between needle-wrapped
boxes. The attenuation of electromagnetic signals when combining the
above two solutions is the total attenuation when applying each
solution. First, electromagnetic waves of intensity E1 (dB) emitting into
space will be attenuated by SE (dB) when passing through the needle
cover. After that, the electromagnetic wave will continue to decrease L
(dB) according to the distance traveled. Equation (2.11) shows the value
of attenuation A (dB) when combining the above two solutions as
follows:
E2 [dB] = E1 [dB] - SE[dB] - L[dB]
(2.9)

=> E1[dB] – E2[dB] = SE[dB] +L[dB]
(2.10)
=> A[dB] = SE[dB] + L [dB]

(2.11)

The decrease of the proposed solution calculated by the formula
(2.11) is shown in Table 2.4.
Table 2.2. The theoretical decline of the proposed solution
Distance
(cm)
3
4
5
6
7
8
9
10
15
20
30
50

1 MHz
270,74
273,24
275,18
276,76
278,10

279,26
280,28
281,20
284,72
287,22
290,74
295,18

Total attenuation A (dB)
20 MHz
50 MHz
100 MHz
996,42
1533,82
2138,02
998,92
1536,32
2140,52
1000,86
1538,26
2142,46
1002,44
1539,84
2144,04
1003,78
1541,18
2145,38
1004,94
1542,34
2146,54

1005,96
1543,36
2147,56
1006,88
1544,28
2148,48
1010,40
1547,80
2152,00
1012,90
1550,30
2154,50
1016,42
1553,82
2158,02
1020,86
1558,26
2162,46

500 MHz
4672,02
4674,52
4676,46
4678,04
4679,38
4680,54
4681,56
4682,48
4686,00
4688,50

4692,02
4696,46


10
2.3. Simulate proposed solution
The thesis will perform the simulation effect of needle coating
method and distance estimation method by CST software.
2.3.1. Simulate needle-wrapped solution
2.3.2. Simulate distance estimation solution
2.3.3. Simulation combines two solutions
Next, the thesis combines the two methods of needle wrapping and
estimating the distance between the needle wrap boxes.

Figure 2.13. Simulation proposed solution on CST
Figure 2.14 illustrates the strength of the electric field caused by the
radiation source in needle box 1 measured at the cover of the 2nd needle
box when the distance d changes from 3 cm, 4 cm, 10 cm and 15 cm (
with the same holes and gaps in the shell).

Figure 2.14. Electric field strength at the 2nd needle box shell


11
2.4. Tested on real circuits
After theoretical analysis and simulation, the thesis will perform
measurements on real circuits to confirm the effectiveness of the
solution combining the needle coating method and estimate the distance
on the actual circuit as shown in Figure 2.15.

Figure 2.15. Test image on actual circuit (Appendix 2)

Figure 2.22. Oscillator and source circuit
spaced d (cm) apart without barrier
The distance d (cm) is varied to different values of 2 cm, 3 cm, 4 cm,
5 cm, 6 cm, 7 cm, 8 cm, 9 cm and 10 cm. The test shows that the effect
of the electromagnetic field between the two circuit blocks is most
reduced when the two circuits are needle coated and spaced 10 cm
apart.


12

Figure 2.23. Signal strength in case of the source circuit and the
oscillating circuit spaced 10 cm apart, without shielding
The obtained results are shown in figure 2.20 (two uncoated and side
by side circuits) and in figure 2.24, figure 2.25, (two needle-coated
circuits spaced close to each other and spaced 10 cm apart), figure 2.26
(comparison the electromagnetic attenuation of the foil and the
uncoated) shows that the attenuation of the electromagnetic signal when
applying the proposed solution compared with the case without the
EMC guaranteed method is about 25 dB - 30 dB.

Figure 2. 24. Oscillating circuit and power circuit
covered with needle spaced d (cm)


13

Figure 2.25. The case signal strength is set 10 cm apart 2.5.

Figure 2.26. Compare the electromagnetic decline
when using needle wrap and changing the spacing
(data are taken from annex 3)
Based on the theoretical results, simulation results and experimental
results in the above cases, we can find out the stated EMC assurance
solutions such as needle wrap, distance estimation or Combining 2
solutions both work to reduce unwanted electromagnetic signals emitted
in electronic equipment. Needle-coated solutions or distance estimation
have separate advantages and disadvantages, we evaluate each solution
and evaluate both solutions at the same time.


14
2.5. Proposing solutions to ensure EMC when designing electronic
telecommunication equipment
Start

- Determine functions
specifications of TBVT
- Affect parameter ai
- EMC limits level btci

Adjust schematic
diagram

and

Design schematic
diagram of TBVT

Adjust schematic
diagram

Divide blocks according
parameter ai and function

Block n

Block 2

Block 1

ai ≤ btci ?

No

Electromagnetic
shielding for each
block

Yes

ai ≤ btci ?

No

Adjust distance of
components

Yes

ai ≤ btci ?

Yes
Make
prototype block
Từ tất cả các khối

No
Make prototype
TBVT
No

Electromagnetic
shielding for TBVT

ai ≤ btci ?

Another
solutions

Yes

ai ≤ btci ?

No

Yes
Adjust distance of

blocks

Another
solutions

No

ai ≤ btci ?

No

Yes

ai ≤ btci ?

Yes

Manufacture
TBVT

End
No

ai ≤ btci ?

Yes

Figure 2.27. Design flow chart of electronic
telecommunication equipment to ensure EMC
2.6. Conclusion of chapter 2

The thesis has implemented a combination solution between the
needle coating method and the method of estimating the distance
between blocks of radio equipment. The author has performed
simulation by CST software and tested the actual circuit, the solution's
effectiveness contributes significantly to reducing radiation intensity,
ensuring proper working function and not disrupting the function of
other equipment when using. From the experimental results, the thesis
proposes a design process to ensure EMC for radio equipment applying
technical solutions combining needle coating method and estimation
method of distance between blocks of radio equipment electronic.


15
Chapter 3. PROPOSED SOLUTIONS FOR ASSESSING THE
NEAREST INTEREST SOURCES IN TOTAL CAPACITY
Based on the research results in the previous chapters and some
methods to assess and ensure EMC for radio devices, chapter 3 will
propose the model of statistical evaluation of the nearest interference
source and ensure EMC for the electronic radio equipment.
Experimental statistical simulation on the computer with assumed
parameters of evaluation models, ensuring EMC to analyze, evaluate
the effectiveness, reliability of the algorithm and make some
recommendations and recommendations .
Visually, we can see that the noise source with the highest power will
have the greatest impact on the probability of interruption of operation
(as analyzed in section 3.1), so the author of the thesis focused on the
analysis. The effect of the strongest noise source is that the probability
of an interruption in that operation receives a reduced form. The results
of analysis and simulation can be seen that at the probability of small
disruption, the probability of receiving the highest power source and the

total noise power is the same (according to the research results in
chapter 3 of thesis).
Consider a number of point (Tx ) and point (Rx) transponders placed
randomly on a limited area of Sm space as a noise model of the physical
network wireless network, m = {1, 2 , 3} is the number of spatial
dimensions (1-D, 2-D or 3-D).

Figure 3.1. Illustration of geographical space
S.Small space area (the vicinity of the node), large space area (the
space expanded around the node does not overlap) and the cyberspace.
The probability for more than one transmitter to fall into dS is
insignificant, P (k> 1, dS) << P (k = 1, dS) when dS → 0. Under these
assumptions, the probability of k machine The emission falls into the S
region given by the Paticona distribution:


16
P(k , S ) 

e N N k
k!

(3.1)



inside, N   dS is the average number of transmitters falling in area.
S

3.1. Proposing the solution to assess the nearest source of

interference
From the network model and the system studied, the thesis considers
fixed position receivers (for example, base stations of a certain user)
and some random noise generators with the same Pt power (eg for
example, other user's mobile devices). In order to simplify mathematical
representation, the thesis assumes that gl = gs = 1 (parameters related to
the phase-nails transmission channel not included in the thesis), that is,
only the station parameter is included in the calculation. The thesis also
assumes that the transmitting and receiving antennas are isotropic and
consider the interference signals located at the input of the receiver.
The thesis defines the skin noise / noise ratio (INR) da (also known as
dynamic range [17]) in the whole interference signal through the
strongest signal at the input Rx (in the small interrupt area, the total
Noise power is affected by the contribution of the strongest signal):
da = Pa1/P0
(3.3)
When the average spatial density of emission sources is constant, ρ =
const, the expressions (3.6) and (3.7) are simplified in the form:
m/v


 N max 
 Pa
 

t v
 Fd ( D)  exp 

c


 m 
   exp  m / v 

 P0 D  

 D 

(3.8)




 N max 
m N max
exp  m / v 
 f d ( D) 
m / v 1
v D

 D 

where c1 = 2, c2 = π và c3 = 4π/3, N max  cm Rmax  is the average
number of emission sources in the sphere of radius Rmax called
"sufficient noise area" or potential noise area. When Rmax = r(1) =
m

 Pa
t  / P0 D 

1/

satisfies Pa(Rmax) = P0, that is, the transmitter is located

at the boundary of "enough noise zone" producing a signal (to the
receiver) equal to the noise level.
Transmitters outside this zone create weaker signals to the receiver,
which should be ignored in situations of limited interference. In Figure


17
3.2, the noise area is sufficiently satisfied: R ≤ Rmax, that is, Pa(R) ≥ P0 =
Pa(Rmax), or in other words this is the area of the noise power exceeding
the receiver noise level; When evaluating the network based on the total
noise power, only the disturbances in this area are considered.

Figure 3.2. Illustrate the noise around the node on a network range
With the above definition of probability of interruption of operation
based on the maximum noise power similar to the total noise power, the
thesis gives the following theorem.
Theorem 1. Consider the probability of interrupt activity in (3.11). At
a low interrupt area, it converges to the probability that the operational
disruption is determined by the total noise power, i.e.:
Pr  i Pai  x
(3.13)
lim
1
x 
Pr Pa1  x
3.1.1. Case of all interference signals (k = 1)
The thesis considers the first case k = 1, ie all interference signals are

active. The probability of an operational interruption can be assessed by
the expressions (3.6) and (3.11). From a practical point of view, the
thesis is concerned with the probability interval of Pout << 1, which
means that the information is highly reliable. Consider the case when





Fd(D) → 1 and use the MacLaurean e N  1  N sequence expansion,
where is the average number of transmitters in the active interference
region, then the expression (3.9) is simplified into:
(3.20)
Pout  N  
 dV
V  r ( D )

Vhen ρ = const receive:

Pout  N max D m/ v

(3.21)


18
To confirm the accuracy of the approximation in (3.13) and the
expressions for the cumulative distribution function and the probability
density function of INR, the thesis performed Monte-Carlo (MC)
simulations. Figure 3.3 gives some representative results of the CCDF
(Complementary Cumulative Distribution Function) curve, including

the INR probability curve according to the maximum noise source
power (expression (3.8)) and the approximate form. its (3.21), and the
INR probability curve according to the total noise power [16], [17],
[18], [19], [20]. Note also that the probability of an operational
interruption is assessed by the total disturbance power and that the
maximum disturbance power is the same in the small interrupt area. In
addition, the approximation becomes very accurate when the probability
of Pout ≤ 0.1. Accordingly, the results obtained are completely
consistent with Theorem 1.

a) v = 2

b) v = 4
Figure 3.3. CCDF probability curve of INR with parameters: m = 2 (2D), P0 = 10−10, Pt = 1, ρ = 10−5


19
3.1.2. The case (k - 1) of the nearest interference source is removed
Assume that (k - 1) the nearest source of noise is removed through
several methods (for example, by receiver processing or resource
allocation). In this case, the expressions (3.9), (3.10) and the expression
(3.20) can be generalized to:

1 k 1  N max 
Pout  N   m v 
k!
k ! D 

k

(3.24)

1 k
Pout ,1  Pout ,1 , inside Pout ,1
k!
is the probability of an operational interruption with k = 1 (see
expression (3.13)). In the area of small probability of disruption of
activity Pout ,1 << 1 và Pout << Pout ,1 , this means that there is
considerable benefit from removing (k - 1) the strongest source of noise,
which is exponentially proportional to k.
From there can be performed Pout 

Figure 3.4. The CCDF probability curve of INR for k = 1 (not
eliminated), k = 2 (latest noise set removed) according to the total
power and approximate (3.24), ν = 4, m = 2, N max = 100, Rmax = 103.
Figure 3.4 illustrates this case. Note that the probability of
interruption operating under the maximum disturbance power and
according to the total noise power is the same in the low interrupt area.
3.1.3. Remove the nearest (k - 1) source of noise
According to [22], one can also consider the case of the type of noise
that is not ideal (this is the case in practice), when (k - 1) the nearest
noise source is attenuated by a coefficient of 0 ≤ α ≤ 1 ( so that the noise
power is αPai, 1 ≤ i ≤ (k - 1) where α = 0 corresponds to the ideal case


20
(completely removed) and α = 1 corresponds to the case not removed.
The closest disturbing source governs the probability of an operational
interruption given by:

Pout   m v N max D m v ,   0

(3.30)
Consider another situation where (k - 2) the nearest source of noise is
completely eliminated (for example, thanks to the appropriate allocation
of resources, divided by frequency or time) and the secondary source of
noise (k - 1) partially removed (for example, by treatment at the
receiver), then k ≥ 3. In this case it may be easy to indicate that the
secondary source of noise (k - 1) is in the region. Proximity to the
potential interference area and the probability of the network disruption
is determined:

Pout 

 ( k 1) m v  N max 


(k  1)!  D m v 

k 1

,  0

(3.31)

Figure 3.5. CCDF probability curve of INR when partial noise is
removed from the nearest source (k = 2) and its approximation to
parameters: ν = 4, m = 2, N max = 100, Rmax = 103 and compare with
situations k = 1 (no noise removal), with complete noise removal from
the nearest source (k = 2).

3.1.4. Case according to the total noise power
If the total noise power is used to determine the probability of an
interrupted network, the result will be exactly the same in the small
disruption region, as indicated by the following theorem (equivalent to
Theorem 1).


21
Theorem 2: Consider the probability of discontinuity in (3.24). At
low discontinuity zones, the probability of interruption is determined by
the total disturbance power, i.e.:
N

Pr  Pai  x 
 1
lim  i  k
x 
Pr  Pak  x

(3.35)

and thus the approximation is obtained:

N

Pr  Pai  x   Pr Pak  x , for large x
 i k


(3.36)

Figure 3.5 shows the result from Theorem 2 through Monte-Carlo
simulation. Note that this theorem also applies when partial noise is
removed and therefore the network interrupt probabilities in expressions
(3.30) and (3.31) are also applied to the total noise power.

Figure 3.6. CCDF probability curve of the skin
with parameters: v = 4, m = 2 (2-D), P0 = 10−10, Pt = 1, ρ = 10−5
Figure 3.6 gives the Monte-Carlo simulation results for the CCDF
curve of the skin according to its maximum noise source capacity and
its approximate form, and the probability curve according to the total
noise power [16], [17], [18], [19], [20].
3.2. The influence of phase-to-phase on the probability of an
operational interruption
Based on the network and system model in the first part of the
chapter, in this section, the thesis analyzes the effect of phase-to-phase
effects on the probability of operational disruption, thereby providing


22
more information on manufacturing mechanisms. noise as well as their
impact. The thesis can prove that the total noise power is governed by
the nearest jamming power for the phase-to-nail effect layer, specific to
each case. This is similar to the case where some of the nearest noise
sources are removed.
3.2.1. Effect of Rayleigh type phase
Without taking into account the phase-to-channel channel factor (it
can be considered that gl = gs = 1), the probability that the INR ratio
exceeds the value of D is Pr{da > D} = Pr{r1 < r(D)} = F1(r(D)) such
that Pa(r(D)) = P0D, the cumulative distribution function of the skin

(section 3.1):



Fd ( D)  1  Pr da  D  exp  N ( D)



(3.37)

Since the probabilities of operation interruption according to
maximum disturbance power and by total disturbance power are the
same in low-active interruption region (in 3.1), figure 3.7 illustrates
results indicating results as total disturbance power. As seen in Figure
3.7, when k = 2 (the latest noise source is eliminated), the probability of
an operational interruption decreases very quickly compared to k = 1
(when no noise reduction), meaning that the network performance
increases significantly.

Figure 3.7. The CCDF probability curve of the skin for k = 1 (no noise
reduction), k = 2 (the most recent set of noise removed) in terms of total power
and approximation to parameters: ν = 4, m = 2,

N max

= 100, Rmax = 103.

Figure 3.8 illustrates the comparison of the proposed model
according to the noise source capacity closest to the model according to
the total power taking into account the impact of Rayleigh type phase.

23
The exponential increase in the Pout in k is conserved under the
influence of the nail-phase, as well as the apparent influence of the
nearest noise source in the region with a small probability of operational
interruption. When Pout ≤ 1, the probability of interruption according to
the power of the nearest interference source and the total power is the
same. The threshold effect is clear and the noise / noise ratio is
D0 = 34 dB.

Figure 3.8. Probability of interrupt for k = 1 (no noise reduction) and k
= 2 (latest noise source removed) according to the nearest power and
total power under Rayleigh type phase-action with parameters

v  4, m  2, N max  50, Rmax  103
3.2.2. The effect of standard log and phase-combined phases
3.2.3. Influence of phase-width distribution layer
3.3. Conclusion of chapter 3
The dissertation has used the power of the nearest noise source
instead of the total noise power as a statistic for the probability of
network interruption and network density, building the correlation
between them for parameter selection compatibility. for network
building strategies. Various types of interference situations are also
analyzed to improve the probability of network interruption.