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MINISTRY OF EDUCATION AND TRAINING

MINISTRY OF NATIONAL DEFENSE

ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY
***************

NGO XUAN MAI

SOLUTION FOR CORRECTING HETEROGENEITY
BETWEEN CHANNELS ON PHASE ARRAY ANTENNA FOR
SATELLITE POSITIONING RECEIVERS
Specialization : Electronic engineering
Code : 9 52 02 03

SUMMARY OF PhD THESIS IN TECHNICAL

Hanoi, 2020


This Thesis has been completed at:
Academy of Military Science and Technology, Ministry of Defense

Scientific Supervisors:
Assoc. Prof. Dr. Nguyen Huy Hoang
Dr. Hoang The Khanh
Reviewer 1: Prof. Dr. Bach Gia Duong
Reviewer 2: Assoc. Prof. Dr. Bui Ngoc My
Reviewer 3: Dr. Ta Chi Hieu

This thesis was defendeb at the Doctoral Evaluating Council at Academy

level held at Academy of Military Science and Technology at ……..,date 2020

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


INTRODUCTION
1. Necessity of the thesis
In recent years, the Global Navigation Satellite System - GNSS
plays an important role, to be applied in almost all areas of social life,
including Civil, industrial and national defense security.
However, the useful signal is transmitted from the GNSS satellites
(about 20,000 km away from the earth) [4] spreading through the
environment to the receiver input will be reduced dramatically (about
1024 times - 26dB) [5] due to many objective factors (extreme weather,
shielded by obstructions, radio frequency interference) as well as
subjective factors (interference, fake signal interference, interfering
sources are created in electronic combat) [6]. Therefore, the research of
improving the anti-interference ability of GNSS receivers in order to
ensure the ability to locate and guide exactly is always an urgent need, is
being and continues to attract the attention of many scientists all over the
world. These types of noise are mainly broard-band noise, the only
solution to be able to withstand these noise is to use phase array antennas.
The process of positioning and navigation signal on phase array antenna
has brought a lot of benefits; however, it also incurred some technical
issues that need to be addressed. One of those problems is heterogeneity
(in terms of phase, amplitude or both) between channels of phase array
antennas. This heterogeneity is usually expressed through group delay
(Group Delay) [7] (Group delay is defined as the negative derivative (or

slope) of a phase response versus frequency. Different frequencies from
input to output in a system).
Stemming from the above reasons, the PhD student proposed
using MPE standard [32] by the method of separate matrix vectors (SVD)
instead of the standard MMSE used in [45] to solve the problem of
correcting inhomogeneous channel errors on the phase array antenna to
reduce the complexity of the algorithm and increase the convergence
speed of the algorithm. Due to the reduction of complexity in the
implementation of the algorithm, the PhD student proposed to increase the
number of phase array antenna elements to 9 to increase the range of anti1


interference capabilities for satellite positioning receivers that are required
for the system computation remains on board the same.
2. Objectives of the study
The study proposes two solutions to correct heterogeneity
between channels on phase array antennas based on self-compensation
and two-stage correction using MPE optimization standard [32] instead of
proposed MMSE standard in [45] to overcome the heterogeneity between
receiving channels, improve the quality of signal to noise ratio (SINR),
improve the reliability of satellite positioning receivers.
3. Objects and scopes of the study
From the above analysis, the PhD student identified the object and
scope of the thesis: GNSS satellite positioning receiver; 3, 4, 7 and 9
elements phase array antennas. The thesis will focus on researching
solutions to correct heterogeneity between receiver channels on 3 and 9
elements phase array antennas.
4. Research contents of the thesis
- Study signal and noise model of GNSS system and receiver
channel model of 3 and 9 elements phase array antennas. Represents the

satellite signal and noise of satellite positioning receiver on 3 and 9
elements phase array antennas under the influence of narrow and
boardband noise.
- Building mathematical models of homogeneous and heterogeneous
receiving channels for 3 and 9 elements phase array antennas.
- Simulate signal processing on 3 and 9 elements phase array
antennas in the case of homogeneous and heterogeneous channels in order
to assess the impact of heterogeneity on the anti-interference quality in
signal processing.
- Study non-working zone and non-working zone's dependence on
receiver sensitivity for 3 and 9 elements phase array antennas with distance
between elements d=2/3.56 and d=/2 when the channel is homogeneous and
inhomogeneous.
- Proposing the application of MPE optimization standard to
replace MMSE standard for solutions to correction heterogeneity between
channels on phase array antennas based on two-stage error channel
2


correction algorithm and self-compensating error channel correction
algorithm for the satellite positioning receiver.
- Perform tests on computers by simulation with Matlab software,
evaluate the research results and the new proposals of the thesis compared
with the previous results, from which give a number of recommendation
with GNSS system model.
5. Research Methods
To solve the above-mentioned contents, the PhD student conducts
research on the theory of probability and mathematical statistics for radio
techniques, coding and channel theory, linear algebra. Based on the basic
theories, build a mathematical model of the problem, thereby proposing

solutions to correct heterogeneous error between the channels on the phase
array antenna. To verify and give visual results of the proposed method,
the PhD student performed the calculation using Matlab software and was
displayed in the form of a chart with different system parameters.
6. Scientific significance and practical meaning of the thesis
- Scientific significance: The research results of the thesis are
novelty, scientific, contributing more basis for the calculation,
construction and design of satellite positioning systems on board. The
proposed solutions to correct heterogeneous error between channels on the
phase array antennas are feasible, which is the initial basis for the research
and development of satellite positioning systems, especially the satellite
positioning systems on board such as UAVs, cruise missiles, and flying
equipment in Vietnam.
- Practical significance: Solutions to correct heterogeneous errors
between channels on phase array antennas combined with spatial - time
signal processing methods to prevent interference, ensure accuracy and
reliability for receiving satellite positioning signals on equipments, hightech equipment (CNC) using satellite positioning and navigation systems
such as UAV, cruise missiles ... So, thesis: "The solution for correcting
heterogeneity between channels on the phase array antenna for satellite
positioning receivers" has high practical significance.
7. Contents of the thesis
In addition to the introduction, conclusion, list of published works of the
author, references, the content of the thesis consists of three chapters:
3


Chapter 1: Overview of GNSS system and anti-interference
solutions for positioning receivers.
Chapter 2: Study and evaluate the performance of antiinterferencing of MPE optimal standard for GNSS receiver.
Chapter 3: Solutions for correcting heterogeneous error between

channels on the phase array antenna for satellite positioning receivers.
CHAPTER 1: OVERVIEW OF GNSS SYSTEM AND ANTIINTERFERENCE SOLUTIONS FOR POSITIONING RECEIVER
1.1. GNSS satellite position and navigation system, types of noise and
signals in the system
Global Navigation Satellite System structure
Signal structure of GNSS system
Nowaday, there are two most widely used satellite systems:
Russia's GLONASS system and US’s GPS system. In the scope of the
thesis, the PhD focuses on solutions to correct heterogeneity error between
channels on phase array antennas for satellite positioning receivers of the
two systems.
1.1.2.1. GPS signal structure
1.1.2.2. GLONASS signal structure
1.2. Noise types in GNSS systems
In GNSS systems, since the useful signal transmitted from
satellites to Earth is strongly degraded (26dB), this signal is very
susceptible to interference by various objective and subjective factors.
These types of disturbances greatly affect GNSS signal reception, which
can be classified into two types: natural noise (multi-path effect,
atmospheric noise) and artificial noise (signal interference, noise
interference ), is the cause of the deterioration of the system.
1.3. Effective STAP processing techniques for GNSS system signals to
enhance the anti-interference properties of recievers
The commonly used optimum are maximize the SINR ratio on the
output of adaptive phase array antennas MSE [19], МMSE [23], ML [23]
and minimize power eigencanceler MPE by Singular Value
Decomposition [32].
4

1.4. Existing methods for solving heterogeneous error correction issues
Two-channel calibration method
x1(t)

1(t )

K 1(jw)

x2(t)

2 (t )

K tq (jw)

K 2(jw)

Fig 1.6. Spatial processing system two channels
Two-channel self-compensating method
L 1
2

Main channel

∑

Sub channel

wL

Output

∑

wk
w2
w1

Fig 1.7. Two-channel self-compensating structure
Noise compensation with one parameter correction
x0(t)

x1(t)

K 0(jw)

K 1(jw)

×

X 

Ʃ

w1
K 2(jw)

×
w2

Fig 1.9. Structure of noise compensation with one parameter correction

1.5. Parameters to assess the anti-interference quality
Table 1.1. Characteristic of anti-interference quality
1.6. Math representation of anti-interference methods based on
processing number of STAP signals
5


The standard of space-time adaptation
1.6.1.1. Minimum mean square errors standard MMSE.

WMMSE  R1RA

(1.1)

1.6.1.2. Minimum mean square errors standard according to limit
condition









Wopt  R1  R A  1  CT R1R A C / CT R1C 



(1.2)

1.6.1.3. Mean square errors standard (MSE)
WMSE   R I  R n  W0 ,
1

(1.3)

1.6.1.4. Minimize the output signal power of the adaptive phase array
antenna according to limit condition
Wopt   R I  R n  W0
1

(1.4)

1.6.1.5. Minimum power eigencanceler standard– MPE[32]





wMPE  Qv v QvH C CH Qv QvH C
x1(n)

w11

Z-1
w12

Z-1
w13

1

Z-1

Z-1

w1k-1

w1k

Z-1

Z-1

w2k-1

w2k

f

(1.5)
FIR

∑
x2(n)
w21

Z-1
w22

Z-1
w23

∑

y(n)

∑
xM(n)
Z-1
wM1

wM2

Z-1

Z-1

wM3

wMk-1

Z-1
wMk

∑

Fig 1.13. Strucure of space-time filter.
Effective anti-jamming algorithms in GNSS systems

1.6.2.1. The algorithm of space-time according to the minimum of limited power
6


The structure of space-time filter is shown above Fig 1.13.

1.6.2.2. The space-time algorithm of minimum mean square deviation (MMSE).
1.7. Overview of domestic and foreign research on issues related research
1.8. Chapter conclusion 1
On that basis, the PhD student has researched and assessed the
anti-jamming effect of the MPE optimal standard for GNSS receiver on
phase array antennas in chapter 2 of the thesis and is the basis for
proposing solutions to correction errors heterogeneity between channels
on the phase array antenna in Chapter 3 of the thesis.
CHAPTER 2: STUDY AND EVALUATE THE PERFORMANCE OF ANTIINTERFERCING OF MPE OPTIMAL STANDARD FOR GNSS RECEIVER
2.1. Signal and noise formation on the receiver elements of adaptive
phase array antennas
The formation of useful input signals

x m   I x m   jQx m 

(1.6)

Noise model


I I (n )  Re exp  j I n t  j I 





Q (n )  Im exp  j I n t  j I 


 I
2.2. Calculate transmission latency in the environment







(1.7)

Fig 2.2. Array antenna geometry structure three elements.
1 x (m ) sin  cos   y(m ) sin  sin  
(m )  
(1.8)

c x (m ) cos  sin 

2.3. Standardize signals and noise
7


x norm (m, n) 

x (m, n) 2

(1.9)

I2  Q2

2.4. Demonstration of noise and GNSS satellite signals on array
antennas with 3 elements and 9 elements
1



A3 (, )  
exp j 2 f0 2(R / c)sin  cos    / 3



exp  j 2 f0 2(R / c)sin  cos 











,










(1.10)



1




exp j 2 f0 2(R / c ) sin  cos   sin  sin  




exp  j 2 f0 2(R / c )sin  cos 




exp j 2 f0 2(R / c ) sin  cos   sin  sin 




A9 (, )  exp  j 2 f0 2(R / c )sin  sin 



exp j 2 f0 2(R / c )  sin  cos   sin  sin 




exp  j 2 f0 2(R / c )( sin  cos )




exp j 2 f0 2(R / c ) sin  cos   sin  sin 



exp  j 2 f0 2(R / c )( sin  sin )
























































(1.11)

2.5. Heterogeneous model of parameters on receiver channels of
phase array antennas.
The group delay model of medium frequency filter.
Create white
noise

Normalize and
add average
values

Low Pass Filter
LPF

Fig 2.8. Algorithm to create group delay.


1, f  F
am
K LPF ( f )  


0, f  Fam



f

f

0

g 0

( f )  0   GD( f )df  0   GD(g )f

In which f  200Hz .
8

Group Delay

(2.24)

(2.27)

Modeling amplitude heterogeneity of medium frequency filter.
A(f )  1  y(t)(1 A)
(2.28)
Which  A determines the maximum oscillation range of
frequency-specific heterogeneity.
The method adds to the heterogeneity of the channel
transmission coefficients of adaptive phase array antennas.


A(m, k ) ej(m,k ), k  k0 ;


K (m, k )  
(2.29)
0, k0  1  k  N  k0 ;


 j (m,k )

A(m, k ) e
, k  N  k0  1,



Fig 2.4. The diagram takes into account the heterogeneity of the receiver
channels in the adaptive phase array antenna.
Is
Ih
S 
I 

y(m, n )     .si (m, n )     .Ii (m, n )  n(m, n )
(2.30)
 N 
 N 
i 1

i

i 1

i

2.6. Determined non-working areas and dependence of non-working
areas on receiver sensitivity with array antennas
The principle of building a non-working zone is to determine the
area that satisfies the inequality:

S / N (, )out  (S / N )threshold

(2.31)

In order to determine the parameters of non-working zones of the
receiver, it is necessary to scan the entire space to receive the GNSS signal,
following the angles ,   .
When scanning, the directional values ( D ) of the phase array
antenna in the direction ( ,  ) are determined:
D(, )  WT A(, )

After standardization D(, ) , we have:
9

(2.37)


D Norm (, ) 

D(, )
D(0 , 0 )

(2.38)

With: (0,0) is the angle values point to the strongest useful signal.
To determine the non-working zones of the receiver, the SINR
input ratio in the direction (,) at the output of the receiver must be less
than the protection factor, ie:
Ps_out
10 lg K
(,  )  S / (N  I )
threshold
 PI_out  N out

(2.42)

i 1





 D2 (, )

Ps_out
  S / N  I 
10 lg  2
(2.45)

threshold
 D (0 , 0 ) K


 PI_out  N out 

i 1
The left of the expression (2.45) can be considered as the spatial
surface. From there, by scanning space, the area of the upper hemisphere
will be calculated, satisfying conditions (2.45). Then, according to the
condition (2.31), determine the working or non-working zone of receiver
2.7. Evaluate the effectiveness of anti-jamming GNSS receiver uses
the MPE standards when the receive channel is homogeneous
with 3 and 9 elements phase array antenna
Evaluate the noise power compression coefficient and SINR
output ratios for GNSS receivers
Evaluate non-working area of the receiver when the receive
channel is homogeneous
 The non-working zones of GNSS receiver using three elements
adaptive phase array antenna
+ In case there is only one source of interference: the elevation angle is
850, azimuths of noise sources are equally distributed

10

Fig 2.16. The working zone at the receiver protection factor is -30dB and 40dB - 1 noise
+ In case there are two sources of interference: the elevation angle is 850,
azimuths of noise sources are equally distributed.

Fig 2.18. The working zone at the receiver protection factor is -30dB
and -40dB - 2 noise
 The non-working zones of GNSS receiver using 9 elements adaptive
phase array antenna.
For 9 elements adaptive phase array antennas, PhD student also
simulates the surface SINR ratio on the antenna output with the number
of variable noise sources of 1, 2, 6, 8 and create the non-working zone of
GNSS receiver with receiver protection factor of -30dB and -40dB
respectively. With assumptions as in the case of 3 elements antenna
+ In case there is only one source of interference: the elevation
angle is 850, azimuths of noise sources are equally distributed.

Fig 2.21. The working zone at the receiver protection factor is -30dB
and -40dB - 1 noise
11


Fig 2.23. The working zone at the receiver protection factor is -30dB
and -40dB - 2 noise

Fig 2.25. The working zone at the receiver protection factor is -30dB
and -40dB - 6 noise

Fig 2.27. The working zone at the receiver protection factor is -30dB
and -40dB - 8 noise

Compare non-working zones of GNSS receiver for 9 elements
adaptive phase array antenna with distance 2/3.56

Fig 2.29. The working zones at the receiver protection factor is -30dB - 8 noise.
12


Su phu thuoc vung khong lam viec vao ty so bao ve - anten 9 phan tu
100

100

1 nhieu - lamda/2
8 nhieu - lamda/2

90
80

80

70

70

60

60

50

50

40

40

30

30

20

20

10
0
-15

Su phu thuoc vung khong lam viec vao ty so bao ve
1 nhieu - d=2lamda/3.56
8 nhieu - d=2lamda/3.56

90

10

-20

-25

-30

-35

0
-15

-40

Ty so bao ve, dB

-20

-25

-30

-35

-40

Ty so bao ve, dB

Fig 2.30. Dependence of nonworking area on protection factor

Fig 2.31. Dependence of nonworking area on protection factor

in case d= /2.

in case d= 2/3.56.

%

%

Compare the non-working areas of GNSS receivers for anten 7 and 9
elements adaptive phase array antenna using the MPE standard

Fig 2.33. Compare the nonFig 2.34. Compare the dependency
working zone of the GNSS receiver
of the non-working zone on the
with the number of antenna
receiver protection factor with 3 and
elements changed
9 antenna elements
Some conclusions about working zone of the phase array antenna
2.8. Evaluate the quality of signal reception on 9 elements adaptive
phase array antenna when the channel is heterogeneous
Evaluate the signal reception quality when the channel is
heterogeneous in phase
The results are simulated with the case that the receiver channel
is not distorted (homogeneous) and heterogeneous in phase between the
receiver channels and the phase amplitude changes respectively: 50 and 100

13


He so nen cong suat nhieu

70

Ty so SINR dau ra

0

60
-10
25dB

50

15dB
-20

40
30

-30

20

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN pha - DltPh0=5
MPE - BĐN pha - DltPh0=5
MMSE - BĐN Pha - DlePh0=10
MPE - BDN Pha - DltPh0=10

10
0

-40

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - DltPh0=5
MPE - BĐN - DltPh0=5
MMSE - BĐN Pha - Dltpha =10
MPE - BĐN Pha - Dltpha =10

-50

-10

-60
0

2

4

6

So buoc tinh toan

8

10

12

0

10 4

2

4

6

So buoc tinh toan

8

10

12
104

Fig 2.35. Compare noise
Fig 2.36. Compare the SINR
compression coefficient when
ratio when heterogeneous in
heterogeneous in phase
phase
Evaluate the quality of the signal reception when channel is
heterogeneous in amplitude
Simulate anti-jamming characteristics when has heterogeneous
between channels on phase array antennas with two optimal standards

MMSE and MPE compared to cases when the receiver channel uses 9
elements adaptive phase array antennas.

Fig 2.37. Compression ratio when
there is distortion of 0.1

Fig 2.38. Output SINR ratio when
there is distortion of 0.1

Fig 2.39. Compression ratio when Fig 2.40. Output SINR ratio when
there is distortion of 0.5
there is distortion of 0.5
2.8.3. Compare the working zone of GNSS receiver when the channel
is heterogeneous with a 9 elements phase array antenna
2.9. Evaluate the convergence of the algorithm through the number of adaptive steps
14


2.10. Conclusion of chapter 2
Chapter 2 has modeled GNSS signal, noise and receiver channel
of array antenna 3 and 9 elements. Simulate anti-jamming characteristics
such as: Noise compression ratio; SINR ratio on the antenna output and
develop a schematic, non-working area of the GNSS receiver for 3 and 9
elements adaptive phase array antennas. Comparing and evaluating the
above parameters with the 4 and 7 elements antenna model has been
studied in the project [45]. From that, we can conclude that the 9 elements
adaptive phase array antenna has the best anti-interference quality.
Thereby, as a basis for evaluating and proposing methods to
correct heterogeneity errors between receivers for satellite-receiver
receivers presented in Chapter 3 of the thesis.

CHAPTER 3: SOLUTIONS FOR CORRECTING
HETEROHENEOUS ERROR BETWEEN CHANNELS ON PHASE
ARRAY ANTENNA FOR SATELLITE POSITIONING RECEIVERS
As mentioned, the heterogeneity between the channels on the
phase array antenna has a great influence on the reception quality,
reducing the reliability of satellite positioning receivers. To overcome the
effects of this heterogeneity, it is necessary to design a multi-channel antijamming filter with the automatic error correction function. Chapter 3 will
propose the use of an MPE optimum standard (with lower computational
complexity, faster algorithm convergence) instead of the MMSE
optimization standard used in [45] and the use of antennas. 9 elements
replacement for 7 elements antenna (more resistant to interference and
non-working area also optimized than antenna 4 and 7 elements).
3.1. Two-stage error channel correction method using MPE standard
Model, structure method
The structure of two-stage filter based on auto-correction and
algorithm flowchart to calculate receiver anti-jamming characteristics
using the above algorithm turn is shown in Fig 3.1 and Fig 3.2

15


SF
x1(n)

Z-1

w11

w12

Z-1

Z-1

Z-1

w1N-1

w13

FIR

w1N

k1

∑
x2(n)

Z-1

w21

w22

Z-1
w23

TF

Z-1

Z-1

w2N-1

w2N
y(n)
k2

∑




xM(n)

Z-1
wM2

wM1

Z-1

Z-1

Z-1

wMN-1

wM3



wMN

kM

∑



∑

MPE optimal
standrad

Fig 3.1. Two-stage filter structure based on auto-correction.
The output of this filter is represented by the formula:
M

N

i 1

j 1

y n    ki (n) vij x n  j  1

(3.1)

The result is:

W  VK

(3.7)

W0  CST (CTST CST )1b1

(3.8)

16


Begin
Enter the input
parameters of the system
Formation of input effects during
processing period
Add heterogeneity on the
receiver channel

Set statistics to 0

jT=1

jT=jT+1

No
jT ≥ NumTest

Two-stage error channel
correction method using
MPE standard

Yes
Calculation of
anti-jamming
properties on
antenna
output

Display results and draw
figures

End

Fig 3.2. Flowchart of Two-stage error channel correction algorithm using MPE standard
17


Stage of signal space processing (automatic error correction).
Step 1:
The signal at the output of the interferer is described by the following
matrix:

y(1)  WT (1)X(1)

(3.11)

y(r )  WT (r )X(r )

(3.13)

Step r  2...q :

Stage of signal time processing (giai đoạn vận hành).
Step q  1 :
The output of the space - time filter is described by the matrix system:

y(q  1)  ZT (q  1)K(q  1)

(3.14)

Step r  q  2 q  p :
The output of the space - time filter is described by the matrix system:

y(r )  ZT (r )K(r )

(3.19)

Simulation results of two-stage error channel correction
method based on auto-correction using MPE standard
To evaluate the signal reception quality of GNSS receivers when
using the two-stage MPE error correction method on the basis of selfcompensation to correct heterogeneous errors between channels on the
phase array antenna. PhD student simulates the anti-interference
characteristics of GNSS receivers when applying the above method in the
case of homogeneous and heterogeneous channels.
He so nen cong suat nhieu thuat toan xu ly khong gian - thoi gian

90

-10

80

-15

Ty so SINR dau ra

-20

70

15dB 7dB

-25

60

10dB

-30
50

30dB

50dB

-35

40
-40
30

-45
MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - Khong hieu chinh

20
10

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - BĐN - Khong hieu chinh

-50
-55

0

-60
0

2

4

6

8

So buoc tinh toan

10

12

0

104

2

4

6

8

So buoc tinh toan

(a)

(b)

18

10

12
104


Fig 3.2. Noise compression factor and SINR ratio situation 1
He so nen cong suat nhieu thuat toan xu ly khong gian - thoi gian

90

-10

80

-15

Ty so SINR dau ra

-20

70

-25

60

9dB

-30
50
-35
40
-40
30

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - BĐN - Khong hieu chinh

-45
MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - Khong hieu chinh

20
10

-50
-55

0

-60

0

2

4

6

8

10

12

0

2

4

104

So buoc tinh toan

6

8

10

12
104

So buoc tinh toan

(a)
(b)
Fig 3.3. Noise compression factor and SINR ratio situation 2
He so nen cong suat nhieu thuat toan xu ly khong gian - thoi gian

70

Ty so SINR dau ra

0

60

-10

50

-20

40
-30
30
-40
20

0

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - Khong hieu chinh

-50

MMSE - Dong nhat
MPE - Dong nhat
MMSE - BĐN - Co hieu chinh
MPE - BĐN - Co hieu chinh
MMSE - Khong hieu chinh

10

-60

-10

-70
0

2

4

6

8

10

12

0

2

4

10 4

So buoc tinh toan

6

8

10

12
10 4

So buoc tinh toan

(a)
(b)

Fig 3.4. Noise compression factor and SINR ratio situation 3
He so nen cong suat nhieu thuat toan xu ly khong gian - thoi gian

40

-15

35

-20

Ty so SINR dau ra

-25

30

-30
25
-35
20
-40
15
-45
MMSE - BĐN - TH1
MPE - BĐN - TH1
MMSE - BĐN - TH4
MPE - BĐN - TH4

10

5

MMSE - BĐN - TH1
MPE - BĐN - TH1
MMSE - BĐN - TH4
MPE - BĐN - TH4

-50
-55

0

-60
0

2

4

6

8

10

12

0

2

4

10 4

So buoc tinh toan

6

8

10

12
104

So buoc tinh toan

(a)
(b)
Fig 3.5. Noise compression factor and SINR ratio situation 4
He so nen cong suat nhieu thuat toan xu ly khong gian - thoi gian

35

-15

30

-20

Ty so SINR dau ra

-25

25

-30
20
-35
15
-40
10
-45
MMSE - TH3
MPE - TH3
MMSE - TH5
MPE - TH5

5
0

MMSE - TH3
MPE - TH3
MMSE - TH5
MPE - TH5

-50
-55

-5

-60
0

2

4

6

8

So buoc tinh toan

10

12

0

10 4

2

4

6

8

So buoc tinh toan

10

12
104

(a)
(b)
Fig 3.6. Noise compression factor and SINR ratio situation 5
Statistics of simulation results
19


3.2. Self-compensating error channel correction method using MPE standard
Model, structure method
x1(n)

Z-1

w11=1

Z-1

w12=1

Z-1

w13=1

w1N-1=1

Z-1

FIR

w1N=1
1

∑
x2(n)

Z-1

w21

Z-1

w22

Z-1

Z-1

w23

w2N-1

w2N

k2

∑




xM(n)

Z-1

wM1

Z-1

wM2

Z-1

wM3

wMN-1




y(n)
∑

Z-1

wMN

kM

∑
MPE optimal
standrad

Fig 3.10. Automatic noise compensation structure with calibration of
heterogeneous channels on phase array antenna.
The output of this filter is represented by the formula:
M

N

i 1

j 1

y n    ki (n ) vij x n  j  1

(3.22)

The expression (3.22) will be rewritten in vector form

y(n)  XT W

(3.23)

W  V K

(3.24)

In which:

20


Begin
Enter the input
parameters of the system

Formation of input effects during
processing period

Add heterogeneity on the
receiver channel

Set statistics to 0

jT=1
jT=jT+1

No
jT ≥ NumTest

Self-compensating error
channel correction method
using MPE standard

Yes
Calculation of
anti-jamming
properties on
antenna
output

Display results and
draw figures

End

Fig 3.11. Flowchart of self-compensating error channel correction algorithm
21


The structure of the automatic noise compensator with the
correction of heterogeneous receiver channels and algorithm flowchart to
calculate receiver anti-jamming characteristics using the above algorithm
turn is shown in Fig 3.10 and 3.11.
Simulate and evaluate the results of error correction methods
in different cases
He so nen nhieu

100

Ty so SINR dau ra – tu bu tru

-10

90
-15
80
-20
70
-25
60

Dong nhat
BĐN - Khong bu tru
BĐN - Co bu tru - MMSE
BĐN - Co bu tru - MPE

50

-30
-35

40

Dong nhat
BĐN - Khong bu tru
BĐN - Co bu tru - MMSE
BĐN - Co bu tru - MPE

-40
-45

30

-50
0

2

4

6

8

10

12

0

2

4

104

So buoc tinh toan

6

8

10

12
10 4

So buoc tinh toan

(a)
(b)
Fig 3.10. Noise compression factor and output SINR ratio situation 1
He so nen nhieu

50

Ty so SINR dau ra – tu bu tru

-10

2 nhieu
6 nhieu
8 nhieu

45
-15
40
-20
35
-25
30
-30
25

2 nhieu
6 nhieu
8 nhieu

-35

20

-40
0

2

4

6

8

10

12

0

2

4

104

So buoc tinh toan

6

8

10

12
10 4

So buoc tinh toan

(a)
(b)
Fig 3.11. Noise compression factor and SINR ratio situation 2
He so nen nhieu

70

Ty so SINR dau ra – tu bu tru

-10
BĐN - MPE - 15dB
BĐN - MPE - 40dB

65

-15

60
55

-20

50

-25

45

-30

40

-35
-40

35

BĐN - MPE - 15dB
BĐN - MPE - 40dB

-45
30
-50
0

2

4

6

8

So buoc tinh toan

10

12

14

0

104

2

4

6

8

10

12

So buoc tinh toan

(a)
(b)
Fig 3.12. Noise compression factor and SINR ratio situation 3

22

14
10 4


He so nen nhieu

Ty so SINR dau ra – tu bu tru

-10

8 nhieu - TH4
8 nhieu - 40dB

-15
-20
-25
-30
-35
101
-40

8 nhieu - TH4
8 nhieu - 40dB

-45
-50

0

2

4

6

8

So buoc tinh toan

10

12

0

104

2

4

6

8

So buoc tinh toan

10

12
10 4

(а)
(b)
Fig 3.13. Noise compression factor and SINR ratio situation 4
3.3. Evaluate the working zone of GNSS receiver when correction
heterogeneity error
3.4. Conclusion of chapter 3
In this chapter, it is proposed to improve methods of correcting
heterogeneity between receivers on adaptive phase array antennas using
MPE adaptive standard instead of MMSE standard proposed in the project
[45]. Through simulation and analysis results for different signal and noise
simulation situations, it is shown that the proposed methods have better
efficiency, faster algorithm convergence speed. When applying a twostage error correction method on the basis of self calibration as well as a
self-compensation method with a 9 elements adaptive phase array antenna
to the MPE standard for both homogeneous and non-homogeneous
channels, then depending on different situations noise ratio SINR better
than standard MMSE from 2dB to 5dB.
CONCLUSION
A) The main results of the thesis.
1. Building mathematical models of signals in GNSS systems under

the influence of broad-band noise and narrow-band noise.
2. Simulate and calculate the non-working zone of the GNSS
receivers by constructing graphs of the SINR ratio on outputting of phase
array antenna with 3 and 9 elements, the dependency of the non-working
zone on the receiver protection factor.
3. Proposed methods to correct heterogeneous channel errors on 9
elements phase array antenna with the distance between the elements is

23