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 R1RA

(1.1)

1.6.1.2. Minimum mean square errors standard according to limit

condition

Wopt R1 R A 1 CT R1R A C / CT R1C

(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 ) ej(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 ) .si (m, n ) .Ii (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 VK

(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

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 R1RA

(1.1)

1.6.1.2. Minimum mean square errors standard according to limit

condition

Wopt R1 R A 1 CT R1R A C / CT R1C

(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 ) ej(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 ) .si (m, n ) .Ii (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 VK

(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

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