This paper presents the author''s research results for heterogeneous channel error correction on phase array antennas in Global Navigation Satellite System in order to improve noise quality for terminals. The error correction method proposed by the author is a two-stage algorithm with automatic correction and error correction algorithm based on self-compensation.
Trang 1PROPOSED METHODS FOR HETEROGENEOUS ERROR
CORRECTION OF RECEIVE CHANNEL FOR GNSS ANTI-INTERFERENCE DEVICES
Abstract: This paper presents the author's research results for heterogeneous
channel error correction on phase array antennas in Global Navigation Satellite
System in order to improve noise quality for terminals The error correction method
proposed by the author is a two-stage algorithm with automatic correction and
error correction algorithm based on self-compensation
Keywords: Heterogeneity on phase array antenna reception channel; Anti-jamming GNSS; Group delay
1 INTRODUCTION
Currently, Global Navigation Satellite Systems (GNSS) play an increasingly important role in all key sectors of both civil, industrial and national security However, signals from satellites positioned to receiver inputs are greatly reduced by many objective and subjective factors Therefore, the studies on improving quality of receivers have been and continues to be attracted by many domestic and international researchers
Solutions using phased array antennas have been widely applied However, one of the technical problems when processing signals on phase array antennas is the heterogeneity between receiving channels This is an unavoidable problem due to the fact that the same phase rotators cannot be produced The heterogeneity on the adaptive phase array antenna receiver channel is represented by the initial phase fluctuations of oscillations, bandwidth fluctuations and the difference in receiver-amplitude-frequency characteristics These factors have a great influence on the anti-interference quality for the terminals in GNSSs
In order to overcome the effect of this heterogeneity, it is necessary to design a multi-channel anti- interference filter by employing heterogeneous error correction function
In this paper, the author proposes two heterogeneous error correction algorithms on receiver channel: A two-phase algorithm with automatic error correction and a heterogeneous error correction algorithm based on self-compensation These algorithms are built based on Frost algorithm with the minimization of signal output over antenna output
This paper consists of four parts: part 1 of the paper raises the question, part 2 presents the theoretical analysis of the channel error correction methods using a two-stage algorithm based on automatic correction and using heterogeneous error correction algorithm based on self-compensation, part 3 shows the results of simulation together with the evaluation of results, part 4 concludes the article and proposes next research direction
2 THEORY 2.1 Method of heterogeneous channel error correction in two stages based on automatic error correction
2.1.1 System model
The structure of the two-stage filter is shown in Figure 1 in which SF - space filter,
TF - time filter The anti-jamming process establishes the minimum point of direction
diagram towards the noise source and the peak of schema towards the signal source by adjusting a time weighting vector K , T i i1,M The heterogeneous error correction of receiver channels is then performed by adjusting the space weighting vector V vector, T
Trang 2i M , jN The Filter works in 2 modes: automatic error correction and operational mode
Fig 1 The two-stage filter structure with automatic error correction
The correction is performed for a period of time determined by the time stability of the adaptive phase array antenna receivers According to the test signal, it produces a uniform spectrum within the processing range The test signal may be white noise transmitted through a bandpass filter with linear frequency response and phase response
An important feature of the proposed method is that during the time of error correction,
it takes place not only in correcting the amplitude-frequency and phase-frequency characteristics of the receiver channels but also eliminating the test signal and useful signals (if it does not coincide with the azimuth of the test signal) transmitted to the output Thus, the automatic error correction filter suitable for signal transmission is useful
in continuous mode
The output of filter is expressed as:
Where N is the number of time branches, M is the number of receiver channels, n is
discrete time, k , i v are the elements corresponding to the weight vector of space – time ij
process ( )x n is vector of the input signal and noise i
Let consider the stage of signal processing space as a separate case of time space processing when ij( ) const
n
v n , then the expression (1) will be rewritten in vector form
as ( )yn X W T
Where X is the class vector of the input signal and noise: T
Trang 31
T
j x j x ji x jM
W is the column vector of weights with elements w ij k v i ij:
1
1
T
j w j w ji w jM
The result is WVK where is the product of vectors by each element
When using high-power broadband signal as a test signal as shown above, it is clear that the automatic balance of the filter channels will be meaningful if the processing power
at the filter output is minimized By optimizing the general adaptation of all coefficients
ij
w while still complying with the same conditions, then the calibration error is optimized
If it is ensured that the test signals being at the input of channels has the same initial phase and k i 1,i1 M then the channels will be aligned to the original phase
At this stage, it is possible to use any adaptive criterion to adjust the weight k when i
( ) const
ij
v n ; in particular, the standard for minimum output power not accompanied by
a useful signal is similar The initial weight vector (NM,1) is in the form:
1
0 ( T ) 1
ST ST ST b
In the case b , the directional schema of the initial antenna is isotropic To prevent 1 1 space-time interference, the limit matrix CT ST is represented in the form:
1 2
C C C C C , with N is the number of branches of the filter of
finite pulse characteristics in each antenna channel, and the component vectors C in the j
limit can be determined from necessary space-frequency limits
The adaptation of the weight vector of time filter is carried out in the loop number p , and the weight vector adaptive of the space filter is performed in loop number q , and the
process is then repeated
+ Signal space processing stage (auto error correction stage)
Step 1:
The signal at the output of the interferer is represented by the following matrix:
(1) (1) (1) ( (1)
(1)
T
N
y
K
K
where K is the weight vector used for the space filter:
Trang 4M
k k
At this step, K(1)1 is the unit vector Hence, V(1)W(1) We can rewrite the formula (2) in the form:
(1) T(1) (1)
*
(1)(1) (0) (1) T(1)
p
, equivalent to the average calculation in the period of the corresponding period or in the
period p T seconds and T is the sampling period
Step r 2 q:
The signal at the output of the interferer is represented by the following matrix:
( ) ( ) ( ) ( ( )
( )
T
N
r
r
K
K
At this step, ( )Kr 1 is the unit vector Hence, ( )Vr W( )r We can rewrite (4) in the form: ( ) T( ) ( )
The correlation matrix is shown corresponding to the calculation according to the formula:R( )r (1) (Rr 1) X*( )r XT( )r
+ Operation stages
Step q : 1
The signal at the output of the interferer is represented by the following matrix:
(q1) T(q1) (q1)
With ( )Zr , T( 1)
i q
V are respectively the output signal and the coefficients of the time
filter on the channel i at step q 1
The weight vector in formula (5) can be calculated according to the formula:K(q1)P K[ 1( )q zR Kzz 1( )]q K 0
For which the initial weight vector can be defined as K0 1 0 0, and z
calculated as the own value of the matrix Rzz(q 1), or as 1 /diag(Rzz(q 1))
*
zz q zz q q q
Step r : q 2 q p
The signal at the output of the interferer is represented by the following matrix: ( )yr ZT( ) ( )r Kr
At this step, the time coefficients are not changed, therefore ( )Vr V(q1)V( )q , Hence K( )r P K[ 1(r 1) zR Kzz 1(r1)]K 0
Trang 5where is defined as the maximum specific value of the matrix z Rzz( )r , or in the form
1 /diag(Rzz( ))r , ( ) (1 ) ( 1) *( ) ( )T
zz r zz r r r
Step p q 1 2q : Output signal and weight vector can be calculated as in the step: p
2
r q
Step: 2 q2p 1 3q2p. The output signal and weight vector are calculated as at
steps:r The process continues so on q 2 q p
2.1.2 Evaluation of simulation results
Computer simulation on MATLAB environment is performed for the case p 50000, 50000
q with signal and noise conditions as follows:
Scenario 1: There is a broadband noise operating on the horizontal plane with a relative power of 40dB The noise is unstable (noise spectrum width of 60000 initial 16Mhz time samples, noise spectrum width of 65000 time samples after 8Mhz)
Scenario 2: There is a broadband noise operation on the horizontal plane with the relative capacity of 40dB Sample signal is used for the comparison selection with 8MHz band Unstable noise (the noise spectrum of the original 60000 time samples is 8 MHz and the noise spectrum of the time samples from 60001 to 125000 is 16Mhz)
Scenario 3: A sample signal of 40dB wide range is transmitted for time samples from 1
to 50000 and from 100001 and the azimuth of the sample signal source is 00 There is broadband noise operating on the horizontal plane with public 40dB relative power The spectral width of noise is 16Mhz and the noise emitter is turned on starting from the 50001
to 100000 time samples and the noise source is 900
Scenario 4: There are 6 broadband noise distributions as in the previous section Sample signal for comparison is selected within 8Mhz range The noise is unstable (the width of the interference spectrum to the 60000 time sample is 8Mhz with the noise spectrum of 65,000 samples after 16Mhz)
a Case of homogeneous receiver channel
For the case of a homogeneous channel, A number of typical situations for a disturbance such as situations 1,2,3 and the situation where there are 6 broad-band noise such as the situation 4 is simulated In order to conduct basic comparison, the evaluation with simulation results for case of receiver channel is heterogeneous
Scenario 1
Trang 6(a) (b)
Scenario 2
-10
0
10
20
30
40
50
60
70
80
Two stages algorithm - Appelbaum (1)
Two stages algorithm - Frost (2)
STAP - Appelbaum (3)
STAP - Frost (4)
(1)
(1)
(2)
(2)
(3)
(3) (4) (4)
-60 -55 -50 -45 -40 -35 -30 -25 -20 -15
Two Statges algorithm - Appelbaum (1) Two Statges algorithm - Frost (2) STAP algorithm - Appelbaum (3) STAP algorithm - Frost (4)
(1)
(2) (3)
(1)
Scenario 3
-10
0
10
20
30
40
50
Two stages algorithm - Appelbaum (1) Two stages algorithm - Frost (2) STAP algorithm -Frost (4)
(1)
(2)
(3) (4)
-60 -50 -40 -30 -20 -10
Two Statges algorithm - Appelbaum (1) Two Statges algorithm - Frost (2) STAP algorithm - Appelbaum (3) STAP algorithm -Frost (4)
(4)
(3)
(1) (2)
Scenario 4
Fig 2 Interference compression ratio (a) and output SINR ratio (b) - homogeneous
b Case of heterogeneous receiver channel
Where the receiver channel is heterogeneous and the filter order number is 4 Heterogeneous characteristics of the channels are as follows: amplitude of the initial phase, amplitude-frequency characteristics, bandwidth of the Mid-range amplifier filter in
Trang 7receiver channels are 50, 0.5dB, 200kHz, respectively The correlation interval is heterogeneous and the frequency response of the mid-frequency amplifier filters is 1 Mhz The results are simulated for the signal and noise case with the assumption similar to the Scenarios 1,2,3,4 above:
-10
-5
0
5
10
15
20
25
30
35
Two stages algorithm - Appelbaum (1) Two stages algorithm - Frost (2) STAP - Appelbaum (3) STAP - Frost (4)
(4)
(4)
Scenario 1
-10
-5
0
5
10
15
20
25
30
35
Two stages algorithm - Appelbaum (1)
Two stages algorithm - Frost (2)
STAP - Appelbaum (3)
STAP - Frost (4)
(1)
(1)
(2)
(2) (3)
(4) (3) (4)
-60 -55 -50 -45 -40 -35 -30 -25 -20
Two Statges algorithm - Appelbaum (1) Two Statges algorithm - Frost (2) STAP algorithm - Appelbaum (3) STAP algorithm -Frost (4)
(3) (4) (1) (2)
(1) (3) (4)
(2)
(2)
Scenario 2
10 4
-20
-15
-10
-5
0
5
10
15
20
25
30
35
interference compression ratio
calculation steps
Two stages algorithm - Appelbaum (1)
Two stages algorithm - Frost (2)
STAP - Appelbaum (3)
STAP - Frost (4)
(2)
(1)
(3) (4)
(3) (4)
-80 -70 -60 -50 -40 -30 -20
SINR output Ratio
Two Statges algorithm - Appelbaum (1) Two Statges algorithm - Frost (2) STAP algorithm - Appelbaum (3) STAP algorithm -Frost (4)
(4) (3) (1) (2)
(2) (1) (3) (4)
Scenario 3
Trang 8calculation steps 10 4
-10
-5
0
5
10
15
20
25
30
Thuat toan hai giai doan - Appelbaum
Thuat toan hai giai doan - Frost
Xu ly khong gian - Appelbaum
Xu ly khong gian - Frost
(1)
(1) (2)
(2)
(3)
(4)
(4) (3) (2)
-60 -55 -50 -45 -40 -35 -30 -25 -20 -15
Two stages algorithm - Appelbaum (1) Two stages algorithm - Frost (2) STAP algorithm -Frost (4)
(3) (4) (2)
(4)
(2)
(1)
(3) (4)
Scenario 4
Fig 3 Interference compression ratio (a) and output SINR ratio – heterogeneous case
2.2 Method of heterogeneous channel error correction based on self-compensating blocks
In the proposed algorithm above, although the anti-interference characteristics are better than even when the channel was homogeneous and when the channel loses its consistency and instability It is still possible to see that there is still specific deterioration
of anti-interference Although this declines in very short time, for devices that require high frequency of information updates (e.g devices moving at high speeds), this reduction range can cause the loss of information control Therefore, the author proposes the heterogeneous channel error correction algorithm based on self-compensating blocks
2.2.1 System model
The filter structure for correcting the heterogeneity of receiver channel based on self-compensation is described in Fig 4
Fig 4 Filter structure corrects heterogeneity receiver channel based on
self-compensation
Trang 9The output of this filter is described by the expression (6) as following
1 1
1
M K
mk
m k
The mixtures of input signals are described by following expressions
With the automatic compensation of all coefficients in the first channel (standard channel) which are equal to 1; hence, the weight vector for an M element antenna is represented in the form:
1
T
Where k 1 N N, is the number of time branches of the filter with finite pulse characteristics Limit vector C and initial weight vector for automatic compensation are T
given by formula (1.8) and (1.9):
7
T
N
(8)
7
T
N
(9)
Where N is the number of time branches of the filter with finite pulse characteristics 2.2.2 Evaluation of simulation results
The anti-interference characteristics are calculated in the case of 4 time branches with automatic compensation blocks on 7 channels The sample signal of broad-band noise (16MHz) is used
The conditions of noise and signal are assumed as follows:
Direction of the satellite signal is (00,00), the value in the first position is the azimuth in the second position the offset angle Relative power of useful signal is -20dB (from individual noise in the processing range)
The relative total power (from individual noise in the processing range) of broad-band noise is 40dB and all sources have the same power The direction of interference sources is:
Scenario 1: offset angles = [850 750 800 450 820 600] and azimuths are evenly distributed
Scenario 2: all noise on the horizontal plane and the azimuth is evenly distributed
Sampling frequency is 25 MHz; transmission bandwidth is 16 Mhz
Trang 101 2 3 4 5 6 7 8
10
20
30
40
50
60
70
80
Number of broad-band noise sources
Scenario 1 - self-compensating
Scenario 1
The dependence of the interference compression ratio
over the number of broad-band noise sources
-40 -35 -30 -25 -20 -15 -10 -5
Scenario 1 - self-compensating Scenario 1
The dependence of SINR ratio over the number of broad-band noise sources
Number of broad-band noise sources
Fig 5 The dependence of the interference compression ratio (a) and the SINR ratio at the
output (b) over the number of broad-band noise sources
10
15
20
25
30
35
Number of broad-band noise sources
Scenario 1 - self-compensating
Scenario 1
The dependence of the interference compression ratio
over the number of broad-band noise sources
-35 -30 -25 -20 -15
Scenario 1 - self-compensating Scenario 1
The dependence of SINR ratio over the number of broad-band noise sources
Number of broad-band noise sources
Fig 6 The dependence of the interference compression ratio (a) and the output SINR ratio
(b) over the number of broad-band noise sources
In Figures 3 and 4, the interference compression ratio and the SINR ratio are valued for the self-compensator where Frost algorithm is applied The distance between elements is
2 / 3.56
d with solid lines representing the symbol of automatic compensator and the dashed lines for STAP algorithm without compensation
2.3 Evaluation of the non-working zone of GNSS receivers
To assess the non-working zone of receiver using the two proposed algorithms above, the non-working zone simulation of the GNSS receiver for cases of phase distortion, amplitude distortion or both phase distortion and amplitude distortion and the use of two proposed algorithms are stimulated to correct heterogeneous errors on the receiver channel with the effect of 6 broad-band noise sources for 7-element array phase antenna with the distance between antenna elements as d 2 / 3, 56
By looking at Fig 7, the curve of the non-working zone dependency on the receiver's protection ratio using the two-stage algorithm shows better error correction than the self-compensating algorithm The curve of non-working zone using both proposed algorithms
is asymptotic to the curve of non-working zone where the receiver channel is homogeneous and is significantly better than the curves where the channel is heterogeneous (red, pink and blue lines, respectively) Therefore, we may conclude that