# A Robust Method to Suppress Jamming for GNSS Array Antenna Based on Reconstruction of Sample Covariance Matrix

Authors: Yanyun Gong; Ling Wang; Rugui Yao; Zhaolin Zhang
Journal: International Journal of Antennas and Propagation
 (2017)

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## Abstract

The Global Navigation Satellite System (GNSS) receiver is vulnerable to active jamming, which results in imprecise positioning. Therefore, antijamming performance of the receiver is always the key to studies of satellite navigation system. In antijamming application of satellite navigation system, if active jamming is received from array antenna main-lobe, main-lobe distortion happens when the adaptive filtering algorithm forms main-lobe nulling. A robust method to suppress jamming for satellite navigation by reconstructing sample covariance matrix without main-lobe nulling is proposed in this paper. No nulling is formed while suppressing the main-lobe jamming, which avoids main-lobe direction distortion. Meanwhile, along with adaptive pattern control (APC), the adaptive pattern of array antenna approaches the pattern without jamming so as to receive the matching navigation signal. Theoretical analysis and numerical simulation prove that this method suppresses jamming without main-beam distortion. Furthermore, the output SINR will not decrease with the main-lobe distortion by this method, which improves the antijamming performance.


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## Body

## 1. Introduction

Satellite navigation system takes advantage of navigating satellites for positioning and navigation [1]. It plays a vital role in transportation management, time service, search and rescue, and geodesy due to its globalized and full-time duration as well as precision [2–6]. Nowadays, GNSS service includes Chinese Beidou Navigation Satellite System (BDS), American Global Positioning System (GPS), and Russian’s GLONASS [7].As the navigation satellites operate on the orbit of 20200 km far away from the Earth surface, the signal emitted by them that is finally received by the GNSS user becomes quite weak [8, 9]. Under this circumstance, navigation signal is vulnerable to active jamming, which leads to the loss of navigation signal. Therefore, the antijamming performance is a prerequisite for the navigation system.Adaptive spatial filtering technology is one of the main antijamming techniques for GNSS as well as a major branch of adaptive array signal processing [10]. Embedding GPS antijamming technology based on power inversion algorithm is proposed which does not require a prior information of navigation signal nor array arrangement [11]. GPS antijamming methods based on spatial time adaptive processing (STAP) increase the tapping of signal’s time domain so that the antijamming performance is improved [12]. An enhanced short-time Fourier transform (STFT) jamming mitigation system is proposed in [13] which employs several windows to increase time-frequency plane resolution.However, the above-listed methods do not constrain the receiving of useful navigation satellite signal, while only nulling the jamming signal. Therefore, it is not guaranteed that the pattern’s main-lobe points to the direction of satellite signal, which posts negative influence on the receiving navigation signal [14]. A robust antijamming algorithm is proposed under this circumstance. Relevant documents take advantage of minimum variance distortionless response (MVDR) to suppress jamming on GPS. This algorithm constrains the antenna pattern and improves the antijamming performance [15]. Then multiple constrained minimum variance-spatial temporal adaptive processing (MCMV-STAP) was proposed in [16] to enhance the desired satellite signals and suppress jamming, which can broaden the width of nulls and provide approximately flat gains in other directions.However, this useful algorithm still forms nulling when active jamming exists in the pattern’s main-lobe, which leads to increased distortion and decreased SINR. Thus, the receiver cannot use navigation signal for positioning [17].A robust method to suppress jamming for satellite navigation by reconstructing sample covariance matrix is proposed in this paper. In this method, adaptive beamforming and antijamming are achieved by combining APC with linearly constrained minimum variance (LCMV) beamformer [18–20]. In proposed method, sample covariance matrix is decomposed first; then jamming components of main-lobe are distinguished by the correlation of eigenvector and desired signal steering vector. The main-lobe jamming eigenvectors are calculated by the correlation between main-lobe jamming eigenvectors and desired signal steering vector. The sampling covariance matrix is reconstructed to eliminate the influence of the main-lobe jamming component on the pattern. Eigen-projection matrix can be constructed after eigenvector of main-lobe jamming is acquired so as to eliminate main-lobe jamming components; thus, main-lobe jamming is suppressed. When suppressing all jamming, the pattern only forms nulling in the side-lobe. Then APC is processed to constrain the weight of the LCMV beamformer so that adaptive pattern approaches the pattern without jamming further.When the main-lobe jamming is suppressed, the proposed method does not form nulling in the main-lobe jamming direction, so that the beam direction will not be offset due to the main-lobe antijamming. This ensures that the beam will point to the navigation satellite still.Therefore, the output SINR of the satellite navigation signal received by the antenna array in the direction of the navigation satellite is higher than that of other methods relatively. The output SINR is guaranteed, it will be easier to calculate the satellite navigation signal after suppressing the jamming for the GNSS receiver. Under the premise of satisfying the tracking sensitivity of satellite navigation receiver, the proposed algorithm in this paper can suppress more jamming than other algorithms.Theoretical analysis and numerical simulation prove that the direction of the pattern is not offset by the suppression of main-lobe jamming. The output SINR of satellite navigation signal will not decrease due to the directional offset of the pattern, and the output SINR is only related to the intensity of the input jamming signal, which will be helpful for the navigation receiver to process the navigation signal.This paper is organized as follows. The array model and signal’s mathematic model are provided in Section2. The details of the proposed method as well as theoretical analysis on reconstruction of covariance matrix and APC are developed in Section 3. Simulations are carried out, which include analysis on the adaptive pattern and the output SINR in Section 4. Section 5 shows the conclusion.


## 2. Problem Formulation

### 2.1. Signal Model

Suppose anN-element uniform linear array which is showed in Figure 1,d is the distance between array elements, and all the array elements are homogeneous and isotropic.Figure 1
The linear antenna array geometry.There is a far-field desired signal andP narrowband jamming signals incident as plane wave (wavelength λ) [21]. The desired signal and the jamming-signal angles of arrival are θ0 and θjj=1,2,…,P; then the signal received by the array can be expressed as(1)Xk=ASk+nk,where Xk refers to the matrix of array received data,(2)Xk=x1k,x2k,…,xNk,and A refers to array steering vector, which is merely relevant to signal incidence angle and can be expressed as(3)A=aθ0,aθ1,…,aθPT.In (3),(4)aθk=1,eiβk,…,eiN-1βkT,k=0,1,…,Pwhich is the array steering vector corresponding to the signal source; meanwhile, βk=2π/λdsin⁡θk.n
k in (1) stands for noise matrix and Sk for signal matrix; the latter one includes the navigation signal s0k and the jamming signal sjk. So Xk can be expressed as(5)Xk=aθ0s0k+∑j=1Paθjsjk+nk,and sample covariance matrix can be reached as(6)RX=EXtXHt,where E∗ and ∗H denote the expectation operator, respectively, and conjugate transpose.


### 2.2. The LCMV Beamformer

The gain constraint by the LCMV beamformer in the expected signal direction is 1 (unit constraint), and the array output power is minimized, in which jamming and noise decrease is suppressed [22]. Weight vector of LCMV beamformer can be reached by this equation(7)minWWHRXW,s.t.WHC=FH,in which C is the constraint matrix and F is the corresponding response constraint vector. The weight vector of LCMV beamformer can be expressed as(8)WLCMV=RX-1CCHRX-1C-1F,in which WLCMV is the weight vector of LCMV beamformer [23].When LCMV beamformer is utilized to suppress main-lobe jamming −5 degrees, its pattern is shown in Figure2. The main-lobe already distorts from the expected angle of the satellite signal when suppressing this jamming signal. The output SINR decreases; meanwhile, the nulling position is not precise.Figure 2
Effect of main-lobe jamming on satellite signal reception.Therefore, in the application of satellite navigation antijamming, both the performance of the interference suppression algorithm and the pattern distortion lead to the loss of positioning function of the receiver prematurely. In the process of suppressing the main-lobe jamming, the pattern distortion also seriously affects the reception of satellite navigation signals. The output SINR of satellite navigation signal is affected by the input jamming-signal intensity and the directional pattern offset. When the output signal to noise ratio of the array is decreased, the performance of the antijamming degrades. This paper focuses on the avoidance of pattern distortion in GNSS antijamming, so that the output signal is only affected by the input jamming intensity.


## 2.1. Signal Model

Suppose anN-element uniform linear array which is showed in Figure 1,d is the distance between array elements, and all the array elements are homogeneous and isotropic.Figure 1
The linear antenna array geometry.There is a far-field desired signal andP narrowband jamming signals incident as plane wave (wavelength λ) [21]. The desired signal and the jamming-signal angles of arrival are θ0 and θjj=1,2,…,P; then the signal received by the array can be expressed as(1)Xk=ASk+nk,where Xk refers to the matrix of array received data,(2)Xk=x1k,x2k,…,xNk,and A refers to array steering vector, which is merely relevant to signal incidence angle and can be expressed as(3)A=aθ0,aθ1,…,aθPT.In (3),(4)aθk=1,eiβk,…,eiN-1βkT,k=0,1,…,Pwhich is the array steering vector corresponding to the signal source; meanwhile, βk=2π/λdsin⁡θk.n
k in (1) stands for noise matrix and Sk for signal matrix; the latter one includes the navigation signal s0k and the jamming signal sjk. So Xk can be expressed as(5)Xk=aθ0s0k+∑j=1Paθjsjk+nk,and sample covariance matrix can be reached as(6)RX=EXtXHt,where E∗ and ∗H denote the expectation operator, respectively, and conjugate transpose.


## 2.2. The LCMV Beamformer

The gain constraint by the LCMV beamformer in the expected signal direction is 1 (unit constraint), and the array output power is minimized, in which jamming and noise decrease is suppressed [22]. Weight vector of LCMV beamformer can be reached by this equation(7)minWWHRXW,s.t.WHC=FH,in which C is the constraint matrix and F is the corresponding response constraint vector. The weight vector of LCMV beamformer can be expressed as(8)WLCMV=RX-1CCHRX-1C-1F,in which WLCMV is the weight vector of LCMV beamformer [23].When LCMV beamformer is utilized to suppress main-lobe jamming −5 degrees, its pattern is shown in Figure2. The main-lobe already distorts from the expected angle of the satellite signal when suppressing this jamming signal. The output SINR decreases; meanwhile, the nulling position is not precise.Figure 2
Effect of main-lobe jamming on satellite signal reception.Therefore, in the application of satellite navigation antijamming, both the performance of the interference suppression algorithm and the pattern distortion lead to the loss of positioning function of the receiver prematurely. In the process of suppressing the main-lobe jamming, the pattern distortion also seriously affects the reception of satellite navigation signals. The output SINR of satellite navigation signal is affected by the input jamming-signal intensity and the directional pattern offset. When the output signal to noise ratio of the array is decreased, the performance of the antijamming degrades. This paper focuses on the avoidance of pattern distortion in GNSS antijamming, so that the output signal is only affected by the input jamming intensity.


## 3. Proposed Method

This section proposes a new antijamming method by overcoming the shortcoming of LCMV beamformer in GNSS antijamming in Section2. This method can deal with the distortion of pattern direction when suppressing main-lobe jamming. The adaptive pattern approaches the pattern without jamming so as to effectively receive navigation signal.Since the navigation signal received by the antenna array is weak in power, this signal can be deemed to be composed of jamming and noise. So sample covariance matrix can be considered to be made up of jamming-and-noise covariance matrix. It meets the requirements of robust beamforming. Therefore, to prevent pattern distortion, coping with main-lobe jamming is the only step to be paid attention to. The detailed process is described as follows.


### 3.1. Covariance Matrix Reconstruction

The eigen-decomposition of a sample covariance matrix can be expressed as(9)RX=∑i=1NλiτiτiH=ΓsΛsΓsH+ΓnΛnΓnH,where λ1≥λ2≥⋯≥λp≥λP+1=⋯=λN=σn2 refers to descending-order eigenvalue of RX. Γs=τ1,…,τP and Γn=τP+1,…,τN are signal-and-jamming subspace and noise subspace, respectively, among which τi is the eigenvector corresponding to λi. Λs=diag⁡λ1,…,λp and Λn=diag⁡λp+1,…,λN are the diagonal matrices of Γs and Γn, respectively [24].Eigenvalue and eigenvector of the main-lobe jamming signal can be achieved by the correlation of decomposed sample covariance matrix and steering vector of signal’s incidence angle [25]. The correlation coefficient equation between a1 and a2 is(10)cora1,a2=a1Ha2a1a2.The correlation coefficient between steering vector of incidence signalaθs and eigenvectors of various-angle jamming Γs=τ1,…,τP can also be achieved by (10).Figure3 shows the curve of correlation coefficient between various-angle steering vectors and the steering vector at 0 degrees based on the seven-element ULA structure.Figure 3
Correlation coefficient between various-angle steering vector and 0 degree steering vector.This figure shows that the correlation coefficient curve descends as the angle increases. Taking advantage of this character, this paper assumes an interval of correlation coefficientε,1, among which ε can be reached by array-element structure.The constant value in Figure3 is the corresponding coefficient of main-lobe boundary angle reached by the seven-element uniform linear array. Main-lobe width can be defined as the 3 dB bandwidth. Eigenvector in this range can be deemed as main-lobe eigenvector of jamming eigenvector.Therefore, it can be assumed that this steering vector is the one corresponding to main-lobe jamming when the steering vector of incident signal and coefficient of jamming eigenvector are within the intervalε,1. This process can be expressed as(11)ε≤corτi,aθs≤1,τi∈Γs,among which Γs=τ1,…,τP is the eigenvector of the various-angle jamming, and(12)corτi,aθs=τiHaθsτiaθs.Eigenvector and eigenvalue of main-lobe jammingτ^i and τ^i can be decided by (11).Eigenvalue analysis tells that the array response of adaptive beamformer can be expressed as the difference of no jamming response and jamming beam response [26](13)Fθ=μσn2aHθsaθ-∑i=1Nλi-σn2λiτiaθsτiHaθ,in which Fθ is the array response of adaptive beamformer, and (14)μ=1aHθsR^-1aθs.Meanwhile, the noise power can be estimated by the mean ofN-P smaller eigenvalues, which can be expressed as (15)σn2=λP+1+⋯+λNN-P.Generally speaking, jamming power is considerably greater than the noise power. Therefore, as the eigenvalue corresponding to jamming signal,λi overwhelms σn2. So this equation is derived(16)λi-σn2λi≈1,i∈1,…,P.That is how the adaptive array response forms nulling in the jamming direction for jamming suppression [18]. It does not form the nulling when λi corresponds to noise eigenvalue.λ
i
^ contains all power of the main-lobe jamming. If the eigenvalue of the main-lobe jamming is reduced to the noise power, the adaptive weight vector will not form a nulling in the main-lobe jamming direction when the adaptive weight vector is calculated.Therefore, when eigenvalue of main-lobe jammingλi^ is replaced by the mean of noise eigenvalue, which results in that the eigenvalue of main-lobe jamming decreases to background noise, the replaced expression is(17)λi^=σn2=λP+1+⋯+λNN-P.In order to deal with noise in the adaptive algorithm,Λn is also replaced by the average value of noise. The reconstructed eigenvalue matrix of Λn can be expressed as(18)Λ⌢=diag⁡λ1,…,λi^,…,λp,σn2,…,σn2.The steering vector matrix makes no change, so the reconstructed sample covariance matrixR~r can be expressed as(19)R~r=ΓΛ⌢ΓH,where Γ=Γs,Γn and R~r excludes main-lobe jamming components. LCMV beamforming adaptive weight value can be calculated as(20)W~LCMV=R~r-1CCHR~r-1C-1F.Adaptive array antenna pattern produces no jamming nulling in main-lobe while suppressing main-lobe jamming.


### 3.2. Adaptive Pattern Control

The weight value of LCMV beamformer computed from the reconstructed jamming-and-noise covariance matrix forms no nulling when suppressing main-lobe jamming and no pattern distortion appears. However, mistakes still appear in adaptive aerial pattern because of other elements. Under this circumstance, APC can be utilized to achieve the pattern without jamming so as to make adaptive management more robust.When experiment data contains merely independent white noise, the array covariance matrix is the unit matrix multiplied by the noise power. Then the weight vector without jamming of LCMV can be expressed as(21)Wq=CCHC-1F.In order to adjust adaptive pattern to the pattern without jamming, The weight vectorWq without jamming of the LCMV is constrained to be W-q, which meets the constraint WHC=HH and approaches the weight vector without jamming Wq. W-q is considered to be the solution to the following constrained least squares fitting:(22)W-q=arg⁡minW--WqHW--Wq,s.t.W-C=FH,where WqHaθ0=1.After Lagrange multiplier method is utilized to solve the following expression, the revised weight vector without jammingW-q is(23)W-q=I-CCHC-1CWq+CCHC-1F.SupposingZ is the block matrix of constraint matrix C and ZC=0, so(24)W-q=ZHZZH-1ZWq+CCHC-1F;if WZ=ZHZZH-1W0, let C-=C,WZ and F-=FWZ2.So the revised the weight vector without jammingW-q becomes W-q=C-C-HC--1F-.Finally, according to formula (8), the LCMV weight vector can be revised as(25)W^LCMV=R~r-1C-C-HR~r-1C--1F-.


### 3.3. Array Antenna Output

Eigen-projection matrix can be constructed after the eigenvector of main-lobe jamming is acquired so as to eliminate main-lobe jamming components. Eigenvector of main-lobe jammingτ^i is the prerequisite for this construction.(26)B=I-τ^iτ^iHτ^i-1τ^iH,in which B is the eigen-projection matrix.The eigen-projection matrix can be utilized for pretreating echo dataX in order to eliminate main-lobe jamming part in the signal.(27)Xb=BX,where Xb refers to the output of the pretreatment, made up of navigation signal, jamming signal, and noise. Equation (27) can get rid of main-lobe jamming but not side-lobe one. This data requires adaptive weight treatment,(28)Y=W^HLCMVBX.After that, remaining side-lobe jamming is suppressed. Until then jamming on array output signal is completely under control, and no main-lobe nulling appears. Therefore, a relatively higher output SINR is acquired.The flowchart of the proposed method is shown in the green frame in Figure4.Figure 4
The flowchart of the proposed method.The jamming suppression processing steps are shown as follows:(1)
The sample covariance matrix of signals received by the array antenna is decomposed and the correlation is calculated. So the main-lobe jamming eigenvectorτ^i is calculated.(2)
Reconstructed sample covariance matrixR~r excludes main-lobe jamming components, eliminating the effect of main-lobe jamming on pattern. At the same time, eigen-projection matrix B can be constructed after the eigenvector of the main-lobe jamming is acquired so as to eliminate the main-lobe jamming components and the main-lobe jamming can be suppressed.(3)
Use LCMV to calculate antijamming weight valueW~LCMV. Since R~r does not contain the main-lobe jamming component, the pattern corresponding to W~LCMV does not form nulls at the main-lobe jamming.(4)
Use APC to make beam pattern approach the pattern without jamming, calculating the final beamformer weight valueW^LCMV.(5)
Calculate beamforming outputY=W^HLCMVBX. The adaptive pattern not only suppresses the jamming but also does not form a nulling in the main-lobe jamming.


## 3.1. Covariance Matrix Reconstruction

The eigen-decomposition of a sample covariance matrix can be expressed as(9)RX=∑i=1NλiτiτiH=ΓsΛsΓsH+ΓnΛnΓnH,where λ1≥λ2≥⋯≥λp≥λP+1=⋯=λN=σn2 refers to descending-order eigenvalue of RX. Γs=τ1,…,τP and Γn=τP+1,…,τN are signal-and-jamming subspace and noise subspace, respectively, among which τi is the eigenvector corresponding to λi. Λs=diag⁡λ1,…,λp and Λn=diag⁡λp+1,…,λN are the diagonal matrices of Γs and Γn, respectively [24].Eigenvalue and eigenvector of the main-lobe jamming signal can be achieved by the correlation of decomposed sample covariance matrix and steering vector of signal’s incidence angle [25]. The correlation coefficient equation between a1 and a2 is(10)cora1,a2=a1Ha2a1a2.The correlation coefficient between steering vector of incidence signalaθs and eigenvectors of various-angle jamming Γs=τ1,…,τP can also be achieved by (10).Figure3 shows the curve of correlation coefficient between various-angle steering vectors and the steering vector at 0 degrees based on the seven-element ULA structure.Figure 3
Correlation coefficient between various-angle steering vector and 0 degree steering vector.This figure shows that the correlation coefficient curve descends as the angle increases. Taking advantage of this character, this paper assumes an interval of correlation coefficientε,1, among which ε can be reached by array-element structure.The constant value in Figure3 is the corresponding coefficient of main-lobe boundary angle reached by the seven-element uniform linear array. Main-lobe width can be defined as the 3 dB bandwidth. Eigenvector in this range can be deemed as main-lobe eigenvector of jamming eigenvector.Therefore, it can be assumed that this steering vector is the one corresponding to main-lobe jamming when the steering vector of incident signal and coefficient of jamming eigenvector are within the intervalε,1. This process can be expressed as(11)ε≤corτi,aθs≤1,τi∈Γs,among which Γs=τ1,…,τP is the eigenvector of the various-angle jamming, and(12)corτi,aθs=τiHaθsτiaθs.Eigenvector and eigenvalue of main-lobe jammingτ^i and τ^i can be decided by (11).Eigenvalue analysis tells that the array response of adaptive beamformer can be expressed as the difference of no jamming response and jamming beam response [26](13)Fθ=μσn2aHθsaθ-∑i=1Nλi-σn2λiτiaθsτiHaθ,in which Fθ is the array response of adaptive beamformer, and (14)μ=1aHθsR^-1aθs.Meanwhile, the noise power can be estimated by the mean ofN-P smaller eigenvalues, which can be expressed as (15)σn2=λP+1+⋯+λNN-P.Generally speaking, jamming power is considerably greater than the noise power. Therefore, as the eigenvalue corresponding to jamming signal,λi overwhelms σn2. So this equation is derived(16)λi-σn2λi≈1,i∈1,…,P.That is how the adaptive array response forms nulling in the jamming direction for jamming suppression [18]. It does not form the nulling when λi corresponds to noise eigenvalue.λ
i
^ contains all power of the main-lobe jamming. If the eigenvalue of the main-lobe jamming is reduced to the noise power, the adaptive weight vector will not form a nulling in the main-lobe jamming direction when the adaptive weight vector is calculated.Therefore, when eigenvalue of main-lobe jammingλi^ is replaced by the mean of noise eigenvalue, which results in that the eigenvalue of main-lobe jamming decreases to background noise, the replaced expression is(17)λi^=σn2=λP+1+⋯+λNN-P.In order to deal with noise in the adaptive algorithm,Λn is also replaced by the average value of noise. The reconstructed eigenvalue matrix of Λn can be expressed as(18)Λ⌢=diag⁡λ1,…,λi^,…,λp,σn2,…,σn2.The steering vector matrix makes no change, so the reconstructed sample covariance matrixR~r can be expressed as(19)R~r=ΓΛ⌢ΓH,where Γ=Γs,Γn and R~r excludes main-lobe jamming components. LCMV beamforming adaptive weight value can be calculated as(20)W~LCMV=R~r-1CCHR~r-1C-1F.Adaptive array antenna pattern produces no jamming nulling in main-lobe while suppressing main-lobe jamming.


## 3.2. Adaptive Pattern Control

The weight value of LCMV beamformer computed from the reconstructed jamming-and-noise covariance matrix forms no nulling when suppressing main-lobe jamming and no pattern distortion appears. However, mistakes still appear in adaptive aerial pattern because of other elements. Under this circumstance, APC can be utilized to achieve the pattern without jamming so as to make adaptive management more robust.When experiment data contains merely independent white noise, the array covariance matrix is the unit matrix multiplied by the noise power. Then the weight vector without jamming of LCMV can be expressed as(21)Wq=CCHC-1F.In order to adjust adaptive pattern to the pattern without jamming, The weight vectorWq without jamming of the LCMV is constrained to be W-q, which meets the constraint WHC=HH and approaches the weight vector without jamming Wq. W-q is considered to be the solution to the following constrained least squares fitting:(22)W-q=arg⁡minW--WqHW--Wq,s.t.W-C=FH,where WqHaθ0=1.After Lagrange multiplier method is utilized to solve the following expression, the revised weight vector without jammingW-q is(23)W-q=I-CCHC-1CWq+CCHC-1F.SupposingZ is the block matrix of constraint matrix C and ZC=0, so(24)W-q=ZHZZH-1ZWq+CCHC-1F;if WZ=ZHZZH-1W0, let C-=C,WZ and F-=FWZ2.So the revised the weight vector without jammingW-q becomes W-q=C-C-HC--1F-.Finally, according to formula (8), the LCMV weight vector can be revised as(25)W^LCMV=R~r-1C-C-HR~r-1C--1F-.


## 3.3. Array Antenna Output

Eigen-projection matrix can be constructed after the eigenvector of main-lobe jamming is acquired so as to eliminate main-lobe jamming components. Eigenvector of main-lobe jammingτ^i is the prerequisite for this construction.(26)B=I-τ^iτ^iHτ^i-1τ^iH,in which B is the eigen-projection matrix.The eigen-projection matrix can be utilized for pretreating echo dataX in order to eliminate main-lobe jamming part in the signal.(27)Xb=BX,where Xb refers to the output of the pretreatment, made up of navigation signal, jamming signal, and noise. Equation (27) can get rid of main-lobe jamming but not side-lobe one. This data requires adaptive weight treatment,(28)Y=W^HLCMVBX.After that, remaining side-lobe jamming is suppressed. Until then jamming on array output signal is completely under control, and no main-lobe nulling appears. Therefore, a relatively higher output SINR is acquired.The flowchart of the proposed method is shown in the green frame in Figure4.Figure 4
The flowchart of the proposed method.The jamming suppression processing steps are shown as follows:(1)
The sample covariance matrix of signals received by the array antenna is decomposed and the correlation is calculated. So the main-lobe jamming eigenvectorτ^i is calculated.(2)
Reconstructed sample covariance matrixR~r excludes main-lobe jamming components, eliminating the effect of main-lobe jamming on pattern. At the same time, eigen-projection matrix B can be constructed after the eigenvector of the main-lobe jamming is acquired so as to eliminate the main-lobe jamming components and the main-lobe jamming can be suppressed.(3)
Use LCMV to calculate antijamming weight valueW~LCMV. Since R~r does not contain the main-lobe jamming component, the pattern corresponding to W~LCMV does not form nulls at the main-lobe jamming.(4)
Use APC to make beam pattern approach the pattern without jamming, calculating the final beamformer weight valueW^LCMV.(5)
Calculate beamforming outputY=W^HLCMVBX. The adaptive pattern not only suppresses the jamming but also does not form a nulling in the main-lobe jamming.


## 4. Simulation Analysis

In this section, five experiments are listed to illustrate the performance of this robust method for jamming suppression. GPS navigation signals are all on frequency point L1 and the input SNR is −20 dB [27].This paper is written with these assumptions: jamming comes from point source. Geometrical aperture is far less than the aerial-radiation distance. Signal received by array is plane wave. Transmission medium is equivalently isotropic and uniform all around. The zero-mean noise is robust, random, and of no relation with expected signal.Power inversion algorithm is utilized for performance comparison, in which STFT algorithm (based on space-frequency structure) and MCMV-STAP algorithm (based on space-time structure) are the two parts [28]. The number of snapshots is 500 throughout the simulation, and all results are the mean of 100 Monte Carlo experiment.Table1 shows angles of navigation signal-and-jamming signal. Each scenario of the simulation chooses satellite and jamming signals of different (incidence) angles.Table 1
Satellite and Jamming Scenarios.
Signal
Angle
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario 6
Scenario 7
Satellite
0 degrees
Satellite
−20 degrees
Satellite
20 degrees
Satellite
70 degrees
Satellite
10 degrees
Satellite
−25 degrees
Satellite
40 degrees
Jamming
−6 degrees
Jamming
12 degrees
Jamming
40 degrees
Jamming
−14 degrees
Jamming
12 degrees
Jamming
24 degrees
Jamming
−22 degrees
Jamming
72 degrees
Jamming
0 degrees
Jamming
−60 degrees
indicates the selected satellite signal or jamming signal.


### 4.1. Influence of Jamming-Signal Incidence Angle on Adaptive Pattern

In this simulation experiment, antenna array uses uniform linear array (ULA) with seven-array elements, with half wavelength width as the distance between array elements.Figure5 takes the first scene in Table 1 for simulation: presuming that incidence angle of satellite signal is 0 degrees. Jamming signal has an incidence angle of −6 degrees and an ISR of 50 dB and produces main-lobe jamming to seven-array antenna. So the algorithm in this paper forms no main-lobe nulling, while the other three algorithms form nulling at −6 degrees. As a result, algorithms of minimum power, STFT, and MCMV-STAP lead to deviation of beam direction: 6 degrees for the first but more on side-lobe and 8 degrees for the last but less on side-lobe. Since no jamming nulling exists in this paper’s algorithm, main-lobe does not distort, and the pattern approaches the pattern without jamming as a whole.Figure 5
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angle of arrival of jamming signal is −6 degrees.Figure6 shows the simulation in the second scene of Table 1: presuming that incidence angle of satellite signal is 0 degrees. Incidence angles of jamming signal are −6 degrees and 12 degrees with an ISR of 50 dB. Although the algorithms of minimum power, STFT, and MCMV-STAP can precisely produce nulling in jamming position, beam direction already distorts terribly. The pattern’s 0-degree gain is 3 dB less than the pattern without jamming, which results in lower output SINR of satellite signal. The method proposed in this paper produces no jamming nulling at −6 degrees. And 12-degree jamming, producing 2-degree main-lobe deviation because of 12-degree nulling, belongs to side-lobe and produces nulling. However, gain of the pattern without jamming, which has a lower side-lobe, is merely 0.3 dB less than one of 0-degree pattern.Figure 6
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees and 12 degrees.Figure7 shows the simulation in the third scene of Table 1: presuming that incidence angle of satellite signal is 0 degrees. Incidence angles of jamming signal are −6 degrees, 12 degrees, and 40 degrees with an ISR of 40 dB. The algorithms of minimum power, STFT, and MCMV-STAP can precisely produce nulling in jamming position, but the deviation of beam direction is bigger than the proposed method. And pattern’s 0-degree gain is 4.7 dB less than the pattern without jamming, and pattern’s 0 -degree gain deteriorates even further. The method proposed in this paper produces jamming nulling at 12 degrees and 40 degrees. However, gain of the pattern without jamming, which has a lower side-lobe, is merely 0.3 dB less than one of 0-degree pattern also.Figure 7
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees, 12 degrees, and 40 degrees.Figures5, 6, and 7 verify the validity of the method proposed in this paper. No nulling or deviation of beam direction appears when suppressing main-lobe jamming. This provides a solid guarantee for effectively receiving navigation signal since output SINR of navigation signal does not decrease because of beam-direction deviation.


### 4.2. Influence of Jamming-Signal Intensity on Output SINR of Satellite Signal

In this simulation experiment, seven-array-element antennas are evenly distributed with a distance of half wavelength width to each other, and ISR of jamming signal increases from 0 dB to 90 dB. Influence of jamming-signal intensity on output SINR of satellite signal is analyzed under this circumstance.Output SINR of navigation signal can be expressed as(29)SINR=W^HLCMVRsW^LCMVW^HLCMVRi+RnW^LCMV,among which Rs refers to sample covariance matrix and Ri+Rn refers to jamming-and-noise sample covariance matrix [29].Figure8 shows the simulation of the first scene in Table 1. Although the beam of minimum power algorithm in Figure 5 deviates 6 degrees, its output SINR curve is the worst because of its higher side-lobe electrical level. In the 0 dB to 40 dB interval, STFT algorithm and MCMV-STAP algorithm’s performance is close. Yet MCMV-STAP one performs better than STFT one between 40 dB and 90 dB. The reason is that MCMV-STAP algorithm utilizes multibeam as well as space-time structure so that it constrains direction of navigation signal. The method proposed in this paper produces the best performance curve, since the pattern does not distort when suppressing main-lobe jamming.Figure 8
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angle of arrival of jamming signal is −6 degrees.Figure9 shows the simulation of the second scene in Table 1, and Figure 10 shows the simulation in the third scene in Table 1. Apparently, the output SINR of navigation is the worst when minimum power algorithm imposes no constraint on direction of navigation signal. Having treated information about frequency domain, STFT algorithm performs equally with MCMV-STAP one in terms of output SINR. Under this circumstance, the method proposed in this paper has the best performance curve of output SINR during jamming suppression.Figure 9
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees and 12 degrees.Figure 10
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees, 12 degrees, and 40 degrees.


### 4.3. Influence of Jamming Signal with Various Incidence Angles on Pattern

This section focuses on influence of jamming signal with various incidence angles on the pattern. In this section, a seven-array-element ULA is evenly distributed with a distance of half wavelength width from each other. But ISR of jamming signal is a constant value of 50 dB.Figure11 shows the simulation of the fourth scene in Table 1: incidence signal of navigation signal is −20 degrees and ones of jamming signals are −14 degrees and 12 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at 12-degree jamming but not at −14-degree main-lobe jamming. The main-lobe direction does not distort.Figure 11
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is −20 degrees and the angles of arrival of jamming signals are −14 degrees and 12 degrees.Figure12 shows the simulation of the fifth scene in Table 1: incidence signal of navigation signal is 20 degrees and ones of jamming signals are 24 degrees and −22 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at −22-degree jamming but not at 24-degree main-lobe jamming. Main-lobe direction does not distort.Figure 12
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 20 degrees and the angles of arrival of jamming signals are 24 degrees and −22 degrees.Figure13 shows the simulation of the sixth scenario in Table 1: incidence signal of navigation signal is 70 degrees and ones of jamming signals are 72 degrees and 0 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at 0-degree jamming but not at 72-degree main-lobe jamming. The main-lobe direction does not distort.Figure 13
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 70 degrees and the angles of arrival of jamming signals are 72 degrees and 0 degrees.


### 4.4. Influence of Jamming Signal among Multisatellite Navigation Signal on Pattern

This subsection simulates the seventh scenario in Table1: incidence angles of navigation signals are −25 degrees, 10 degrees, and 40 degrees. Ones of jamming signals are −60 degrees, −22 degrees, −14 degrees, and 24 degrees, among which the second one is at the main-lobe. LCMV beamformer produces three beams, pointing at incidence angles of three navigation signals relatively.In Figure14, seven-array-element aerials are evenly distributed with a distance of half wavelength width from each other, and ISR of jamming signal is 40 dB, fixed. Jamming nulling only appears in adaptive pattern at −60 degrees, −14 degrees, and 24 degrees, yet none at −22-degree main-lobe jamming. Furthermore, pattern direction does not distort, which is in favor of effectively receiving navigation signal.Figure 14
The array antenna pattern of the proposed method: the angles of arrival of the satellite signal are 10 degrees, −25 degrees, and 40 degrees and the angles of arrival of jamming signals are −14 degrees, −22 degrees, −60 degrees, and 24 degrees.


### 4.5. Influence of Jamming Signal on a Seven-Sensor Uniform Circular Array Pattern

The method proposed in this paper is applied in the seven-sensor uniform circular array pattern (Figure15): seven-array elements are evenly distributed on the circle with half wavelength (the array-element’ distance is d) as radius R. Signal incidence angle is θ,ϕ; the former one refers to azimuth and the latter to pitching angle [30]. So corresponding steering vector can be expressed as(30)aθ,ϕ=exp⁡j2πRsin⁡θcos⁡ϕ-γ0λexp⁡j2πRsin⁡θcos⁡ϕ-γ1λ⋮exp⁡j2πRsin⁡θcos⁡ϕ-γM-1λamong which γm=2πm/Nm=0,1,…,6.Figure 15
The seven-sensor uniform circular array geometry.In order to verify the validity of this method in real condition, the simulation in this subsection is implemented at 11 o’clock on 14 April, 2016, at 40°N, 108.45°E. Table2 shows the actual position of GPS satellite.Table 2
Azimuth and elevation angles of visible satellites.
PRN
Az (degree)
El (degree)
Sky plot
1
24
5
4
98
10
10
170
19
12
221
6
14
320
10
18
112
39
22
99
35
25
270
62
32
312
81
33
58
52The following Jamming Scenario shows the parameters of jamming with respect to satellite’s coordinate position in Table2:Four-CW jammingAzimuth = 81, 146, 201, 342Elevation = 17, 67, 15, 48The results of simulation by this method are shown by Figures16 and 17; the former one is three-dimensional (3D) antenna pattern and the latter one shows two-dimensional (2D) direction and pitching angle. Meanwhile, Figure 17 illustrates positions of navigation signal and jamming: jamming 1 and jamming 2 are at main-lobe but form no nulling, while jamming 3 and jamming 4 form precise nulling. Navigation signals are at respective beam main-lobe, where no deviation appears. This conforms to the result of theoretical analysis.Figure 16
Beams and nulls 3D pattern of the proposed method according to the scenario in Table2 and Jamming Scenario in Section 4.5.Figure 17
Beams and nulls 2D pattern of the proposed method according to the scenario in Table2 and Jamming Scenario in Section 4.5.


## 4.1. Influence of Jamming-Signal Incidence Angle on Adaptive Pattern

In this simulation experiment, antenna array uses uniform linear array (ULA) with seven-array elements, with half wavelength width as the distance between array elements.Figure5 takes the first scene in Table 1 for simulation: presuming that incidence angle of satellite signal is 0 degrees. Jamming signal has an incidence angle of −6 degrees and an ISR of 50 dB and produces main-lobe jamming to seven-array antenna. So the algorithm in this paper forms no main-lobe nulling, while the other three algorithms form nulling at −6 degrees. As a result, algorithms of minimum power, STFT, and MCMV-STAP lead to deviation of beam direction: 6 degrees for the first but more on side-lobe and 8 degrees for the last but less on side-lobe. Since no jamming nulling exists in this paper’s algorithm, main-lobe does not distort, and the pattern approaches the pattern without jamming as a whole.Figure 5
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angle of arrival of jamming signal is −6 degrees.Figure6 shows the simulation in the second scene of Table 1: presuming that incidence angle of satellite signal is 0 degrees. Incidence angles of jamming signal are −6 degrees and 12 degrees with an ISR of 50 dB. Although the algorithms of minimum power, STFT, and MCMV-STAP can precisely produce nulling in jamming position, beam direction already distorts terribly. The pattern’s 0-degree gain is 3 dB less than the pattern without jamming, which results in lower output SINR of satellite signal. The method proposed in this paper produces no jamming nulling at −6 degrees. And 12-degree jamming, producing 2-degree main-lobe deviation because of 12-degree nulling, belongs to side-lobe and produces nulling. However, gain of the pattern without jamming, which has a lower side-lobe, is merely 0.3 dB less than one of 0-degree pattern.Figure 6
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees and 12 degrees.Figure7 shows the simulation in the third scene of Table 1: presuming that incidence angle of satellite signal is 0 degrees. Incidence angles of jamming signal are −6 degrees, 12 degrees, and 40 degrees with an ISR of 40 dB. The algorithms of minimum power, STFT, and MCMV-STAP can precisely produce nulling in jamming position, but the deviation of beam direction is bigger than the proposed method. And pattern’s 0-degree gain is 4.7 dB less than the pattern without jamming, and pattern’s 0 -degree gain deteriorates even further. The method proposed in this paper produces jamming nulling at 12 degrees and 40 degrees. However, gain of the pattern without jamming, which has a lower side-lobe, is merely 0.3 dB less than one of 0-degree pattern also.Figure 7
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees, 12 degrees, and 40 degrees.Figures5, 6, and 7 verify the validity of the method proposed in this paper. No nulling or deviation of beam direction appears when suppressing main-lobe jamming. This provides a solid guarantee for effectively receiving navigation signal since output SINR of navigation signal does not decrease because of beam-direction deviation.


## 4.2. Influence of Jamming-Signal Intensity on Output SINR of Satellite Signal

In this simulation experiment, seven-array-element antennas are evenly distributed with a distance of half wavelength width to each other, and ISR of jamming signal increases from 0 dB to 90 dB. Influence of jamming-signal intensity on output SINR of satellite signal is analyzed under this circumstance.Output SINR of navigation signal can be expressed as(29)SINR=W^HLCMVRsW^LCMVW^HLCMVRi+RnW^LCMV,among which Rs refers to sample covariance matrix and Ri+Rn refers to jamming-and-noise sample covariance matrix [29].Figure8 shows the simulation of the first scene in Table 1. Although the beam of minimum power algorithm in Figure 5 deviates 6 degrees, its output SINR curve is the worst because of its higher side-lobe electrical level. In the 0 dB to 40 dB interval, STFT algorithm and MCMV-STAP algorithm’s performance is close. Yet MCMV-STAP one performs better than STFT one between 40 dB and 90 dB. The reason is that MCMV-STAP algorithm utilizes multibeam as well as space-time structure so that it constrains direction of navigation signal. The method proposed in this paper produces the best performance curve, since the pattern does not distort when suppressing main-lobe jamming.Figure 8
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angle of arrival of jamming signal is −6 degrees.Figure9 shows the simulation of the second scene in Table 1, and Figure 10 shows the simulation in the third scene in Table 1. Apparently, the output SINR of navigation is the worst when minimum power algorithm imposes no constraint on direction of navigation signal. Having treated information about frequency domain, STFT algorithm performs equally with MCMV-STAP one in terms of output SINR. Under this circumstance, the method proposed in this paper has the best performance curve of output SINR during jamming suppression.Figure 9
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees and 12 degrees.Figure 10
The output SINR of different method when suppress jamming: the angle of arrival of the satellite signal is 0 degrees and the angles of arrival of jamming signals are −6 degrees, 12 degrees, and 40 degrees.


## 4.3. Influence of Jamming Signal with Various Incidence Angles on Pattern

This section focuses on influence of jamming signal with various incidence angles on the pattern. In this section, a seven-array-element ULA is evenly distributed with a distance of half wavelength width from each other. But ISR of jamming signal is a constant value of 50 dB.Figure11 shows the simulation of the fourth scene in Table 1: incidence signal of navigation signal is −20 degrees and ones of jamming signals are −14 degrees and 12 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at 12-degree jamming but not at −14-degree main-lobe jamming. The main-lobe direction does not distort.Figure 11
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is −20 degrees and the angles of arrival of jamming signals are −14 degrees and 12 degrees.Figure12 shows the simulation of the fifth scene in Table 1: incidence signal of navigation signal is 20 degrees and ones of jamming signals are 24 degrees and −22 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at −22-degree jamming but not at 24-degree main-lobe jamming. Main-lobe direction does not distort.Figure 12
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 20 degrees and the angles of arrival of jamming signals are 24 degrees and −22 degrees.Figure13 shows the simulation of the sixth scenario in Table 1: incidence signal of navigation signal is 70 degrees and ones of jamming signals are 72 degrees and 0 degrees. Algorithms of STFT and MCMV-STAP form two sets of jamming nulling and beam-direction deviation. The method proposed in this paper produces nulling at 0-degree jamming but not at 72-degree main-lobe jamming. The main-lobe direction does not distort.Figure 13
The array antenna pattern of antijamming for different method: the angle of arrival of the satellite signal is 70 degrees and the angles of arrival of jamming signals are 72 degrees and 0 degrees.


## 4.4. Influence of Jamming Signal among Multisatellite Navigation Signal on Pattern

This subsection simulates the seventh scenario in Table1: incidence angles of navigation signals are −25 degrees, 10 degrees, and 40 degrees. Ones of jamming signals are −60 degrees, −22 degrees, −14 degrees, and 24 degrees, among which the second one is at the main-lobe. LCMV beamformer produces three beams, pointing at incidence angles of three navigation signals relatively.In Figure14, seven-array-element aerials are evenly distributed with a distance of half wavelength width from each other, and ISR of jamming signal is 40 dB, fixed. Jamming nulling only appears in adaptive pattern at −60 degrees, −14 degrees, and 24 degrees, yet none at −22-degree main-lobe jamming. Furthermore, pattern direction does not distort, which is in favor of effectively receiving navigation signal.Figure 14
The array antenna pattern of the proposed method: the angles of arrival of the satellite signal are 10 degrees, −25 degrees, and 40 degrees and the angles of arrival of jamming signals are −14 degrees, −22 degrees, −60 degrees, and 24 degrees.


## 4.5. Influence of Jamming Signal on a Seven-Sensor Uniform Circular Array Pattern

The method proposed in this paper is applied in the seven-sensor uniform circular array pattern (Figure15): seven-array elements are evenly distributed on the circle with half wavelength (the array-element’ distance is d) as radius R. Signal incidence angle is θ,ϕ; the former one refers to azimuth and the latter to pitching angle [30]. So corresponding steering vector can be expressed as(30)aθ,ϕ=exp⁡j2πRsin⁡θcos⁡ϕ-γ0λexp⁡j2πRsin⁡θcos⁡ϕ-γ1λ⋮exp⁡j2πRsin⁡θcos⁡ϕ-γM-1λamong which γm=2πm/Nm=0,1,…,6.Figure 15
The seven-sensor uniform circular array geometry.In order to verify the validity of this method in real condition, the simulation in this subsection is implemented at 11 o’clock on 14 April, 2016, at 40°N, 108.45°E. Table2 shows the actual position of GPS satellite.Table 2
Azimuth and elevation angles of visible satellites.
PRN
Az (degree)
El (degree)
Sky plot
1
24
5
4
98
10
10
170
19
12
221
6
14
320
10
18
112
39
22
99
35
25
270
62
32
312
81
33
58
52The following Jamming Scenario shows the parameters of jamming with respect to satellite’s coordinate position in Table2:Four-CW jammingAzimuth = 81, 146, 201, 342Elevation = 17, 67, 15, 48The results of simulation by this method are shown by Figures16 and 17; the former one is three-dimensional (3D) antenna pattern and the latter one shows two-dimensional (2D) direction and pitching angle. Meanwhile, Figure 17 illustrates positions of navigation signal and jamming: jamming 1 and jamming 2 are at main-lobe but form no nulling, while jamming 3 and jamming 4 form precise nulling. Navigation signals are at respective beam main-lobe, where no deviation appears. This conforms to the result of theoretical analysis.Figure 16
Beams and nulls 3D pattern of the proposed method according to the scenario in Table2 and Jamming Scenario in Section 4.5.Figure 17
Beams and nulls 2D pattern of the proposed method according to the scenario in Table2 and Jamming Scenario in Section 4.5.


## 5. Conclusion

On the basis of reconstructing sample covariance matrix, this paper proposes a method to suppress jamming on satellite navigation. No main-lobe nulling is formed by the proposed method. Combined with APC, the adaptive pattern of array antenna approaches the pattern without jamming so as to receive the matching navigation signal.This proposed method suppresses the jamming by constructing eigenvector matrix, because of the sampling covariance matrix reconstruction. The main-lobe jamming does not null. This pattern always accurately points to the direction of navigation satellite. The pattern accurately formed deep nulling at the side-lobe jamming. Compared with other methods, it has the highest output SINR. This is helpful for the navigation receiver to solve the navigation signal and can effectively improve the navigation system antijamming capacity.Numerical simulation and case study results in this paper show that the pattern always precisely points to the direction of navigation satellite during jamming suppression. Deep nulling is achieved only on the position of side-lobe jamming. The proposed method has the highest output SINR compared with other methods. This is beneficial to the navigation signal receiving as well as improving the antijamming performance of the GNSS receiver.



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*Source: 9764283-2017-03-12.xml*