Research ArticleSpace-Time-Frequency Adaptive Processor for MultipleInterference Suppression in GNSS Applications

Qiang Guo, Lian-gang Qi , and Jianhong Xiang

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Correspondence should be addressed to Lian-gang Qi; qiliangang@hrbeu.edu.cn

Received 23 August 2017; Revised 9 January 2018; Accepted 17 January 2018; Published 24 April 2018

Academic Editor: Sotirios K. Goudos

Copyright © 2018 Qiang Guo et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To enhance the multiple interference suppression performance of global navigation satellite system (GNSS) receivers without extraantenna elements, a space-time-frequency adaptive processor (STFAP) is investigated. Firstly, based on the analysis of theautocorrelation function of the multicomponent signal, we propose a common period estimation and data block technique tosegment the received signal data into blocks. Secondly, the signal data in each block are short-time Fourier transformed intotime-frequency (TF) domain, and the corresponding TF points with similar frequency characteristics are regrouped to structurespace-time-frequency (STF) data matrixes. Finally, a space-time-frequency minimum output power- (STF-MOP) based weightcalculation method is introduced to suppress multiple interfering signals according to their sparse characteristics in TF andspace domains. Simulation results show that the proposed STFAP can effectively combat more wideband periodic frequency-modulated (WBPFM) interferences even some of them arriving from the same direction as GNSS signals without increasing thenumber of antenna elements.

1. Introduction

In recent years, with the rapidly increasing complexity ofthe electromagnetic environment, interference suppressiontechniques for global navigation satellite system (GNSS)receivers have become an increasingly prominent role [1].Many researchers have been devoting themselves in the studyof interference mitigation to ensure the reliability and conti-nuity of GNSS services, and much progress have been alreadyachieved. According to the required number of antennaelements, existing interference suppression methods canbe classified into single-antenna interference suppressiontechniques and multiple-antenna interference suppressiontechniques. The single-antenna interference suppressionmethods, such as frequency-domain filtering [2], adaptivetime-domain filtering [3, 4], and time-frequency (TF) fil-tering [5], have the advantages of small volume and lowhardware complexity; however, they can only deal with theinterferences with sparse characteristics in time and fre-quency domains (such as narrowband interferences andlinear chirp interferences) and are not able to cope with mul-tiple interferences [6] effectively. The space processing based

on an antenna array, such as power inversion technology andspace-only MPDR (S-MPDR) beamformer, can nullify wide-band interferences (WBI) and narrowband interferences(NBI) regardless of their time and frequency characteristics[7]. But the number of interferences coped with by space-only-based methods is limited to the number of antenna ele-ments. To deal with this shortcoming, the space-time adap-tive processing (STAP) is introduced in GNSS applicationsand widely studied [8–10]. By combining time and spatialprocessing, it increases the number of suppressed NBI with-out extra elements in the array; nevertheless, it still cannotdeal with the scenario in which the number of WBI exceedsthat of antenna elements. With the rapid development ofjamming technology and the increasingly complex electro-magnetic environment, how to effectively deal with moreinterferences with a limited number of antenna elementshas aroused the concern of people [11]. Recently, [12] drewthe attention on suppressing the multiple interferencesaccording to their direction of arrival (DOA) and power byusing an open-loop antijam approach. The key idea is to sup-press the strong interferences (interference-to-signal ratio(ISR) >30 dB) by spatial processing and ignore the weak

HindawiInternational Journal of Antennas and PropagationVolume 2018, Article ID 2301052, 9 pageshttps://doi.org/10.1155/2018/2301052

interferences. Obviously, it failed when the number of stronginterferences exceeds that of antenna elements. In addition,the methods mentioned above are not able to cope with theWBI arriving from the same direction as GNSS signals verywell. Reference [13, 14] drew the attention on cascaded inter-ference suppression methods based on sparse decompositionand spatial filtering. In the first stage, the interfering signalswhose waveform characteristics are known are detected andcanceled by utilizing their sparsity in the overcompletedictionary, and the residual interferences are suppressedby spatial filtering in the second stage. However, they needthe prior information of interfering signals dealt with bysparse decomposition.

In view of the above problems, this paper proposes aspace-time-frequency adaptive processor (STFAP) by com-bining TF analysis and spatial processing. More specifically,our main contributions are as follows: firstly, in order toavoid the repeated consumption of the spatial degree of free-dom (DoF), we propose a common period estimation anddata block technique which can obtain the common periodof generalized periodic signals and segment received signaldata into blocks; then, the signal data in each block areshort-time Fourier transformed (STFT) into TF domain,and the corresponding TF points with similar frequencycharacteristics are regrouped to structure space-time-frequency (STF) data matrixes. Secondly, to avoid the degra-dation of interference suppression performance when thenumber of interferences falling into a TF point exceeds thelimitation that an antenna array can cope with, we proposea space-time-frequency minimum output power- (STF-MOP) based interference suppression method to modifythe conventional weight calculation formula by using a refer-ence TF point.

2. Signal Model

The analog signals received by an N-element antenna arraycan be expressed as follows:

x t = as t + 〠I

i=1bi J i t + η t , 1

where x t = x1 t x2 t ⋯ xN t T is the array signal, eachrow corresponding to one antenna, and “ • T” representsthe transpose; i = 1, 2,… , I represents the number of inter-fering signals; a and bi denote the steering vector of the GNSSsignal and the ith interfering signal, respectively; s, Ji and ηare defined as the GNSS signal, the ith interfering signal,and the receiver thermal noise, respectively.

According to their frequency characteristics, interferencescan be divided into NBI (e.g., single-tone (S-T) interferingsignals) and WBI (e.g., wideband periodic frequency-modulated (WBPFM) and Gaussian noise (WBGN) interfer-ing signals). The WBPFM interfering signal is one of themost efficient interferences due to its wideband and nonsta-tionary characteristics in the frequency domain, and theWBGN interference is considered to be the most costly inter-ference because of the requirement of large transmit power

[15, 16]. Reference [17] pointed out that using different com-binations of multiple WBPFM and S-T interfering signalsand fewer WBGN interferences, we can effectively disablethe STAP with lower costs. Therefore, this paper focuses onthe research of mixed interference suppression in the pres-ence of these interfering signals. In general, the S-T andWBPFM interfering signals can be expressed as follows:

JMkt = Ake

−j2π f Mkt +f k+φk , 2

where f Mk• is the frequency-modulated (FM) function with

the period Tk, where k = 1, 2,… , K represents the number ofWBPFM interfering signals; Ak, f k, and φk are the amplitude,the carrier frequency, and the phase, respectively.

3. The Proposed STFAP

From [1], we have known that, in a relatively short time, thebandwidth of the WBPFM signal is narrow; however, sinceits frequency is rapidly varying compared to the receiver inte-gration time, it acts like a WBI. And as we have known, thetime domain finite impulse response (FIR) filter in the con-ventional STAP is not able to make full use of the time-frequency sparse characteristics of interference signalsbecause it only has frequency-resolving ability. Then, theWBPFM interference is treated as a global WBI. It resultsin the waste of the spatial DoF.

It is aware that since WBPFM interfering signals havesignificant concentrated energy distribution and periodicityin the time-frequency domain, there are a few TF pointsaffected by the interferences. For the convenience ofexpression, an analysis is carried out by taking two linearfrequency-modulated continuous wave (LFMCW) interfer-ing signal as an example, and their spectrogram is shownin Figure 1, where f c and B are the carrier frequency andbandwidth, respectively; f m f

, mf = 1, 2,… ,M2, denotes thefrequency bins; Tc and l represent the integer multipleof two modulation period of the two LFMCW interferingsignals and a positive integer, respectively; and tl,mt

mt =1, 2,… ,M1 mt = 1, 2,⋯,M1 is the number of signal datain time domain. And the TF point (tl,mt

, f m f) is named as

the (mt,mf )th TF point belonging to the lth block, and wedefined that the “ mt,mf th TF point” represents the“ mt,mf th TF point” belonging to all blocks. From it, wecan find out that although the bandwidth of the two interfer-ing signals are the same, their frequencies are different atmost times due to their different modulation periods and ini-tial frequencies. In theory, WBPFM interferences can betreated as NBI by using a single TF point data, and the num-ber of interferences falling into one TF point may be less thanthe total number of interferences in the receiving environ-ment. However, we need huge amounts of snapshot datato ensure the performance of interference suppressiondue to the unknown nature of interferences and the ther-mal noise. Looking closely at Figure 1, the frequency charac-teristics of the two interfering signals in TF points (tl,mt

, f m f)

and (tl+ln,mt, f m f

), such as (t1,1, f1) and (t2,1, f1), are consis-tent, where ln is a positive integer. In other words, all of the

2 International Journal of Antennas and Propagation

mt ,mf th TF points consist the same WBPFM interfer-ences. Then, we are able to regroup the TF points withsimilar TF characteristics to obtain the required numberof snapshot data.

Accordingly, we proposed a STFAP which is to improvethe multiple interference suppression performance of GNSSreceivers by using sparse characteristics of interfering signalsin time, frequency, and space domains. The diagram of theproposed STFAP is shown in Figure 2. It can be found thatcompared with the conventional multiple-antenna interfer-ence suppression techniques, such as S-MPDR beamformerand STAP, the proposed method requires no extra antennaelements, RF modules, and analog to digital conversion

modules. The difference between conventional methods andthe proposed one is the digital signal processing. And theproposed method is composed of the common period esti-mation and data block technique, the STF data matrix con-struction method, and the STF-MOP-based interferencesuppression. Firstly, the unbiased autocorrelation analysis iscarried out for the received signal data in one of the channelsto estimate the common period of WBPFM interferingsignals. Then, the received signal data in all channels are seg-mented into blocks according to the estimated period.Secondly, the signal data in each block are STFT into TFdomain, and the corresponding TF points with similar fre-quency characteristics are grouped to structure STF data

0

fc + B

fc

t1,1, t1,2, t1,3, t1,4, t1,5

f1

f2

fM2

t1,M1−1, t1,M1, t2,1, t2,2, t2,3 t2,M1−1, t2,M1 tl,M1−1, tl,M1

Tc 2Tc lTc

f

t

…

… … …

… … … …

Figure 1: The frequency variation of two LFMCW interfering signals.

Time-frequencydomain

STF-MOP

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

… …

t2, fM2 … tM1, fM2

t2, fM2 tM1, fM2…

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

… …

t2, fM2 … tM1, fM2 ISTFT

Σ

Σ

Σ…

t1, f1 t1, f1 … t1, f1

t1, f2 t1, f2 … t1, f2

tM1, fM2 tM1, fM2 … tM1, fM2

t1, f1 t1, f1 … t1, f1

t1, f2 t1, f2 … t1, f2

tM1, fM2 tM1, fM2 … tM1, fM2

……

Commonperiod

estimation

Data block

Time-frequency domain

f

t

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

Block 1

Block 2

…

Block L

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t1, f2

t1, fM2

t2, f2 … tM1, f2

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

…… …

t2, fM2… tM1, fM2

STFT

STFT

Data block

Time-frequency domain

f

t

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

Block 1

Block 2

…

Block L

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

t1, f1 t2, f1 … tM1, f1

t1, f2

t1, fM2

t2, f2 … tM1, f2

… …

t2, fM2 … tM1, fM2

STFT

STFT

…

…

…

A/D

A/D

Fron

t—en

d 1

Fron

t—en

d N

…

…

…

…

…

……

………

STFT

STFT

Figure 2: The diagram of the proposed STFAP.

3International Journal of Antennas and Propagation

matrixes. Thirdly, the optimum weight vectors are computedby using STF-MOP-based weight calculation method, andthe TF data after interference suppressing are inverse short-time Fourier transformed (ISTFT) into the time domain.

3.1. The Autocorrelation-Based Common Period Estimationand Data Block Technique. Since the energy of GNSS signalsat ground receivers is much lower than that of the receiverthermal noise, they are able to be negligible in the followinganalysis. Then, the signal in the nth channel can be writtenas follows:

xn t = 〠K

k=1JMk

t +ℵ t , 3

where JMkrepresents the kth WBPMF interfering signal;

ℵ t =∑I−Ki=1 Jgi t + ηn t , in which Jgi and ηn are the ith

WBGN interfering signal and the receiver thermal noise cor-responding to the nth channel, respectively. Since Jgi and ηnare independent of each other, ℵ can be regarded as aWBGN. Because all signals are independent of each other,the cross-correlation function of different signals is 0: theautocorrelation function of xn should be as follows:

Rx τ = 〠K

i=1RMkMk

τ + Rℵℵ τ , 4

where RMkMkand Rℵℵ are the autocorrelation function of the

kth WBPFM interfering signal and the autocorrelation func-tion of ℵ, respectively. Since ℵ is the Gaussian white noise,Rℵℵ τ = 0 τ ≠ 0 . And the autocorrelation function of theperiodic signal is still a periodic function. Then, when τ ≠ 0,

Rx τ = 〠K

k=1RMkMk

τ

= 〠K

k=1

A2k

2 e−j2πf kτ limT→∞

1T

−T

Te−j2π f Mk

t −f ∗Mkt−τ dt

≤ 〠K

k=1

A2k

2 ,

5

where “ • ∗” represents the conjugate. If and only if f Mkt

− f Mkt − τ = 0 and f ki − f kj τ = α, in which α is an integer,

the equality holds. Because f Mkis a periodic function over τ

and the period is Tk, Rx τ has many maximums whichappear at Tc.

Tc ∣ Tc = T1, T2,… , TK CM & f ki − f kj Tc = α , 6

where “ • CM” is defined as the function for computing thecommon multiple of a list of numbers.

Based on the above analysis, an autocorrelation-basedcommon period estimation method in practical applicationsis proposed. And the details are described as follows. The dig-ital signals with sampling period T s can be written as follows:

x m = x1 m x2 m ⋯ xN m T 7

And the unbiased estimation of the autocorrelationfunction can be obtained by using finite-length receivedsignal data.

R̂x mτ = 1MR −mτ

〠MR

m=mτ+1xn m x∗n m −mτ , 8

where MR is the length of sampled signal data. Because itis impossible to get infinite-length sampled signal data, theautocorrelation function of WBGN may not be 0 whenmτ ≠ 0. And the maximums of R̂x mτ appearing at Tcmay not have strict equality. To estimate the commonperiod of multiple WBPFM interfering signals, eliminatethe value of R̂x mτ near mτ = 0, then a normalizationprocessing is carried out:

R̂c mτ =0, 0 ≤mτ ≤m0,

R̂x mτ

max   R̂x mτ

, others,9

wherem0 is the minimum of the search range of the commonperiod. Then, the time corresponding to the first peak whichis greater than ρ frommτ = 0 is the block sizeMc (T̂c =McTsis the estimated common period). ρ 0 5 < ρ < 1 is a thresh-old to judge whether the peak is required.

Let the number of blocks in every channel be L, then thesignal vector of the lth block at the nth channel can be writtenas follows:

Xnl = xn l − 1 Mc + 1 ,… , xn l − 1 Mc +McT 10

3.2. The STF Data Matrix Construction Method. The digitalsignal data in each block are STFT into TF domain:

Xn mt,mf , l =〠m

Xnl m ω mt −m e−j 2π/Mc m fm, 11

where “ω • ” represents the analysis window; mt = 1, 2,… ,M1 andmf = 1, 2,… ,M2 denote the number of sampled dataand the number of frequency bins, respectively; Xn mt ,mf , lis named as the “ mt,mf th TF point” belonging to the lthblock in the nth channel, which represents the TF character-istics of signals in the corresponding TF point. And WBPFMinterferences in the mt,mf th TF points belonging to allblocks have similar TF characteristics. To obtain enoughsnapshot data with similar frequency characteristics, weshould regroup the TF point data. Then, every batch of themt,mf th TF points should be treated as an input matrixof spatial filtering:

X mt ,m f= X1 mt ,m f

, X2 mt ,m f,… , XN mt ,m f

T, 12

in which

Xn mt ,m f= Xn mt,mf , 1 , Xn mt,mf , 2 ,… , Xn mt,mf , L T

13

4 International Journal of Antennas and Propagation

3.3. The STF-MOP-Based Weight Calculation Method. TheMPDR beamformer is employed to nullify the interferencesin each batch of TF points, whose optimization problemcan be expressed as follows:

minw

 wHmt ,m f

R mt ,m fw mt ,m f

 s t  wHmt ,m f

a = 1, 14

where w mt ,m frepresents the array weight vector for the

mt,mf th TF point; R mt ,m fis the covariance matrix esti-

mated by using the maximum likelihood criterion:

R mt ,m f= 1LXH

mt ,m fX mt ,m f

, 15

where “ • H” denotes the conjugate transpose. Then, theoptimal weight vector is

w mt ,m f opt=

R−1mt ,m f

aaHR−1

mt ,m fa= β mt ,m f

R−1mt ,m f

a 16

As shown in (16), w mt ,m f optis calculated by only using

the information of the mt,mf th TF point and having noth-ing to do with other TF points. And β mt ,m f

is real and makesall weights in the same order of magnitude. But when thenumber of interference falling into a TF point exceeds thelimitation that an antenna array can cope with or there areinterferences arriving from the same direction as GNSS sig-nals, it will naturally cause the interferences not to be sup-pressed. In order to solve these problems, a STF-MOP-based weight calculation method by using the informationof the TF point whose energy is minimal is proposed, whichcan be expressed mathematically as follows:

w mt ,m f opt=

R−1mt ,m f

aC + aHR−1

mt ,m fa, 17

where C is defined as follows:

mmaxt ,mmax

f = arg maxmt ,m f

 aHR−1mt ,m f

a,

C = aHR−1mmax

t ,mmaxf

a18

Then, the TF signal data after spatial filtering are asfollows:

Y mt + l − 1 Mc,mf =wHmt ,m f opt

X mt ,m f: , l , 19

where X mt ,m f: , l is the lth column of matrix X mt ,m f

.Finally, Y is ISTFT into the time domain to obtain the

output data for subsequent processing.

4. Experiments and Simulation Results

Two simulations have been carried out to assess the perfor-mance of the proposed method. In all simulations, a linearhalf-wavelength space antenna array with 4 elements isadopted. And there is only one GNSS signal operating on1.023MHz with C/A code, whose DOA is 80°. If there is nospecial explanation, the analog signal with signal-to-noiseratio (SNR = −15 dB) is sampled at 4.096MHz. The parame-ters of interference signals are shown in Table 1, where T FMis the period of FM; LFMCW, SFMCW, and CF representthe linear frequency modulation, sinusoid frequency modu-lation interferences, and the center frequency ofWBI, respec-tively. And the length of ω • is 65; L = 20; ρ = 0 95.

4.1. Influence of M2 on the Performance of the ProposedMethod. To show the influence of M2 on the performanceof the proposed method, an interference scenario in the pres-ence of all the interfering signals listed in Table 1 has been

Table 1: Interference signal characteristics.

Name Type DOA Broadband CF T FM μs INR (dB)1 S-T 50° 0 1 023MHz / 55

2 LFMCW 80° 2MHz 1 023MHz 31 25 55

3 LFMCW 110° 2MHz 1 023MHz 20 83 55

4 SFMCW 30° 2MHz 1 023MHz 62 56 55

5 SFMCW 165° 2MHz 1 023MHz 50 05 55

6 WBGN 20° 2MHz 1 023MHz / 50

7 WBGN 155° 2MHz 1 0MHz / 50

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.975

0.98

0.985

0.99

0.995

1

1.005

False alarm probability

Det

ectio

n pr

obab

ility

M2 = 64M2 = 32M2 = 16

Figure 3: ROC curves of different M2.

5International Journal of Antennas and Propagation

considered. Then, the receiver operating characteristic(ROC) curves obtained from 500 Monte Carlo are used as ameasure of the performance for different M2.

As shown in Figure 3, the greater theM2 is, the better thereceiver performance is. It is because the bandwidth of theinterfering signal in each frequency bin decreases with theM2 increasing. And the greater the bandwidth of the inter-fering signal in each frequency bin is, the greater the proba-bility of multiple interferences falling into one TF point is.And the number of interferences falling into one TF pointexceeding the limitation that the antenna array can deal withmay bring lower interference suppression performance.However, the computational complexity increases with theincrease of M2. Then, the value of M2 should be selected byconsidering the computational complexity and interferencesuppression performance.

4.2. Advantages of the Proposed Method. In this section, theproposed multiple interference suppression method is com-pared with the well-known space-only MPDR (S-MPDR)beamformer [7], the distortionless space-time MPDR pro-cessor (DST-MPDR) [9], and the combining method basedon double-chain quantum genetic matching pursuit-sparsedecomposition and MPDR beamformer (DCQGMP-SD &MPDR) [14]. The number of time delay taps of DST-MPDR is Nτ = 9 for the proposed method, M2 = 32 Andassume that we only knew the prior information of S-T and

LFMCW interfering signals, then the signal processing flowand parameters of DCQGMP-SD & MPDR are the sameas in [14].

In order to evaluate the performance of the four methodsand to provide a direct and precise description, the computa-tional complexities of each processing module of differentmethods are given in Table 2, where “/” represents that themodule is not needed. N J,NG, and NQ denote the numberof interferences can be dealt with by DCQGMP-SD, thenumber of iterations, and the population size in theDCQGMP, respectively. Ns andNω are the length of sampledsignal data and the total number of windows occurs for theobservation length Ns, respectively. From Table 2, we canfind that the computational complexity of the proposedmethod is less than that of DCQGMP-SD & MPDR, butcompared with S-MPDR and ST-MPDR, the computationalcomplexity of the proposed method may increase. It isbecause the M1 increases with the increase of Tc, the com-mon period of multiple WBPFM interferences. Fortunately,most digital signal processors completely satisfied therequired computing power for a GNSS receiver equippedwith a small number of antenna elements.

To adequately show the advantages of the proposedmethod, four interference scenarios, denoted I, II, III,and IV, were considered. In the scenario I, interference1, 3, and 5 are used; in the scenario II, interference 1, 3, 4,and 5 are employed; in the scenario III, interference 1, 2,

Table 2: Computation complexities of the proposed method and the compared methods.

Name DCQGMP-SD Periodic estimation STFT and ISTFT Interference suppression

S-MPDR / / / O(N3)

ST-MPDR / / / O(N3τN

3)

DCQGMP-SD & MPDR O N JNGNQN2S / / O(N3)

Proposed / O Nslog2 Ns O NωM2log2 M2 O M1M2N3

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6 International Journal of Antennas and Propagation

and 5 are adopted; and scenario IV consists all interferencesin Table 1. And the acquisition results after interferencesuppression obtained by coherent integration are used tomeasure the performance of different methods for interfer-ence suppression. The integration time of the correlator isset to 5 ms.

For scenario I, since the number of interferences is lessthan that of antenna elements, all methods are effective tosuppress interferences. It is consist of the acquisition resultsas shown in Figure 4, where the correlation peaks of C/Acode are particularly obvious.

For scenario II, although the number of interferencesexceeds the DoF of the antenna array, the number ofantenna array is more than that of WBI. Then, fromFigure 5, it can be found out that DST-MPDR, DCQGMP-

SD & MPDR, and the proposed method are all able to sup-press these interferences, but the S-MPDR failed to deal withso many interfering signals. And for scenarios III and IV,Figures 6(a) and 6(b) and Figure 7(a) and 7(b) show thatthe S-MPDR and DST-MPDR failed to mitigate the interfer-ences due to the presence of the interference with the sameDOA as the GNSS signal or excessive number of WBI. FromFigure 6(c), DCQGMP-SD & MPDR can deal with theLFMCW interference with the same DOA as the GNSS sig-nal; it is because the prior information of S-T and LFMCWinterfering signals is known, and they can be canceled bysparse decomposition in the first stage of the method. Butas shown in Figure 7(c), since the prior information ofSFMCW interferences is unknown and the WBI is too muchin the residuary interferences, after processing by DCQGMP-

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Figure 5: Correlation peaks after interference suppression for scenario II.

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Figure 6: Correlation peaks after interference suppression for scenario III.

7International Journal of Antennas and Propagation

SD, DCQGMP-SD &MPDR failed in scenario IV. However,for both the two scenarios, from Figure 6(d) and Figure 7(d),it is obvious that the proposed STFAP can effectively dealwith all interferences. It is because the idea of regroupingprocessing in the TF domain and the improved weight calcu-lation technique using the information of reference TF pointscan make full use of the sparse characteristics of interferencesignals in time, frequency, and space domains.

5. Conclusions

Considering the different energy distribution and the period-icity of interfering signals in TF domain and their sparseproperty in spatial domain, a STFAP has been proposed. Byregrouping the TF points according to the common periodofWBPFM interferences and calculating the weight of spatialfilters using the information of reference TF points, the pro-posed method can deal with more WBPFM interferences.Simulation results have shown that with the same configura-tion of an antenna array, the proposed STFAP outperformsthe compared methods for multiple interference suppression.Especially, it can effectively cope with WBPFM interferenceswith the same DOA as the GNSS signal.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this article.

Acknowledgments

This work has been supported by the International S & TCooperation Program of China (ISTCP) (no. 2015DFR-10220), the National Major Research & Development projectof China (no. 2016YFC0101700), the Application Technol-ogy Research and Development of Heilongjiang Scienceand Technology Agency (no. GX16A007), the National

Natural Science Foundation of China (no. 61371172), theApplication Technology Research and Development ofHeilongjiang Science and Technology Agency (no. GC13-A307), and the Provincial Technique Research of Zhejiang(no. 2016C31095).

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