A Two Stage GPS Anti jamming processor for Interference Suppression and Multip ath mitigation Dan Lul'2,Renbiao Wul,Zhigang Sul,Wei Huang'
I.Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China, Tianjin,300300, P.R.China 2. National Key Lab for Radar Signal Processing, Xidian University, Xi'an, 710071,P.R.China E-mail:
[email protected] Abstract-Global Positioning System (GPS) has found wide application in many areas. However, due to the low power of the received signal, GPS is susceptible to a variety of interferences and multipath. In this paper, a two stage GPS anti-jamming processor based on adaptive arrays is proposed. Firstly, the array received signals are projected onto the orthogonal subspace corresponding to interference to suppress interferences. Then the interference free signals are further processed by a conventional data-independent beamforming to enhance the GPS direct-path signal and mitigate GPS multipath signals. Simulation results are provided to demonstrate the performance of the proposed algorithm.
Key words: Global Positioning System, Anti-jamming, Adaptive arrays, Multipath mitigantion
interference orthogonal subspace to suppress interferences in the first stage. After the suppression of the interference, interference free signal is further processed to enhance direct-path signal and attenuate multipath signals by a conventional data-independent beamformer. II.
SIGNAL MODEL
In Fig.1, after down-conversion and A/D conversion, the received signal model from an M-element uniform linear array can be written as [4] KPk
x
L
(n) =ZZYc4 (nTS-rkP)a k ri=ip)akp,I+Z(n) b + v(n)
()
(1)
where T, is Nyquist sample interval, K is the number of GPS satellite signals, and P. is the number of path corresponding to the kth GPS satellite. Irp is the time delay of the pth path of the kth satellite signal. cp is the waveform of the pth path of kp the kth satellite signal and p =0 denotes the direct-path signal. I, is the waveform of the /th interference. v(n) is additive white Gaussian noise vector, a denotes the spatial
I. INTRODUCTION Global Positioning System (GPS) has been widely used in civil and military applications and will gradually become a main tool of global navigation, because GPS can provide the accurate position, velocity and timing information for user in all weather conditions, anywhere in the world and anytime in the day. However, GPS signal is susceptible to intentional or P unintentional interference due to the extremely low power, if the interference signal's power exceeds the 30 dB processing signature of the pth path of the kth satellite signal and b gain offered via the dispreading of the GPS C/A code, the denotes the spatial signature ofthe /th interference. receiver is unable to recover navigation data. On the other hand, Note that, since the transfer characteristics and position of GPS multipath caused by signal reflections and diffractions Nte thay arheassfer beristics andpos between the GPS satellite and the GPS receiver is one of the antenna array are assumed to be known, akp and b1 is a main error sources for user's position. Therefore, it is function of direction of arrival (DOA) [5]. For an M-element necessary to make some measure to suppress interference and uniform linear array, there is the following form mitigate miltipath in order to provide accurate navigation information for GPS user. A s'n 1 Okp) ..exp(j 2T(MA - I)d s'nI 0,,7 (2) a(Okp) = Il exp(,l2.Td In recent years, the promising solution to the interference where i problem is use of adaptive antenna array (AAA) system[1-3]. K The AAA system sets in an anti-jamming processor between . . receiver, ^ . . which . . .is .shown p~~~~ath. deote th)ric P Let s (n =Zk=1 ckonT koaGP denotes the driect path GPS antenna array and conventional GPS as Fig. 1. In Fig. 1, the received signal vector from the antenna L array is processed in the anti-jamming module after signals vector, I (n) = )I, (n)b, denotes the interferences vector, 1=1 down-conversion and A/D conversion and the output of the anti-jamming module is fed into a conventional GPS for further then (2) can be rewritten as (3) x(n) = s (n) + Sm (n) + I (n) + v (n) processing after up-conversion and D/A conversion. The key K Pk problem of AAA system is how to design anti-jamming where sm (n) = ZZ ckP (nTs - ckp )a4p denotes the GPS processor. k=i p= In this paper, we propose a two stage anti-Jamming saelt multph signlsetr processor. The array received signal iS projected onto the
.
-
This work is supported in part by the National Natural Science Foundation of China under grant 60325102 and 60428101 and the 863 High Tech Project of China under grant 2006AA1 2Z321
1-4244-0284-0/07/$20.OO ©2007 IEEE
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V=l-U(UHU) UH
If we are assumed that the GPS signals, interferences, and noise are independent each other, then the covariance matrix of the received signals are
(6)
=le
where U eL ] is an M x L matrix, I is an MxM matrix, V is orthogonal projection matrix. Due toel. eL is the orthogonal basis of the interference subspace, where E{.} denotes the statistical expectation, (.)H denotes (7) reduces to the following equation conjugate transpose operation, RS' RI and RV represent the (7) V=I-UU covariance matrices of the GPS signals, interferences and noise B. Conventional data-independent Beamformer respectively. R ,= E {x(n)xH (n)} = R, + R, + R,
III.
(4)
Interference signals are cancellation by projecting array
Two STAGE ANTI-JAMMING PROCESSOR
data onto the interference orthogonal subspace. But anti-jammingpocessorproposdisreceived shw the GPS signal and GPS multipath signals are still direct-path prop anti-jAmming ed is stage The2 provessior,the i Fig., the A/ conveors accurately C/A codesignal order to acquire below the noise level. the received Fig.2.tIn ontor tinterfrence tho subspae by for the conventional GPSIn receiver, GPS direct-path must projected proecton rasfomatonmatix n he irs sage The two
two stage
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Aferbe
enhanced and
multipath signals
are
mitigated.
The
perforance of cnetio nala amfomingawillilbbe interference cancellation, free interference output data in the promneo ovninlaatv emomn t enhance GPS direct-path signal and first stage iSis synthesized to degraded due to the GPS direct-path signal and its multipath mitiateultiath signls b th methods conentinalarer coherent. modified beamforming oeet Some oemdfe emomn ehd for o data-independent beamforming technique in the second stage. d coherent signal processing are proposed in recent years, but these methods need to know the direction of arrival (DOA) of A. Interference Orthogonal Subspace Interference spatial signature is usually unknown and coherent signal or only are applied to the uniform linear difficult to obtain. But in GPS application, the GPS signals are array[6,7]. In the second stage, considering the fact that the well below the noise floor (typically 20-30 dB below the noise affection of GPS multipath signals on the acquisition of C/A floor) and interference signals are far above the noise floor. In code can be neglected if GPS multipath signals power is far this case, the covariance matrix of the array receiver signals is below GPS direct-path signal[8]and the DOA of GPS signal can be obtained by inertial navigation system mainly dominated by interference covariance matrix. Therefore direct-path interference subspace can be obtained by the eigenvalue (INS), the conventional data-independent weight vector may be to adjust beampattern of array to aim at the DOA of the decomposition (EVD) of the covariance matrix of the array used GPS direct-path signal and further control peak sidelobe level receiver signals. to fall any unknown direction GPS multipath signals. Making singular value decomposition (SVD) for Rx, we From the above discussion, the weight vector of anti-jamming processor proposed in this paper can be written can obtain the following form
firstigstae ltsynthesizd eignhan GbS direct-pathnsignal
RX where
A, (i = 1,
M =
eeZ
L)
L
M
eH + EA eeH i=L+ I= e
as
(5)
w = Vaq
is the L largest eigenvalues, e1 (i 1,* L) is the ith eigenvector corresponding to the ith largest eigenvalue. A, (i = L + 1... M) is the M - L smallest eigenvalues, e, (i = L +.1... M) is the ith eigenvector corresponding to the ith smallest eigenvalue. Due to the fact that the GPS signal is very weak and the interference signals are very strong, ei (i= 1, L) only span the interference subspace and e, (i= L+l... M) span the signal plus noise subspace. Note that spatial signature vector {bl, bL} also span the interference subspace. So eigenvectors{e1,...eL} may replace interference spatial signature vector{bl...bL},Then we can obtain the interference subspace by finding the eigenvectors corresponding to the L largest eigenvalues of RXX. Once the interference subspace is determined, we can find the orthogonal subspace of interference by the following formula =
(8)
where w is weight vector and aq is select to Chebyshev quiescent weight vector in the next simulation experiments.. IV. SIMULATION RiESULTS In our simulation, we employ a uniform linear array with the half-wavelength interelement spacing and sample array received data with T= 200 ns. DOAs of the GPS direct-path signal and two GPS multipath signal are 1O, -1 50 and 25 respectively, an interference signal impinges on the antenna array from -45 The noise is white Gaussian and has a power of OdB and SNR is -20dB and INR is 40dB. The time delay needed for the direct-path signal to travel from the satellite to receiver is300,us, which is equal to 1500 sample intervals. Time delay of two multipath signals from the satellite to receiver is 300.9,us and 301,us respectively. The interference suppression and multipath mitigation performance of the proposed anti-jamming processor is shown as Fig.3. From the Fig.3, we can see that the array beampattern generate high gain toward the GPS direct-path signal direction
747
.
and place deep null at the interference location, while falling the GPS multi-path signals. In order to further illuminate the performance of the proposed anti-jamming processor, the simulation experiment on the receiver's synchronization capabilityis is made. In the synchronizationcapability macievd by experiment, the synchronization iS achieved cross-correlating the received signal with the locally generated C/A code. When the receiver synchronizes with the satellite, there is a maximum correlation. The delay time corresponding with the maximum correlation is the delay time of the local C/A code, which is also time delay of GPS direct-path signal travel. Note that in this simulation experiment, the delay of
ththereceiver's
processor is proposed. Simulation results show that the scheme proposed is a good candidate for GPS interference cancellation and multipath mitigation. REFERENCES 1]
y
local C.AiS code at 1500 Sample local C/A code at maximum correlation
max
D. Moelker, T. V. Pol, and Y. Bar-Ness, "ADAPTIVE ANTENNA ARRAY for INTERFERENCE CANCELLATION in GPS and
GLONASS RECEIVERS," in Proceeding of the IEEE 1996 Position Location and Navigation Symposium, pp. 191-198, 1996. [2] R. L. Fante and J. J. Vaccaro, "WIDEBAND CANCELLATION of INTERFERENCE in a GPS RECEIVER ARRAY," IEEE Transaction on Aerospace and Electronic Systems, vol.36, no. 2, pp.549-564, April 2000. and M. Zoltowski, "LOW COMPLEXITY [3] W. Myrick, J. Goldstein, in SPACE-TIME PROCESSING for
m
cANTI-JAMMING Proceedings of the 2001
IEEE International Conference on GPS," Acoustics,
Speech, and Signal Processing, vol. 4, pp. 1332-1336, 2001. intervals. Fig.4 shows the simulation result of normalized cross-correlation for GPS receiver. Fig.4(a) is normalized [4] W. Sun and M. Amin, "MAMMUM SIGNAL-to-NOISE RATIO GPS ANTI-JAMMING RECEIVER WITH SUBSPACE TRACKING", IEEE cross-correlation curve with only GPS direct-path signal using International Conference on .Acoustics, Speech, and Signal Processing an antenna. Fig.4(b) is normalized cross-correlation curve with (ICASSP )., Philadelphia, PA, March 2005. GPS direct-path signal and multipath signals using an antenna. and R.New Moses, 'ANALYSIS of SIGNAL SPECTRUM", Pearson cross-correlation curve with . GPS [5] P.Stoica Hall, Fig.4(c) is normalized Jersey 2005. * r 1 r* *1 * * using an [6] ~~~~~~~~~Prentice signals* and* interference direct-path signal,- multipath T.J.Shan and T. Kailath, "ADAPTIVE BEAMFORMING for Fig'4diiSs normalize antenna. antenna. normalized cross-correlation curve with Fig.4(d) SIGNALS and INTERFERENCE", IEEE Trans. Acoust., COHERENT Speech, Signal Processing, vol. ASSP-33, pp.527-536, June 1985. interference suppression but without multipath mitigation using antenna array. Fig.4(e) is normalized cross-correlation curve [7] T.S.Lee and T.T.Lin, "COHERENT INTERFERENCE SUPPRESSION with COMPLEMENTALLY TRANSRORMED ADAPTIVE proposed anti-jamming processor. Comparison Fig.4(a) with BEAMFORMER", IEEE Trans on Antennas and Propagation, Vol.46, Fig.4(b), we can see that the receiver is unable to acquire No.5, pp.609-616, May 1998 accurate code delay time since GPS multipath signals impinge A.Brown, "MULTIPATHof ION REJECTION through SPATIAL for [8] ~~PROCESSING",Proceeding on the receiver (i.e maximum is at .. 1504 sample intervals GPS 2000, Salt Lake City, Utah, .> . . . . . . .......... Septerber, 2000. is of> the receiver multipath). Fig.4(c) indicates the performance very poor with strong interference. Fig.4(d) shows multipath still effects on the acquisition of C/A code delay after interference is cancelled (i.e maximum is at 1505 sample intervals ). Fig.4(e) shows the receiver can acquire code delay time comparison with Fig.4(a). cross-co
n
c
e
w
V. CONCLUSION In this paper, we have considered the development of GPS anti-jamming processor in AAA system. Combining the
subspace projection technique with the data-independent beamforming technique, a two stage GPS anti-jamming
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