# A Novel GPS Antijamming Receiver Based on Noncircularity

Authors: Chen Xian-Ning; Qun Wan; Yang Wan-Lin
Journal: Journal of Electrical and Computer Engineering
 (2010)

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## Abstract

We present a novel antijamming global position system (GPS) receiver that relies on the unique noncircularity of the GPS signal. Since the GPS signal is BPSK modulated, it is a noncircular signal while most interferers are circular signals. The proposed receiver utilizes this circular difference property to excise interferences while preserve the GPS signals. It is shown that the proposed receiver is a blind receiver that does not require any angular information of the satellites.


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## Body

## 1. Introduction

A Global Positioning System (GPS) is a satellite-based all-weather navigation system and having a large success in civil application because its low prize receives its global coverage and its precision in navigation solutions [1]. However, the intentional interferences and the increasing pollution of electromagnetic environment may make GPS receivers lose their efficacy. Interference suppression in GPS can be conducted in the time, space, or frequency domain, or in a domain of joint variables [2–4]. It is noted, however, that the existing GPS interference cancellation techniques do not fully utilize the noncircularity property of the GPS signal.Recently, more and more researches concerned on using the non-circularity of signals to improve the performance of signal processing such as root-MUSIC algorithm [5] and enhanced unitary ESPRIT [6] for non-circular sources DOA estimation, enhanced blind estimator [7], and nondata aided carrier frequency offset estimation in non-circular transmissions through frequency-selective channels [8]. GPS signal is BPSK modulated and is a non-circular signal while most interferers are circular signals.This letter proposes a new interference suppression technique using, in effect, the circular difference between the GPS signal and the interferes. Unlike previous contributions in this area, the proposed GPS receiver exploits the unique non-circular property to suppress a large class of narrowband and broadband interferers. Furthermore, neither the knowledge of the satellite locations nor the synchronization between the satellite and the receiver is required to perform interference cancellation.Section2 describes the system model and introduces the proposed method. Section 3 will present simulation results and show that the proposed method can achieve a similar performance as an MMSE receiver. Section 4 will make conclusions.


## 2. Proposed Antijamming Receiver

A block diagram of the GPS receiver with an M-element spatial uniform linear array(ULA) is depicted in Figure1.Figure 1
Block diagram of the GPS receiver.The waveforms impinging on the array are those of the GPS signals, interferences, and noise. After down-conversion and sampled by chip-rate, the discrete-time format of the received signal vector form can be presented as(1)x(n)=as·s(n)+∑p=1Pajp·jp(n)+v(n),
where s(n) is signal component, as steer vector of the signal; as=[1,ej2π(d/c)sinθs,…,ej2π(d/c)(M-1)sinθs]Tθs is steer vector of the GPS signal,where d is the sensor spacing, c is the propagation speed of the waveform, and θs represents the arriving angle of the signal; jp(n) is the waveform of the pth interfere; ajp=[1,ej2π(d/c)sinθjp,…,ej2π(d/c)(M-1)sinθjp]T is steer vector of the pth interferer, where θjp represents the arriving angle of the pth interferer; v(n) is additive white Gaussian noise sample vector  with variance σv.Equation (1) can be rewritten as(2)x(n)=s(n)+j(n)+v(n)
where s(n) denote the signal vector and  j(n)=∑p=1Pajp·jp(n) is the compound interference vector.Under the assumption that GPS signals, interference, and noise are independent, the normal covariance matrixRxx of the received signal becomes(3)Rxx=E{x(n)·xH(n)}=Rs+Rj+Rv,
where E{·} represents the statistical expectation. (·)H denotes complex conjugate transpose, and Rs, Rj, and Rv are covariance matrices of the GPS signals, the interference, and the noise, which are defined, respectively, as(4)Rs≜E{s(n)·sH(n)},Rj≜E{j(n)·jH(n)},Rv≜E{v(n)·vH(n)}=σvI,
where I is an M×M identity matrix.GPS signal is BPSK modulated and is a non-circular signal while jammers and noise are circular signals. The elliptic covariance matrixRxx′ of the received signal should be(5)Rxx′=E{x(n)·xT(n)}=Rs′+Rj′+Rv′,
where (·)Tdenotes transpose, and Rs′,Rj′, and Rv′  are elliptic covariance matrices of the GPS signals, the interference, and the noise. To circular signals, its elliptic covariance matrix is equal to zero, which means that(6)Rj′≜E{j(n)·jT(n)}=0,Rv′≜E{v(n)·vT(n)}=0.
Then, (5) becomes(7)Rxx′=Rs′.
Let w be the M×1 weight vector. Then, the output of the beamformer is given by(8)z(n)=wH·x(n),
and the beamformer w is obtained by Maximizing the Non-circular to Circular Ratio (MNCR) of the output signal:(9)wMNCR=argmaxwE{|z(n)·zT(n)|}E{|z(n)·zH(n)|}=argmaxw|wHRxx′w*|wHRxxw,
where (·)*denotes complex conjugate.Since the denominator of (9) is positive real, we notice that (9) is unchanged when w undergoes an arbitrary phase rotation. Then, by choosing a w such that Im{wHRxx(T)w*}=0 where Im{·} denotes the imagine part, then, (9) can be rewritten as(10)wMNCR=argmaxwRe{wHRxx′w*}Re{wHRxxw}.
Let(11)wr=Re{w};wi=Im{w},Rxxr=Re{Rxx};Rxxi=Im{Rxx},Rxxr′=Re{Rxx′};Rxxi′=Im{Rxx′},
where Re{·} denotes the real part. Then we can expand (10) in complex form as(12)wMNCR=argmax(wr,wi)Re{(wrT-jwiT)(Rxxr′+jRxxi′)(wr-jwi)}Re{(wrT-jwiT)(Rxxr+jRxxi)(wr+jwi)}=argmaxw̅w̅T(R̅xx′)w̅w̅T(R̅xx)w̅,
where j=-1 and w̅=[wrwi] is a 2M×1 real vector; R̅xx′=[Rxxr′Rxxi′Rxxi′-Rxxr′] and R̅xx=[Rxxr-RxxiRxxiRxxr] are both 2M×2M real matrices.Thus, the optimumw̅ is the eigenvector corresponding to the maximum eigenvalue of the following generalized eigenvalue problem:(13)R̅xx′·w̅=λmax·R̅xx·w̅,
where λmax denotes the maximum eigenvalue, which is also the maximum NCR.In practice,Rxx′ and Rxx are replaced by their sample estimate:(14)R̂xx′≜1KXK·XKT,R̂xx≜1KXK·XKH,
where M×K data matrix is XK≜[x(n),…,x(n-(K-1))].The updating algorithm may now be outlined as follows:(1)
estimatingR̂xx′ and R̂xx using data sample matrix XK;(2)
forming matricesR̅xx′ and R̅xx using real and imagine part of  R̂xx′ and R̂xx;(3)
determining an estimatew̅ according to (13);(4)
finally, the  estimate ofwMNCR can be written as(15)wMNCR=wr+jwi.


## 3. Simulations

A 7-element uniform linear array with half-wavelength spacing is used in the simulation. GPS navigation symbols are in the BPSK format and spread by the Gold code with processing gainP = 1023. At the receiver, chip-rat sampling is performed, and K = 800 samples are collected. Jammers used in the simulations are generated as broadband binary signals having the same rates as the C/A-codes but with a different structure than that of the C/A signals.In the first simulation, to examine the performance of the proposed GPS receiver in presence of multiple strong jammers, we compare the proposed GPS receiver with the MMSE receiver in [4]. In the simulation, the satellite is located at -20°, and the three jammers are at 10°, 40°, and 60°. It is noted that the proposed receiver need no prior information of the satellite location while the MMSE receiver does need the knowledge in order to compute the power of the GPS signal. Figure 2 shows that both receivers are capable of suppressing strong jammer while preserving the GPS signal, with the proposed receiver having the advantage of being a blind receiver.Figure 2
Comparison of Antenna gains between the self-coherence receiver and the MMSE receiver with SNR =-20 dB, JSR = 60 dB.In the second simulation, consider the same condition of the first simulation; we examine the effectiveness of the proposed GPS receiver. In GPS, the receiver is ultimately evaluated based on its ability to provide accurate pseudorange measurements. This is achieved by establishing synchronization between the receiver and the satellite, which is decided based on the cross-correlation between the beamformer outputs and a locally generated Gold sequence [1]. The normalized cross-correlations before and after the jammer removal in Figure 3, show that the proposed GPS receiver can effectively cancel directional jammers and achieve synchronization even when the JSR is as high as 60 dB (Figure 3(b)). Without interference suppression, however, synchronization fails, as is evident in Figure 3(a).(a) Normalized cross-correlation before jammer removal. (b) Normalized cross-correlation after jammer removal.
(a)(b)


## 4. Conclusion

We have presented a new GPS receiver that is based on the non-circularity of the GPS signals. Due to the different circularity between the GPS signal and interferers, we present new adaptive beamforming criteria—the Maximum Non-circular to Circular Ratio (MNCR) criteria. Utilizing this criterion, an anti-jamming GPS receiver is constructed to mitigate a wide class of interferers. Simulations have shown that the proposed receiver is capable of suppressing strong jammers while preserving GPS signals, without requiring any knowledge of the angular information of the satellites.



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*Source: 451214-2009-12-14.xml*