A hybrid beamforming approach to anti jamming for multi channel GNSS receivers

We consider the problem of anti-jamming in GNSS navigation. In this work, we introduce the novel concept of a hybrid beamforming approach to antijamming for multi-channel GNSS receivers.

A HYBRID BEAMFORMING APPROACH TO ANTI-JAMMING

FOR MULTI-CHANNEL GNSS RECEIVERS

Nguyen Huu Trung1*, Nguyen Minh Duc1, Thai Trung Kien2

Abstract: We consider the problem of anti-jamming in GNSS navigation In this

work, we introduce the novel concept of a hybrid beamforming approach to anti-jamming for multi-channel GNSS receivers In this method, three separate techniques are integrated: a) the system suppresses jams by nulling based on eigen-decomposition of correlation matrices; b) the direction of desired satellite is estimated by phase difference based on antenna geometry and carrier-phase measurements; and c) an adaptive beamformer is used to optimize desired signal while minimizing interferences The characteristics of the proposed system model is demonstrated using Monte-Carlo simulations

Keywords: GNSS, Anti-jamming, Interference mitigation, Hybrid beamforming, Multi-channel GNSS receivers

1 INTRODUCTION

The Global Navigation Satellite System (GNSS) includes the Global Positioning System (GPS) operated by the United States, the Global Orbiting Navigation Satellite System (GLONASS) and various other systems such as COMPASS operated by China and GALILEO operated by Euro in future With GNSS, multi-constellation signals will be available to increase the performance of receivers operating with some or all of these systems [1] Global Navigation Satellite Systems (GNSS) plays an important role in many aspects of life, from military and defense to transportation, rescue, surveying maps, marine navigation, aviation… with high demanding requirements for security and integrity [2]

GNSS receivers have to operate at very low signal levels and in the presence of

RF interference including jams, multipath and noise For GPS system, the satellites have an orbit altitude of 20200Km from earth GPS L1 signals are transmitted with

a power of 44.8 W at 1575.43MHz and GPS satellite antenna gain is 12dBi Assume receiver antenna gain is 4dBi, the power level received by user located near the Earth surface is -125dBm using free space loss model while background inband noise (2.046MHz) is -110dBm However, spread spectrum processing gain

is 43dB (10log1.023Mbs/50bps ≈ 43dB), so the signals are recovered at power level of -110dBm - 43dB = -153dBm In fact, the received power strength requirement will be several dB above the theoretical level [3]

With this very low signal levels, it is easy for GNSS receivers to be subjected to unintended and intended jams In the case of jams, the signals are unable to be synchronized Especially in military applications, GNSS receivers have to operate

in the ruggedenvironment and mitigate interferences in order to provide reliable navigation solutions [4]

The effect of multipath on GNSS receiver performance has been widely analyzed, whereas many anti-jamming and multipath mitigation algorithms have been proposed [5-10] In order to mitigate interferences, a single-antenna receiver can make use of time and frequency diversity, such asadaptive space-time equalization techniques [11] A remarkable approach is based onthe use of antenna

arrays that can benefit from spatial-domain processing and thus mitigate the effects

of multipath Their capability is usually applied to the signal tracking operation of GNSS receivers, and there exists an extensive bibliography on this topic [12] Recently, multi-antenna techniques have been presented in [13] for interference mitigation A digital beamformer works as a spatial filter to mitigate the interferences and acquire the signal using the beamformer output [14] The beamformer design relies on a priori knowledge of a reference waveform or the spatial signature of the signal using DOA estimation [15]

Antenna arrays and beamforming algorithms may estimate direction-of-arrivals (DOAs) [16] But, in a GNSS receiver, due to the extremely low receiving power

of the satellite signals, it is difficult to estimate the DOA before signal correlation, and DOA-based beamforming techniques usually need a calibrated array [17].However, if we make use of plural of correlators that work by carrier-phase measurements then we can estimate the direction of desired satellite by phase difference based on antenna geometry and carrier-phase measurements

In this paper, weproposeahybrid beamforming approach to anti-jamming for multi-channel GNSS receivers design The approach suppresses jams by nulling based-on subspace orthogonal projectionand maximizesthe gain of useful GNSS signals by minimum variance distortionless response beamformer We overcome the problem of the DOA estimation by using differential carrier-phase measurements

The rest of the paper is organized as follows In section 2, the necessary background is given about notations and GNSS signal structure and carrier-phase measurement for satellite direction estimation In section3, the proposed system is shown with beamforming scheme Section 4 provides simulation results and characteristics of the proposed system Finally, the conclusions of this paper are for concluding remarks, and suggestions for further researches

2 PRELIMINARIES 2.1 Notations

Throughout the paper, following conventions are used Bold capital letters are denoted for matrices, while low-case bolt letters are for vectors.ℝ{ } stands for real, { } for either expectation or average value of { } The super scripts ρ(.), (.)T

, (.)H, (.)+, Re{.} stand for rank, transpose, conjugate transpose, pseudo-inverse, real part of (.) Non-negative (positive) definite matrix ≽ 0 is a symmetric one having only non-negative (positive) eigenvalues

2.2 GNSS Signal model

The term GNSS means interoperability and compatibility between different satellite navigation systems: Modernized GPS + GLONASS + GALILEO GNSS makes use of CDMA, BOC modulation (binary offset carrier) and QPSK Transmitted signal for the normalized complex envelope (i.e base-band version) ( ) of a RF signal ( )( ) ( ) includes inphase component and quadrature component ( )( ), ( )( ) of kth satellite respectively [18] We have:

( )

( ) = 2 ( )( ( )( ) − ( )( )) ( ( )( ) ( )) (1)

where: Re{}: Real part of the signal; ( )( ): Average signal power of satellite k

at frequency of ; ( ): Phase of the signal transmitted from satellite k

The components data ( )( ) and pilot ( )( ) are modulated by DS-CDMA and BOC (in order to minimize interference to existing available GPS signals) typical of modernized global positioning system [19] The BOC modulation is a signal subcarrier modulation where the signal is multiplied by a rectangular

subcarrier (sine or cosine phased) Both the subcarrier frequency fs and the

pseudo-random noise sequence (PRN code) with chip rate fc are an integer multiple of the

reference frequency f0=1,023MHz BOC signal is denoted as BOC( , ) or BOC( , ) where the integer represents the ratio between fs and reference

frequency f0 and the integer represents the ratio between code rate and f0

( )

( )

where: [.] is integer part, ( ), , ( ), : Brimary spreading sequences for data (D) and pilot (P), ( ): Navigation message, : Carrier frequency, Tc: Chip rate and ( ): Unit pulse

2.3 GNSS carrier-phase measurement

Since the carrier-phase measurement have higher resolution than that of the code phase measurement, it can be used for the attitude determination of vehicles with multiple antennas confuguration In this case, we use carrier-phase measurements to estimate phase shifts relative to the reference antenna for steering vector in beamforming stage

In general, the carrier-phase measurement model is as follows [20]:

( )

( )

+ (4)

where the subscript k indicates the k-th receiver (for master, denote b, for slave, denote r), the superscript i indicates the i-th satellite, λ is the wavelength, ( ) is the

true range between the receiver antenna k and GNSS satellite i, c is the speed of

light, is receiver clock error from GNSS time, ( ) is the satellite clock offset from GNSS time, ( ) is ionospheric delay error, ( ) is tropospheric delay error, ( ) is delay error due to satellite ephemerides error, ( ) is the carrier-phase integer ambiguity and represents other errors such as multipath, inter channel receiver biases, thermal noise , = ( ), ( )= ( )( ) are phases at initial time

The phase‐range is expressed as:

Φ( ) = λ ( ) (5)

The single and double carrier-phase difference is modeled as shown in Figure 2:

∇∆ ( ) = ∆ ( )− ∆ ( ) (7) Given that the common clock is used in the system, the satellite clock error

( )can be removed by a single difference as:

(8)

Due to the short baselines used, common mode error terms

∆ ( ) , ∆ ( ) , ∆ ( ) between satellites and receivers can be eliminated or greatly reduced, we have:

Figure 1 Vector Diagram for phase shift calculation

3 PROPOSED HYBRID BEAMFORMING SCHEME

FOR GNSS RECEIVERS 3.1 System model

The RF Front-end consist of a low-noise amplifier (LNA), a ceramic filter (BPF), a mixer to form the IF frequency signal, an IF filter and an ADC It converts the RF signal at the output of each antenna elements to a digitally sampled signal There are mixer modules in the array working with the same common clock which is synchronized to local oscillator

Consider the array with K elements The sample from ADC of each element of

the array is multiplied with a weight ∗ where the superscript * represents the complex conjugate The weighted signals are added together from K elements to form the output signal:

Master ⃗Slave

∆ ( ) = ∆ ( )+ ∆ ̅( )

∆ ( )

θ

Satellite i direction

= ∑ ∗ = (11)

Where represents the weighted vector of length , is received vector signal:

Figure 2 Block diagram of proposed system

The × 1 observation vector of the array at time t is given by:

( ) = ∑ ( ) , + ∑ ( ) + ( ) (13) Where ( ) is GNSS signal of interest (SOI) arriving from pth

satellite

(p=1 P) is a steering vector, ( ) and ( ) are broad band interference and

noise vector, respectively Number of satellites in view is P and number of jammers is Q Steering vector is expressed as:

3.2 Nulling based-on subspace orthogonal projection

For simplicity, we omit the parameter of time in the equations The covariance matrix of input signals is:

The covariance matrix can be divided into GNSS signal, interference and

noise component as:

= + + (16)

GNSS signal level is far below noise floor, so that:

≈ + (17)

Where is the average noise power The eigen-decomposition of the covariance matrix is given by:

= (18) Where the columns of = , , … , , … are the K eigenvectors of

, and = diag( , , … , , , … , ) contains the corresponding K

eigenvalues , , … , are the Q largest eigenvalues corresponding to Q

jammers Denote interference subspace as = span{ , , … }, then its orthogonal complementary space is:

= − ( ) (19)

And the subspace orthogonal projection matrix is:

= ( ) (20)

New steering vector for interference nulling is:

, = , (21)

3.3 Beamforming based-on carrier-phase measurements

Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal beamforming techniques include maximization of SNR, Minimum Mean Squared Error (MMSE), Linearly Constrained Minimum Variance (LCMV), minimum variance distortionless response (MVDR) are widely applied [21], [22] Design of the beamformer under statistically optimal method requires statistical properties of the source and the statistical characteristics of the channel

In this case, after interference nulling by subspace orthogonal projection, the output power of the beamformer is minimized andthe response according to direction of arrival of the desired signalis fixed in order to preserve desired signal while minimizing the impact of undesired components including noise and remaining interference We have the output response of signal source with direction of arrival and frequency is determined by ( , ) Linear constraint for the weighs satisfy ( , ) = , where c is a constant to ensure

that all signals with frequency come from direction of arrival are passed with

response c Minimization of output due to interference is equivalent to minimizing

the output power (minimum output power):

Using the method of Lagrange multipliers, find min[ ( ; λ)], where:

Solution of the equation [23]:

is the constraint steering vector toward the target satellite after interference

nulling The steering vector is set as phase shifts relative to the reference antenna, which are represented by:

(27)

Where ∆ , is the phase difference based on antenna geometry and the direction

of desired satellite ∆ , is the phase resulting from the difference of cabling and RF chain including down converter and digitization among elements of antenna array

∆ , can be calculated via carrier-phase measurement model by (10)

The covariance matrix is estimated by computing sample covariance matrix with assuming the sample mean is zero as follows:

[ ] =

(28)

Where N is the number of samples to compute the covariance matrix The

overline sign denotes complex conjugation

In practice, uncorrelated noise component ensures is invertible If c = 1 the

beamformer is called minimum variance distortionless response, MVDR, beamformer The MVDR beamformer does not require the knowledge of the direction of the interferences for weight vector calculation, it requires only the direction of the SOI [19] The minimization process minimizes the total noise including interference and uncorrelated noise

4 NUMERICAL RESULTS

The performance of the system is performed by means of the Monte-Carlo simulation The simulation estimates the influence of some parameters on the performance of the system These parameters include ISR (Interference to Signal Ratio); SNR (Signal to Noise Ratio), array configuration (UCA); Number of

antennas (M); Sampling rate f s; Difference DOA between transmited signal and

interference Δθ

Monte-Carlo simulation algorithm includes sequence steps: generation of transmit signal, interference and AWGN by parameters of SNR, INR and DOAs;

Reception of signal by steering vector a(t), interference and AWGN at sensors;

Beamforming weights calculation by processing signal samples; Compare output signal to source signal and evaluate NRMSE by Monte-Carlo method The number

of samples to compute the covariance matrix N = 103

Transmitted signal is determined narrow band sine wave signal Signal is transmitted continuously through the training sequence and the amplitude of the signal can vary or change in order to get the desired SNR at each antenna The transmit signal is of the form:

Where f c is carrier frequency, f s is sampling frequency, is phase of signal,

= [1: ] with N is simulated number of samples

Interference can be narrow band with the same frequency as signal or broadband interference as:

AWGN ( )= (0,1) has normal standard deviation 1 appears at every antennas

The system performance in simulation is Normalized Root Mean Square Error,

NRMSE, the final value is the average value of all Q values after each simulation:

Besides the simulation of system performance according to SNR we also simulate the performance of the system according to the interference The severity

of the interference is determined by INR (interference to noise ratio):

[ ] (interference to signal ratio) is in dB

In the simulations, Uniform Circular Arrayhave been used, array element spacing is 1/2 signal wavelength; GPS navigation symbols are in the BPSK symbols transmitted at 50 b/s; The C/A-code is a Gold code with a chip rate of

1.023 Mcps (or code period P = 1023) and repeats every millisecond; Carrier frequency Fc = 1.57542GHz; its DOA θs=30o, Jammers used in the simulations are generated as broadband binary signals with DOAs = -20, 30, 55 degrees Monte-Carlo experiment number is 200

(a)

(b)

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5

Angle [degree]

-45 -40 -35 -30 -25 -20 -15 -10 -5

Angle [degree]

(c)

(d)

Figure 3 Beamforming patterns (a): Subspace orthogonal projection, DOA

interferences = -20, 20 degrees; (b): MVDR algorithm, DOA signal = 30 degree, DOA interference = -20; (c) LCMV algorithm, DOA signal = 30 degrees, DOA interference = -20 degrees; and (d) Frost algorithm, DOA signal = 30 degrees,

DOA interference = 20 degrees

We first consider the problem of placing nulls in the directions of interferences

Jj(t) while preserving GPS signals si(t) If the relative received power of interference and desired signal at an antenna is taken as a reference, then the rejection of interference with respect to desired signal, is the change in relative power after the null has been placed To evaluate the rejection of the proposed system, we setup the simulation with two jammers at DOA of ±20 degrees, and a signal at DOA of 30 degrees and SNR = 0dB The rejection level is approximately35dB However, this is ideal case In practice, RF component, array mismatch,… decrease the performance

-45 -40 -35 -30 -25 -20 -15 -10 -5

Angle [degree]

-18 -16 -14 -12 -10 -8 -6 -4 -2

Angle [degree]

Beamforming patterns of beamforming algorithms under the influence of interference sources are shown in Figure4 Figure 4 (a) illustrated the nulling of two jammers;(b), (c), (d) show the responses of the various beamformers including MVDR, LCMV and Frost We see that the response at the incident angle of interference is suppressed

(a)

(b)

Figure 4 NRMSE according to SNR (a) Othorgonal Subspace projection only

and (b) NRMSE of the proposed system and various beamformers

The simulation results are presented in Figure4 (a,b) according to SNR range Figure 4 (a) shows NRMSE of othorgonal subspace projection method only and (b) shows NRMSE of the proposed system and various beamformers in performance comparing In the figure, we see that the proposed system yields significant result That is, the system is more robust to jamming and multipath due to hybrid beamforming method

5 CONCLUSIONS

This paper presented a hybrid beamforming approach to anti-jamming for multi-channel GNSS receivers for optimum performance We first apply nulling

0 1 2 3 4 5 6

SNR [dB]

Orthogonal Subspace Projection

1 1.5 2 2.5 3 3.5 4 4.5 5

SNR [dB]

MVDR LCMV FrostBeamformer Orthogonal Subspace Projection only Proposed Hybrid Method