MVDR Radar Signal Processing Approach for Jamming Suppression in Satellite Navigation Receivers
Vera Behar1, Christo Kabakchiev2, Hermann Rohling3
1Institute for Parallel Processing, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., bl. 25-A, 1113 Sofia, Bulgaria
e-mail:
2Faculty of Mathematics & Informatics, Sofia University, 125, Tzarigradsko shose Blvd.
bl. 2, fl 3 (soufh), room 301. Sofia 1113, Bulgaria, e-mail:
3Technical University Hamburg-Harburg, Eibendorfer Str. 40, D-21073 Hamburg, Germany
e-mail:
Abstract
The Minimum Variance Distortionless Response (MVDR) technique which is well-known in radar signal processing will be applied in this paper for jamming suppression in a satellite navigation receiver. Two different beamforming schemes, conventional and MVDR, are applied to a satellite navigation receiver for mitigation of strong jamming before acquisition of the C/A code. The effect of beamforming on the cross-correlation performance is evaluated in terms of two quality factors: the signal-to-interference-plus-noise ratio (SINR) improvement factor estimated at the beamformer output and the post correlation signal-to-noise ratio (SNR) which will be estimated at the cross-correlator output. The simulation results demonstrate that the more effective jamming protection and as a consequence the improved performance of the C/A code acquisition are achieved using the MVDR beamformer procedure compared to the conventional one.
1. Introduction
In satellite navigation systems, Binary Phase Shift Keying (BPSK) modulated signals are transmitted by the satellites. The transmit power is relatively low but an adequate signal-to-noise-ratio (SNR) for accurate position estimation is assumed. However, the observed SNR at the satellite navigation receiver shows very low values between -20 and -30 dB in realistic situations. This makes it more or less impossible for the receiver to detect the C/A code with sufficient accuracy especially in situations where jamming will occur. If a strong broadband jamming source is nearby to the receiver, the noise component may rise to the level where the post correlation SNR of the receive signal is below the detection threshold.
One way to overcome this situation is to use some beamforming technique for broadband jamming suppression. This procedure has some advantages if the receive signal and the jamming signal originate from different spatial locations [1]. The conventional non-adaptive beamformer is the simplest technique, where all weights are of equal magnitudes and the phases which have been selected to steer the array in particular direction [2]. However, it is not effective in the presence of directional jamming signals, intentional or unintentional. The MVDR beamformer overcomes this problem by suppressing interfering signals from off-axis directions [3]. It requires only the information for the expected direction-of-arrival of the receive signals from different satellites.
In this paper, the capability of two beamforming procedures, conventional and MVDR, to suppress jamming signals and as a result of this to improve acquisition of the satellite signals is analyzed for two small 2D antenna arrays. The effect of array configuration, sampling rate of the incoming data and steering vector mismatch on the effectiveness of the joint “beamforming plus acquisition” algorithm is evaluated using the Monte Carlo approach.
2. Signal model
The input signal of a satellite navigation receiver is composed of the satellite signal, thermal noise and a variety of interference. In conditions of jamming, the complex valued samples of the received signal at time instant k can be mathematically described as:
(1)
where x(k) is the (M x 1) data vector, s(k) is the desired satellite signal sample, jl(k) is the lth broadband jamming sample, ac and bl are (M x 1) antenna array response vectors of the satellite signal and the lth broadband interference, respectively, n(k) is the noise sample and L is the number of broadband interference sources. The satellite signal is given by:
(2)
where Ps is the received signal power, c(k) is the C/A coded signal of length (20 x 1023), separate for each satellite, d(k) is the GPS data bit which remains constant over the length of one cycle of the C/A code, and f0 is the carrier frequency. The jamming signal j(k) occupies the entire receiver bandwidth and can be modeled as bandlimited additive white Gaussian noise (AWGN).
3. Signal processing
The conventional satellite navigation receiver is a multi-channel device, where each channel realizes acquisition and tracking of the signal from a single satellite. Here we consider the acquisition stage only. In our case, the signal processing includes two stages (Fig.1). Firstly, the digital beamforming is performed in order to mitigate broadband interference and secondly, the standard acquisition algorithm is performed in the frequency domain [1].
Fig.1: The flow-chart of the evaluation process
Beamforming stage: The digital beamformer increases the gain in the direction of arrival of the desired signal, and decreases the gain in all other directions (interference). The output signal of an antenna array with M elements is formed as:
, where k=1… N (3)
and (.)H denotes conjugate transpose. In a conventional beamformer, the complex vector of weights W is equal to the array response vector ac defined by the array configuration [3,4]:
(4)
The objective of the adaptive beamforming is to preserve the gain in the direction of arrival of the desired signal and mitigate broadband interference incoming from the other directions. The easy solution can be found by maintaining the distortionless response toward signal and minimizing the power at the filter output. This criterion of optimization is formulated as:
to subject (5)
The solution of (5) is the minimum variance distortionless response (MVDR) beamformer:
(6)
Acquisition stage: The main purpose of the acquisition stage is to identify the visible satellites in the incoming data and then find the beginning point of the C/A code and estimate the rough Doppler shift by cross-correlating the incoming signal with the local signal replica [1]. When both parameters, the beginning point of the C/A code and the carrier frequency, are found, this information is passed on to the tracking algorithm.
4. Simulation results
The impact of each beamforming technique is evaluated in terms of the SINR improvement factor estimated at the beamformer output and the post correlation SNR estimated at the cross-correlator output. The SINR improvement factor achieved by the beamformer is evaluated as:
(7)
The post correlation SNR at the output of a cross-correlator is evaluated as:
(8)
where Pmax is the peak power at the correlator output, and SLBave is the average sidelobe level. In this study, 500 computer simulations of the joint “beamforming plus acquisition” algorithm are performed in order to evaluate the influence of different factors on the capability of the algorithm to operate effectively in conditions of strong jamming. The impact of the antenna array configuration on the algorithm performance is evaluated by simulating the beamforming with two 2D arrays: (i) -Uniform Rectangular Array with 9 elements (URA-9) and (2) -Uniform Circular Array with 7 elements (UCA-7). These antenna arrays have the same overall dimension. Both jamming and signal parameters are given in Table 1.
Variant / Jamming / GPS signal1. IF carrier: 1.2513 MHz
Sampling: 5.0053 MHz / Four jamming sources:
Elevation: θ=40°
Azimuth: φ1=-70°; φ2=60°; φ3=60°; φ4=70°
ISR: 10dB … 100dB / Elevation: θ=40°
Azimuth: φ=0°
Doppler shift:5 kHz
SNR: -20dB; Duration: 1ms
C/A code: satellite 19
2. IF carrier: 2.4967 MHz
Sampling: 9.9868 MHz
Table 1: Jamming and signal parameters
In jamming conditions the effectiveness of the acquisition algorithm depends on the capability of the beamforming algorithm as much as possible to suppress jamming. In order to compare the effectiveness of the two beamforming algorithms, the SINR improvement factor at the beamformer output is evaluated as a function of the Interference–to-Signal Ratio (ISR) at the receiver input (Fig.2). The results from Fig.2 show that in contrast to the conventional beamformer the adaptive MVDR-algorithm is able to almost completely suppress jamming. The sensitivity of each beamformer to angular (azimuth and elevation) errors in satellite location is shown in Fig.3 for ISR=100dB. It is seen that the mean loss due to steering vector mismatch is less than 10 dB in the diapason of errors [-30°, 30°].
Fig.2: SINR improvement for URA-9 and UCA-7 Fig.3 SINR losses due to steering vector mismatch
According to [1], for the stable GPS signal tracking, the post correlation SNR must be of at least 10 dB. The results illustrated in Fig.4 and Fig.5 show that the SNR at the cross-correlator output rises with increase of the sampling rate of the incoming data and on the contrary quickly degrades with increase of the jamming intensity. The results shown in Fig.6 and Fig.7 demonstrate the sensitivity of the cross-correlator performance to steering vector mismatch depending on the sampling rate. It can be seen that at the sampling frequency of 5 MHz, only the antenna array URA-9 can guarantee the post correlation SNR of above 10dB. However, when the sampling frequency is doubled, the array UCA-7 can also be used if the maximal angular errors in satellite location are no greater than 10°.
Fig.4: Correlator SNR for fs=5.0053 MHz Fig.5 Correlator SNR for fs=9.8968 MHz
Fig.6 SNR losses due to steering vector mismatch Fig.7 SNR losses due to steering vector mismatch
5. Conclusion
The results obtained show that the MVDR signal processing approach used for jamming suppression in a satellite navigation receiver significantly improves the signal processing quality factors. It is shown that the joint “beamforming plus acquisition” algorithm has good anti-jamming capability if the MVDR-algorithm comes before cross-correlation. It is also shown that the influence of angular errors in satellite location on the cross-correlation performance can be reduced by increasing of the sampling rate of the incoming data.
Acknowledgment
This work is partially supported by the Bulgarian Science Fund (the project MU-FS-05/2007)
Reference
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3. L. Tummonery, I. Proudler, A. Farina, J. McWhirter, “QRD-based MVDR algorithm for adaptive multi-pulse antenna array signal processing”, in Proc. Radar, Sonar, Navigation, vol.141, No 2, 1994, 93-102
4. P. Vouras, B. Freburger, “Application of adaptive beamforming techniques to HF radar”, in Proc. IEEE conf. RADAR’08, May, 2008, 6.
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