Global Positioning System (GPS), a satellite based radio navigation system, is widely used in various fields because it provides positioning, navigation and timing (PNT) services with affordable price, easy installation, and other beneficial factors. In addition to GPS by the United States (US), Russia's GLOASS NAvigation Satellite System (GLONASS) and China's Beidou are currently being operated as a satellite based navigation system. Also, Europe's Galileo declared initial services in December, 2016 and its full operational capacity (FOC) is expected to be complete by 2020. The satellite based navigation system is called Global Navigation Satellite System (GNSS), and GPS is commonly used as a typical GNSS system. GPS signal is protected by the international radio regulation and relatively immune to the radio interference due to a spreading gain of the spread spectrum scheme. However, since the signal is received at a very low-power (nominal level : -130 dBm) below the thermal noise level, the GPS receiver is vulnerable to malicious and excessive interference. In order to deal with this problem, the beam steering and spatial nulling based on adaptive beamforming have been considered as effective methods in GPS receivers. Generally, an adaptive beamforming technique determines the weight vector of the array antennas by using the steering vector based on the known direction information of the satellites. However, for instance, if the cold start mode (where there is no valid information on almanac, user location, or time data) is entered under the persistent presence of strong jamming, it is difficult to receive the navigation messages including satellite position information. Therefore, the blind adaptive beamforming method is needed because it is capable of automatically steering the beam to the satellite direction by receiving only GPS signals without requiring a known information. Moreover, it does not suffer from performance degradation by the mismatch between the direction vector of the desired signal and the steering vector because antenna array calibration is not necessary.
It is known that the blind beamforming is achieved by some known property of self-coherence signals exhibited in most communication signals. An estimate of the desired signal can be obtained by optimizing a proper cost function based on this property. A spectral self-coherence restoral (SCORE) algorithm has been presented to deal with the problem of a blind adaptive signal extraction. It has been shown that the performance of the cross-SCORE algorithm approaches that of the conventional adaptive beamforming when infinite time-averaging interval is available. Utilizing the self-coherence properties of GPS L1 coarse/acquisition (C/A) code, an anti-jamming GPS receiver based on the cross-SCORE algorithm has been proposed. However, it can only suppress the jamming signals that have different self-coherence properties from those of the GPS signals. It cannot remove even the simple jamming like the continuous wave (CW) having similar self-coherence properties to those of GPS C/A signals or spoofing signals having the same structure as GPS C/A signals. In particular, the sample blocks used for estimating the correlation matrices are very important part in determining the beamforming weight vector. The anti-jamming scheme is completely unable to resolve various bit transition problems of multiple GPS signals caused by the time of arrival (TOA) differences between multiple satellites and the receiver. Also, the real-world environment with the signal strength differences between multiple satellites is seldom considered in the anti-jamming scheme. Consequently, this scheme creates high gain only to the direction of the strongest signal strength because its weight vector is determined by the eigenvector which maximizes a measure of the self-coherence feature of the beamformer output.
In order to overcome this practical problems that occur when the blind beamforming technique is applied to the GPS receiver, we propose a blind beamforming based on a robust cross-SCORE algorithm for GPS receiver against various types of interference such as jamming or spoofing. First, we examine the cross-SCORE algorithm through an asymptotic analysis and propose the robust cross-SCORE algorithm based on interference-free (IF) subspace. Then, the transition-free block search (TFBS) algorithm is developed to estimate the sample correlation matrices using the common block, which is free from the bit transitions under various TOAs of multiple GPS signals. Moreover, we consider the real-world situation where the signal power differences exist between multiple satellites. GPS signal subspace constrained beamforming (GSCB) method is suggested to provide an equivalent level of antenna gains to multiple GPS satellites under various received strengths of multiple GPS signals. The beamforming weight is determined by imposing constraints on the eigenvectors corresponding to GPS signal subspaces extracted from the robust cross-SCORE algorithm.
Finally, we have performed the beampattern simulations with uniform linear array (ULA) and uniform circular array (UCA) antenna under the realistic GPS signal environment in order to verify the performance of the proposed methods. Consequently, the simulation results have shown that the proposed blind beamforming scheme provides better performance than the anti-jamming scheme and eventually leads to a performance close to that of the linearly constrained minimum variance (LCMV) scheme (non-blind beamforming), which is one of the optimum beamformers.