# Noncoherent Channel Combining for GNSS Signal Tracking with an Adaptive Antenna Array
## 1 Introduction  
Recently, position, navigation, and timing (PNT) information has become increasingly important to our modern society [1]. The Global Navigation Satellite System (GNSS) has been widely used to provide PNT information due to its easy availability. Unfortunately, the GNSS signal is extremely weak, making it vulnerable to both intentional and unintentional interference [2]. Therefore, it is of great importance to mitigate the effects of interference to keep GNSS receivers operating continuously. The adaptive antenna array with anti-jamming array processing techniques is the state-of-the-art approach to interference suppression [3]. The minimum variance distortionless response (MVDR) algorithm [4] is one of the most popular techniques. It can not only suppress interference but also maximize the signal-to-noise ratio (SNR). However, the implementation of the MVDR algorithm requires prior knowledge of the satellite steering vector. This increases the complexity of the implementation and also limits the application during cold start of the GNSS receiver. Blind anti-jamming array processing techniques, such as the power inversion (PI) algorithm [5], can adaptively suppress the interference without any prior knowledge. This type of technique is more attractive in practical engineering due to its ease of implementation and wide range of applications. However, the PI algorithm cannot provide an array gain for the satellite signal, and it often results in satellite signal attenuation [6]. This reduces the signal tracking precision and thus degrades the measurement accuracy. To address this issue, many other blind algorithms have been studied. The direction-of-arrival (DOA) estimation methods can be used to extract the spatial information of the satellite signal for beamforming [7]. To reduce the complexity of DOA estimation, the angle-locked loop has been proposed to achieve closed-loop angle tracking [8]. However, this type of approach requires accurate knowledge of the array manifold, which is not easily determined without costly array calibration [9]. This is because the antenna array and its associated electronics are subject to many errors, some of which are even environment-dependent [10]. Moreover, the performance of angle estimation or tracking is degraded in coherent signal environments, such as the multipath environment. The spectral self-coherence restoral technique has been proposed in the literature [11; 12]. It can form high-gain beams toward the satellites by using the repetitive feature of the GNSS code without requiring the knowledge of the satellite direction. However, this technique cannot mitigate the interference that has similar self-coherence properties to the GNSS signal, such as the continuous wave interference. The beamforming algorithm in [13; 14] reconstructed the spatial signature vector of the satellite signal using the carrier phase measurements obtained from the tracking channel of each antenna. However, it is not suitable in an interference scenario because signal tracking will fail in this case. The minimum mean square error (MMSE) algorithm [15] is known to use the waveform information of the reference signal for beamforming. However, the reference signal should be obtained by the receiver tracking loop, so it inevitably contains estimation errors that degrade the performance of the algorithm. Different from the above approaches, this paper considers the adaptive antenna array from the perspective of a multichannel system. Then, a new method for GNSS signal tracking using adaptive antenna arrays is proposed based on the concept of channel combining. The main contributions of this work are summarized as follows:  
1. Conventional anti-jamming methods are explained as a unified two-stage processing architecture, where the first stage is interference suppression and the second stage is channel combining. 2.