# Two-Stage Beamforming Technique for GNSS Applications +
## 1 Introduction  
Navigation services currently deploy the state-of-the-art Global Navigation Satellite System (GNSS) for outdoor positioning. However, due to the long communication link, the Carrier-to-Noise ratio (CN0) values of the GNSS signals received on the ground are low. Accordingly, the GNSS services are very limited in urban and canyon-like environments. In such environments, the received signals will be either obstructed by a physical barrier or distorted by the multipath effect. To overcome this limitation, several techniques have been proposed in the literature. Some techniques rely on the super correlator approach [1]. This approach depends heavily on the mobility of the GNSS receiver; therefore, it is not suited for static scenarios. Other techniques that rely on a dual polarization antenna (DPA) have also been proposed in the literature [2]. Those techniques are very appealing due to the exploitation of a compact antenna that consists of a right-hand circular polarization (RHCP) antenna and a left-hand circular polarization (LHCP) antenna. Nonetheless, the performance of those techniques is limited and dependent on the correct characterization of the DPA; therefore, those techniques are not entirely suitable for low-cost COTS hardware. The final and most effective approach, which can mitigate the multipath effect and increase the received CN0 level, involves spatial diversity techniques by means of array antenna systems [3].  
Array antenna systems have been exploited in various applications, e.g., multipath and interference mitigation; angle of arrival (AoA) estimation; and localization [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. Consequently, over the past years, array antennas have been deployed in GNSS receivers either to provide a spatial filter or to improve the CN0 level by using beamforming techniques. [PERSON] et al. [5] provided an overview of the GNSS receivers that utilize array antennas to mitigate interference signals (and the multipath effect) and to improve the received signal strength. Nonetheless, the current multipath mitigation techniques depend mostly on either the subspace decomposition (i.e., eigen-based beamforming); or Minimum Variance Distortionless Response (MVDR). The performance of those algorithms deteriorates significantly in the presence of correlated signals, which is the case for the multipath effect [11].  
In this paper, we address the aforementioned shortcoming by providing a robust beamforming technique using array antennas. The proposed solution constitutes two stages; the first stage exploits an array antenna system to decompose the received signals into direct and reflected signals. The proposed solution deploys the space-alternating generalized expectation-maximization (SAGE) algorithm with the acquired complex samples (from every antenna during the acquisition stage). The second stage, on the other hand, exploits the MVDR algorithm to produce the weight vector that steers the main beam towards the satellite's direction and the nulls towards the multipath effect. The main difference between the proposed two-stage beamforming technique and a traditional MVDR beamformer is that we deploy the MVDR technique using the de-correlated signals' covariance matrix. Those signals are decomposed using the SAGE algorithm in the first stage. On the other hand, the traditional MVDR technique directly exploits covariance matrix of the received signals.  
In the following sections, the proposed technique will be introduced; followed by the experimental results and discussion; and finally, the conclusions of this paper will be drawn.