# Beamforming Techniques for Resilient Navigation with Small Antenna Arrays +
## 1 Introduction  
Wireless communications and navigation applications are experiencing a massive proliferation in urban environments thanks to the increasing widespread deployment of enabling technologies such as 5G, the Internet-of-Things (IoT) and Global Navigation Satellite Systems (GNSSs). This has unveiled the need to cope with signal propagation impairments such as interference, multipath and spoofing that are abundant in such urban environments [1, 2]. Multipath is certainly a major concern, and it appears whenever the line-of-sight signal (LOSS) of interest is received from multiple paths and different directions of arrival (DoA) due to reflection in nearby objects. The signal replicas exhibit an additional delay and carrier phase offset with respect to the LOSS, thus distorting the latter and hampering the receiver's performance. Of particular concern is the case of coherent multipath, the worst yet most frequent form of multipath in dense urban cities. It appears that the signal reflections are highly correlated to the LOSS due to the fact that they are received very closely spaced in time, coming from reflecting objects very close to the user's receiver. The need to mitigate coherent signal replicas also appears when the receiver is subject to a spoofing attack, a threat of increasing concern in positioning and navigation applications whereby a malevolent party forges the receiver position after gaining illegitimate control over the latter [3]. The use of array-processing techniques, also known as spatial filtering or beamforming, is known to be the most powerful approach to combat the above impairments [4]. The goalis to steer the array beam toward the LOSS for signal-to-noise ratio (SNR) maximization, and to place nulls at the DoA of the undesired signals. Some examples of conventional beamformers are the phased array, the Capon [5] and the linear minimum mean square error (LMMSE) [6] techniques. However, more advanced beamformers have recently been proposed in the literature, such as the LMMSE-Capon hybrid [7] and the power-based Capon [8] techniques, which have been specially designed to deal with coherent reflections, thus becoming of particular interest for multipath and spoofing mitigation in challenging environments. An unexplored problem appears, though, when moving to the arena of handheld devices such as tablets or smartphones, which are driven by constraints on miniaturization, low power consumption and low-cost components. The advent of 5G cellular networks has definitely paved the way for the deployment of antenna arrays in such devices as a de-facto standard in the context of multiple-input, multiple-output (MIMO) systems [9; 10; 11]. This is motivated by the use of millimeter-wave signals, allowing the implementation of arrays in an area with tiny dimensions. Some examples can be found in [12; 13] for 5G applications. However, this is not the case for other technologies such as GNSS, where the terminal dimensions are still and will be, in the long-term, comparable to the signal carrier wavelength. This poses a serious concern for the practical use of spatial filtering in these devices. While extensive research on antenna arrays has been performed for professional GNSS receivers [14; 15], where external arrays with many antennas are used, the case of mass-market handheld receivers where just a small number of embedded antennas can be used still remains, to our best knowledge, an open problem. Hence, the objective of this paper is to explore the feasibility of performing robust multipath and spoofing mitigation in handheld GNSS devices with a small number of antenna elements. Additionally, the paper evaluates the suitability of new beamformers such as the LMMSE-Capon hybrid and the power-based Capon for compensating the limitations and technological challenges posed by such small arrays. To these ends, a benchmarking of the above-mentioned conventional and new beamforming techniques is carried out in two representative scenarios, namely urban and suburban.