## 1 Introduction
Line-of-sight (LOS) signals are ideal; however, non-line-of-sight (NLOS) signals can also reach the antenna through reflections. Additionally, intentional interference signals (jammers) can be present. providing greater control over the phase delay between feedlines, at the expense of higher computation cost [10]. However, every antenna must be directly connected to an ADC, which must be able to sample synchronized signals at a high sampling frequency, requiring ADCs that are usually expensive, making the overall system costly and complex [11]. Other beamforming techniques, such as Direct Digital Synthesizer and Phase Lock Loop (DDS-PLL), are also available. In DDS-PLL, the signal of each antenna is downconverted twice, with two mixers that use synchronized local oscillators (LOs). By varying the phase of the second LO relatively to the first LO, that same phase shift is induced in the output of the second mixer [12]. The use of antenna arrays for GNSS multipath and interference mitigation has been attempted and reported in literature, with the solution based on four-antenna planar arrays being the most prominent design reported. In [13], the authors use a 2 \(\times\) 2 planar array composed of E1/E5 dual-band patch antennas placed just under \(\lambda_{0}/2\) from each other to demonstrate the mitigation of jamming and spoofing signals in realistic scenarios with good results. Similarly, in [14], a 190 \(\times\) 190 mm 2 \(\times\) 2 planar array composed of commercial off-the-shelf (COTS) patch antennas at \(\lambda_{0}/2\) spacing was used as part of a system for multipath detection. Resorting to a software-defined radio (SDR), the MUSIC algorithm was implemented and, with beamforming, an increase in C/N\({}_{0}\) of up to 8 dB was achieved. In [15], a four-element half-wavelength circular array was used in combination with a COTS GNSS receiver and an FPGA to evaluate nulling capabilities for intentional interference mitigation. A field test demonstrated that up to two sources of interference could be countered while maintaining a sufficient carrier-to-noise ratio for the GNSS receiver. In [16] a 140 \(\times\) 140 mm\({}^{2}\) planar 2 \(\times\) 2 array of patch antennas with d = \(\lambda_{0}/3\) was presented. Different designs can also be found, with a 1 \(\times\) 4 linear array of custom-made patch antennas being presented in [17]. Each patch is 40.9 \(\times\) 40.9 mm\({}^{2}\) (0.21\(\lambda_{0}\)\(\times\) 0.21\(\lambda_{0}\)), and the center-to-center distance in the array is 66 mm, around 0.35\(\lambda_{0}\) at 1.57542 GHz. The array was controlled by a hardware beamformer, and its beamforming was demonstrated. Being a linear array, the beamforming capabilities were limited from design, and mutual coupling compensation was not considered, which was a considerable design flaw given the close distance between antenna elements in the array. In [18] a circular array of seven dual-band (L1/L2) antennas was reported. The array had a diameter of 500 mm, and the antennas were spaced by 125 mm. The array was tested for its nulling capabilities with both hardware and software beamforming systems. However, N-antenna systems can perform nulling operations on N-1 interferences. With the commonly seen four-antenna system, this means filtering three interferences. As such, arrays with more antenna elements may be necessary to optimize the performance of GNSS receivers in complex environments like urban canyons, where multiple interferences may be present (multipath and man-made). The reported arrays are mostly composed of four antennas, since the complexity of the hardware and software required for more antennas will increase rapidly with the number of antennas. The cost is greater due to more components, not only antennas but also ADCs, amplifiers, and filters. For an increase in beamsteering capabilities, the antennas must be maintained at a certain distance from each other, also increasing volume and substrate material demands.