Multi-band or multi-frequency antennas have become essential for many GNSS applications [1]. These antennas allow a receiver to simultaneously receive from multiple bands such as L1, L2, L2C, E5A, L5, and so on, which is essential for ionosphere corrections, can help mitigating multipath induced biases, and improve overall system availability. Furthermore, they also allow for multiple GNSS to be used simultaneously, improving accuracy and robustness due to the larger number of satellites available.Another advancement that has recently attracted attention in the GNSS community is the usage of antenna arrays at the receiver [2], [3]. These arrays, which can assume multiple shapes and sizes, can be used to enhance system performance in multiple ways. Beamforming can be used to null out interferers or multipath components and improve gain over a designated direction of arrival. Some antenna array geometries can also enable a receiver to estimate its attitude while relying solely on received GNSS signals.While both multi-band antennas and antenna arrays offer attractive advantages for precise GNSS positioning, merging such systems on a single receiver can be challenging. Antenna arrays have their performance largely dictated by their geometries and the spacing between antenna elements [4]. This spacing is defined with respect to the frequency of the signal that is received at the antenna array. If the spacing is too large the receiver will suffer from inaccuracy introduced by ambiguities that will be present when trying to filter out undesired signals or when trying to estimate the direction of arrival of received signals. If the spacing is too small, the total array directivity will be lower, which will lead to more biased direction of arrival estimations or to beamformers with lobes that are too broad to filter out undesired signals.The relationship between frequency and geometry makes it impossible to create a multi-band antenna array that is optimal for every frequency received, as optimizing one frequency will inevitably lead to performance degradation in the remaining ones. To tackle this issue, a technique known as array interpolation can be employed [5]. Array interpolation consists of creating a mathematical transformation that projects the signal received at a real and imperfect array onto an ideal and abstract receiver. This allows arrays whose geometries are not optimal, and even heavily distorted with respect to an optimal geometry, to achieve high levels of performance, with improved direction of arrival estimation accuracy. A different array interpolation can be constructed for each individual frequency received at the array. Thus, array interpolation can be a valuable tool for allowing multi-band antenna arrays to achieve high performance over the entire range of frequencies they are designed to receive.This work studies the effects of optimizing antenna array geometries for a given frequency band while applying array interpolation over the array response for the remaining frequency bands. Furthermore, the possibility of choosing a geometry that is not optimal for any given array geometry but achieving an overall improved performance over the entire range of frequency bands to which the array is tuned is also studied. The performance of multiple array interpolation methods is verified, and the tradeoffs between performance and computational complexity is studied.[1] J. Li, H. Shi, H. Li, and A. Zhang, “Quad-band probe-fed stacked annular patch antenna for GNSS applications,” IEEE Antennas Wirel. Propag. Lett., vol. 13, pp. 372–375, 2014.[2] S. Caizzone, “Miniaturized E5a/E1 antenna array for robust GNSS navigation,” IEEE Antennas Wirel. Propag. Lett., vol. 16, pp. 485–488, 2016.[3] S. Caizzone, W. Elmarissi, M. A. M. Marinho, and F. Antreich, “Direction of arrival estimation performance for compact antenna arrays with adjustable size,” in IEEE MTT-S International Microwave Symposium Digest, 2017.[4] Y. T. Lo, S. W. Lee, and Q. H. Lee, “Optimization of directivity and signal-to-noise ratio of an arbitrary antenna array,” Proc. IEEE, vol. 54, no. 8, pp. 1033–1045, 1966.[5] M. A. M. Marinho, F. Antreich, S. Caizzone, J. P. C. L. da Costa, A. Vinel, and E. P. de Freitas, “Robust Nonlinear Array Interpolation for Direction of Arrival Estimation of Highly Correlated Signals,” Signal Processing, vol. 144, 2018. © 1995-2021, The Institute of Navigation, Inc.
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