The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension

High-dimensional Lagrange interpolation plays a pivotal role in finite element methods, where ensuring the unisolvence and symmetry of its interpolation space and nodes set is crucial. In this paper, we leverage group action and group representation theories to precisely delineate the conditions for unisolvence. We establish a necessary condition for unisolvence: the symmetry of the interpolation nodes set is determined by the given interpolation space. Our findings not only contribute to a deeper theoretical understanding but also promise practical benefits by reducing the computational overhead associated with identifying appropriate interpolation nodes.Comment: 18 page

Experimental Validation and Applications of mm-Wave 8x8 Antenna-in-Package (AiP) Array Platform

Phased array antennas play an indispensable role in millimeter-wave (mmWave) communications. The Antenna-in-package (AiP) system combines advanced antenna and packaging technology, making it highly valuable for various cellular, radar and automative applications. The benefits it brings in terms of small size, low development costs, low power consumption and fast beam-steering capability further drive the vast deployment of phased array antennas in mmWave systems. In this paper, an 8 × 8 AiP experimental platform is presented and its operating performance is measured and analyzed. Further, two application examples of the AiP are presented, namely, a platform for investigating the phased array calibration performance of different methods, and an AiP-based channel sounder for channel characterization. The performance of the channel sounder is verified by analysing the angle of arrival (AoA), angle of departure (AoD) and propagation delay of the measured dominant propagation components (DPCs)