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The millimeter-wave (mmWave) scanner is a system built a few years ago by the phased array antenna research and development group (PAARD) in the Advanced Radar Research Center (ARRC) with the purpose of measuring, characterizing, and calibrating mmWave antennas without significantly changing the setup. The most important reason for developing a multitasking system is to utilize a vector network analyzer (VNA), in many applications. This thesis proposes upgrades to this system, starting with the software, which restricts the system with poor motion flow, and addition of new features to the system that allow faster and reliable measurements. A relevant feature that was added is the calibration and measurement of a W-band active phased array antenna in a package that was manufactured for commercial purposes. Due to the nature of the active element in a phased array antenna, calibration of the system is required for precise and correct performance, which is critical for radio frequency systems. Over-the-air (OTA) calibration is a powerful technique used in phased array antennas in real-world environments. This thesis proposes a novel measurement system to calibrate and characterize the antenna. The system is a multi-axis hybrid system with nine degrees of freedom, used to perform the calibration process and also to scan the antenna radiation pattern in both near-field (NF) and far-field (FF) regions. Experimental results of the calibration method show high precision in the element radiation values, and excellent agreement between the antenna array radiation pattern measured in the near-field and far-field is achieved.

We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the L1 distance between the predicted values and the set of predictions that are perfectly calibrated in hindsight. This is analogous to a calibration measure recently proposed by Błasiok, Gopalan, Hu and Nakkiran (STOC 2023) for the offline setting. The calibration distance is a natural and intuitive measure of deviation from perfect calibration, and satisfies a Lipschitz continuity property which does not hold for many popular calibration measures, such as the L1 calibration error and its variants. We prove that there is a forecasting algorithm that achieves an O(√T) calibration distance in expectation on an adversarially chosen sequence of T binary outcomes. At the core of this upper bound is a structural result showing that the calibration distance is accurately approximated by the lower calibration distance, which is a continuous relaxation of the former. We then show that an O(√T) lower calibration distance can be achieved via a simple minimax argument and a reduction to online learning on a Lipschitz class. On the lower bound side, an Ω(T^(1/3)) calibration distance is shown to be unavoidable, even when the adversary outputs a sequence of independent random bits, and has an additional ability to early stop (i.e., to stop producing random bits and output the same bit in the remaining steps). Interestingly, without this early stopping, the forecaster can achieve a much smaller calibration distance of polylog(T).