Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Existing methods of defining stored energy in radiating systems are then reviewed in a framework based on technical commonalities rather than chronological order. Equivalences between some methods under common assumptions are highlighted, along with the strengths, weaknesses, and unique applications of certain techniques. Numerical examples are provided to compare the relative margin between methods on several radiating structures.

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Antenna current optimization is often used to analyze the optimal performance of antennas. Antenna performance can be quantified in e.g., minimum Q-factor and efficiency. The performance of MIMO antennas is more involved and, in general, a single parameter is not sufficient to quantify it. Here, the capacity of an idealized channel is used as the main performance quantity. An optimization problem in the current distribution for optimal capacity, measured in spectral efficiency, given a fixed Q-factor and efficiency is formulated as a semidefinite optimization problem. A model order reduction based on characteristic and energy modes is employed to improve the computational efficiency. The performance bound is illustrated by solving the optimization problem numerically for rectangular plates and spherical shells.