In most multiple-input multiple-output (MIMO) communication systems, antennas are spaced at least half a wavelength apart to reduce mutual coupling. In this configuration, the maximum array gain is equal to the number of antennas. However, when the antenna spacing is significantly reduced, the array gain of a compact array can become proportional to the square of the number of antennas, greatly exceeding that of traditional MIMO systems. Achieving this "superdirectivity" requires complex calculations of the excitation coefficients (beamforming vector), which is a challenging task. In this paper, we address this problem with a novel double coupling-based superdirective beamforming method. In particular, we categorize the antenna coupling effects to impedance coupling and field coupling. By characterizing these two coupling in model, we derive the beamforming vector for superdirective arrays. We prove that the field coupling matrix has the unique solution for an antenna array, and itself has the ability to fully characterize the distorted coupling field. Based on this proven theorem, we propose a method that accurately calculates the coupling matrix using only a number of angle sampling points on the order of the number of antennas. Moreover, a prototype of an independently-controlled superdirective antenna array is developed. Full-wave electromagnetic simulations and real-world experiments validate the effectiveness of our proposed approaches, and superdirectivity is achieved in reality by a compact array with 4 and 8 dipole antennas.

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