  In most multiple-input multiple-output (MIMO) communication systems, the
antenna spacing is generally no less than half a wavelength. It helps to reduce
the mutual coupling and therefore facilitate the system design. The maximum
array gain equals the number of antennas in this settings. However, when the
antenna spacing is made very small, the array gain of a compact array can be
proportional to the square of the number of antennas - a value much larger than
the traditional array. To achieve this so-called ``superdirectivity" however,
the calculation of the excitation coefficients (beamforming vector) is known to
be a challenging problem. 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. In order to obtain the field
coupling matrix, we propose a spherical wave expansion approach, which is
effective in both simulations and realistic scenarios. Moreover, a prototype of
the 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 5 dipole antennas.
