Superdirective beamforming under limited excitation power ranges

The array gain of a superdirective antenna array can be proportional to the square of the number of antennas, which is much larger than the traditional array. However, the realization of the so-called superdirectivity entails accurate calculation and application of the excitations (beamforming vector). Moreover, the excitations require a large dynamic power range, especially when the number of antennas increases and the antenna spacing decreases. In this paper, we derive the closed form solution to the superdirective beamforming vector and characterize the distribution of the excitation power range for the superdirective array. We prove that as the antenna spacing tends to 0, the amplitude range of the superdirective excitations for an M-antenna array can be expressed as a list of binomial coefficients of order M-1. Moreover, to alleviate the high power range requirement, two beamforming methods are proposed to obtain the beamforming vector under a certain excitation range constraint based on Particle Swarm Optimization and convex approximation, respectively. Full-wave electromagnetic simulations validate the effectiveness of our proposed methods.