Robust Beamforming for Superdirective Antenna Arrays and Experimental Validations

Superdirective antenna arrays have the potential to increase array directivity proportional to the square of the number of antenna elements. However, the high sensitivity problem of superdirectivity has posed a major challenge for practical applications. To address this issue, we propose a robust superdirective beamforming method that accounts for mutual coupling between antenna elements. We first introduce a universal sensitivity measurement applicable to coupled arrays and derive its closed-form expression, termed the degree of sensitivity (DoS). A beamforming optimization problem is then formulated to maximize the directivity factor while satisfying a DoS constraint, resulting in a parameterized beamformer where the parameter is difficult to determine. To solve this optimization problem, we propose an efficient orthogonal complement-aided quadratic constraint least squares (OC-QCLS) algorithm, which achieves the maximum possible directivity under the sensitivity constraint. Specifically, the framework of the least squares problem with a quadratic constraint is utilized to provide useful insights, and the intractable secular equation for the parameter is transformed into an easy-to-solve polynomial equation using the orthogonal complement. Numerical and electromagnetic (EM) simulations verify the effectiveness of the DoS and the OC-QCLS algorithm. The improvement in communication performance achieved by the OC-QCLS algorithm is demonstrated through its superior average spectral efficiency. Furthermore, an eight-dipole superdirective antenna array prototype with 0.20λ element spacing operating at 1.6 GHz is built, and real-world experiments validate the proposed method. Notably, the distributions of directivity metrics are analyzed and demonstrated in both simulation and experimental results.