Convex Minimization of Active Reflection Coefficients in Antenna Arrays with Radiation Pattern Constraints

Increasing the output power of high-power amplifiers (HPAs) in active electronically-scanned arrays (AESAs) may lead locally to problematic temperature rises because of rises in reflected power at the antenna-elements' terminals, which originates from both self and mutual coupling. One way to reduce the reflected power is to determine excitation coefficients of the antenna elements such that their active reflection coefficients (ARCs) are minimized, while gain, sidelobe level (SLL), and cross polarization are not significantly compromised. In this paper, we describe a convex relaxation of the optimization problem, based on semi-definite programming. We illustrate the effectiveness of the algorithm by optimizing the excitation coefficients of an 8 x 8 array of half-wavelength dipoles, operating in the radio band, whose S-parameters and embedded element patterns are simulated by a commercial solver. Specifically, we show that the maximum ARC values are significantly reduced by 8% to 33%, where the highest percentages are achieved for the highest maximum ARCs occuring for extreme scanning to 50° off-broadside in the three principal planes. Also, we demonstrate that gain, SLL, and cross polarization are reasonably well maintained as compared to the case of linear phase tapering.