Novel Algorithm to Synthesize the Tapering Profile for Enhanced Linearization of RF Beamforming Arrays Over a Wide Steering Range

This article proposes an algorithm to synthesize a tapering profile that reduces the extent of the variation of the active reflection coefficients seen by the power amplifiers (PAs) in a radio frequency (RF) beamforming array, and accordingly reduces the variation in the array nonlinearity versus steering angle. Specifically, it starts by theoretically analyzing the following: 1) the dependence of the RF beamforming array nonlinearity on the antenna active reflection coefficients as well as the PA output reflection coefficients and 2) the dependence of the antenna active reflection coefficients on the tapering profile. A novel algorithm that uses the antenna array scattering parameters is then devised to synthesize a tapering profile that both hold the following: 1) reduces the extent of the variation of the active reflection coefficients seen by the PAs and 2) constrains the maximum reduction in the antenna array factor compared with uniform tapering. The performance of the proposed algorithm is validated in simulation and experimentally using an $8\times $ 8 RF beamforming array. The simulation revealed that applying the tapering profile obtained from the proposed algorithm reduced the variation in the antenna active reflection coefficients by 6 dB or more for 25% of the antenna elements (3.9-dB median) compared with when a uniform tapering profile is applied. Furthermore, experimental results showed that the application of the synthesized tapering profile enhanced the capacity of digital predistortion (DPD) with a single set of coefficients to linearize the RF beamforming array over a wide steering range. Specifically, when the elevation angle $\theta $ is steered between −50° and 50°, the variations in the adjacent channel power ratio (ACPR) and error vector magnitude (EVM) after DPD are $\leq 0.5$ and $\leq 0.3$ dB for the designed taper compared with 6 and 4 dB, respectively, for a uniform taper.