Analysis and Linearization of Frequency-Multiplier-Based RF Beamforming Transmitters Over a Wide Steering Range

• Published in: IEEE transactions on microwave theory and techniques Vol. 70; no. 8; pp. 3987 - 4001
• Main Authors: Ben Ayed, Ahmed, Jaffri, Ifrah, ElAdwy, Mahitab, Darwish, Ali M., Mitran, Patrick, Boumaiza, Slim
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-08-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antenna arrays; Array signal processing; Arrays; Beamforming; Behavioral sciences; Circuits; Digital predistortion (DPD); Frequency doublers; Frequency modulation; frequency multiplier; Load modeling; millimeter wave (mm-wave); Modulation; Multipliers; Nonlinearity; OFDM; Orthogonal Frequency Division Multiplexing; Power amplifiers; Radio frequency; radio frequency (RF) beamforming transmitters (TXs); Sensitivity; Steering; Transmitters
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2022.3186340

This article first analyzes the nonlinear behavior of frequency-multiplier (FM)-based radio frequency (RF) beamforming transmitters TXs) over a wide range of steering angles. Then, based on this analysis, a digital predistortion (DPD) scheme is proposed to linearize FM-based TX arrays. Specifically, a dual-input behavioral model of FM-based TX arrays is derived. This dual-input model is then transformed into an angle-dependent single-input-single-output (SISO) model. Next, the effect of load modulation on FM nonlinearity is studied using a circuit-inspired behavioral model, and a very distinctive feature is revealed. Notably, it is shown that FM-based RF beamforming arrays have reduced sensitivity to load modulation when compared to last-stage power-amplifier (PA)-based arrays. This is first validated in simulation using a frequency doubler and PA terminated with load impedances extracted from an 8 <inline-formula> <tex-math notation="LaTeX">\times </tex-math></inline-formula> 8 electromagnetically simulated array. Furthermore, experimental results are obtained using a 2 <inline-formula> <tex-math notation="LaTeX">\times </tex-math></inline-formula> 2 planar frequency-doubler-based RF beamforming TX operated at 28 GHz and driven with up to 400-MHz-wide orthogonal frequency-division multiplexing (OFDM) signals where the subcarriers are modulated using up to 256-QAM. It is experimentally demonstrated that a single set of SISO DPD coefficients can significantly improve the adjacent channel power ratio (ACPR) and error vector magnitude (EVM) over a wide steering range. Specifically, for the case of a 100-MHz signal, the ACPR and EVM improved from 20 dBc and 23% to, at worst, 48 dBc and 1%, respectively, when the array is steered from <inline-formula> <tex-math notation="LaTeX">-40^\circ </tex-math></inline-formula> to 40° and measured along the main beam direction. In light of the FM-based arrays reduced sensitivity to load modulation, this article also investigates different TX observation receiver (TOR) methods for DPD function training, namely, far-field-based TOR, coupler-based TOR, and single-element-based TOR, and their impacts on the linearizability of the FM-based RF beamforming TXs.