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

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
$\times $
8 electromagnetically simulated array. Furthermore, experimental results are obtained using a 2
$\times $
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
$-40^\circ $
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.