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.

中文翻译：

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宽转向范围内基于倍频器的射频波束成形发射机的分析和线性化


本文首先分析了基于倍频器 (FM) 的射频 (RF) 波束成形发射机 TX (TX) 在大范围转向角下的非线性行为。然后，基于此分析，提出了数字预失真 (DPD) 方案来线性化基于 FM 的 TX 阵列。具体来说，推导了基于 FM 的 TX 阵列的双输入行为模型。然后，该双输入模型被转换为角度相关的单输入单输出（SISO）模型。接下来，使用受电路启发的行为模型研究负载调制对 FM 非线性的影响，并揭示了一个非常独特的特征。值得注意的是，与基于末级功率放大器 (PA) 的阵列相比，基于 FM 的射频波束形成阵列对负载调制的敏感度降低。这首先在仿真中得到验证，使用倍频器和 PA，其端接负载阻抗是从 8 $\times $8 电磁仿真阵列中提取的。此外，实验结果是使用 2 $\times $2 基于平面倍频器的 RF 波束成形 TX 获得的，该 TX 在 28 GHz 下运行，并由高达 400 MHz 宽的正交频分复用 (OFDM) 信号驱动，其中子载波为使用高达 256-QAM 进行调制。实验证明，单组 SISO DPD 系数可以在较宽的转向范围内显着改善邻道功率比 (ACPR) 和误差矢量幅度 (EVM)。具体来说，对于 100 MHz 信号的情况，当阵列从 $-40^\circ $ 转向到40°并沿主波束方向测量。 鉴于基于 FM 的阵列降低了对负载调制的灵敏度，本文还研究了用于 DPD 功能训练的不同 TX 观测接收器 (TOR) 方法，即基于远场的 TOR、基于耦合器的 TOR 和单元件 TOR。基于 TOR，以及它们对基于 FM 的 RF 波束形成 TX 线性化的影响。