Fourier-Gated Transformer and MLP-Enhanced REV: Noise-Robust Phased-Array Antenna Calibration Using Power-Only Measurements

Accurate calibration of active phased array antennas (APAAs) is essential during field operation, but phase-based methods are often costly and challenging due to the need for precise phase measurement equipment. To enable efficient online calibration using only output power measurements, we build on the rotating element electric field vector (REV) method and propose three neural network-based approaches. Each approach relies on N power samples obtained by sweeping the phase shifter (e.g., 32 samples for a 5-bit shifter). The first approach, multilayer perceptron neural-network enhanced REV (MLPeREV), uses an MLP to estimate the REV input parameters ϕ and r from the power sequence and then applies the REV equations to compute phase errors. The second approach, transformer neural network-based phase error estimation (Tran-PhEr), replaces explicit parameter estimation with an encoder-only transformer that directly processes the raw power sequence and predicts phase errors via self-attention. The third approach, Fourier-gated transformer neural network-based phase error estimation (FGTran-PhEr), augments Tran-PhEr with a Fourier transform layer and Gaussian gating to focus attention on the sequence’s maxima and minima. This yields noise-robust predictions and reduces the need for repeated measurements. These transformer-based approaches use only the REV measurement procedure, not the REV equation directly. We evaluate the three approaches in simulation and experimentation on a 1024-antenna planar phased array operating at 18–21 GHz. Experimental validation was conducted on a representative C-module (16 antennas) of the 1024-element array, with results generalizable to the full aperture. MLPeREV achieves a mean absolute error (MAE) and root-mean-square error (RMSE) of 2.30° and 2.80°, respectively, in simulation, and 4.15° and 5.07° in experimentation. Tran-PhEr yields an MAE of 1.91° (simulation) and 2.86° (experimentation), and an RMSE of 2.46° (simulation) and 3.67° (experimentation), converging in 37 epochs. FGTran-PhEr outperforms both, with an MAE of 1.36° (simulation) and 1.75° (experimentation), and an RMSE of 1.93° (simulation) and 2.48° (experimentation), converging in 24 epochs. We further quantify estimator bias and the peak-index MSE–SNR law under phase-quantization (DNL/INL) and VGA nonlinearity, and validate the analysis through Monte-Carlo simulation (2–20 dB). The results confirm the efficacy of neural-network-based calibration for achieving robust and online phased-array calibration.