Clever Trick and Dual Neural Networks Crack the Phaseless Antenna Puzzle

One of the most stubborn problems in antenna engineering has just been tamed by an unlikely combination of signal processing and deep learning. Researchers report a new method that recovers the complete, complex behavior of planar antenna arrays using only intensity measurements — no phase data required — and it does so with an accuracy that conventional approaches cannot approach. In numerical experiments, the proposed framework achieved a coefficient of determination of roughly 0.98, while a standard phaseless reconstruction method managed only about 0.40 on the same task.

The core of the difficulty lies in what happens when phase information is thrown away. Full near-field measurements of an antenna’s radiated field capture both the amplitude and the phase of the electromagnetic waves, and with them, engineers can accurately reconstruct the distribution of currents flowing across the array. But such measurements are expensive and experimentally demanding, requiring specialized equipment to preserve and record phase. Phaseless measurements — recording only the squared magnitude of the field — are far more practical, yet they turn the reconstruction into a nonlinear and ill-posed inverse problem. Many different source configurations can produce nearly identical intensity patterns, and the reconstruction can become fundamentally ambiguous.

The ambiguity has a particularly cruel mathematical structure. Two current distributions with exactly identical amplitudes but exactly opposite phase profiles generate indistinguishable radiation intensities on a scanning plane. In other words, the measured data for two physically different antennas can be perfectly identical, and no amount of computational cleverness applied to conventional phaseless data can tell them apart. Earlier attempts to break this symmetry involved scanning multiple planes at different distances from the antenna to collect extra information, but the added measurement overhead and computational burden substantially reduced their practical appeal.

The new work, published in Frontiers in Antennas and Propagation by Mehdi Masoodi of the Institute for Electromagnetic Sensing of the Environment at Italy’s National Research Council, Haniyeh Taromideh of the University of Guilan, and Naser Omrani of the University of Science and Technology in Tehran, attacks the problem at its source — literally. Before the antenna radiates at all, the researchers apply a preprocessing step to the source current distribution, adding a phase-dependent term to the original currents. This modified current source produces intensity measurements that are far more informative, because the extra term breaks the symmetry that made opposite-phase sources look identical.

The effect is subtle but decisive. In the conventional configuration, the radiation operator maps the amplitude and phase of each array element’s excitation into a field whose squared magnitude is all that survives at the observation plane, and the sign flip of the entire phase profile vanishes in the squaring operation. After the phase-dependent perturbation, that cancellation no longer occurs: the nonlinear coupling between the source coefficients and the measured field is enhanced, and the two formerly indistinguishable sources now generate distinct, identifiable intensity patterns. The measurement plane, sampled at a fixed distance from the array, effectively carries a fingerprint of the phase structure that was previously erased.

Turning these enriched measurements back into a full complex current distribution is the job of a dual U-Net architecture. U-Net, originally developed for biomedical image segmentation, consists of an encoder that extracts increasingly abstract features from the input image while progressively reducing its spatial resolution, and a decoder that rebuilds the output through transposed convolutions. Its signature skip connections shuttle fine spatial detail from the encoder directly to the decoder, which proves crucial for preserving structural information in reconstruction tasks. In the new framework, two independent but identically configured U-Nets run in parallel: one predicts the real part of the array coefficients, and the other predicts the imaginary part. Both receive the same phaseless radiation pattern as input.

The network details follow well-established practice. Four encoding and decoding levels process the input, with successive convolutional layers and ReLU activations at each stage, zero-padding to preserve spatial dimensions, and max-pooling that halves the resolution while doubling the number of filters, starting from 32. The bottleneck is followed by a symmetric decoder that upsamples and concatenates encoder features at every stage. Training used the ADAM optimizer with an initial learning rate reduced by half every 20 epochs over 50 epochs, with a mini-batch size of eight, optimized through a pixel-wise regression loss.

The dataset was deliberately designed to stress-test the approach. It contains 2,000 samples of two-dimensional antenna array current distributions, with randomly positioned amplitude peaks and phases drawn uniformly across the full interval. Critically, half the samples pair each amplitude distribution with an opposite-phase counterpart, so the network is forced to confront the most ambiguous cases head-on. The underlying source is a planar array of ideal omnidirectional magnetic dipole elements, and phaseless near-field intensities are collected on a scanning plane at a dense grid of observation points satisfying the standard near-field sampling criterion. Input measurements and output current maps are resized to a common resolution using nearest-neighbor interpolation, which minimally disturbs the pixel values before training, with the reconstruction resized back after prediction.

The performance gap between the conventional and processed configurations was stark. During training, the networks fed with phaseless data from the processed current distribution showed dramatically lower loss values for both real and imaginary components, while the conventional model’s losses remained high and nearly flat — the signature of a learning problem whose training data simply do not contain the information needed to distinguish the answers. Validation curves tracked the training curves closely, indicating stable convergence and no overfitting. On a held-out test set of 200 unseen samples, the average root-mean-square error fell from approximately 0.208 for the conventional approach to approximately 0.029 for the proposed method, for both the real and imaginary parts. Histograms of the errors showed most proposed-method predictions clustered at very small values, whereas the conventional errors concentrated broadly around 0.3.

Robustness testing added further weight to the results. When additive white Gaussian noise was injected into the phaseless inputs at signal-to-noise ratios of 30 dB and 20 dB, the reconstructed current distributions remained highly consistent with the ground truth, with only limited degradation as noise increased — an encouraging sign for real measurement environments, which are never noise-free. Scatter plots of predicted versus observed pixel values for the full test set showed the proposed model’s points tightly hugging the ideal prediction line, with R-squared values near 0.98 for both components, compared with wide dispersion and values near 0.4 for the conventional formulation. Reconstructed amplitude and phase maps from the predicted currents closely matched the true distributions in representative examples.

The implications reach beyond antenna diagnostics. Phase retrieval problems of this kind arise in microwave imaging, biomedical imaging, and inverse scattering, and the strategy demonstrated here — modifying the signal before measurement rather than struggling to untangle ambiguity afterward — offers a template for other ill-posed inverse problems in electromagnetics. Because the method retains a practical single-plane measurement configuration, it avoids the multi-plane scanning overhead of earlier remedies. The authors note that future work will extend the strategy to gradient-descent-based optimization problems, where additional signal processing must be applied to the unknown parameters themselves to compensate for the processing introduced at the source, a task they acknowledge will be considerably more demanding. For now, the result stands as a striking demonstration that sometimes the best way to solve a hard inverse problem is to change the question being asked of the data before the measurement is ever taken.

Subject of Research: Deep learning reconstruction of planar antenna array currents from phaseless near-field intensity measurements

Article Title: Ambiguity-reduced phaseless reconstruction of planar antennas using deep learning

Article References: Masoodi, M., Taromideh, H., & Omrani, N. (2026). Ambiguity-reduced phaseless reconstruction of planar antennas using deep learning. Frontiers in Antennas and Propagation, 4, Article 1894538. https://doi.org/10.3389/fanpr.2026.1894538

Image Credits: AI Generated

DOI: 10.3389/fanpr.2026.1894538

Keywords: antenna arrays, deep learning, phase retrieval, U-Net, inverse problems, near-field measurements, electromagnetics, phaseless reconstruction, convolutional neural networks, antenna diagnostics, ill-posed problems, Ambiguity-reduced