Learning antenna imperfections to better locate incoming signals

When the antenna model is wrong

Direction-of-arrival estimation determines the angle at which a wave reaches an antenna array. It matters for integrated sensing and communication, where information about incoming signals can help guide wireless transmission. Accurate estimation depends not only on the algorithm, but also on how faithfully its mathematical model represents the hardware.

Real antennas can depart from their intended positions and respond differently in amplitude and phase. These discrepancies alter the pattern an incoming wave produces across the array. An estimator using an idealized array model can therefore mistake hardware errors for differences in direction.

In their preprint, Model-based learning for DoA estimation and array calibration via continuous sparse recovery, Chatelier and colleagues address both hardware mismatch and the limited precision of angular search grids. Their evidence comes from simulations, not a physical antenna demonstration.

A structured alternative to black-box learning

The method builds on simultaneous orthogonal matching pursuit, or SOMP. This algorithm represents measurements using a small selection from a dictionary of predicted array responses. Each dictionary entry corresponds to a candidate arrival angle. SOMP selects entries that best match the unexplained portion of the measurements, combining information across multiple measurement snapshots.

A conventional dictionary contains only a finite grid of angles. A source between grid points cannot be represented exactly by its true direction. Finer grids reduce this restriction but increase computation and make neighboring dictionary entries harder to distinguish.

The proposed approach instead starts with a coarse grid and refines selected responses continuously. Its learned variables have physical meanings: antenna positions, complex gains, and arrival angles, rather than the many weights of a general-purpose neural network.

Calibration first, direction estimation second

Although formulated as a joint problem, the practical procedure separates calibration from subsequent direction estimation. Calibration happens offline using batches of previously collected measurements. For each batch, SOMP supplies initial direction estimates using the current array model. Those angles are then held fixed while the antenna parameters are adjusted.

The unsupervised objective minimizes measurement energy that the selected array responses cannot explain. No ground-truth direction labels are required. Gradient-based updates are followed by constraints: antenna positions remain within a quarter-wavelength of their nominal locations, and the gain vector is normalized.

Once calibrated, the array model is fixed. For each new measurement, SOMP provides initial angles, followed by continuous angular refinement using the same residual-energy principle. The resulting estimates need not lie on the original grid. A supervised calibration variant substitutes known directions for the initial estimates.

What the simulations found

The default setup used 16 antennas, five far-field sources and 100 snapshots per measurement. Unsupervised calibration used 500 measurement samples, while the initial angular dictionary contained 50 points. Results were evaluated on 1,000 test measurements for each hardware realization, with median performance reported across 100 realizations.

The researchers tested independent signals and fully coherent signals, where every source emits the same waveform. Ordinary MUSIC, a comparison method based on separating signal and noise subspaces, struggled with coherent sources even when supplied with the true array parameters. The sparse-recovery methods remained effective in that setting.

The unsupervised calibrated continuous method outperformed the discrete baselines in the reported noise comparisons, including discrete SOMP given perfect hardware knowledge. In grid-resolution experiments, continuous variants using 50 candidate angles already matched or surpassed their discrete counterparts using 1,000. The supervised continuous variant closely matched the continuous estimator supplied with the true hardware parameters.

Accuracy and computational cost

Continuous refinement adds work, but it can avoid searching an extremely fine grid. Runtime measurements on one core of an NVIDIA Grace CPU showed operating points where continuous SOMP achieved better accuracy than discrete SOMP at equal runtime. MUSIC remained the least computationally demanding method in these comparisons, but failed for coherent sources.

Calibration also carries an upfront cost. Because the method performs it offline, that cost can be shared across subsequent estimates. These results establish a measured trade-off, not a universal speed advantage.

What remains unresolved

Good direction estimates do not imply uniquely recovered hardware parameters. Different combinations of antenna geometry, gain phase and arrival angles can explain the same measurements. Unsupervised calibration inherits a residual scaling and offset in the sine of the angles from its initial direction estimates; parameter errors can consequently plateau as noise decreases.

The method also assumes the number of sources is known and uses narrowband, far-field signals. Mutual coupling between antennas, unknown source counts, near-field operation and wideband signals remain future work. The simulations support the approach under the tested models, but do not establish performance on deployed hardware or demonstrate downstream communication gains.