The Radon Transform, True Time Delay Beamforming, and Ultra-Wideband Antenna Arrays (Invited Paper)

The FR3 band has emerged as the major focus of 6G wireless research. FR3 cellular operation presents the challenge of extreme bandwidth combined with physically large antenna arrays. In this regime, conventional phase-shift beamforming entails a loss of coherence (beam-squint), and has to be replaced by true time delay beamforming (TTD). It happens that TTD is mathematically equivalent to taking the Radon transform of the space/time measurements. We exploit fifty years of research in the application of the Radon transform to computer tomography and to seismic exploration to elucidate the workings of TTD. We use the Radon transform combined with semblance detection and Radon slowness filtering to remove far-field signals from the measured space/time signals from a linear array, leaving only near-field signals. In turn we partition the array into sub-arrays. For each sub-array we estimate, via the semblance Radon transform, the angles-of-arrival of the near-field signals. We then use triangulation to estimate the coordinates of the near-field sources. Finally we integrate the original space/time data along hyperbolic trajectories to extract the individual near-field signal envelopes.