Harmonic amplitude-based DOA estimation in time-modulated array via asynchronous sampling

A harmonic amplitude-based method for direction-of-arrival (DOA) estimation using time-modulated arrays (TMAs) is presented. In the proposed scheme, DOAs are estimated from a limited number of harmonic amplitudes without requiring harmonic phase information, thereby allowing asynchronous sampling between the radio frequency (RF) front end and the analog-to-digital converter (ADC). The received signals are modulated through multi-phase schemes with fixed delays, and the desired harmonic amplitudes are extracted via a zoom fast Fourier transform (FFT). The mathematical relationship between the amplitude ratio and the incident angle is derived, where the ratio is jointly determined by the time delay, baseline spacing, and harmonic order. A specific amplitude ratio, defined as the ratio of amplitudes at different harmonic orders, may correspond to multiple angles, leading to ambiguity. Under certain delay conditions, this mapping simplifies to a one-to-two correspondence, which is resolved by exploiting two sets of effective amplitude ratios to obtain common angle solutions. Simulation results demonstrate that the proposed approach achieves accurate DOA estimation and maintains robustness under synchronization errors. Experimental validation in the S-band confirms the effectiveness of the method. © 2026 Elsevier Inc.