In the field of signal processing, modulation signals, including phase shift keying (PSK) and quadrature amplitude modulation (QAM), can significantly enhance the signal‐to‐noise ratio (SNR) through aliasing transmission following clustering and sorting. This article presents two novel approaches to compressed time difference of arrival (TDOA) estimation, leveraging amplitude‐phase clustering signals. A carefully designed compression matrix is constructed based on the unique amplitude and phase characteristics of the signals. The study then analyzes the Cramér–Rao lower bound (CRLB) under full‐sampling conditions. Finally, TDOA estimation is performed using the approximate maximum likelihood (AML) method. Simulation results demonstrate that the proposed compressed sampling TDOA estimation methods, based on amplitude‐phase clustering, achieve accuracy within an order of magnitude of full‐sampling performance. Additionally, this article explores the application of OFDM‐QAM signals, which exhibit amplitude‐phase convergence in the frequency domain, for time difference estimation in compressed sampling. A novel frequency‐domain aliasing time difference estimation algorithm based on amplitude‐phase convergence is proposed. Experimental results indicate that under high SNR conditions, the algorithm incurs only a minor SNR degradation of ~4 dB compared to time difference estimation in uncompressed transmission.
Jiao et al. (2026) studied this question.