Two-Dimensional ESPRIT-Like Shift-Invariant TOA Estimation Algorithm Using Multi-Band Chirp Signals Robust to Carrier Frequency Offset

In this paper, a two-dimensional (2-D) ESPRIT-like shift-invariant time-of-arrival (TOA) estimation (ELSITE) algorithm for multi-band chirp signals in the presence of a carrier frequency offset (CFO) is presented. For the shift invariant TOA estimation, the received signals must be transformed into a sinusoidal form. When the received signals are perturbed by a CFO, the frequency of the transformed sinusoids is also shifted such that the TOA estimation results are biased. The TOA-induced phase shift of the multi-band chirp signals is determined according to the parameters of the signal, while the CFO-induced phase shift is only proportional to the elapsed time. Based on this property, the proposed ELSITE algorithm achieves robust TOA estimation against CFO from the signal subspace of the stacked matrix. The root mean square error of the proposed algorithm was analyzed and verified in both an AWGN channel and a multipath channel with CFO via Monte-Carlo simulations.