On the CRLB of TDOA/FDOA estimation from MIMO signals

Passive localization of a radio emitter on the ground is an important subject in military and security contexts. In passive localization, the time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) combination of the received signals can be used to determine the location of an emitter. The performance of the TDOA/FDOA estimation using single-input-single-output (SISO) signals is well-known in the literature. However, multiple-input-multiple-output (MIMO) signals and how they affect the TDOA/FDOA estimation accuracy have not studied before. In this paper, we investigate the problem of the TDOA/FDOA estimation using MIMO signals. The Cramér-Rao lower bound (CRLB) of the TDOA/FDOA estimation is derived as a benchmark to evaluate the impact of MIMO transmission. To make the derivations easier to understand, the CRLB is first formulated for SISO signals. Then, the results are extended to MIMO signals with any arbitrary number of transmit antennas. The maximum likelihood (ML) estimator of TDOA/FDOA is shown to be determined by calculating the cross ambiguity function. The performance of the ML estimator is compared with the CRLB through computer simulations.