Direct Localization and Synchronization for High-Mobility Agents With Frequency Shifts in MIMO-OFDM Systems

The direct position determination (DPD) technique utilizes raw received signals to localize agents in a single step, eliminating the need for intermediary measurements. The DPD is recognized for its accuracy superiority over the two-step approach, especially under low signal-noise-ratio (SNR) condition. However, few existing DPD research has focused on scenarios involving moving or unsynchronized agents. In this article, we develop a novel and extended problem, direct localization and synchronization (DLAS) for highly mobile agents with unsynchronized frequency shifts in collocated multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The base stations (BSs) sequentially broadcast signals in a time-division multiple access (TDMA) manner, and both Doppler effect and oscillator's nondeterminism lead to frequency shifts at the agent side. In order to compensate for the position variation of the fast-moving agent, we construct a motion model with uniform acceleration. Next, we propose a computationally efficient DLAS method based on the maximum-likelihood (ML) principle. Specifically, we first decouple the frequency shifts from other unknowns by exploiting the periodicity of block-type pilots and determine a nonlinear optimization problem. We then develop an iterative solution using the frequency shifts to optimally extract real DLAS parameters from complex signal observables. Moreover, we present the closed-form Cramér-Rao lower bound (CRLB) for our estimators determined from the derived general bounding result in complex field. We theoretically analyze the performance gain owing to prior information, and compare the computational complexity among different algorithms. Finally, we provide extensive numerical results to establish the superiority of our proposed method.