Super-Resolution Joint DoA and ToA Estimation with Virtual Antenna Array

Conventional direction of arrival (DoA) estimation techniques require multi-antenna arrays at the transceiver, leading to high hardware costs. To address this issue, this paper investigates the joint DoAs and time of arrivals (ToAs) estimation in a single-input single-output (SISO) multi-carrier system. Specifically, the DoAs are estimated using a virtual antenna array (VAA), which is constructed by integrating signals received at different positions of a moving receiver. Since the receiver trajectory is irregular and there is a relatively large time interval between two neighboring positions, mainstream estimation methods in VAA face two challenges: i) The VAA lacks the advantageous antenna geometry of a uniform linear array (ULA) for signal processing, and ii) There exist phase errors caused by the oscillator frequency offset between the transmitter and receiver. We overcome the first challenge using an array manifold separation technique, which transforms the irregular VAA to the ULA geometry via the Jacobi-Anger expansion. After manifold separation, we accomplish super-resolution recovery of DoAs and ToAs by formulating an atomic norm minimization (ANM) problem. To address the second challenge, we propose an alternating optimization approach that iteratively solves the ANM and frequency offset problems. In each iteration, the frequency offset is solved through a bounded univariate minimization problem given the DoAs and ToAs. Numerical experiments consolidate that the proposed estimators for DoAs and ToAs exhibit superior performance, and their errors are close to the Cramer-Rao Lower Bound (CRLB) when SNR ≥ 5dB.