High-precision and low-latency wireless localization is a key objective for future networks. The majority of existing localization methods rely on multi-antenna arrays (MAAs) to estimate directions of arrival (DoAs), but the size and cost of MAAs limit their application in portable electronic devices. Virtual antenna arrays (VAAs), constructed from signals received at different positions by a moving single-antenna receiver, offer a promising alternative. However, VAA-based localization is challenged by the local oscillator frequency offset (LOFO) in transceivers, the irregular array geometry caused by the receiver’s movement, and the non-line-of-sight (NLoS) environments due to physical blockage. To address the above challenges, this paper proposes a VAA-based online localization approach. Specifically, we employ a manifold separation technique based on the Jacobi-Anger expansion to maintain a uniform linear array-like channel representation for the irregular VAA geometry. This enables us to transform the joint estimation of multi-path DoAs, times of arrival (ToAs), and LOFO into a modified two-dimensional atomic norm minimization problem, which is solved using an alternating convex search algorithm. Additionally, we introduce an unscented Kalman filter-based simultaneous localization and mapping algorithm for real-time position tracking in NLoS environments. Extensive simulations validate the effectiveness of our approaches, showing a 70.15% reduction in DoA estimation error and a 54.02% reduction in localization error compared to benchmark methods.

Previous studies on time-of-arrival (ToA) estimation with phase ambiguity have largely relied on correlation matrices constructed from multi-shot signals. However, only a single-shot signal with binary phase ambiguity is available in Bluetooth low energy (BLE) ranging systems, rendering traditional methods ineffective. To address the above limitation, this paper proposes an efficient method for the joint estimation of ToA and phase ambiguity in BLE ranging systems. By leveraging the idea of beamforming among multiple frequency channels, the proposed method is comprised of three phases. In the first phase, we extract the one-way time differences of arrival (TDoAs) from the two-way channel frequency response measurements based on a modified atomic norm minimization algorithm by further addressing a component-dominating issue. In the second phase, we solve the matching problem related to the topological order of TDoAs by employing an alternating optimization framework and the Hungarian matching algorithm. In the final phase, we cope with the remaining first-arriving delay estimation problem by solving a series of low-rank MaxCut semidefinite programs. In particular, we prove the uniqueness and the global optimality of the obtained solution under certain conditions that can be easily satisfied in practice. Simulation shows that the proposed method can achieve the nanosecond-level accuracy in ToA estimation at a signal-to-noise ratio of 25 dB, with approximately 90% of ToA estimations exhibiting errors of less than 18 nanoseconds.

The dense distribution of access nodes in next-generation networks enables ultra-high-precision localization using time of arrival (ToA) measurements. However, in complex environments, some ToA measurements may originate from non-line-of-sight (NLoS) paths, degrading localization accuracy. Traditional robust methods for mitigating NLoS errors typically rely on high-complexity convex optimization or extensive data collection, imposing large localization overhead for ultra-dense networks. This paper proposes a novel robust method for joint NLoS identification and localization, which requires only a limited number of ToA measurements and scales efficiently to ultra-dense network deployments. To select an appropriate subset of ToAs for localization, we formulate a robust least-squares regression problem from a combinatorial optimization perspective. We design a solution algorithm with a computational complexity of$\mathcal{O}(N\log N)$, where$N$is the number of ToAs. This complexity is lower than most robust localization methods. Our algorithm iteratively refines the localization result using a coarse-to-fine positioning step and an adaptive ToA selection step. We provide theoretical error analysis to ensure the convergence of NLoS identification and localization results toward the optimal solution under mild conditions. Simulation results show that even with up to 32% of ToAs being NLoS, the proposed algorithm achieves an NLoS identification accuracy exceeding 85% and a localization error below 1 m.

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.

Configuring the reflection coefficients of a reconfigurable intelligent surface (RIS) is essential in harvesting the RIS benefits. When using beam training methods for the configuration, a large-sized codebook is required to reflect signals in all possible directions, incurring high beam training overheads. To address this issue, this paper considers a RIS beam training system operated in millimeter wave (mmWave) bands and proposes a fingerprint-based technique to reduce the codebook size using prior knowledge of the channel. The fingerprint database tensor records signal powers received at different positions and RIS reflection coefficients so that one can recommend a small-sized codebook for the RIS beam training. To reduce the fingerprint construction overhead, we exploit the mm Wave channel sparsity and channel spatial consistency to propose a sparse sampling strategy, which collects fingerprint data in only 35% of positions and 10.75% of codewords under the signal-to-noise (SNR) = 15dB. The other unsampled data is inferred by a formulated tensor completion problem. To efficiently solve the problem, we develop the conjugate gradient (CG) method to accelerate the alternating direction method of multipliers (ADMM), reducing 80.40% of running time. Numerical results show a similarity between the completed tensor and the benchmark tensor acquired in full sampling. The size of the recommended codebook is 2% of the full codebook, and the optimal achievable rate is approached by the recommended small-sized codebook.