Reduced-Complexity Decimeter-Level Bluetooth Ranging in Multipath Environments

Abstract

In this paper, we investigate enhanced super-resolution range estimators with decimeter-level accuracy for multi-antenna and multipath Bluetooth systems. To enhance the traditional MUSIC range estimator for a two-way frequency-hopping Bluetooth channel model, we apply forward-backward averaging and bandwidth extrapolation using Burg's algorithm to improve ranging accuracy, which is limited by the used Bluetooth bandwidth and the quality of the estimated sample covariance matrix. For the multiantenna case, we compare the Summed Antenna Processing and Individual Antenna Processing methods to process multiple-antenna Bluetooth channel measurements and enhance the range estimation accuracy compared to the single-antenna case. In addition, we investigate a sparsity-aware range estimator which exploits the sparsity of Bluetooth channel impulse response and achieves comparable ranging accuracy to the enhanced MUSIC estimator but at a much lower computational complexity. We apply the greedy Orthogonal Matching Pursuit algorithm to heuristically solve the sparsity-constrained optimization problem for Bluetooth ranging. Furthermore, we evaluate the computational complexity of our investigated Bluetooth range estimators with two complexity-reduction techniques to further reduce the complexity of MUSIC range estimator. Moreover, we analyze the Cramer-Rao Lower Bound (CRLB) on unbiased range estimation using the frequency-hopping Bluetooth channel model and derive a new insightful CRLB expression for a two-path channel model. Finally, we evaluate the Root-Mean-Square Error and Empirical Cumulative Distribution Function performance of our investigated range estimators both on simulated and real-world Bluetooth data that we collected in line-of-sight (LOS) and non-line-of-sight (NLOS) multipath scenarios. Our proposed enhancements on the range estimators improved the ranging accuracy by 58% for our collected Bluetooth data.

A Multichannel Approach and Testbed for Centimeter-Level WiFi Ranging

“…The smoothing subarray size for all cases is set as N ≈ K Ds /2 following insights from [63], [70] and preliminary evaluations. The number of MPCs specified is scaled with bandwidth as higher resolution estimation of the MPC ToFs is possible with higher bandwidths [57]. Finally, the number of search points for MUSIC is fixed at J M = 751 with a 2 cm resolution for complexity evaluations since a centimeter-level resolution is often sufficient in practice.…”

“…, K B describes the uniformly spaced unique subcarrier frequencies after stitching across B channels. Following this signal model, a derivation for the Cramér-Rao Lower Bound (CRLB) in the case of two MPCs is provided in [57] which demonstrates the relationship of the bound to the ToF spacing between MPCs, signal-to-noise ratio (SNR), bandwidth, and CFR measurement spacing.…”

“…is the calibrated one-way CFR, H While we assume known gains for the SDRs utilized in our testbed, in practice, these gains may not be known, and an estimate may be necessary for the gain shifts across channels. For cases with unknown G T X,b and G RX,b , alternative methods for aligning CFR magnitude measurements of adjacent channels can be based on overlapping CFR measurements from channels available in the 2.4 GHz band or CFR extrapolation using Burg's algorithm for forward and backward autoregressive modeling of the CFR [57], [58]. The alignment factor can then be estimated from the least squares solution of…”

“…We employ the MUSIC algorithm for ToF estimation due to its properties as an asymptotically efficient and unbiased estimator and popularity as a super-resolution estimator for signal processing problems of the form in (10) [9], [10], [37], [57], [59]- [61]. For the subspace decomposition necessary for MUSIC, a sample covariance matrix must be computed.…”

WiFi 5GHz CSI-Based Single-AP Localization With Centimeter-Level Median Error

“…However, linear interpolation would degrade the channel quality between the U-NII-2C and U-NII-3 bands due to the large amount of gap between them. To address this issue, we utilize Burg's prediction method [38] to propose an interpolation scheme that fills in the gap between these two bands with sufficient CFR estimation accuracy. For the received two-way CFR vector y(k), we can divide the CSI from the two bands as follows…”