Estimating Angle-of-Arrival and Time-of-Flight for Multipath Components Using WiFi Channel State Information

Abstract

Channel state information (CSI) collected during WiFi packet transmissions can be used for localization of commodity WiFi devices in indoor environments with multipath propagation. To this end, the angle of arrival (AoA) and time of flight (ToF) for all dominant multipath components need to be estimated. A two-dimensional (2D) version of the multiple signal classification (MUSIC) algorithm has been shown to solve this problem using 2D grid search, which is computationally expensive and is therefore not suited for real-time localisation. In this paper, we propose using a modified matrix pencil (MMP) algorithm instead. Specifically, we show that the AoA and ToF estimates can be found independently of each other using the one-dimensional (1D) MMP algorithm and the results can be accurately paired to obtain the AoA⁻ToF pairs for all multipath components. Thus, the 2D estimation problem reduces to running 1D estimation multiple times, substantially reducing the computational complexity. We identify and resolve the problem of degenerate performance when two or more multipath components have the same AoA. In addition, we propose a packet aggregation model that uses the CSI data from multiple packets to improve the performance under noisy conditions. Simulation results show that our algorithm achieves two orders of magnitude reduction in the computational time over the 2D MUSIC algorithm while achieving similar accuracy. High accuracy and low computation complexity of our approach make it suitable for applications that require location estimation to run on resource-constrained embedded devices in real time.

Keywords: MUSIC algorithm; WiFi channel state information; angle of arrival estimation; indoor localization; joint AoA–ToF estimation; matrix pencil; multipath propagation; time of flight estimation.

Figure 1

Signal impinging on a linear antenna array.

Figure 2

Multipath propagation simulated by the Wireless Insite software.

Figure 3

Simulation with no noise. (a) performance of MMP with no noise. Simulation time is 0.044 s; (b) performance of 2D MUSIC with no noise. Simulation time is 8.66 s.

Figure 4

2D Music spectrum with no noise.

Figure 5

Simulation with ambient noise. (a) performance of MMP with $\mathrm{SNR}=35$ dB for 1000 runs. The RMSEs for AoA and ToF are 2.34 deg and 6.24 ns and the bias for AoA ToF are −1.53 deg and −0.49 ns. Simulation time is 0.79 s; (b) performance of 2D MUSIC with $\mathrm{SNR}=35$ dB for 1000 runs. The RMSEs for AoA and ToF are 2.60 deg and 13.69 ns and the biases for AoA and ToF are −1.97 deg and 16.95 ns. Simulation time is 152.21 s.

Figure 6

2D Music spectrum with $\mathrm{SNR}=35$ dB.

Figure 7

Performance of 2D MUSIC with $\mathrm{SNR}=35$ dB and a higher resolution gird for 1000 runs. The RMSEs for AoA and ToF are 1.97 deg and 13.69 ns. Simulation time is 201.45 s.

Figure 8

Performance using CSI from experiment. (a) performance of MMP with real CSI data. Algorithm runtime is 0.013 s; (b) performance of 2D MUSIC with real CSI data. Algorithm runtime is 2.24 s.

Figure 9

Simulation with no noise. (a) performance of MMP with $\mathrm{SNR}=35$ dB for 1000 runs. The RMSEs for AoA and ToF are 0.057 deg and 0.023 ns. Simulation time is 0.83 s; (b) performance of 2D MUSIC with $\mathrm{SNR}=35$ dB and a lower resolution grid for 1000 runs. The RMSEs for AoA and ToF are 8.4661 deg and 6.271 ns. Simulation time is 2.3 s.

Figure 10

2D MUSIC spectrum with $\mathrm{SNR}=35$ dB and a lower grid resolution.

Figure 11

Performance of MMP when bandwidth is 80 MHz for 1000 runs. The RMSEs for AoA and ToF are 1.80 deg and 0.44 ns. Simulation time is 0.80 s.

Figure 12

Ordering performance. (a) performance of MMP estimating AoA first for 1000 runs. The Average RMSEs for ToF and AoA are 2.20 ns and 0.65 deg; (b) performance of MMP estimating ToF first for 1000 runs. The RMSE for ToF and AoA are 0.089 ns and 0.61 deg.

Figure 13

Multi-packet CSI aggregation performance. (a) performance of MMP with $\mathrm{SNR}=20$ dB for 1000 runs. The RMSEs for AoA and ToF are 12.39 deg and 22.92 ns. Simulation time is 0.76 s; (b) performance of MMP using the multi-packet CSI aggregation method when $\mathrm{SNR}=20$ dB for one run using CSI of 1000 packets. The RMSEs for AoA and ToF are 2.29 deg and 0.46 ns. Simulation time (including CSI aggregation) is 0.14 s.