# A Novel Time Delay Estimation Algorithm for 5G Vehicle Positioning in Urban Canyon Environments
## 1 Introduction
[29] proposed a novel TDOA algorithm with super resolution based on a multi-dimensional cross-correlation function, namely the volume cross-correlation function (VCC). Numerical simulations showed an excellent time resolution capability of the algorithm in multipath environment. [PERSON] et al. [22] made comparisons of the super-resolution TOA/TDOA estimation algorithms and the experience showed that the MUSIC-CR algorithms have the highest resolution and lowest SNR threshold. [PERSON] et al. [30] proposed a super-resolution TDOA estimate algorithm based on orthogonal frequency division multicarrier, the experimental results showed that the approach can be useful for several applications needing accurate positioning. [PERSON] et al. [31] proposed two 2-D DOA and TOA estimators called FFT-MUSIC and two-step FFT-MUSIC. Simulation results showed that both estimators can reduce the computation cost by 1-2 orders of magnitude. All the above methods effectively improve the accuracy and robustness of time delay estimation. However, few researchers have addressed the problem of non-line of sight (NLOS) propagation scenarios which is common for mobile communication signals in urban canyon environments. In some cases, the signal strength of direct path is weaker than non-direct path in NLOS propagation scenario, e.g., when there is an obstruction between the transmitting antenna and the receiving antenna, and the obstruction absorbs electromagnetic waves more heavily (such as thick walls), the direct path will receive severe degradation from the obstruction, while the NLOS path still has strong signal strength through the transmission to the receiving antenna. The direct path will be submerged by the non-direct path in conventional MUSIC algorithm and this problem will cause a large delay estimation error as shown in Figure 1. In Figure 1, we simulated a typical channel in an NLOS propagation scenario, and the peak of direct path in MUSIC spectral function of the received signal is submerged by the non-direct path. In order to solve this problem, we propose a novel time delay estimation algorithm called non-line of sight cancellation multiple signal classification (NC-MUSIC). In this algorithm, the time delay spread of received signal is roughly estimated through the cross-correlation method,and the NLOS path with strong signal strength is cancelled while the direct path is retained. This step will reduce the peak of NLOS path and make the peak of direct path more obvious. Then, the covariance matrix of the received signal is calculated and the eigenvalue decomposition (EVD) is carried out. An unsupervised multipath estimation method is used to estimate the number of multipath in the propagation channel. With the number of multipath and the EVD, the noise subspace of covariance matrix is solved. The MUSIC spectral function is calculated from the noise subspace. Finally, the time delay of the direct path is estimated by searching the peak of the MUSIC spectral function. The contributions of this paper are:  
* The proposal of a novel accurate time delay estimation algorithm based on NLOS cancellation and MUSIC super-resolution method. * The proposal of an unsupervised multipath estimation method to estimate the multipath number of received baseband signal. * Improvement of the MUSIC spectral function calculation method in conventional MUSIC super-resolution to make the peak of direct path more obvious. The proposed algorithm in this paper is used to eliminate the NLOS error due to the signal propagation. In practice, there is still a synchronization error between the vehicle and the base station in addition to the NLOS error. This error will also lead to errors in the positioning results. The distance between RX and TX can be measured by round-trip time (RTT) and the synchronization error between RX and TX can also be ignored by calculating TDOA. The rest of the paper is organized as follows. The system model is developed in Section 2. The NC-MUSIC algorithm is defined in Section 3.