High Resolution ToA Estimation via Optimal Waveform Design

This paper introduces a novel method to improve the Time of Arrival (ToA) estimation resolution for a fixed available bandwidth in the presence of unknown multipath frequency selective (MPFS) channels. Here, the maximum rising level detector technique is proposed which utilizes oversampling and multiple correlation paths to evaluate with high resolution the path corresponding to the maximum rising level of matched filters output. However, employing such technique demands for transmission of waveform that creates a very high rising level at autocorrelation center. This paper proposes an efficient technique to design proper waveforms (very high rising level at autocorrelation center) via minimization of weighted integrated sidelobe level, exploiting the trust-region algorithm. The performance of the proposed technique is evaluated via simulations of the ToA mean square error, and compared with the state-of-the-art approaches considering the same bandwidth, and Cramer-Rao lower bound as benchmark. Simulations confirm that the ToA resolution is improved as the number of correlation paths increases and verify the feasibility of the proposed technique compared with the available approaches for the MPFS channels.

I. Introduction

Time-of-arrival (TOA) estimation is desired in variety of applications such as digital communications, wireless sensor network, radar and sonar and wireless indoor and outdoor localization [1]–[7]. The ToA estimation techniques are divided into two different categories, the traditional techniques that are based on the matched filter output, and the super resolution techniques. The former incorporates a pre-designed waveform with autocorrelation properties close to the delta function at the output of matched filter. Although correlation based techniques propose excellent performance in the presence of unknown multipath frequency selective (MPFS) channels, however, their proposed ToA resolution is limited by transmitted waveform bandwidth. In later, the ToA is calculated via maximizing the pseudo-spectrum of the corresponding signal sub-space. This is achievable via matched filter output decomposition in frequency domain [8], [9]. Examples of super resolution techniques are independent component analysis (ICA) [10], maximum likelihood (ML) [11], multiple signal classification (MUSIC) [12]- and estimation of signal parameter via rotational invariance technique (ESPRIT) [15]. However, the frequency domain techniques only improve the ToA resolution in flat fading channels or in the presence of multiple resolvable paths which are not feasible assumptions in many ToA applications.