# Multipath Mitigation for BOC Signals Based on Prompt-Assisted-Offset Correlator
## 1 Introduction  
Global navigation satellite systems (GNSS) are widely used in high-precision positioning applications, such as surveying, remote sensing, and unmanned ground vehicles (UGV) [1]. Differential techniques can effectively eliminate the errors of ionosphere, troposphere, and satellite ephemeris by exploiting the spatial correlation of these GNSS error sources [2]. However, differential techniques can hardly eliminate multipath errors because multipath signals change with the environment. Therefore, multipath has become the dominant error source in high-precision GNSS positioning. Multipath is the phenomenon where the direct signal is reflected or diffracted by obstacles. The modulation method, code rate, and carrier frequency of GNSS signals have a direct impact on multipath effects, so the multipath performance is an important factor to be considered in the design of GNSS signals. Modernized GNSS signals generally adopt binary offset carrier (BOC) modulation [3, 4]. BOC modulation introduces a subcarrier in the binary phase-shift keying (BPSK) modulation, which moves the main energy from the center to the edge of the frequency band [5, 6]. As a result, the BOC signal has more high-frequency components and larger root-mean-square bandwidth than the BPSK signal with the same code rate, indicating that the BOC signal has better ranging capability and multipath resistance in theory. How to make full use of the ranging potential of BOC signals is a topic of great interest. Tracking ambiguity is a major threat in processing the BOC signal because its autocorrelation function (ACF) has multiple peaks. The typical delay lock loop (DLL) probably locks on side peaks of the BOC signal, resulting in large ranging errors. Therefore, many three-loop tracking methods have been proposed to solve the tracking ambiguity problem, such as the Dual Estimate Technique (DET) [7], the Double Phase Estimator (DPE) [8], and Dual BPSK Tracking (DBT) [9; 10]. In addition to the DLL and carrier phase lock loop (PLL), three-loop tracking methods use a subcarrier lock loop (SLL) to track the subcarrier delay. In the DPE and DBT methods, the SLL is replaced with a subcarrier phase lock loop (SPLL). With limited signal bandwidth, the SPLL has lower computational complexity and similar thermal noise performance compared to the SLL [8]. Although three-loop tracking methods address the threat of tracking ambiguity, their ranging performance deteriorates severely in the presence of multipath. Therefore, GNSS receivers need to be equipped with multipath mitigation techniques to reduce ranging errors in practice. There are various GNSS multipath mitigation techniques, among which the receiver signal processing techniques using advanced correlator architectures are of great concern. These correlator-based techniques can be divided into two categories: parametric and non-parametric [11]. Parametric correlator-based techniques, such as the multipath estimation delay lock loop (MEDLL) [12], require a large amount of computation and may not converge when there are many multipath signals. By contrast, non-parametric correlator-based techniques require a small amount of computation, so they are more widely used in GNSS receivers. There are many non-parametric correlator-based techniques that can effectively mitigate multipath, such as the narrow correlation (NC) [13] and double delta (DD) correlator variants (high resolution correlator (HRC) [14] and strobe correlators [15]). These multipath mitigation techniques were originally designed for BPSK signals and gradually applied to BOC signals [16; 17; 18; 19]. Specifically, the NC and DD techniques are usually used in the DLL to mitigate code multipath errors for BOC signals [20; 21; 22]. Since the code ranging measurement is used to fix the integer ambiguity of subcarrier ranging measurement, the code multipath error needs to be suppressed to be less than half of the subcarrier wavelength. The pseudo-range used for positioning is the subcarrier ranging measurement after fixing integer ambiguity.