## 1 Introduction  
In recent decades, an evolving global navigation satellite system (GNSS) receiver landscape fueled the discussion of further introductions of new GNSS signals to meet emerging market needs. For instance, Galileo (GAL) E5-AltBOC and BeiDou Navigation Satellite System (BDS) B2-ACEBOC were added to the signal portfolio to offer a signal with increased bandwidth and therefore higher-ranging capabilities in the lower L-band. Options to broadcast new broadband signals in the upper L-band are limited due to spectrum restrictions as well as possible intra- and inter-system interference issues. In the upper L-band, a wideband open service (OS) ranging signal is missing, but to meet market demands, the introduction of a quasi-pilot signal for low-complexity receivers [1; 2; 3] with a potential offset to the L1 carrier was proposed by previous studies [4; 5; 6]. Adding this new signal with a frequency offset may enable meta-signal processing (MSP) of the GAL E1B/C with the E1D signal. The concept of MSP was first discussed in the context that a GNSS transmits a multitude of satellite navigation (satnav) signals across multiple frequencies [7; 8]. MSP aims to track a combination of ranging signals which have different carrier frequencies and therefore have a larger Gabor bandwidth, which can in theory greatly increase tracking performance [9; 10].  
However, meta-signals have a severe ambiguity problem since their auto-correlation functions (ACFs) contain a large number of side-peaks which leads to larger probabilities of false locks in high-noise regimes [11]. To solve this issue, research has focused on developing tracking algorithms that optimize the benefits of meta-signals in particular for the BDS III signals in the upper L-band [10]. Notably, the extension of the double estimator/double phase estimator [12; 13] and the wideband high-accuracy joint tracking technique [14] have been developed to improve the tracking performance of the BDS B1I-B1C meta-signal while reducing the number of required correlators [15].  
The theoretical gains in terms of ranging performance and the mitigation of the ambiguity problem were the subject of previous work [9]. In [16], [PERSON] et al. conducted a first analysis of cross-correlation function (CCF) property changes in the presence of linear distortions. This study was limited to a meta-signal comprising a binary offset carrier (BOC)(1,1) and binary phase-shift keying (BPSK)(1)/BOC(1,1) with a frequency offset of \(12\times 1.023\) MHz. However, there is a lack of further findings regarding the influence of distortions on MSP performance dependent on the modulation and chosen frequency offset. In this paper, we present an extended analysis through a systematic assessment of the robustness of the time of arrival (TOA) estimation error standard deviation (stdev.) of several potential meta-signal options enabled by a forthcoming GAL E1D signal for different levels of distortions caused by a transmitter and a receiver. The results suggest that MSP may enable an improvement in the ranging performance depending on the exact shape and placement of the GAL E1D signal. Certain GAL E1D signal options were found to be sub-optimal in the context of MSP since the ambiguity problem is elevated in the presence of distortions.