## 1 Introduction  
As global navigation satellite systems (GNSS) have developed and upgraded, new civil signals are designed and employed, in order to support a wide and growing range of navigation services. For the applications including surveying, timing, vehicle navigation and consumer electronics, the level of performance demanded are different. To meet those requirements simultaneously in the modernized GNSS signal for civil use, complicated modulations and multiplexing techniques are employed, represented by Alternative BOC (AltBOC) and multiplexed BOC (MBOC). These new GNSS signals can be deconstructed with multiple components, thus different level of accuracy can be obtained by processing different number of components. When all of the components are employed to process as an integral, that the local despreading signal is matched with the received signal, the up-bound of the pseudo-ranging accuracy can be obtained. Also, by choosing different number of components or different forms of local despreading signal, a great many strategies are available for the signal receiving. By using these strategies, it is able to promote the positioning accuracy or robustness, such as unambiguous tracking of BOC signal [1] and multipath mitigating techniques [2]. Also, it is possible to reduce the receiver complexity by locally generating a simplified form of the signal, such as the BPSK-like receiving of BOC signal [3; 4; 5]. Because of these benefits, the various receiving strategies are widely used by receivers in the processing of the MBOC, AltBOC signals. Theoretical evaluation is an objective and convenient method to acknowledge the performance of a signal. In this context, since the obtained performance is largely associated with the processing techniques implemented by receivers, the theoretical evaluation of signal should also take comprehensive consideration of the receiving strategies. In the aspect of signal design, to provide better performance for a wide range of users, not only the performance under traditional matched receiving, but also the performance under the various pervasive applied receiving strategies, should be considered and optimized, where the theoretical evaluation criteria are treated as the guidance and objective of signal design process. In the aspect of receiving, the theoretical evaluation is a convenient method to compare the performance under various receiving strategies, thus providing useful information for the strategies choosing and configuration for receiver manufactures. Accordingly, the theoretical evaluation of signal performance becomes an essential topic for both the signal design and receiving in GNSS. In addition, to reveal the properties of signals, the theoretical evaluation criteria should focus on key factors associated with the signal and its processing. A myriad of factors related to the receiving performance can be concluded in the evaluation, including the receiving bandwidth, signal to noise ratio (SNR), interference type and strength, sampling and quantification, etc. However, considering all these factors exaggerate the sophistication of signal evaluating process, making the results coupled with the external factors such as specific working scenarios or receiver implementations, from which it is hard to observe the inherent performance of signal. Therefore, in theoretical evaluation of signals, a concise model decoupled from the unnecessary factors not only increases the objectivity of evaluation, but also facilitates the calculation, which is required by the research in signal design and receiver configuration. As signal evaluation theory has developed, various routines for choosing the set of related factors in the evaluating model have been proposed. In terms of code tracking evaluation, the initial work comes from communication [6], which is applicable for a BPSK signal under an infinite receiving bandwidth and thermal noise. The paper [7] proposes a model with one equivalent front-end filter and also considers the non-white Gaussian noise and interference.