## 1 Introduction  
The BeiDou Navigation Satellite System (BDS) is a relatively new member of the Global Navigation Satellite System (GNSS) family. Its global role has recently been recognized by formal acceptance by the International Maritime Organization (IMO) as a key part of its World-Wide Radio-Navigation System (WWRNS). This is in addition to the adoption of 1575.42 MHz for the future B1c component (instead of 1561.098 MHz currently used by B1 signal) for interoperability with other GNSS's. For both mass-market and professional GNSS users, BDS will provide improved accuracy, integrity, continuity and availability. There are several factors that determine a GNSS receiver's tracking sensitivity, one of which is self-interference. This is due to cross-correlation between codes from other satellites, within the same GNSS constellation. Self-interference problem is present in GNSS with short (1023 or 2046 chips in one code period) spreading codes. The fact that this problem has little influence on existing GNSS such as GPS indicates it is not a major problem, but in some exceptional cases when signal is extremely weak (down to 20 dB-Hz or even weaker), this could cause trouble for receiver correlators, which requires close investigation. Take acquisition for example, the effects could be two-fold. First, the self-interference between a strong and a weak signal may surpass the weak signal autocorrelation peak. Second, the very same self-interference contributes to the pre-detection noise floor, effectively reducing the processing gain of a weak signal; this could amount to a 9 dB processing gain degradation in weak signal acquisition [1]. In addition, in reseach such as multiple access capacity of GNSS, self-interference is a non-negligible factor when considering the upper limit of navigation satellites in the sky [2]. All these examples necessitates evolution of existing self-interference evaluation methods. Since GPS achieved full operational capability (FOC), research and development activities on the understanding and mitigation of self-interference were historically focused on GPS L1 C/A code. Typically, there are two methods to study this effect: simulation or an analytical way. Simulation can provide highly accurate results but at a cost in terms of computation time. A single location on earth surface takes about 11 CPU hours to gather the data for a whole day: 30-s data sets spaced every 15 min [3], and this translates into 13.752 CPU seconds for each second of simulated data. The accuracy of the simulation approach is 0.5 degrees (1 \(\sigma\)) for carrier tracking standard deviation, with coherent integration time equal to 0.02 s [4]. The analytical method is expected to achieve a lower but acceptable accuracy with a much reduced computation overhead. This paper intends to introduce a method for BDS self-interference evaluation on top of existing GPS self-interference models. The analytical model of GPS L1 C/A self-interference has long been investigated. Self-interference when introduced as extra noise injected into a receiver, like cross correlation between different GNSS's, is evaluated using spectrum separation coefficient (SSC) [5; 6]. It is common practice that analytical models treat the short code as a simple wide sense stationary (WSS) random process using a single parameter auto-correlation function (ACF) [7]. However, this simple model for C/A code self-interference ignores the fact that the spreading code repeats every 1023 chips and treats C/A code as an infinite long sequence of random plus/minus '1' s. Efforts to improve the accuracy of the analytical model were made by [PERSON] and [PERSON] [8], [PERSON] and [PERSON] [9], [PERSON] and [PERSON] [10] and [PERSON] et al. [11]. More complex WSS models were derived to predict C/A code self-interference by considering the real L1 C/A signal comprised of 20 repetitions (which was previously ignored) of spreading code of 1 ms long in one navigation data bit.