# Method for Estimating the Optimal Coefficient of L1C/B1C Signal Correlator Joint Receiving
## 1 Introduction
To ensure that global users obtain the best service performance while minimizing terminal costs, a new implementation of MBOC-modulated signals was proposed on civil interoperability signals, realizing that BDS B1C signals are interoperable user levels with GPS LIC and Galileo E1 OS [19; 20; 21; 22]. In particular, the three implementations corresponding to pilot and data components have been proposed to comply with the composited BOC (CBOC) modulated on Galileo E1, the time multiplexed BOC (TMBOC) modulated on GPS III L1, and the orthogonal multiplexed BOC (QMBOC) modulated on BDS III B1 [23; 24]. These three designs of MBOCs have different transmission and reception performances to ensure compatibility. Among the three MBOC signals, GPS-L1C and BDS-B1C adopt the signal modulation method, in which the power of the data and pilot channels is not equal, at 1:3. The conclusions, based on an analysis of the data/pilot joint receiving algorithm with equal power, cannot be completely applied to situations where the powers of the two are not equal by simple derivation, which attracts researchers to study joint reception of the data/pilot with an unequal power distribution in more depth. The weighting coefficient of the traditional discriminators joint algorithm is determined by the variance in the loop noise, which depends on the power ratio of the data/pilot. Therefore, the traditional discriminator joint algorithm adapts to the data/pilot with an unequal power distribution. For example, [PERSON]. [25; 26; 27] introduced the combined method of BDS3 B1C signal discriminator output with the power weighting coefficient determined by the variance in the loop noise. The traditional correlator combination is superimposed with the integration results of the data and the pilot, which cannot show the optimal performance in cases where the two powers are not equal. However, there are still some works that use the traditional methods. For example, [PERSON]. [28; 29] introduced the traditional correlator coherent and non-coherent joint acquisition and tracking method with consistent power distribution methods for GPS L1C signals, which directly superimpose the results of the correlator integration by equal weight ratio after the symbol decision. It was concluded that a better acquisition performance and tracking sensitivity were still obtained than single-component receivers. Later scholars made some changes to the coefficients of the correlator joint. Acquisition and tracking of correlator joint based on the data/pilot power ratio are introduced in [30; 31; 32], and the receiving performance is improved. Reference [30] is a coherent joint tracking algorithm based on the L1C and L1 CA correlators, and proposes a weighted joint determined based on the signal power ratio to minimize noise. To maximize the advantages of the correlator joint, Reference [33] proposed an improved non-coherent power-weighted joint acquisition algorithm. The least squares method is used to fit the optimal weighting coefficient based on the false alarm rate and monitoring probability of the joint acquisition. It is concluded that the optimal weighting coefficient is related to the received signal strength and power distribution ratio. However, the carrier-to-noise ratio (C/N0) cannot be obtained until the receiver has completed acquisition and tracking. Therefore, an optimal acquisition performance cannot be obtained for the real-time received signal. Ref. [34] analyzed the acquisition performance difference between the power ratio weighting coefficient and the optimal weighting coefficient to be less than 0.5 dB based on Ref. [33]. To avoid the complexity of the receiver, it is recommended that the user select the power ratio weighting coefficient. These references are based on the optimization combination coefficients discussion of acquisition.