# Asymmetric Dual-Band Tracking Technique for Optimal Joint Processing of B1I and B1C Signals
## 4 The ASYM-DBT Method and Thermal Noise Performance Analysis
### The ASYM-DBT Method
#### 4.1.2 Processing Unit  
The processing unit supports two working modes of single-band and dual-band processing, and can smoothly switch between the two modes without any hardware modifications. While the single-band processing mode allows separate discriminating and filtering for the B1I and B1C signals at the same time, the dual-band processing mode is used to track the whole wideband signal, B1-ADS. Figure 5 depicts the processing flow of the two working modes. During the channel initialization phase, the single-band processing mode is first adopted to achieve reliable tracking of both the B1I and B1C signals, respectively and simultaneously. Once separate tracking obtains stable code and carrier parameters of both signals, the processing unit may shift smoothly to the dual-band processing mode to track the B1-ADS signal to obtain the optimal ranging performance. When one sideband undergoes narrow-band interference, the processing unit can shift back to the single-band mode to ensure that at least the signal on the other sideband can be reliably tracked. Obviously, the dual-band working mode of the processing unit is more complicated and needs to deal with the asymmetry resulting from different modulation schemes and the unequal power of the upper and lower sidebands of B1-ADS. The following will detail those algorithms under this working mode. * Discriminators for subcarrier and carrier phases  
The phase discrimination results of both carrier and subcarrier are calculated based on the prompt branches of two groups of correlators. In the DBT method designed for the AltBOC signal, by virtue of the symmetry between the upper and lower bands and the existence of pilot channels, the coherent combinations of the correlator outputs are directly implemented with the aim of decoupling the subcarrier and carrier phases and hence obtaining their respective estimates. However, this method cannot be applied directly to the B1-ADS signal because the B1I and BIC signals have different power and the B1I signal is only a data channel modulated by the navigation message. Consequently, the carrier and subcarrier phase discriminations of the B1-ADS signal can only be acquired after stripping the B1I navigation message and compensating for the unequal power of the two signals. To strip the navigation message of B1I, it is necessary to provide an estimation of the message data bit, \(\widetilde{D}_{B1I}\). This can be achieved in two ways [26]. When the signal-to-noise ratio meets the requirement of reliable demodulation, the estimation of the data bits of the message can be directly obtained from the sign of \(IP_{B1I}\). Otherwise, the bits may be provided through the assistance data in an Assisted-BDS system. To compensate for the unequal power of both signals, it is necessary to know the amplitude ratio between two signals, \(\gamma\). Under the assumption that the local codes are approximately aligned with the received signal, for the prompt branches of two groups of correlators we have \(\Delta\tau\approx 0\); then \(R_{\text{BIC}}(\Delta\tau)\approx 1\) and \(R_{B1I}(\Delta\tau)\approx 1\). Because the propagation paths to the receiver antenna are the same, the amplitude ratio \(A_{B1I}/A_{B1C}\) of the received signal is approximately equal to that of the transmitted signal from the satellite, i.e., \(\gamma=2:\sqrt{3}\). Given the estimated B1I data bit \(\widetilde{D}_{B1I}\) and the theoretical amplitude ratio of B1I and BIC \(\gamma\), and further assuming that both the B1I and BIC are stably tracked--viz., \(\alpha\) and \(\beta\) in Equation (14) approach zero--then the following coherent combinations can be formulated by applying the trigonometric function equation:  
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