# Band-Pass Sampling in High-Order BOC Signal Acquisition
## 1 Introduction  
The BOC modulation has been adopted in modernized global positioning system (GPS), European Galileo project, and China's BeiDou-3. BOC signals are characterised by a rectangular subcarrier, which split the signal spectrum around two main lobes at \(\pm f_{\mathrm{sc}}\), the subcarrier repetition frequency. It can improve the tracking performance, and enhance spectrum compatibility due to the narrow ACF, and split spectrum [1]. More detail and characteristics of BOC modulation can be found in literature [2; 3; 4; 5].  
However, the acquisition process of BOC signals becomes more complex, due to the multiple peaks in the ACF envelope, which requires a large number of timing hypotheses to search a given uncertainty window [6]. Thus the acquisition becomes more computationally expensive and time consuming. Another problem in BOC acquisition is the high Nyquist sampling frequency [7], which increases the computational burden and power consumption.  
Some techniques have been reported to remove the impact of the secondary peaks in the ACF. The subcarrier phase cancellation technique (SPCT) [8] introduces a quadrature squared subcarrier, called QBOC, to eliminate the ambiguity problem. In the autocorrelation side-peak cancellation technique (ASPeCT) proposed in [9], subtraction of the cross-correlation between the BOC and PRN signals from the BOC autocorrelation is employed; but the technique is applicable only to sine-BOC(\(n\),\(n\)). The Pseudo-Correlation Function (PCF) [10] method constructs a single-peak ACF using a special designed reference signal. However, it will suffer from severe detection performance degradation forhigh-order BOC signal. The techniques mentioned above can remove the impact of the secondary peaks in the ACF, but they all process the upper and lower sidebands together, resulting in a high sampling frequency and computational complexity.  
The main idea behind the BPSK-like method is that the BOC signal can be obtained as the sum of two BPSK signals, located at positive and negative sub-carrier frequencies. The effect of sub-carrier modulation can be removed by using a pair of single-sideband correlators. A receiver may use a single-side band (SSB), either the upper or lower sidebands, or use dual-side band (DSB), where both bands are combined non-coherently. Due to filtering and correlation losses, the BPSK-like methods bring some degradation. The losses are 3 dB for SSB and about 0.5 dB for DSB [11]. However, the BPSK-like method needs two RF channels, mixers and analog-to-digital converters (ADC), which increase the implementation complexity [11].  
In this paper, the band-pass sampling technique [12; 13; 14; 15; 16] is introduced in BOC signal sampling to remove the secondary peaks, as well as to reduce the sampling frequency. Band-pass sampling is the technique of under-sampling a band-pass signal to achieve a frequency translation via intentional aliasing [17]. If the sampling frequency is \(f_{s}\), then the spectrum of the sampled signal can be obtained by replicating the spectrum of the original signal at multiples of \(f_{s}\)[18]. Since a BOC signal can be treated as the sum of two BPSK signals with adjacent center frequencies [19], the band-pass sampling technique for multiple signals [14; 17; 20] can be used. Furthermore, taking into account the subcarrier Doppler, a dual-loop based acquisition structure is proposed to acquire the sampled signal.  
The remainder of this paper is organized as follows. Section 2 introduces the dual-sideband model of BOC signals, which is the basis of band-pass sampling; in Section 3, the band-pass sampling is applied and the sampling parameters are derived. The dual-loop based acquisition structure is also described in detail. The detection probability and computational complexity are analysed in Section 4. The conclusions are drawn in Section 5.