## 1 Introduction  
With the development of Global Navigation Satellite System (GNSS), high-sensitivity receiver design in weak signal environments such as urban canyons, tunnels and dense foliage has become an important issue [1; 2; 3; 4; 5; 6; 7]. In high-sensitivity receivers, the extension of integration time is a typical strategy to enhance the signal-to-noise ratio (SNR) [8]. However, such extension is limited by data bit reversions [9]. The BeiDou Navigation Satellite System is called BeiDou System for short and is scheduled to be completed in 2020. A secondary modulation of the Neumann-Hoffman (NH) code is adopted by the BeiDou System, which plays an important role in spectral separation and narrowband interference protection [10]. However, the periodicity of the transmitted sequence is modified by the NH codes, leading to more polarity changes [11; 12]. The data bit rate increases to 1 kbps and the integration time is limited to 1 millisecond. In the Beidou System, once signal acquisition phase is completed, a bit synchronization phase should be used to detect the position of the data bit edges and NH codes in order to extend the coherent integration time of the tracking loops [13]. The classic algorithm for GPS data bit synchronization is the _histogram method_. It labels the sign changes in consecutive correlation results [14]. If the sign change occurs, the corresponding counter would increase. When the largest counter value exceeds the threshold, the bit boundary is found. Because of its simplicity, the histogram method has been widely used in consumer-level receivers, but it is only adequate for carrier-to-noise ratio (C/N0) above 30 dB-Hz, which is the normal condition for most outdoor GNSS receivers. When the C/N0 is less than 30 dB-Hz, the performance slides fast. The Viterbi algorithm is also used for bit synchronization [15]. It is adequate for C/N0 even of less than 20 dB-Hz, but its disadvantage is the complicated calculation and increased complexity. For GPS weak signals, the maximum likelihood (ML) bit synchronization method is more popular [16; 17]. The ML method calculates the bit energy of all possible navigation bit boundaries. The peak of bit energies corresponds to the bit boundary. This method still has good performance when C/N0 is 20 dB-Hz, but the ML method is sensitive to the frequency deviation. If the frequency deviation is larger than 25 Hz, the ML method is nullified [16; 18]. Furthermore, under low C/N0, the frequency deviation is unavoidable and the ML is unreliable. An efficient differential coherent accumulation algorithm (EDCAA) for weak GPS signal bit synchronization in [19] can eliminate the influence of frequency deviation by adopting the differential coherent value of two consecutive correlation outputs. Authors in [20] proposed a balance differential coherent bit synchronization algorithm for GPS signals, which adopts two complementary differential distances to avoid the unbalanced problem and the accumulation attenuation. Because these two algorithms adopt consecutive correlation outputs to do differential coherent process and the data bit rate of BeiDoi is 1 kbps due to NH codes, these algorithms are appropriate for legacy GPS signals but not BeiDoi signals. Because of the NH codes, the data bit rate of BeiDoi signals increases to 1 kbps and the integration time is limited to 1 ms. In order to extend the coherent integration time of the tracking loops, a bit synchronization algorithm is necessary to detect the position of the data bit edges and NH codes. In general, for BeiDoi weak signals without frequency deviation, the maximum likelihood method can be used for bit synchronization, but considering a frequency deviation larger than 25 Hz, a more appropriate and effective bit synchronization algorithm for BeiDoi signals is necessary. The paper proposes a bit synchronization algorithm for BeiDoi weak signals with large frequency deviation.