## 1 Introduction
In the GNSS community, the bandpass sampling theory was adopted to design a direct conversion of GNSS carrier signal [27; 28; 29; 30] in order to reduce the sampling frequency of the direct RF sampling front end of GNSS receivers. However, currently mainstream commercial GNSS receivers generally employ the intermediate frequency (IF) sampling front end. In the design of IF sampling front end for multi-frequency GNSS receivers, its bandwidth is generally much larger than that of the single-frequency front end, in order to incorporate multiple signals located at adjacent frequency points in one channel of the IF front end. Owing to the fact that signals of each frequency point are acquired separately, signal acquisition can be realized within the lower bandwidth. It exactly inspires us to apply the bandpass sampling theory to the efficient and fast signal acquisition of the IF sampling GNSS receivers. As another important solution contributing to the signal acquisition challenge, massive correlation-related approaches also have been widely investigated. From the perspective of correlation period, [PERSON] et al. [31] introduced an interesting chip-wise correlation strategy that accumulated code samples in one period and calculated correlation values for each chip period to reduce the search space and computation. In contrast, [PERSON] et al. [32] extended the correlation time to an entire duration of navigation data bit, aiming at enhancing the sensitivity of receivers. Further, [PERSON] et al. [33] proposed a variable time parallel acquisition scheme and different accumulation schemes over multiple code periods to detect weak signals. [PERSON] et al. [34] exploited a fusion acquisition method of multiple correlation strategies to reduce correlation loss caused by sign transition of high data rate signals. Especially, a small increase of computation emerged using the delay-accumulation method [35] and data-pilot optimized combining acquisition methods [36]. Additionally, [PERSON] et al. [37] presented a partial acquisition algorithm using specially-designed matched filters and differential post-correlation techniques to simplify computational complexity of signal acquisition. Although increasing correlation time is an effective way to ensure acquisition accuracy, computation and time consumption generally present higher expense due to the longer correlation time. Further, it is difficult to find out many researches that have done detailed exploration on the relationship between acquisition performance and correlation time, and that have been applied effectively to signal acquisition of GNSS receivers. With regard to broadband multi-frequency GNSS receivers, we propose a resampling strategy and variable circular correlation time in this paper to decrease computational complexity and time consumption of signal acquisition. Inspired by the bandpass sampling theory, the resampling strategy reduces greatly the data size of the sampled signal with just slight loss of signal quality. It lays the computational foundation for FFT, correlation and convolution operations of signal acquisition. In particular, the resampling strategy is implemented step-by-step to demonstrate the capability of combining with existing FFT-/correlation-based acquisition algorithms. Taking the longer code period into consideration, the relationship between circular correlation time and acquisition performance is concerned for the potential of shortening circular correlation time to adapt to different signal strength conditions and thereby increase the operation flexibility of GNSS signal acquisition. Moreover, the acquisition threshold is defined as the ratio of the highest and second highest correlation results in the search space of carrier frequency and code phase. Computational complexity is formulated by amounts of multiplication and summation operations in the signal acquisition.