## 1 Introduction  
Inter-satellite links play an important role in satellite navigation systems, where they provide a direct link within the space segment without the need of an intermediate ground segment to relay the data. Spread spectrum technology is widely applied in present-day inter-satellite link systems. A common form of spread spectrum is direct sequence spread spectrum (DSSS) where incoming binary data is multiplied by a pseudo-noise (PN) code before they are transmitted [1]. Since long PN-codes achieves higher tolerance for jamming and spoofing, and greater multiple access capabilities compare with short codes, ranging mode of inter-satellite link in GPS and BDS systems both adopt the long code spread spectrum system [2; 3]. Among the signal synchronization steps of spread spectrum technology, code acquisition is one of the most critical functions of receivers [4]. It is of great significance to study the acquisition of long PN-code. However, with the code period getting longer, the time cost and burdens on hardware are becoming unacceptable [5; 6]. The inter-satellite link adopts time-division-multiple-access (TDMA) technology. Each link is assigned a short time-slot, which means signal acquisition and tracking need to be completed in a short time [7]. Moreover, inter-satellite link is characterized by complex electromagnetic interference and low signal-to-noise ratio (SNR). Interference and noise bring great challenges to exact acquisition [8; 9]. With the rapid development of the inter-satellite link, an essential concern is how to ensure rapid and exact acquisition. Long code acquisition methods perform in time or frequency domain depending on how the correlation is done. There are some other methods that estimate the initial states of long PN-code generating shift registers similar to channel decoding algorithms [10; 11]. However, these methods converge slowly at low SNR and the applications of them are limited to few types of PN codes like gold codes. In time domain methods, each correlator can search only few code phases, and using multiple correlators would occupy extra hardware resources. Serial search (SS) [12; 13] is one typical method in the time domain which detects code phases one by one. Many tests are required and thus the process is too long. Reference [14] proposes an improved double dwell search scheme that uses a 2D compressed correlator (TDCC) in the 1 st dwell search and the convention correlator in the 2 nd dwell search. But Signal-to-noise ratio (SNR) deterioration arises as the compression rate is increased. With great advances in digital processing boards, algorithms based on frequency domain search are more investigated [15]. These methods exploit the property of Fourier transform. Many methods are proposed based on FFT search. Zero-Padding method (ZP) is a popular one among them. The method adds \(\frac{\mathbb{N}}{2}\) zeros to extend the incoming samples to length \(N\). With fast Fourier transform (FFT) technique, ZP can search \(\frac{\mathbb{N}}{2}+1^{2}\) code phases in parallel. Many methods have been developed based on the ZP scheme [16]. [PERSON] [17] proposed a method named Generalized Zero Padding(GZP) that optimizes the length of zeros according to SNR. [PERSON] [18] proposed another modified ZP method that applies interpolation to achieve higher acquisition accuracy. These methods have reasonable performance for Doppler and jamming mitigation but are still inadequate for long codes. Among proposed long code acquisition methods, folding local PN-code and averaging input and local samples are mostly used in practice. A typical example of the former is XFAST proposed by [PERSON] [19] and the latter is known as Direct Average Method(DAM) [20]. For XFAST, an incoming code segment is simultaneously compared with local code segments to find a match. The use of circular correlation via FFT to determine if a match occurs permits the simultaneous search through all code phase across multiple code segments.