# An Unambiguous Delay-And-Multiply Acquisition Scheme for GPS L1C Signals
## 1 Introduction  
The Global Positioning System (GPS) has become an essential technology for positioning, navigation, and timing after the full operational capability (FOC) in early 1995, and GPS modernization has now been in progress since January 1999 [1; 2; 3]. As a modernization program, two civil signals have been added at the L2 and L5 frequencies, which are denoted as the L2C and L5 signals, respectively [1]. The L2C signal has been transmitted from the GPS Block IIR-M satellite since September 2005, while the L5 signal from GPS Block IIF satellite has been transmitted since May 2010 [4; 5]. The fourth civil signal, denoted as L1 Civil (L1C) signal, will be transmitted from the next generation satellites (GPS Block III) on the L1 carrier frequency [6; 7]. One feature of the L1C signal is the use of binary offset carrier (BOC) modulation, which enables compatibility, and reduces interference between the legacy L1 signal and L1C signal, despite their use of same carrier frequency. The BOC modulation is also used in Galileo [8; 9], the European Global Navigation Satellite System (GNSS) that is like the GPS of the United States, and enables Galileo E1 open service (OS) signal to use the same GPS L1 carrier frequency. The BOC modulation results in split spectrum signal, and thus enables frequency sharing [10; 11; 12; 13]. After many years of research, MBOC (multiplexed BOC) is applied to GNSS, such that composite BOC (CBOC) is used for Galileo E1 OS signal, and time multiplexed BOC (TMBOC) for GPS L1C signal. GPS L1C signal consists of data and pilot channels with powerratio (75%/25% for the pilot/data) [14], where the data channel uses \(BOC_{(1,1)}\) modulation, and the pilot channel uses TMBOC modulation. One drawback of using BOC modulation are the multiple peaks which appear in the correlation between the received signal and the generated signal, complicating the signal acquisition and tracking process, and termed the ambiguity problem. To deal with the BOC modulation, many techniques have been suggested [9; 14; 15; 16; 17], and several unambiguous methods, such as the \"BPSK-like\" technique, sub-carrier phase cancellation (SCPC) technique, and bump-jumping technique, have been suggested to deal with the ambiguities of the traditional BOC modulation [9; 14]. Recently, the delay-and-multiply (DM) concept has been suggested for unambiguous acquisition of Galileo E1 OS signals in [18; 19; 20]. The DM concept exists from early GNSS history [3], but has not been studied in depth, since the DM method causes the multiplication of noise, which greatly deteriorates the signal acquisition performance. However, one advantage of the DM concept is the elimination of the Doppler frequency. That is, the DM method can reduce the two-dimensional acquisition process to a one-dimensional search. The Doppler frequency can be obtained after finding the code phase first. The DM concept also eliminates the effect of data symbol transition [19], which comes from the same length of the data symbol and the period of ranging code, so the non-coherent integration can be greatly increased. The acquisition problem for GPS L1C signal has been studied in [21; 22; 23; 24], but it is hard to find any research on the ambiguity problem for the GPS L1C signal. The DM acquisition method is attractive for the GPS L1C signal despite the multiplication of noise, since the L1C signal has a severe ambiguity problem and long search time, because of its long 10 ms ranging code. Even though [18; 19; 20] used the DM method in the Galileo E1 OS signal, which uses CBOC modulation, the GPS L1C signal uses TMBOC modulation. Thus the DM approach for the GPS L1C signal is a new problem and it is necessary to find optimal delay and the generated DM scheme again for the GPS L1C signal. In this paper, we propose new DM acquisition schemes for the GPS L1C signal to eliminate the ambiguity of the correlation function between the received signal and the generated signal.