N and tracking [4,7]. S(t) = Sdata (t) jS pilot (t) (1) where
N and tracking [4,7]. S(t) = Sdata (t) jS pilot (t) (1) exactly where Sdata (t) denotes the information element, which is an in-phase component of signals, j is an imaginary unit, and S pilot (t) denotes the pilot element, which can be a quadrature component of signals. The data component Sdata (t) is generated as a PRN code Cdata (t) modulated using a navigation message Ddata (t) and a subcarrier scdata (t) for the data element, and the pilot component S pilot (t) is generated in the PRN code C pilot (t) modulated having a subcarrier sc pilot (t) for the pilot element. When the energy ratio with the two components is assumed to be 1:3, the two components may be expressed as shown by Equation (2). Table two can be a summary of detailed facts around the Legendre sequence-based GPS L1C [4] signals and BDS B1C [7] signals.1 Sdata (t) = two Ddata (t)Cdata (t)scdata (t)S pilot (t) =Table 2. GPS L1C and BDS B1C signals. Signal Property Frequency (MHz) Modulation Information code (Cdata ) Pilot code (C pilot ) Code rate (Mcps)three two C pilot ( t ) sc pilot ( t )(2)GPS L1C 1575.42 (L1) TMBOC Plain code Tiered code 1.BDS B1C 1575.42 (L1) QMBOC Plain code Tiered code 1.two.two. Legendre Sequence-Based PRN Code Generation To enable receivers to distinguish satellite signals, every satellite transmits signals with person PRN codes, including Cdata (t) and C pilot (t), shown in Equation (2). The PRN codes are divided in line with the configurations into plain codes consisting of only primary codes and tiered codes in which primary codes and secondary codes are combined. The generation strategy will be the very same for both major codes and secondary codes. Firstly, a Legendre sequence is generated; subsequent, a Weil sequence is configured Tianeptine sodium salt web according to the Legendre sequence, and also a major code or maybe a secondary code is generated by way of the post-processing from the Weil sequence. Inside the case of a plain code, the primary code becomes the final PRN code, and, in the case of a tiered code, the final PRN code is determined by the mixture from the major code along with the secondary code. To examine the foregoing in terms of formulas, initially, a Legendre sequence, the length of which is NL , is defined as shown in Equation (three). 0, k = 0 L(k) = 1, k = 0 and k = x2 modNL (integer x ) 0, else (3)where k is the index of Legendre sequence for (0 k NL ). Then, a Weil sequence, of which the length is NW , is calculated by means of the modulo-2 addition operation of two Legendre sequences with a phase GS-626510 medchemexpress difference as shown in Equation (4). W (k; w) = L(k) L(k ) (4)Electronics 2021, ten,five ofwhere k is definitely the index of Weil sequence for (0 k NW ) and is definitely the phase difference among two Legendre sequences. Lastly, a post-processing approach is carried out to generate a major code or even a secondary code, of which the length is NC , applying the Weil sequence expressed as shown in Equation (four). Inside the case of GPS L1C signals, a postprocessing course of action via which a 7-bit fixed sequence 0,1,1,0,1,0,0 is inserted according to the insertion point is carried out. 0, k = – 1, 2, four, five C (k; w; ) = 1, k = , 1, 3 W (k; ), else(five)exactly where k is the index of GPS L1C code for (0 k NC ) and is the insertion point. Every single GPS satellite in a GPS satellite program features a unique phase difference and an insertion point and generates a special code by way of the phase difference and insertion point. Also, within the case of BDS B1C signals, a post-processing approach is carried out via which the Weil code, of which the length is NW , is periodically truncated as.