Chapter 3: SIGNAL CHARACTERISTICS AND INFORMATION EXTRACTION

Why is the GPS signal so complex? GPS was designed to be readily accessible to millions of military and civilian users. Therefore, it is a receive-only passive system for a user, and the number of users that can simultaneously use the system is unlimited. Because there are many functions that must be performed, the GPS signal has a rather complex structure. As a consequence, there is a correspondingly complex sequence of operations that a GPS receiver must carry out in order to extract desired information from the signal. In this chapter we characterize the signal mathematically, describe the purposes and properties of the important signal components, and discuss generic methods for extracting information from these components.

3.1 MATHEMATICAL SIGNAL WAVEFORM MODELS

Each GPS satellite simultaneously transmits on two L-band frequencies denoted by L₁ and L₂, which are 1575.42 and 1227.60 MHz, respectively. The carrier of the L₁ signal consists of an in-phase and a quadrature-phase component. The inphase component is biphase modulated by a 50-bps (bits per second) data stream and a pseudorandom code called the C/A-code consisting of a 1023-chip sequence that has a period of 1 ms and a chipping rate of 1.023 MHz. The quadraturephase component is also biphase modulated by the same 50-bps (bits per second) data stream but with a different pseudorandom code called the P-code, which has a 10.23-MHz chipping rate and a one-week period. The mathematical model of the L₁ waveform is

where P_I and P_Q are the respective carrier powers for the in-phase and quadrature-phase carrier components, d(t) is the 50-bps (bits per second) data modulation, c(t) and p(t) are the respective C/A and P pseudorandom code waveforms, ω is the L₁ carrier frequency in radians per second, and θ is a common phase shift in radians. The quadrature carrier power P_Q is approximately 3 dB less than P_I .

In contrast to the L₁ signal, the L₂ signal is modulated with only the 50-bps (bits per second) data and the P-code, although there is the option of not transmitting the 50-bps (bits per second) data stream. The mathematical model of the L₂ waveform is

Figures 3.1 and 3.2 show the structure of the in-phase and quadrature-phase components, respectively, of the L₁ signal. The 50-bps (bits per second) data bit boundaries always occur at an epoch of the C/A-code. The C/A-code epochs mark the beginning of each period of the C/A-code, and there are precisely 20 code epochs per data bit, or 20,460 C/A-code chips. Within each C/A-code chip there are precisely 1540 L₁ carrier cycles. In the quadrature-phase component of the L₁ signal there are precisely 204,600 P-code chips within each 50-bps (bits per second) data bit, and the data bit boundaries always coincide with the beginning of a P-code chip [61, 84].

Why is the GPS signal so complex? GPS was designed to be readily accessible to millions of military and civilian users. Therefore, it is a receive-only passive system for a user, and the number of users that can simultaneously use the system is unlimited. Because there are many functions that must be performed, the GPS signal has a rather complex structure. As a consequence, there is a correspondingly complex sequence of operations that a GPS receiver must carry out in order to extract desired information from the signal. In this chapter we characterize the signal mathematically, describe the purposes and properties of the important signal components, and discuss generic methods for extracting information from these components.

3.1 MATHEMATICAL SIGNAL WAVEFORM MODELS

Each GPS satellite simultaneously transmits on two L-band frequencies denoted by L₁ and L₂, which are 1575.42 and 1227.60 MHz, respectively. The carrier of the L₁ signal consists of an in-phase and a quadrature-phase component. The inphase component is biphase modulated by a 50-bps (bits per second) data stream and a pseudorandom code called the C/A-code consisting of a 1023-chip sequence that has a period of 1 ms and a...