Finally, the product of the incoming signal and local code, which represents the correction between the incoming and carrier frequencies, is applied to an inverse Fourier transform whose squared output feeds back to the decision logic. The FFT-based frequency domain has proven to be a low consumer of computation. For the example mentioned earlier, the complexity of acquisition is roughly 20,000/500 = 40 FFT operations.

Thus, the serial-search method has the simple logic and control architecture necessary for a convenient ASIC implementation. The huge search space, however, imposes complexity on the software algorithm. The serial-search method is therefore not a good choice for software GPS receivers. In contrast, the low complexity of the parallel-code acquisition method makes it ideal for the software implementation. Its logic architecture, however, is far more complex than that of the serial-search method, making it difficult to implement in an ASIC.

Tracking Refines Alignment

Figure 3. The DLL circuit multiplies the incoming signal by threelocal replicas of the PRN code (positioned in time at ±0.5 chip),which represent early, prompt, and late arrivals with respect to theincoming signal. The one with the highest correlation value is thenselected and retained.

The DLL circuit multiplies the incoming signal by three local replicas of the PRN code (positioned in time at ±0.5 chip), which represent early, prompt, and late arrivals with respect to the incoming signal. After integration, each of these signals represents a correlation between the incoming signal and a local replica. The one with the highest correlation value is then selected and retained (Figure 3). Carrier-frequency tracking is carried out by a phase-lock loop (PLL) or Costas loop⁸. The purpurpose of carrier tracking is to tune the locally generated frequency to the exact frequency of the incoming signal.