Combining and Integration Schemes for Acquisition of Weak GNSS Split-Spectrum Signals

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A multitude of GNSS signals are transmitted at the same frequency band, and even the same signal may have several components with different codes. For examples, different signals are modulated onto the in-phase and quadrature components (e.g., L1C-I and L1C-Q, I5 and Q5) and are time-division multiplexed (e.g., odd and even chips of M-code). Most of these signals adopt the binary offset carrier (BOC) modulation and thus have a split-spectrum as compared to the legacy signals that use binary phase shift keying (BPSK) and have a dominant lobe at the band center. BOC is used not only for the ease of spectrum sharing but also for its improved ranging performance due to a larger Gabor bandwidth. Both weak signals and in particular the presence of strong interference lead to an effective signal to noise ratio (SNR) that is very low. To pull such a signal out of noise and interference, it is necessary to combine multiple signal components available at the same time and then integrate them over time so as to add up the signal strength while averaging the noise and interference out in a burn-through process. However, it is not straightforward to apply the linear additive coherent operation due to the difference in phase and frequency between signal components as well as the presence of unknown data bits, which may become counterproductive if not treated properly. In this paper, we investigate several nonlinear multiplicative schemes including non-coherent, semi-coherent, and cross-conjugate-multiply for signal accumulation (combining and integration), and compare them to the coherent scheme. The study shows that according to the SNR definition at the output of nonlinear operations, some of the schemes may have the same SNR level per analysis of second-order statistics, yet they exhibit different Pd vs. Pfa characteristics, which can be attributed to different distribution tail behaviors (higher order statistics). Understanding of the detection performance is thus important in trading off combining and integration schemes for implementation. Extensive computer simulation results are presented to illustrate the functionality and performance of the schemes.