Simulated Annealing-Guided Geometric Descent-Optimized Frequency-Domain Compression-Based Acquisition Algorithm

Global Navigation Satellite System (GNSS) signal acquisition in high-dynamic environments faces significant challenges due to large Doppler frequency offsets and stringent computational constraints. This paper proposes a frequency-domain compressed acquisition algorithm that reformulates the conventional two-dimensional code-phase/Doppler search as a set of independent one-dimensional sparse recovery problems. Doppler uncertainty is modeled as sparsity in a discretized frequency dictionary, and a low-coherence measurement matrix is designed offline via projected gradient descent with a two-stage annealing strategy. The resulting matrix significantly reduces maximum coherence and supports reliable sparse recovery from a small number of compressed measurements. During online operation, the receiver forms compressed observations for all code phases through efficient matrix operations and recovers sparse Doppler spectra using lightweight orthogonal matching pursuit. Simulation results show that the proposed method achieves a several-fold reduction in computational cost compared with classical parallel code-phase search while maintaining high detection probability at low carrier-to-noise density ratios and under large Doppler offsets, providing an effective solution for resource-constrained GNSS receivers in high-dynamic scenarios.