Compressive-Sensing-Based Fast Acquisition Algorithm Using Gram-Matrix Optimization via Direct Projection

This paper proposes a compressive-sensing (CS) acquisition algorithm for low-power, high-dynamic GNSS receivers based on low-dimensional time-domain measurements, a non-iterative compressive-domain direct-projection peak-search pipeline, and a coherence-optimized sensing-matrix design. Unlike most existing GNSS-CS acquisition approaches that rely on explicit sparse-recovery formulations (e.g., OMP/BP/LS-type iterative reconstruction) to identify the delay–Doppler support—often incurring substantial computational burden and acquisition latency—the proposed method performs peak detection directly in the compressive measurement domain and is supported by unified Gram-matrix optimization and perturbation/detection analyses. Specifically, the measurement Gram matrix is optimized on the symmetric positive-definite (SPD) manifold to obtain a diagonally dominant and well-conditioned structure with reduced inter-column correlation, thereby bounding reconstruction-induced perturbations and preserving the main correlation peak. Simulation results show that the proposed scheme retains the low online complexity characteristic of direct-projection baselines while achieving a 2–3 dB acquisition sensitivity gain, and it requires substantially fewer operations than iterative OMP-based CS acquisition schemes whose cost scales approximately linearly with the sparsity level K. The proposed framework enables robust, low-latency acquisition suitable for resource-constrained GNSS receivers in high-dynamic environments.