Non-Iterative Shrinkage-Thresholding-Reconstructed Compressive Acquisition Algorithm for High-Dynamic GNSS Signals

Owing to the intrinsic sparsity of GNSS signals in the correlation domain, compressed sensing (CS) is attractive for the rapid acquisition of high-dynamic GNSS signals. However, the compressed measurement-associated noise folding inherently amplifies the pre-measurement noise, leading to an inevitable degradation of acquisition performance. In this paper, a novel CS-based GNSS signal acquisition algorithm is, for the first time, proposed with the efficient suppression of the amplified measurement noise and low computational complexities. The offline developed code phase and frequency bin-compressed matrices in the correlation domain are utilized to obtain a real-time observed matrix, from which the correlation matrix of the GNSS signal is rapidly reconstructed via a denoised back-projection and a non-iterative shrinkage-thresholding (NIST) operation. A detailed theoretical analysis and extensive numerical explorations are undertaken for the algorithm computational complexity, the achievable acquisition performance, and the algorithm performance robustness to various Doppler frequencies. It is shown that, compared with the classic orthogonal matching pursuit (OMP) reconstruction, the NIST reconstruction gives rise to a 3.3 dB improvement in detection sensitivity with a computational complexity increase of <10%. Moreover, the NIST-reconstructed CS acquisition algorithm outperforms the conventional CS acquisition algorithm with frequency serial search (FSS) in terms of both the acquisition performance and the computational complexity. In addition, a variation in the detection sensitivity is observed as low as 1.3 dB over a Doppler frequency range from 100 kHz to 200 kHz.