Abstract
A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.
Highlights
In software implementations, massive parallel correlation is done by exploiting the Fourier transformation
By having all the intermediate frequency (IF) samples in memory, we can transform to the frequency domain, perform a simple multiplication by the Fourier transform of the Pseudorandom noise (PRN) code, and later perform an inverse transform back to the time domain, this approach requires a large amount of random access memory RAM to store the data being received from the IF, and it is more of a store and process approach [1]
A novel global navigation satellite system (GNSS) signal acquisition algorithm based on compressed sensing (CS) and Singular Value Decomposition (SVD) is proposed aiming to reduce the computational complexity of Global Positioning System (GPS) and BOC satellite signals
Summary
Massive parallel correlation is done by exploiting the Fourier transformation. By having all the IF samples in memory, we can transform to the frequency domain, perform a simple multiplication by the Fourier transform of the Pseudorandom noise (PRN) code, and later perform an inverse transform back to the time domain, this approach requires a large amount of random access memory RAM to store the data being received from the IF, and it is more of a store and process approach [1]. Due to digital processing technology and the implementation of software-based GNSS receivers, researchers are motivated to try new acquisition and tracking methods of the GNSS signal with the advantages of robustness, sensitivity, and anti-jamming capabilities [2]. GPS satellites simultaneously transmit several ranging codes and navigation data using binary phase-shift keying keying (BPSK). 0 dBicarrier user receiving antenna when Figure the satellite elevation angle is and both use composite-binary offset (CBOC) modulation(see.
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