Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)

Area of Science:

• Signal Processing
• Electrical Engineering
• Satellite Navigation

Background:

• Global Navigation Satellite System (GNSS) signal processing traditionally requires high sampling rates, posing a significant challenge.
• Compressed Sensing (CS) theory offers a potential solution by enabling signal processing at lower sampling rates, provided the signal has a sparse representation.
• Sparse representation is crucial for CS applicability, necessitating methods to achieve it for complex signals like GNSS.

Purpose of the Study:

• To propose and validate a novel algorithm for sampling GNSS signals at sub-Nyquist rates using Compressed Sensing (CS) and Singular Value Decomposition (SVD).
• To demonstrate the effective reconstruction of compressed GNSS signals.
• To show the enhancement of GNSS signal acquisition through noise filtering and signal power optimization.

Main Methods:

• Constructing a rectangular Toeplitz matrix (TZ) of the transmitted GNSS signal.
• Utilizing SVD to calculate left singular vectors from the TZ, achieving a sparse signal representation.
• Obtaining M-dimensional observation vectors based on SVD left singular vectors for sub-Nyquist sampling, followed by signal reconstruction using L1 minimization and convex optimization.

Main Results:

• The proposed algorithm successfully samples GNSS signals at rates significantly lower than the Nyquist rate.
• Accurate reconstruction of the compressed intermediate frequency (IF) GNSS signals in the time-discrete domain was achieved.
• The method demonstrated an enhancement in GNSS signal acquisition by retaining useful signal components and filtering noise via projection onto significant proper orthogonal modes (PODs).

Conclusions:

• The developed algorithm effectively addresses the challenge of high sampling rates in GNSS signal processing.
• The integration of CS and SVD provides a viable approach for low-rate sampling and accurate reconstruction of GNSS signals.
• The proposed method offers added value through improved GNSS signal acquisition performance and noise reduction.