Compressed sensing based sub-Nyquist sampling of multiple sinusoids with dual rate channels

Area of Science:

• Signal Processing
• Information Theory
• Applied Mathematics

Background:

• Reconstructing complex signals often requires a high sampling rate, posing limitations in data acquisition and storage.
• Efficient signal reconstruction from limited samples is crucial for various applications, including communications and sensor networks.

Purpose of the Study:

• To propose a novel reconstruction approach for multiple-sinusoidal signals.
• To enable signal reconstruction using a minimal number of samples via a sub-Nyquist sampling scheme.

Main Methods:

• A sub-Nyquist sampling scheme with dual-rate channels is proposed, grouping samples into multiple cosets.
• The Whittaker-Shannon interpolation formula is used to relate sub-Nyquist samples to the original signal, forming a measurement matrix.
• Compressed sensing theory is applied due to the signal's frequency-domain sparsity for reconstruction.

Main Results:

• The proposed sampling scheme requires relative coprime channel sampling rates to generate sufficient cosets.
• The method successfully reconstructs multiple-sinusoidal signals from a small number of samples.
• Simulation results validate the feasibility and effectiveness of the reconstruction approach.

Conclusions:

• The developed approach offers an efficient method for multiple-sinusoidal signal reconstruction.
• This technique significantly reduces the number of required samples, enhancing practical applicability.
• The integration of sub-Nyquist sampling and compressed sensing proves effective for sparse signal recovery.