Blind power spectrum reconstruction for multi-sinusoid signals with generative multicoset sampling

Abstract

As the target frequency increases, the Nyquist rate is hard to reach due to hardware limitations. Alternatives to high-rate sampling have attracted considerable research interest. Compressed covariance sensing based on multicoset sampling (MCS) is a prevalent sub-Nyquist sampling strategy for blind power spectrum reconstruction. However, it requires the sampling pattern of MCS to be a minimal sparse ruler. In this paper, a generative multicoset sampling (GMCS) is proposed to minimize the number of cosets. In sampling stage, a minimal MCS, delay coprime scheme is proposed to ensure the recoverability of the power spectrum. In recovery stage, a new function, i.e., multifold correlation is constructed for blind power spectrum reconstruction. We prove that the power spectrum of a multi-sinusoid signal (MSS) can be estimated by its multifold correlation and the sample density of multifold correlation can be increased by correlation operations. Owing to multifold correlation, GMCS can generate virtual cosets satisfying the sparse ruler criterion through only two physical cosets and then efficiently recover the power spectrum by least-squares estimation. Moreover, we demonstrate the feasibility of GMCS for linear frequency modulation (LFM) signals. Finally, the effectiveness of GMCS are verified by numerical simulations and blade tip timing experiments (a non-contact vibration measurement). By reducing the average sampling rate and hardware complexity, GMCS opens new avenues for blind sampling and power spectrum reconstruction.