Phased Fractional Lower-Order Cyclic Moment Processed in Compressive Signal Processing

Tao Liu,Fangxiao Jin,Shengyang Luan,Tianshuang Qiu,Stephanie Wilcox

doi:10.1109/access.2019.2929434

Tao Liu, Fangxiao Jin + Show 3 more

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https://doi.org/10.1109/access.2019.2929434

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In signal processing research, cyclostationarity and fractional lower-order statistics (FLOS) are two important solutions to non-stationary signals and non-Gaussian noises, respectively. In the last five years, many methodologies combining the two technologies were proposed to achieve the two tasks simultaneously. Unfortunately, these methodologies need to be based on the Shannon/Nyquist sampling theorem. As phased fractional lower-order cyclic moment (PFLOCM) theoretically cooperates with compressive signal processing (CSP), this paper studies PFLOCM to apply in CSP at sub-Nyquist sampling rates. Using this technical foundation, a complete procedure is novelly proposed to rebuild phased fractional lower-order cyclic moment spectrum (PFLOCMS), which functions as a crucial factor in signal detection, system identification, parameter estimation, and other applications. In addition, various experiments verify the performance of the proposed procedure. It is believed that this paper will have implications for non-stationary and non-Gaussian signal processing at sub-Nyquist sampling rates.

Highlights

Stationarity in transmission signals and Gaussianity in background noises are usually assumed in traditional system modeling research
Inspired by the rapid development of compressive signal processing (CSP) originated from compressive sensing, we further study phased fractional lower-order cyclic moment (PFLOCM) processed in the framework of CSP since PFLOCM theoretically cooperates with CSP
Due to the non-existence of the second-order statistics of the background noise modelled by SαS distribution, a corresponding concept called the generalized signal-to-noise ratio (GSNR) is used instead of the conventional signal-to-noise ratio (SNR)

Summary

INTRODUCTION

Stationarity in transmission signals and Gaussianity in background noises are usually assumed in traditional system modeling research. Proposed to address non-Gaussian noise modeled by alpha-stable distribution in 1993, covariation and fractional lower-order moment (FLOM) established FLOS theory [3]. Inspired by the rapid development of compressive signal processing (CSP) originated from compressive sensing, we further study phased fractional lower-order cyclic moment (PFLOCM) processed in the framework of CSP since PFLOCM theoretically cooperates with CSP. The theory states that if a signal (vector) is compressible or sparse, it can be represented at a sampling rate far below the recommendation by the Shannon/Nyquist sampling theorem. The comparison between the frameworks of CSP and DSP + CS is shown, where CS and SR represent compressive sensing and sparse reconstruction, respectively. Rxp and p x are different, by the projection matrices G in (22a) and B in (25), the two matrices mutually convert into vector Rxp which functions as a bridge between the two routes

9: Return B

THE DESIGN OF SIMULATION

CONCLUSION