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This paper describes a novel multichannel signal denoising approach based on multivariate variational mode decomposition (MVMD). MVMD is the extended version of the variational mode decomposition (VMD) algorithm for multichannel data sets. Unlike previous MEMD (multivariate empirical mode decomposition)-based denoising methods, the proposed scheme not only has a precise mathematical framework but also can better align the common frequency modes of the signals. Therefore, it has good robustness for non-stationary signals with low SNR. Based on the similarity measurement between the probability density function (pdf) of the input signal and each mode by Hausdorff distance(HD), the interval thresholding and partial reconstruction denoising of band-limited intrinsic mode functions (BLIMFs) are performed in the algorithm. Besides, to take advantage of the characteristics of channel diversity, the subspace projection method is used to further denoise the multivariable signals. We demonstrate the effectiveness of the proposed approach through results obtained from extensive simulations involving test (synthetic) and real-world multivariate data set.INDEX TERMS MVMD, VMD, oscillatory modes.

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ELF can be generated by HF heating the low ionosphere for submarine communication. QPSK has been used on ELF carried generated via modulated ionosphere heating to transmit digital data. However, ELF band is disturbed frequently by the power frequency harmonic interference, and QPSK modulation can’t effectively suppress interference. In this paper, the Chirp-BOK(Binary Orthogonal keying) modulation method for ELF communication based on ionosphere heating is proposed. The up-chirp and the down-chirp modulation waveforms are designed to transmit the symbols “0” and “1” respectively. Simulation results show that the variation of electron temperature and conductivity in the ionosphere is basically consistent with the frequency modulation characteristics of power modulation when the ionosphere is heated by Chirp-BOK power modulation high frequency wave. The performance of Chirp-BOK and QPSK under harmonic interference is compared, and the simulation results show that Chirp-BOK has better anti-interference performance.