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Complex variational mode decomposition (CVMD) has been proposed to extend the original variational mode decomposition (VMD) algorithm to analyze complex-valued data. Conventionally, CVMD divides complex-valued data into positive and negative frequency components using bandpass filters, which leads to difficulties in decomposing signals with the low-frequency trend. Moreover, both decomposition number parameters of positive and negative frequency components are required as prior knowledge in CVMD, which is difficult to satisfy in practice. This paper proposes a modified complex variational mode decomposition (MCVMD) method. First, the complex-valued data are upsampled through zero padding in the frequency domain. Second, the negative frequency component of upsampled data are shifted to be positive. Properties of analytical signals are used to get the real-valued data for standard variational mode decomposition and the complex-valued decomposition results after frequency shifting back. Compared with the conventional method, the MCVMD method gives a better decomposition of the low-frequency signal and requires less prior knowledge about the decomposition number. The equivalent filter bank structure is illustrated to analyze the behavior of MCVMD, and the MCVMD bi-directional Hilbert spectrum is provided to give the time–frequency representation. The effectiveness of the proposed algorithm is verified by both synthetic and real-world complex-valued signals.

Utilizing the difference in phase and power spectrum between signals and noise, the estimation of direction of arrival (DOA) can be transferred to a spatial sample classification problem. The power ratio, namely signal-to-noise ratio (SNR), is highly required in most high-resolution beamforming methods so that high resolution and robustness are incompatible in a noisy background. Therefore, this paper proposes a Subspaces Deconvolution Vector (SDV) beamforming method to improve the robustness of a high-resolution DOA estimation. In a noisy environment, to handle the difficulty in separating signals from noise, we intend to initial beamforming value presets by incoherent eigenvalue in the frequency domain. The high resolution in the frequency domain guarantees the stability of the beamforming. By combining the robustness of conventional beamforming, the proposed method makes use of the subspace deconvolution vector to build a high-resolution beamforming process. The SDV method is aimed to obtain unitary frequency matrixes more stably and improve the accuracy of signal subspaces. The results of simulations and experiments show that when the input SNR is less than −27 dB, signals of decomposition differ unremarkably in the subspace while the SDV method can still obtain clear angles. In a marine background, this method works well in separating the noise and recruiting the characteristics of the signal into the DOA for subsequent processing.