Multivariate singularity power spectrum distribution and its application to radar target detection

The singularity power spectrum (SPS) characterizes the energy distribution of signals through a power measure defined in the singularity exponent domain. However, existing SPS methods are restricted to univariate analysis and cannot capture the joint energy distribution of multichannel signals in a unified singularity exponent space. To overcome this limitation and inspired by the dimensional joint analysis framework of the multivariate multifractal spectrum (MV-MFS), this paper proposes—to the best of our knowledge—the first formulation of a bivariate singularity power spectrum (BV-SPS) and its generalization, the multivariate singularity power spectrum (MV-SPS). The theoretical definition and model of MV-SPS are established by extending the conventional SPS framework. Taking the bivariate case as an illustrative example, we detail the algorithmic implementation, which involves constructing two-dimensional joint singularity subsets and estimating the bivariate joint power spectrum using a geometric-mean power measure. The approach is then generalized to the multivariate case through the construction of high-dimensional joint singularity subsets and the introduction of a multivariate geometric-mean power function, thereby enabling the characterization of energy-distribution features across multiple signals in a unified high-dimensional singularity exponent space. Experimental validation on the IPIX radar dataset demonstrates the superior performance of the proposed MV-SPS in sea-clutter classification and low-resolution weak-target detection. This study establishes a novel technical pathway for multidimensional information fusion, target feature extraction, and detection/recognition based on fractal-domain signal analysis.