Advanced Signal Processing for Multidimensional Harmonic Retrieval

Description

The problem of harmonic retrieval (HR) is to extract the parameters from noisy sinusoids, which has been an important topic in science and engineering because many real-world signals can be well described by the sinusoidal model. Although one-dimensional (1-D) HR is the most common, multidimensional HR in fact has numerous applications such as wireless communication channel estimation, nuclear magnetic resonance (NMR) spectroscopy and multiple-input multiple-output (MIMO) radar imaging. For example, the measurements in NMR spectroscopy which is a powerful technique for protein research in food and nutritional industries, can be modeled as a sum of multidimensional damped sinusoids where the frequencies and damping factors are crucial to determining the protein structures. Moreover, the sinusoidal parameters of the MIMO radar data contain the position information of multiple targets of interest.Analogous to 1-D HR, the key step in the multidimensional scenarios is to find the damping factor and frequency parameters because they are nonlinear functions in the observed signals. However, multidimensional HR is much more challenging than the 1-D counterpart. First, it is difficult to align the parameters at all dimensions particularly when there are identical frequencies in at least one dimension. Second, processing of multidimensional data corresponds to enormous computations and thus algorithm complexity is a main concern. Third, even the data dimension is more than two, the multidimensional signals are stored in matrices by means of stacking operations for manipulation in most of the existing approaches, implying that the harmonic structure may not be fully utilized in the estimation procedure.The aim of this research is to develop advanced multidimensional HR approaches that are efficient in both aspects of accuracy and complexity. To fulfill the challenging demands, we propose to effectively exploit tensor algebra which perfectly aligns with multidimensional data as well as principal singular vectors and values determined from the observed signals for optimal parameter estimation. Moreover, we will extend the proposed methodology for estimating the number of sources in case it is not known a priori. The performance of the devised multidimensional HR schemes will also be analyzed and evaluated in different applications.