An NN Framework for Target Number Detection in FMCW Radar Systems via Hankelization: A Low-Dimensional Data Representation Perspective

In this paper, we introduce a novel neural network (NN)-based algorithm that significantly improves the target number detection in frequency modulated continuous wave (FMCW) radar systems. By integrating the mathematical processes of Hankelization and singular value extraction, we can perform input data manipulation for effective target number detection, resulting in constructing an efficient NN framework. This is based on the following mathematical properties: 1) A sequence obtained by uniform sampling of the superposition of K radio waves can be represented as a superposition of K geometric sequences; 2) A Hankelized matrix formed by the superposition of K geometric sequences exhibits low-rank characteristics; and 3) In an FMCW radar system with K targets, if the received signal, which is represented as a matrix, is ideal, the vectors obtained by extracting this matrix in row, column, diagonal, and anti-diagonal patterns can all be modeled as a superposition of K geometric sequences. The proposed NN framework showcases remarkable improvements in accuracy and efficiency for target number detection, leveraging a small sized dataset and a compact NN design to achieve unprecedented performance levels. Numerical results validate the superiority of our method across various scenarios, establishing a new benchmark for low-dimensional data representation in radar systems.