Represent Micro-Doppler Signature in Orders

Non-line-of-sight sensing of human activities in complex environments is enabled by multiple-input multiple-output through-the-wall radar (TWR). However, the distinctiveness of micro-Doppler signature between similar indoor human activities such as gun carrying and normal walking is minimal, while the large scale of input images required for effective identification utilizing time-frequency spectrograms creates challenges for model training and inference efficiency. To address this issue, the Chebyshev-time map is proposed in this paper, which is a method characterizing micro-Doppler signature using polynomial orders. The parametric kinematic models for human motion and the TWR echo model are first established. Then, a time-frequency feature representation method based on orthogonal Chebyshev polynomial decomposition is proposed. The kinematic envelopes of the torso and limbs are extracted, and the time-frequency spectrum slices are mapped into a robust Chebyshev-time coefficient space, preserving the multi-order morphological detail information of time-frequency spectrum. Numerical simulations and experiments are conducted to verify the effectiveness of the proposed method, which demonstrates the capability to characterize armed and unarmed indoor human activities while effectively compressing the scale of the time-frequency spectrum to achieve a balance between recognition accuracy and input data dimensions. The open-source code of this paper can be found in: https://github.com/JoeyBGOfficial/Represent-Micro-Doppler-Signature-in-Orders.