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.

翻译：多输入多输出穿墙雷达（TWR）实现了复杂环境中人体活动的非视距感知。然而，在类似室内人体活动（如持枪行走与正常行走）之间，微多普勒特征的区分度较低，而利用时频谱图进行有效识别所需的大规模输入图像对模型训练和推理效率提出了挑战。为解决该问题，本文提出切比雪夫-时间映射方法，这是一种利用多项式阶次表征微多普勒特征的技术。研究首先建立了人体运动的参数化运动学模型与穿墙雷达回波模型，进而提出基于正交切比雪夫多项式分解的时频特征表征方法。通过提取躯干与肢体的运动包络，将时频谱切片映射至鲁棒的切比雪夫-时间系数空间，从而保留时频谱的多阶形态细节信息。数值仿真与实验验证了所提方法的有效性，结果表明该方法能够有效表征持械与非持械室内人体活动，同时显著压缩时频谱数据规模，在识别精度与输入数据维度间取得平衡。本文开源代码位于：https://github.com/JoeyBGOfficial/Represent-Micro-Doppler-Signature-in-Orders。