本研究針對連續波雷達於多接收端架構下，當多個目標的角度間距小於系統理論解析度時所面臨的波束成型困境，提出一套整合週期卷積虛擬陣列、Khatri-Rao 子空間重建與Chebyshev窗函數的多階段演算法架構。此方法成功突破傳統均勻線性陣列因通道數限制所造成的解析度瓶頸。以八通道5.8 GHz微帶天線雷達為平台，透過週期卷積可將物理通道擴展至15個虛擬通道，並使角度解析度自原本的12.344°提升至6.732°，達成近兩倍改善。進一步結合 Khatri-Rao 共變異數矩陣重構與Chebyshev窗設計後，解析度進一步優化至3.719°，提升幅度達三倍以上。實驗結果顯示，所提出的PC-KR-Chebyshev-CBF架構在本研究設計之實驗場景下，其方向估計表現優於MUSIC演算法，有效突破物s理限制。
在生理訊號應用方面，針對心跳訊號的量測，本研究模擬胸腔中心跳與呼吸振幅相差十倍的真實情境，發現透過週期卷積擴展後會加劇此振幅差異，導致心跳訊號於頻譜中易被呼吸造成的頻譜洩漏所遮蔽。為提升心跳信號可辨識度，本文提出以零點差分波束方法進行訊號提取，並事先量測系統之零點位置作為波束設計依據。在人體生理訊號實驗中，以BIOPAC量測的心跳頻率為1.203 Hz下，該方法可準確估得1.217 Hz，誤差率僅1.16%，訊雜比達11.31 dB；相較之下，單一波束提取出的心率誤差率高達 31.01%，訊雜比僅3.78 dB，顯示差分波束法能顯著提升頻率估計的準確性與頻譜品質。

This work presents a multi-stage processing framework that combines periodic convolution-based virtual array expansion, Khatri-Rao subspace reconstruction, and Chebyshev window-based weight optimization. The proposed method effectively addresses the resolution bottleneck caused by the limited number of physical elements in uniform linear arrays. Using an eight-channel 5.8 GHz microstrip radar system, the PC operation increases the effective channel count from 8 to 15. Further enhancement is obtained by applying Khatri–Rao covariance reconstruction together with Chebyshev weighting, narrowing the resolution to a threefold improvement. Experimental evaluations confirm that the proposed PC-KR-Chebyshev-CBF achieves superior direction-of-arrival estimation compared to the MUSIC algorithm, demonstrating its ability to surpass physical constraints of the array and deliver high-resolution performance in scenarios with closely spaced targets.
This study performs human vital signal measurements. It was observed that after periodic convolution, the amplitude disparity becomes more pronounced, causing the heartbeat signal to be masked by spectral leakage from respiration. To mitigate this, a differential beam technique is introduced to enhance spectral discriminability of the heartbeat signal, supported by pre-measured beam null points for accurate design. Experimental results confirm the effectiveness of the proposed approach: with reference to the 1.203 Hz obtained from ECG, the differential beam method estimates 1.217 Hz with only 1.16% error and achieves a signal-to-noise ratio of 11.31 dB. In contrast, CBF yields a large estimation error of 31.01% and an SNR of only 3.78 dB.

[1] G. W. Fang, C. Y. Huang, and C. L. Yang, "Switch-Based Low Intermediate Frequency System of a Vital Sign Radar for Simultaneous Multitarget and Multidirectional Detection," IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, vol. 4, no. 4, pp. 265-272, 2020, doi: 10.1109/JERM.2020.2969100.
[2] H. Hong et al., "Microwave Sensing and Sleep: Noncontact Sleep-Monitoring Technology With Microwave Biomedical Radar," IEEE Microwave Magazine, vol. 20, no. 8, pp. 18-29, 2019, doi: 10.1109/MMM.2019.2915469.
[3] J. Xiong, H. Hong, H. Zhang, N. Wang, H. Chu, and X. Zhu, "Multitarget Respiration Detection With Adaptive Digital Beamforming Technique Based on SIMO Radar," IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 11, pp. 4814-4824, 2020, doi: 10.1109/TMTT.2020.3020082.
[4] H. Cox, R. Zeskind, and M. Owen, "Robust adaptive beamforming," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35, no. 10, pp. 1365-1376, 1987, doi: 10.1109/TASSP.1987.1165054.
[5] Z. Hao, W. Biyang, W. Shicai, and L. Xiaofeng, "Linear time-frequency MUSIC algorithm," in Proceedings of the IEEE 6th Circuits and Systems Symposium on Emerging Technologies: Frontiers of Mobile and Wireless Communication (IEEE Cat. No.04EX710), 31 May-2 June 2004 2004, vol. 2, pp. 689-692 Vol.2, doi: 10.1109/CASSET.2004.1321981.
[6] C. Zhizang, G. Gopal, and Y. Yiqiang, Introduction to Direction-of-Arrival Estimation. Artech, 2010, p. 1.
[7] H. Krim and M. Viberg, "Two decades of array signal processing research: the parametric approach," IEEE Signal Processing Magazine, vol. 13, no. 4, pp. 67-94, 1996, doi: 10.1109/79.526899.
[8] V. V. Chudnikov, B. I. Shakhtarin, A. V. Bychkov, and S. M. Kazaryan, "DOA Estimation in Radar Sensors with Colocated Antennas," in 2020 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), 1-3 July 2020 2020, pp. 1-6, doi: 10.1109/SYNCHROINFO49631.2020.9166072.
[9] Y. Zeng, "DOA Estimation for Non-uniform Linear Array without Knowing the Number of Sources," in 2012 International Conference on Industrial Control and Electronics Engineering, 23-25 Aug. 2012 2012, pp. 904-907, doi: 10.1109/ICICEE.2012.240.
[10] E. O. Owoola, K. Xia, T. Wang, A. Umar, and R. G. Akindele, "Pattern Synthesis of Uniform and Sparse Linear Antenna Array Using Mayfly Algorithm," IEEE Access, vol. 9, pp. 77954-77975, 2021, doi: 10.1109/ACCESS.2021.3083487.
[11] B. Kim, S. Kim, and J. Lee, "A Novel DFT-Based DOA Estimation by a Virtual Array Extension Using Simple Multiplications for FMCW Radar," Sensors (Basel), vol. 18, no. 5, May 14 2018, doi: 10.3390/s18051560.
[12] W. K. Ma, T. H. Hsieh, and C. Y. Chi, "DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri–Rao Subspace Approach," IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 2168-2180, 2010.
[13] X. Wang, Y. Zhu, M. Huang, J. Wang, L. Wan, and G. Bi, "Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise," IEEE Access, vol. 7, pp. 73719-73728, 2019, doi: 10.1109/ACCESS.2019.2920707.
[14] S. Kim, B. S. Kim, Y. Jin, and J. Lee, "Extrapolation-RELAX Estimator Based on Spectrum Partitioning for DOA Estimation of FMCW Radar," IEEE Access, vol. 7, pp. 98771-98780, 2019, doi: 10.1109/ACCESS.2019.2930102.
[15] J. Li, Z. Dunmin, and P. Stoica, "Angle and waveform estimation via RELAX," IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 3, pp. 1077-1087, 1997, doi: 10.1109/7.599338.
[16] X. Li, X. Wang, Q. Yang, and S. Fu, "Signal Processing for TDM MIMO FMCW Millimeter-Wave Radar Sensors," IEEE Access, vol. 9, pp. 167959-167971, 2021, doi: 10.1109/ACCESS.2021.3137387.
[17] J. Li and P. Stoica, "MIMO Radar with Colocated Antennas," IEEE Signal Processing Magazine, vol. 24, no. 5, pp. 106-114, 2007, doi: 10.1109/MSP.2007.904812.
[18] A. D. Droitcour, O. Boric-Lubecke, V. M. Lubecke, J. Lin, and G. T. A. Kovacs, "Range correlation and I/Q performance benefits in single-chip silicon Doppler radars for noncontact cardiopulmonary monitoring," IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 3, pp. 838-848, 2004, doi: 10.1109/TMTT.2004.823552.
[19] C. Li, Y. and J. Lin, "Complex signal demodulation and random body movement cancellation techniques for non-contact vital sign detection," in 2008 IEEE MTT-S International Microwave Symposium Digest, 15-20 June 2008 2008, pp. 567-570, doi: 10.1109/MWSYM.2008.4633229.
[20] C. Li, Y. Xiao, and J. Lin, "Experiment and Spectral Analysis of a Low-Power $Ka$-Band Heartbeat Detector Measuring From Four Sides of a Human Body," IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 12, pp. 4464-4471, 2006, doi: 10.1109/TMTT.2006.884652.
[21] F. Daum, "Radar Handbook, 3rd Edition (M.I. Skolnik, Ed; 2008) [Book Review]," IEEE Aerospace and Electronic Systems Magazine, vol. 23, no. 5, pp. 41-41, 2008, doi: 10.1109/MAES.2008.4523916.
[22] X. Chen, J. Xin, N. Zheng, and A. Sano, "Direction-of-arrival estimation of coherent narrowband signals with arbitrary linear array," in 2017 IEEE International Workshop on Signal Processing Systems (SiPS), 3-5 Oct. 2017 2017, pp. 1-5, doi: 10.1109/SiPS.2017.8109984.
[23] S. Hong, S. Lee, B. H. Lee, J. Kim, Y. H. Kim, and S. C. Kim, "Radar Signal Decomposition in Steering Vector Space for Multi-Target Classification," IEEE Sensors Journal, vol. 21, no. 22, pp. 25843-25852, 2021, doi: 10.1109/JSEN.2021.3116712.
[24] Z. JianXiong, S. ZhiGuang, and Z. YongFeng, "Superresolution Performance of Different Spatial Smoothing Methods for Short Uniform Linear Array," IEEE Antennas and Wireless Propagation Letters, vol. 21, no. 6, pp. 1144-1147, 2022, doi: 10.1109/LAWP.2022.3159768.
[25] P. Chen, J. Gao, and W. Wang, "Linear Prediction-Based Covariance Matrix Reconstruction for Robust Adaptive Beamforming," IEEE Signal Processing Letters, vol. 28, pp. 1848-1852, 2021, doi: 10.1109/LSP.2021.3111582.
[26] M. Hur, K. Han, and S. Hong, "Multiple Human Heart Rate Variability Detection Using MIMO FMCW Radar With Differential Beam Techniques," IEEE Transactions on Radar Systems, vol. 1, pp. 698-706, 2023, doi: 10.1109/TRS.2023.3333628.
[27] K. Han and S. Hong, "Differential Phase Doppler Radar With Collocated Multiple Receivers for Noncontact Vital Signal Detection," IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 3, pp. 1233-1243, 2019, doi: 10.1109/TMTT.2018.2884406.
[28] K. Han and S. Hong, "MIMO differential radar using null point beams for vital sign detection in the presence of body motions," 2022: IEEE, pp. 177-180.
[29] T. Yamaoka and T. Oshima, "Sidelobe Reduction for Window Functions by Multiplication of Cosine-Sum Windows," IEEE Access, vol. 13, pp. 35588-35596, 2025, doi: 10.1109/ACCESS.2025.3544540.
[30] M. Alizadeh, G. Shaker, J. C. M. D. Almeida, P. P. Morita, and S. Safavi-Naeini, "Remote Monitoring of Human Vital Signs Using mm-Wave FMCW Radar," IEEE Access, vol. 7, pp. 54958-54968, 2019, doi: 10.1109/ACCESS.2019.2912956.
[31] M. Safarpour and O. Silvén, "LoFFT: Low-Voltage FFT Using Lightweight Fault Detection for Energy Efficiency," IEEE Embedded Systems Letters, vol. 15, no. 3, pp. 125-128, 2023, doi: 10.1109/LES.2022.3212776.
[32] X. Liu and B. Qi, "Beamspace-based underdetermined DOA estimator via Khatri-Rao subspace for quasi-stationary signals," Digital Signal Processing, vol. 141, p. 104158, 2023/09/01/ 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1051200423002531.
[33] J. Xiong, H. Hong, L. Xiao, E. Wang, and X. Zhu, "Vital Signs Detection With Difference Beamforming and Orthogonal Projection Filter Based on SIMO-FMCW Radar," IEEE Transactions on Microwave Theory and Techniques, vol. 71, no. 1, pp. 83-92, 2023, doi: 10.1109/TMTT.2022.3181129.
[34] F. Riaz, A. Hassan, S. Rehman, I. K. Niazi, and K. Dremstrup, "EMD-Based Temporal and Spectral Features for the Classification of EEG Signals Using Supervised Learning," IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 24, no. 1, pp. 28-35, 2016, doi: 10.1109/TNSRE.2015.2441835.
[35] K. Dragomiretskiy and D. Zosso, "Variational Mode Decomposition," IEEE Transactions on Signal Processing, vol. 62, no. 3, pp. 531-544, 2014, doi: 10.1109/TSP.2013.2288675.
[36] P. D. H. Re et al., "FMCW radar with enhanced resolution and processing time by beam switching," IEEE Open Journal of Antennas and Propagation, vol. 2, pp. 882-896, 2021.
[37] M. Rameez, M. Dahl, and M. I. Pettersson, "Adaptive digital beamforming for interference suppression in automotive FMCW radars," 2018: IEEE, pp. 0252-0256.
[38] Z. Peng, L. Ran, and C. Li, "A $ K $-band portable FMCW radar with beamforming array for short-range localization and vital-Doppler targets discrimination," IEEE Transactions on Microwave Theory and Techniques, vol. 65, no. 9, pp. 3443-3452, 2017.
[39] S. Abouzaid, T. Jaeschke, S. Kueppers, J. Barowski, and N. Pohl, "Deep learning-based material characterization using FMCW radar with open-set recognition technique," IEEE Transactions on Microwave Theory and Techniques, vol. 71, no. 11, pp. 4628-4638, 2023.
[40] L. R. Cenkeramaddi et al., "A novel angle estimation for mmWave FMCW radars using machine learning," IEEE Sensors Journal, vol. 21, no. 8, pp. 9833-9843, 2021.
[41] J. Benny, N. N. Moudhgalya, M. Khan, H. K. Meena, M. Wajid, and A. Srivastava, "Scalable Multi-Subject Vital Sign Monitoring with mmWave FMCW Radar and FPGA Prototyping," IEEE Sensors Journal, 2024.