關於設計單模波形以抑制干擾：基於連續都卜勒位移最小化峰值旁瓣等級

Abstract

在主動感測系統中，設計適當的探測波形對於偵測和估計目標物體的重要參數（如在雷達系統中的距離和速度）至關重要。在匹配濾波器組接收器中，波形應具有低模糊函數旁瓣，以減少干擾。精確來說，峰值旁瓣等級是一個更理想的準則，因為它決定了誤報率。此外，從硬體角度來看，採用單模波形有助於最大化功率放大器的效率。現有文獻已在特定離散化的距離-都卜勒區域內，最小化了模糊函數的格點峰值旁瓣等級。然而，由於目標產生的都卜勒頻率位於連續區間，基於該方法設計的波形可能會導致在都卜勒頻率格點之間出現預料之外的旁瓣，造成如誤報和目標遮蔽等偵測問題。因此，GPSL準則在這種情況下可能不是最合適的。本論文採用了真實峰值旁瓣等級來取代格點峰值旁瓣等級準則，以評估在連續都卜勒頻率區間內的峰值旁瓣等級。我們提出了一個波形設計問題，該問題在單模約束下，考慮了在特定距離-都卜勒區域內連續都卜勒頻率下將真實峰值旁瓣等級最小化。此外，我們引入了涉及三角多項式技巧的凸迭代算法來解決真實峰值旁瓣等級最小化問題。驗證結果顯示，與先前的研究相比，本論文所提出的方法在真實峰值旁瓣等級上取得了更佳的表現，這代表著該方法在整個連續都卜勒頻率區間內保證了低旁瓣等級。

In active sensing systems, designing appropriate probing waveforms is crucial for detecting and estimating valuable parameters of the objects of interest, such as range and velocity in radar systems. In a matched filter bank receiver, the waveform should exhibit low ambiguity function sidelobes to mitigate interference. Specifically, the peak sidelobe level is a more desirable criterion since it determines the false alarm rate. Moreover, from a hardware perspective, unimodular waveforms are preferable to maximize power amplifier efficiency. Existing literature has minimized the grid peak sidelobe level (GPSL) of the ambiguity function over a specific discretized range-Doppler region. However, since the Doppler frequency produced by the target falls within a continuous interval, using waveforms based on the method may lead to unexpected sidelobes between Doppler frequency samples, causing detection issues such as false alarms and target masking. Therefore, the GPSL criterion may not be the most suitable criterion in this scenario. In this thesis, the true peak sidelobe level (TPSL) is used instead of the GPSL criterion to evaluate the peak sidelobe level along a continuous Doppler frequency interval. A waveform design problem that minimizes the TPSL, considering continuous Doppler frequency over a specific range-Doppler region under unimodular constraints, is proposed. Also, convex iterative algorithms, involving the technique of trigonometric polynomials, are introduced to solve the TPSL minimization problem. Validation results show that the proposed method achieves a better TPSL compared to previous work, which implies the proposed method guarantees low sidelobe levels across the entire continuous Doppler frequency interval.