An Enhanced MUSIC DoA Scanning Scheme for L-shaped Antenna Array Systems

本論文提出一適用於L形陣列天線系統之改良式多重訊號分類入射角度掃描技術，主要應用於建立周遭環境的障礙地圖，以輔助盲人行走。我們以傳統的多重訊號分類演算法(Multiple Signal Classification Algorithm)為基礎，將其延伸至二維的角度估測，並進行演算法的改良以降低硬體實現的複雜度。傳統多重訊號分類入射角度掃描技術中包含了自相關矩陣、特徵值分解以及頻譜掃描等大量的運算，故其運算複雜度極高。這對於角度估測演算法的實現造成很大的障礙。為了提高演算法實現的可能性，勢必需要降低運算複雜度。本論文提出以正交投影矩陣(Orthogonal Projection Matrix)取代特徵值分解(Eigenvalue Decomposition)的方法，並利用QR分解來實現正交投影矩陣內的反矩陣運算。另外，在二維的入射角估測中，傳統使用矩形天線陣列的作法，雖然可以獲得較高的估測精準度，但不論是在天線系統或是base band的訊號處理複雜度都很高，因此我們採用較低複雜度的L形陣列天線系統來進行估測，並將仰角與方位角合併在一起同時進行頻譜的掃描。如此可以解決分成兩次估測所衍生的角度匹配問題，角度估測上的精準度也可以獲得提升。從模擬結果可以得知，我們所提出的低複雜度多重訊號分類入射角度掃描技術用於L形天線陣列和矩形天線陣列時，當訊號雜訊比大於15dB，兩者的估測精確度相當。 在對應的硬體實現上，我們規劃了縝密的時序安排與管線化架構，以提升運算的速率。為了降低硬體運算複雜度，採用座標旋轉數位計算器(Coordinate Rotate Digital Computer，CORDIC)來實現QR分解內所需的三角函數運算。整體電路架構針對60度×60度的FOV，2度的掃描解析度，每次的估測掃描必須進行31×31次的估測。以系統目標的204.8MHz工作頻率，每次掃描需要花費2079 clock cycles。加上auto-correlation矩陣計算資料蒐集所需的512 clock cycles，可以在一個chirp period (40us)的時間內完成估測掃描，相當於50kHz的掃描速率。In this thesis, we present an enhanced MUltiple SIgnal Classification (MUSIC) scheme for Direction of Arrival (DoA) scanning using a L-shaped antenna array system. The goal is to construct an obstruction map based on the DoA scanning results, which helps blind people to learn their surrounding environment when walking on the street. A low complexity two-dimension DoA estimation scheme based on the conventional MUSIC Algorithm is developed. Conventional MUSIC scheme is computationally intensive, requires various computations such as auto-correlation matrix estimation, Eigenvalue decomposition and spectrum scanning. In particular, Eigen Value Decomposition (EVD) has the highest computation complexity. The auto-correlation matrix estimation is also time consuming. To achieve an efficient hardware accelerator design for DoA estimation, it is essential to reduce the computing complexity firstly. In this thesis, we propose to use an Orthogonal Projection Matrix (OPM) scheme in lieu of Eigenvalue Decomposition. Furthermore, a QR decomposition method is employed to implement the pseudo inverse matrix calculation required in the OPM scheme. The proposed one-dimensional DoA estimation scheme is next extended to the two-dimensional case. Instead of using a rectangular antenna array, which yields better estimation accuracy at the expense of hardware complexity, a low complexity L-shaped array antenna system is used. To avoid the matching problem between azimuth and elevation angles, both angles are estimated simultaneously for better accuracy. Extensive simulations are conducted to show the effectiveness of the proposed 2-D DoA estimation scheme. The simulation results show that DoA estimation accuracy of the proposed scheme when applied to the L-shaped antenna array is comparable to that of rectangular array if SNR is greater than 15dB. After algorithm development, a hardware accelerator design is investigated. We employ careful scheduling and pipelined architecture to improve the speed of the operations. To reduce the circuit complexity, a Coordinate Rotate Digital Computer (CORDIC) technique is used to implement the trigonometric functions required in QR decomposition. The proposed accelerator design supports a FOV of 60 (degree) × 60 (degree), and a scanning resolution of 2 (degree). This means that 31×31 angles are scanned within the FoV. It takes 2,079 clock cycles to perform the scanning and an additional 512 clock cycles are needed to auto-correlation matrix estimation. With a target clock rate of 204.8MHz, the proposed design can accomplish one complete scan within a chirp period of 40us, which is equivalent to a 25kHz scan rate.摘要 i Abstract ii 目錄 iv 圖目錄 vi 表目錄 viii 第一章 緒論 1 1.1 研究背景 1 1.2 研究動機及研究目標 1 1.3 論文架構 2 第二章 應用於頻率調變連續波雷達系統之入射角度掃描技術 3 2.1 頻率調變連續波雷達系統 3 2.1.1 頻率調變連續波雷達 3 2.1.2天線陣列模型 5 2.2 方位估測技術及文獻回顧 9 第三章 基於雷達掃描之方位估測演算法模擬分析 11 3.1 一維方位估測演算法 11 3.1.1 傳統多重訊號分類演算法 11 3.1.2 改良式多重訊號分類演算法 14 3.1.3 傳統與改良式一維多重訊號分類演算法之模擬分析 17 3.2 二維方位估測演算法 25 3.2.1 傳統方形天線陣列之二維多重訊號分類演算法 25 3.2.2 基於方形天線陣列之改良式二維多重訊號分類演算法 34 第四章 適用於L形天線陣列之改良式多重訊號分類入射角度掃描技術 42 4.1 適用於L形天線陣列之改良式多重訊號分類架構 43 4.2 適用於L形天線陣列之改良式多重訊號分類架構 49 4.3 傳統與改良之角度估測演算法模擬分析 53 4.4 演算法運算複雜度分析與比較 62 第五章 硬體電路設計 65 5.1 整體硬體架構 65 5.2 系統及時序規劃 67 5.3 定點模擬與分析 69 5.4 硬體實現與模組設計 73 5.4.1 自相關矩陣硬體模組 73 5.4.2 基於座標旋轉數位計算器之QR分解模組 74 5.4.3 投影矩陣模組 78 5.4.4 空間頻譜掃描模組 79 5.5 硬體架構設計總結 80 第六章 結論與未來展望 81 參考文獻 8