壓縮感知(compressive sensing)是一個得到許多關注的新興研究領域。壓縮感知的概念是基於信號的稀疏性和不相關性，前者和信號本身的特性相關，後者則是與信號量測方法有關。壓縮感知可以在許多的領域中被應用。在雷達系統方面，壓縮感知可以藉由消除matched filter以及減少ADC頻寬需求，來對系統進行改善。壓縮感知的訊號重建問題可以被訊號重建演算法解決，例如Orthogonal Matching Pursuit(OMP)便是其中一種相當熱門的訊號重建演算法，訊號重建演算法是壓縮感知的關鍵核心部位。但是很不幸地，對於壓縮感知雷達系統而言，訊號重建演算法的複雜度是跟隨著系統的解析度而增加，因此複雜度便成為壓縮感知雷達的重要議題。所以這份研究提出了一個適用於壓縮感知雷達的兩階段訊號重建演算法。這份研究所提出之兩階段訊號重建演算法除了擁有比傳統OMP演算法更好的定位效能，也同時擁有更低的複雜度。除此之外，這份研究為了獲得更精確以及更加真實的模擬結果，路徑損失模型(path loss model)以及呼吸訊號模型(human respiratory signal model)皆在模擬中被使用。同時在這份研究中，也呈現了所提出的兩階段訊號重建演算法中，其中兩個最耗費時間以及複雜度最高的兩個步驟(coarse和fine positioning)的硬體架構設計。此研究所提出的兩階段訊號重建演算法在block size被設定為4時，其計算複雜度僅約是傳統OMP演算法的25%而已。

Compressive sensing is a novel research field which gains many interest. The idea of compressive sensing is based on sparsity and incoherence, which is related to signal characteristic and measurement scheme respectively. Many research fields have the motivation using the compressive sensing. For radar applications, compressive sensing can improve radar system by eliminating the need of matched filter and reducing the bandwidth requirement of analog to digital converter. The signal reconstruction problem of compressive sensing can be solved by reconstruction algorithms, for example, orthogonal matching pursuit(OMP) is one of the popular algorithms. The signal reconstruction algorithms are the key component of compressive sensing applications. Unfortunately, the complexity of reconstruction algorithms for compressive sensing radar increases with the resolution of compressive sensing radar system. Hence, complexity has become a critical issue of compressive sensing radar system. This work proposes a two-stage reconstruction algorithm for compressive sensing radar. The proposed two-stage reconstruction algorithm for compressive sensing radar has better positioning performance and lower complexity than conventional OMP algorithm under noisy environment. Furthermore, path loss model and human respiratory signal model are applied for simulations in this work, in order to improve the reality of simulation results. This work also presents a architecture design of two time consuming steps, coarse and fine positioning step, of proposed two-stage reconstruction algorithm. The computational complexity of proposed algorithm with block size b=4 is approximately 25% of conventional OMP algorithm.

1 Introduction 1
1.1 Compressive Sensing Radar System . . . . . . . . . . . 1
1.2 Research Motivation . . . . . . . . . . . 4
1.3 Organization of This Thesis . . . . . . . . . . . 5
2 Compressive Sensing Radar 7
2.1 Signal Model of Compressive Sensing. . . . . . . . . . . 7
2.2 Compressive Sensing Radar System . . . . . . . . . . . 11
2.2.1 SISO Compressive Sensing Radar . . . . . . . . . . . 11
2.2.2 MIMO Compressive Sensing Radar . . . . . . . . . . . 15
2.2.3 Path Loss and Human Respiration Signal Model . . . . . . . . . . . 19
2.3 Reconstruction Algorithms for Compressive Sensing . . . . . . . . . . . 22
2.3.1 Orthogonal Matching Pursuit . . . . . . . . . . . 22
2.3.2 Orthogonal Matching Pursuit via Matrix Inversion Bypass . . . . . . . . . . . 24
3 Proposed Two-Stage Reconstruction Algorithm 29
3.1 Two-Stage Reconstruction Algorithm . . . . . . . . . . . 29
3.2 Computational Complexity Analysis . . . . . . . . . . . 38
3.2.1 Orthogonal Matching Pursuit Algorithm . . . . . . . . . . . 38
3.2.2 OMP via Matrix Inversion Bypass Algorithm . . . . . . . . . . . 39
3.2.3 Proposed Algorithm . . . . . . . . . . . 39
3.3 Simulation and Performance Analysis . . . . . . . . . . . 42
3.3.1 Environment Setup . . . . . . . . . . . 43
3.3.2 Simulation Result . . . . . . . . . . . 45
4 Architecture Design 57
4.1 Architecture of OMP via MIB processor . . . . . . . . . . . 58
4.2 Matching Result Update and Index Selection Unit . . . . . . . . . . . 59
4.2.1 Initialization and Matching Result Update Circuit . . . . . . . . . . . 59
4.2.2 Index Selection Circuit . . . . . . . . . . . 64
4.3 Parameter Update Unit . . . . . . . . . . . 66
4.4 Timing Schedule . . . . . . . . . . . 69
5 Conclusion 73

[1] E. Candes and M. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE, vol. 25, no. 2, pp. 21–30, 2008.
[2] D. Donoho, “Compressed sensing,” Information Theory, IEEE Transactions on, vol. 52, no. 4, pp. 1289–1306, 2006.
[3] S. Qaisar, R. Bilal, W. Iqbal, M. Naureen, and S. Lee, “Compressive sensing: From theory to applications, a survey,” Communications and Networks, Journal of, vol. 15, no. 5, pp. 443-456, Oct 2013.
[4] M. Wakin, “Sparse Image and Signal Processing: Wavelets, curvelets, morphological diversity (starck, J.-L., et al; 2010) [Book Reviews],” Signal Processing Magazine, IEEE, vol. 28, no. 5, pp .144-146, 2011.
[5] M. Mishali, Y. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: Analog to digital at sub-nyquist rates,” Circuits, Devices Systems, IET, vol. 5, no. 1, pp. 8–20, 2011.
[6] M. Mishali, Y. Eldar, and A. Elron, “Xampling: Signal acquisition and processing in union of subspaces,” Signal Processing, IEEE Transactions on, vol. 59, no. 10, pp. 4719–4734, 2011.
[7] M. Mishali and Y. Eldar, “Xampling: Analog data compression,” in Data Compression Conference (DCC), 2010, 2010, pp. 366–375.
[8] M. Skolnik, Introduction to RADAR SYSTEMS. McGraw Hill, 1962.
[9] R. Baraniuk and P. Steeghs, “Compressive radar imaging,” in Radar Conference, 2007 IEEE, April 2007, pp. 128–133.
[10] T. Strohmer and B. Friedlander, “Compressed sensing for mimo radar -algorithms and performance,” in Signals, Systems and Computers, 2009 Conference Record of the Forty-Third Asilomar Conference on, Nov 2009, pp. 464–468.
[11] M. Herman and T. Strohmer, “Compressed sensing radar,” in Radar Conference, 2008. RADAR ’08. IEEE, May 2008, pp. 1–6.
[12] M. Herman and T. Strohmer, “High-resolution radar via compressed sensing,” Signal Processing, IEEE Transactions on, vol. 57, no. 6, pp. 2275–2284, June 2009.
[13] Z. jiankui and D. Ziming, “Some mimo radar advantages over phased array radar,” in Industrial Mechatronics and Automation (ICIMA), 2010 2nd International Conference on, vol. 2, May 2010, pp. 211–213.
[14] E. Fishler, A. Haimovich, R. Blum, R. Cimini, D. Chizhik, and R. Valenzuela, “Performance of mimo radar systems: advantages of angular diversity,” in Signals, Systems and Computers, 2004. Conference Record of the Thirty-Eighth Asilomar Conference on, vol. 1, Nov 2004, pp. 305–309 Vol.1.
[15] Y.-H. KAO, “Radar cross section measurement,” May 2013.
[16] Y.-F. Chiu, “A low-complexity uwb-radar signal processing system for real-time human respiratory feature extraction,” Master’s thesis, National Tsing Hua University, Taiwan, september 2013.
[17] J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” Information Theory, IEEE Transactions on, vol. 53, no. 12, pp. 4655–4666, Dec 2007.
[18] G. Huang and L. Wang, “High-speed signal reconstruction with orthogonal matching pursuit via matrix inversion bypass,” in Signal Processing Systems (SiPS), 2012 IEEE Workshop on, 2012, pp. 191–196.
[19] A. Bjorck, “Numerical methods for least squatres problems,” 1996.
[20] S. Chatterjee, K. V. S. Hari, P. Handel, and M. Skoglund, “Projection-based atom selection in orthogonal matching pursuit for compressive sensing,” in Communications (NCC), 2012 National Conference on, 2012, pp. 1–5.
[21] W. Dai and O. Milenkovic, “Subspace pursuit for compressive sensing signal reconstruction,” Information Theory, IEEE Transactions on, vol. 55, no. 5, pp. 2230–2249, 2009.
[22] A. Septimus and R. Steinberg, “Compressive sampling hardware reconstruction,” in Circuits and Systems (ISCAS), Proceedings of 2010 IEEE International Symposium on, 2010, pp. 3316–3319.
[23] J. Stanislaus and T. Mohsenin, “High performance compressive sensing reconstruction hardware with qrd process,” in Circuits and Systems (ISCAS), 2012 IEEE International Symposium on, 2012, pp. 29–32.
[24] D. Bailey and H. Ferguson, “A strassen-newton algorithm for high-speed parallelizable matrix inversion,” in Supercomputing ’88. [Vol.1]., Proceedings., 1988, pp. 419–424.
[25] D. Donoho, Y. Tsaig, I. Drori, and J.-L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” Information Theory, IEEE Transactions on, vol. 58, no. 2, pp. 1094–1121, 2012.
[26] R. V. Deanna Needell, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Foundations of Computational Mathematics -FoCM, vol. 9, pp. 317–334, 2009.
[27] S. Chatterjee, D. Sundman, and M. Skoglund, “Look ahead orthogonal matching pursuit,” in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, 2011, pp. 4024–4027.
[28] Z. Tian and G. Giannakis, “Compressed sensing for wideband cognitive radios,” in Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, vol. 4, 2007, pp. IV–1357–IV–1360.