近年來，壓縮感知(Compressive Sensing)是一個熱門的研究主題。壓縮感知的基本概念是基於信號本身的稀疏特性以及信號量測方法的不相關性所組成。可藉由減少取樣率以移除冗餘資訊的信號特性，使壓縮感知的技術具有廣泛的應用。在雷達系統中，matched filter以及ADC的頻寬需求非常高，壓縮感知的技術能改善此問題。所有壓縮感知的問題都在追求高速度(低運算複雜度)與完美重建表現，例如Orthogonal Matching Pursuit(OMP)是其中一種熱門的訊號重建演算法。壓縮感知技術的核心部分為訊號重建演算法。然而，訊號重建的複雜度會隨著壓縮感知雷達的解析度而增加，因此複雜度為壓縮感知雷達應用中，重要的議題。這份研究提出一個適用於分散式壓縮感知超寬頻雷達系統之低複雜度定位演算法與架構。提出的演算法可有效降低運算上的複雜度，縮短運算時間。也可與兩階段訊號重建演算法結合，擁有比傳統OMP更低的複雜度以及更好的定位效能。其節省的運算耗費時間與稀疏性呈線性關係。模擬中使用分散式雷達系統可減少更多的定位死角，提升涵蓋能力。最後為此研究所提出多向量選取訊號重建演算法的硬體架構並驗證於FPGA。

In recent years, Compressive Sensing (CS) has been a hot research topic. The idea
of compressive sensing is based on sparsity and incoherence, which is related to signal
characteristic and measurement scheme respectively. Owing to signal characteristic of
removing redundant information by reducing the sampling rate, CS technique has a wide
range of applications. In the radar system, matched lter and the bandwidth requirement
of analog to digital converter are very high, which can improve radar system by CS
technique. All the CS problems pursue the high speed (low computational complexity)
and high signal reconstruction performance, for example, orthogonal matching pursuit
(OMP) is one of the popular algorithms. The signal reconstruction algorithm is the
essentials of CS technique. Nevertheless, the complexity of reconstruction algorithms
for CS radar increases with the resolution, which is the critical issue of CS radar applications.
This study proposed Low-Complexity Localization Algorithm and Architecture for Distributed Compressive Sensing Ultra-Wideband Radar System. Proposed algorithm can reduce computation complexity efficiently, so it has a shorter operation time.
Furthermore, this study also presents to combine with Two-Stage algorithm, which has lower complexity and better positioning performance than conventional OMP algorithm.
The saving computation time and sparsity is linear relationship. We use the distributed radar system, in order to reduce the positioning blind spot, and improve the coverage ability in the simulation. The architecture of the proposed algorithm is implemented and veried by FPGA in the end.

[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] ||, "High-resolution radar via compressed sensing," Signal Processing, IEEE
Transactions on, vol. 57, no. 6, pp. 2275{2284, June 2009.
[13] C. S. S., D. D. L., and S. M.A., "Atomic decomposition by basis pursuit," vol. 58, 1999, pp. 33-61.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] Y.-H. KAO, "Radar cross section measurement," May 2013.
[19] 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.
[20] A. Bjorck, "Numerical methods for least squatres problems," 1996.
[21] K. C. Tsao and Y. H. Huang, "A low-complexity two-stage signal reconstruction algorithm for compressive sensing ultra-wideband radar positioning systems."
[22] N. D. and T. J. A., "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," vol. 26, 2008, pp. 93-100.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[29] 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.
[30] 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.
[31] 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.