壓縮感知是一項被應用在許多領域的訊號處理技術。透過壓縮感知，可以由較少量的資訊高機率地復原未知數，藉此達成資源的節省。在無線通訊領域上，由於多重路徑通道的稀疏特性，我們可以藉由以壓縮感知為基礎的方法來處理在正交分頻多工中的稀疏通道估測問題。其中在領航信號的樣式的設計上，有別於一般藉由最小化測量矩陣的最大相關性值的方法，本文提出了新的設計準則，藉此有較高的機率能挑選出正交性較高的測量矩陣。模擬結果顯示，相對於被廣泛採用的準則，由本文提出的設計準則所產生的領航信號，在稀疏通道估測上可以有更低以及更穩定的均方誤差表現。

Compressed sensing (CS) is a signal processing technique which has been applied in lots of fields. Through CS, unknown parameters can be recovered with high probability from smaller amounts of information so that resources are saved. Due to the sparse nature of multipath channels, we settle the channel estimation problem in orthogonal frequency division multiplexing (OFDM) systems using CS -based method. On the design of pilot patterns, instead of a general way of minimizing the mutual coherence of the measurement matrix, a novel criterion is proposed by which measurement matrices with higher orthogonality can be picked with higher probability. Simulation results display that, in comparison to the widely used criterion, the pilot patterns generated by proposed criterion give better and more stable mean square error (MSE) performances in sparse channel estimation.

[1] Y. Shen and E. F. Martinez. “Channel Estimation in OFDM Systems,” AN3059, Freescale Semiconductor, Inc., Jan. 2006.
[2] I. J. Fevrier, S. B. Gelfand, and M. P. Fitz, “Reduced complexity decision feedback equalization for multipath channels with large delay spreads,” IEEE Trans. Commun., vol. 47, no. 6, pp. 927–937, Jun. 1999.
[3] M. Kocic, D. Brady, and M. Stojanovic, “Sparse Equalization for Real-Time Digital Underwater Acoustic Communications,” in Proc. OCEANS Conf., pp. 1417–1422, Oct. 1995. .
[4] X. He and R. Song, “Pilot pattern optimization for compressed sensing based sparse channel estimation in OFDM systems,” in Proc. IEEE Int. Conf. Wireless Commun. Signal Process., pp. 1–5, Oct. 2010.
[5] J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 30, no. 2, pp. 210–227, Feb. 2009.
[6] M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72–82, Mar. 2008.
[7] D. L. Donoho, M. Elad, and V. N. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6–18, Jan. 2006.
[8] L. Najjar, “Pilot allocation by Genetic Algorithms for sparse channel estimation in OFDM systems,” in Proc. of European Signal Process. Conf. (EUSIPCO), pp. 1–5, Sep. 2013.
[9] X. He, R. Song, and W. Zhu, “Pilot allocation for sparse channel estimation in MIMO-OFDM systems,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 60, no. 9, pp. 612-616, Sep. 2013.
[10] C. Qi, G. Yue, L. Wu, and A. Nallanathan, “Pilot Design for Sparse Channel Estimation in OFDM-Based Cognitive Radio Systems,” IEEE Trans. Veh. Technol., vol. 63, no. 2, pp. 982–987, Feb. 2014.
[11] X. He, R. Song, and W. P. Zhu, “Optimal pilot pattern design for compressed sensing-based sparse channel estimation in OFDM systems,” Circuits Syst. Signal Process., vol. 31, pp. 1379–1395, 2012.
[12] M. Babaie-Zadeh and C. Jutten, “On the stable recovery of the sparsest overcomplete representations in presence of noise,” IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5396–5400, Oct. 2010.
[13] E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math., vol. 59, no. 8, pp. 1207–1223, Aug. 2006.
[14] J. Tropp and A. C. Gilbert, “Signal recovery from partial information via orthogonal matching pursuit,” IEEE Trans. Inf. Theory, vol. 53, no.12, pp. 4655–4666, Dec. 2007.
[15] T. Cai and L. Wang, “Orthogonal matching pursuit for sparse signal recovery with noise,” IEEE Trans. Inform. Theory, vol. 57, no. 7, pp. 4680–4688, 2011.
[16] D. L. Donoho and X. Huo, “Uncertainty principles and ideal atomic decomposition”, IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845–62, Nov. 2001.
[17] C. Qi and L. Wu, “A hybrid compressed sensing algorithm for sparse channel estimation in MIMO OFDM systems,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process, pp. 3488–3491, May 2011.
[18] H. Wolkowicz and G. P. H. Styan, “Bounds for eigenvalues using traces,” Linear Algebra Its Appl., vol. 29, pp. 471–506, 1980.
[19] R. Jain, “Channel Models: A Tutorial, ” WiMAX Forum AATG, Feb. 2007.