臺灣博碩士論文加值系統

摘要
在本篇論文中, 我們提出了一種可同時精確估測二維方位角與載波
頻率之演算法, 此演算法主要架構是運用正交投影矩陣, 將接收訊號拆解成二
維方位角所生成之訊號子空間與載波頻率所生成之訊號子空間, 再運用二維
Unitary-ESPRIT 及一維Unitary-ESPRIT 演算法將接收訊號中的參數估測出
來; 之後, 我們更將上述演算法之架構作進一步延伸, 將接收訊號分解成三個
一維的訊號子空間, 再利用一維Unitary-ESPRIT 估測出精準的方位角與載波
頻率以降低整體複雜度。另一方面,我們也可利用相同的架構來估測二維方位
角與時間延遲之接收訊號。最後, 在本篇論文模擬結果中, 可以顯示我們所提
出的演算法, 可同時準確的估測接收訊號之二維方位角與載波頻率或二維方
向角與時間延遲等相關參數。
關鍵字: 二維方位角, 載波頻率, 時間延遲, 正交投影矩陣, 二維Unitary-
ESPRIT, 一維Unitary-ESPRIT , 參數估測。
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ABSTRACT
In this thesis, we propose low-complexity, yet high accuracy algorithms to
jointly estimate two-dimensional directions of arrival (DOAs) and carrier frequency
using a uniform rectangular array. To achieve this, we utilize the (2-D) unitary
Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT)
and one-dimensional (1-D) unitary ESPRIT to estimate the 2-D DOAs and frequencies
of the incoming rays, respectively. Also, to enhance the performance, a
signal partitioning process, implemented by a set of projection matrices, is invoked
in between the unitary ESPRIT algorithms. To further reduce the computation,
we also decompose the 2-D DOA estimation process, so that only 1-D unitary
ESPRIT algorithm are required. Similar techniques are also employed for joint
2-D DOA and delay estimation. Conducted simulations show that the new algorithms
can provide satisfactory performance compared with previous works, but
with drastically reduced computational complexity.
Keywords: 2D DOA, carrier frequencies, time delay, projection matrices, 2D
Unitary-ESPRIT, 1D Unitary-ESPRIT, parameter estimation

目錄
第一章緒論1
1.1 介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 內容章節概述. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
第二章一維與二維訊號模型與入射方位角之估測演算法之介紹4
2.1 訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 一維信號模型. . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 二維訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . 7
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2.2 ESPRIT型式之入射方位角估測演算法. . . . . . . . . . . . . . . 8
2.2.1 ESPRIT基本型式. . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Unitary-ESPRIT演算法. . . . . . . . . . . . . . . . . . . . 13
2.2.3 二維Unitary ESPRIT 演算法. . . . . . . . . . . . . . . . 17
2.2.4 三維Unitary-ESPRIT 演算法. . . . . . . . . . . . . . . . 20
2.3 結語. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
第三章二維方位角及載波頻率之聯合估測法29
3.1 訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 估測二維方位角與載波頻率基於結合二維Unitary-ESPRIT 及
一維Unitary-ESPRIT 架構之演算法. . . . . . . . . . . . . . . . 31
3.3 估測二維方位角與載波頻率基於一維Unitary-ESPRIT 架構之
演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
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3.5 結語. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
第四章二維方位角及時間延遲之聯合估測法51
4.1 訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 估測二維方位角與時間延遲基於二維Unitary-ESPRIT 及一維
Unitary-ESPRIT 架構之演算法. . . . . . . . . . . . . . . . . . . . 53
4.3 估測二維方位角與時間延遲基於一維Unitary-ESPRIT 架構之演
算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4 模擬結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 結語. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
第五章結論與未來展望64

[1] T. S. Rappaport, Wireless Communications. Prentice Hall PTR, 1996.
[2] Simon Haykin, Adaptive Filter Theory, 4e. Prentice-Hall, 2002.
[3] H. L. Van Trees,Optimun Array Processing. Wiley-Interscience, 2002.
[4] R. Schmidt,“Multiple emitter location and signql parameter estimation,”
IEEE Transactions on Antennas and Propagation, Vol. AP-34, NO.3,pp 276-
280 March 1986
[5] R. Roy and T. Kailath, “ESPRIT-estimation of signal parameters via rotational
invariance techniques,” IEEE Transcation on Acoustics. Speech. and
Signal Processing, pp. 984-995, Vol 37. NO 7. July 1989
[6] M. Haardt and J.A. Nossek,“Unitary ESPRIT: how to obtain increased estimation
accuracy with a reduced computational burden,” IEEE Transcation
on Signal Processing, Vol. 43,NO.5,pp 1232 - 1242 , May 1995,
[7] M. D. Zoltowski, M. Haardt and C.P. Mathews, “Closed-form 2-D angle estimation
with rectangular arrays in element space or beamspace via unitary
ESPRIT,” IEEE Transaction on Signal Processing, Vol. 44, NO. 2,pp 316 -
328, Feb. 1996
[8] M. Haardt and J.A. Nossek, “Simultaneous Schur decomposition of several
nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic
retrieval problems,”IEEE Transaction on Signal Processing, Vol. 46,
NO. 1,pp Jan. 1998.
[9] G.H. Gloub and C.F. Van Loan, Matrix Computations, 3rd ed. Johns Hopkins
University Press, 1996
[10] P. Strobach, “Total least squares phased averaging and 3-D ESPRIT for joint
azimuth-elevation-carrier estimation,” IEEE Transactions on Signal Processing,
Vol. 49, NO. 1,pp 54 - 62 Jan. 2001.
66
[11] M. Haardt and J. A. Nossek, “3-D unitary ESPRIT for joint 2-D angle and
carrier estimation”Acoustics, Speech, and Signal Processing, Vol 1,pp 21-24,
Apr. 1997.
[12] C. Qi, Y. Wang, Y. Zhang and H. Chen. “A space-time processing approach
to joint estimation of signal frequency and 2-D direction of arrival” in proc.
Antennas and Propagation Symposium,Vol 2B,pp 370 - 373, July 2005.
[13] T. S. Rappaport, J. H. Reed and B. D. Woerner, “Position location using
wireless communications on highways of the future,”IEEE Commun. Mag,
Oct. 1996.
[14] M. Wax, T. J. Shan and T. Kailath, “ Spatio-temporal spectral analysis by
eigenstructure methods,” IEEE Trans on ASSP,Vol. 32,pp. 817-827, Apr.
1984.
[15] Y H. Chen and C. H. Chen, “Direction-of-arrival and frequency estimation
for narrowband sources using two single rotation invariance algorithms with
the marked subspace,” IEE Proceedings-F,Vol. 139,pp. 297-300, Apr. 1992.
[16] A. N. Lemma, A. J. Veen and E. F. Deprettere, “Analysis of joint anglefrequency
estimation using ESPRIT,” IEEE Trans. Signal Processing,Vol.
51,pp. 1264-1283, May. 2003.
[17] M. A. Zatman and H. J. Strangeways, “An efficient joint direction of arrival
and frequency ML estimator,” Antennas and Propagation Society International
Symposium,Vol 1. ,pp 431-434 June. 1995.
[18] A. L. Swindlehurst, “Time delay and spatial signature estimation using known
asynchronous signals,” IEEE Trans. Signal Processing,Vol. 46, pp. 449-461,
Feb. 1998.
[19] A. Jakobsson, A. L. Swindlehurst and P. Stoica, “Subspace-based estimation
of time delays and doppler shifts,” IEEE Trans. Signal Processing,Vol. 46,pp.
2472-2483, Sept. 1998.
[20] A. L. Swindlehurst and J. H. Gunther, “Methods for blind equalization and
resolution of overlapping echos of unknown shape,” IEEE Trans. Signal Processing,
Vol. 47,pp. 1245-1254, May. 1999.
[21] M. P. Clark and L. L. Scharf, “Two-dimensional modal analysis based on
maximum likelihood,” IEEE Trans. Signal Processing,Vol. 42,pp.1443-1452,
June. 1994.
[22] EIA/TIA Interim Stand. IS-136, Dec. 1994.
[23] “European telecommunication standard institute (ETSI),” Europeon
Telecomm. Stand. Inst., rec. ETSI/GSM 05.02, 1990.
67
[24] V. M. Baronkin, Y.V. Zakharov and T. C. Tozer, “Cramer-Rao lower bound
for frequency estimation in multipath Rayleigh fading channels” Acoustics,
Speech, and Signal Processing,Vol. 4,pp 2557-2560, May. 2001.
[25] S. Chaudhuri and S. Chatterjee, “Performance analysis of total least squares
methods in three-dimensional motion estimation” IEEE Robotics and Automation
Society,Vol. 7,pp 707-714, Oct. 1991.
[26] M. J. D. Rendas and J. M. F. Moura, “Cramer-Rao bound for location
systems in multipath environments” IEEE Transactions on Signal Processing,
Vol. 39,pp 2593-2610, Dec. 1991.
[27] C. Joseph and S. Theodore, Smart Antennas for Wireless Communication
Prentice Hall, 1999.
[28] J.-D. Lin, W.-H. Fang, Y.-Y. Wang, and J.-T. Chen, “FSF MUSIC for joint
DOA and frequency estimation and its performance analysis,” accepted by
IEEE Trans. Signal Processing.
[29] C.-H. Lin, K.-H.Wu, J.-D. Lin, and W.-H. Fang, “A one-dimensional ESPRIT
based algorithm for joint azimuth, elevation and frequency estimation,” in
Proc. IEEE Int’l Symposium Antennas and Propagations, 2006.
[30] G.G. Raleigh and T. Boros, “Joint space-time parameter estimation for wireless
communication channels” IEEE Trans. Signal Processing,Vol. 46,pp 1333-
1343, May. 1998
[31] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, 1985.
[32] J.-D. Lin, W.-H. Fang and J.-T. Chen, “Constrained TST MUSIC for joint
spatial-temporal channel parameter estimation” Acoustics, Speech, and Signal
Processing,Vol. 5,pp 193-196, 2003.
68