臺灣博碩士論文加值系統

本篇論文呈現一個藉由空間資源與時間資源結合估計波達角與頻率的方式。巢狀陣列偵測照射在非均勻感應器的訊號，並且於巢狀多重延遲的時間點作取樣，接著我們就能從取樣的資訊中獲得共變數矩陣。在經過空間平滑技術後，可以取得巢狀共陣列共變數矩陣而這看起來像更長的均勻平面時空陣列的型式。這可以降低估測波達角與頻率的方均根誤差。然而常見方法如多訊號分類法採用預定的時間、空間網格，並找出極值坐落的格子點處，以此來使用矩陣做波達角與頻率的估測，這會造成龐大的運算量。為了解決這個問題，我們採用旋轉不變技術訊號參數估測演算法，因此本方式可以在共陣列領域中還原出無網格狀態的波達角與頻率。在本篇論文以方均根誤差與解析度分析的模擬證實了本方式的有用性質。

This thesis presents a method of jointly estimating directions-of-arrival (DOAs) and frequencies with the use of spatial resource and temporal resource. Nested arrays detect the signals impinged on the sensors which are located at nonuniform positions and sample them at nested multiple-delay time. Then we can get a covariance matrix from the sampled data. After spatial smoothing technique, the nested coarray covariance matrix is obtained and it looks like a longer uniform planar space-time array form. It may decrease the root mean square errors of the estimated DOAs as well as frequencies. However conventional algorithm, the MUSIC algorithm exploits the matrix to estimate DOAs and frequencies by adopting predefined spatial and temporal grids and finding which lattice points the peaks locate on. It may cause too huge computational complexity. In order to resolve this problem, we adopt the Estimation of Signal Parameters via Rotational Invariance Techniques. As a result, the proposed method can retrieve the off-grid DOAs and frequencies in coarray domain. The simulations of root mean square errors and the resolution analyses verify the useful characteristic of the proposed method in the thesis.

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 The Signal Model and Coarray Domain 6
2.1 Data Model of ULA . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Nested Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Nested Time delayed Outputs . . . . . . . . . . . . . . . . . . 15
3 The Proposed Joint DOA and Frequency Estimation Method 17
3.1 Spatial Smoothing . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 DOA Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . 29
4 Simulation Results 30
5 Conclusion 40

[1]J. Zhang, H. Wang, and X. Zhu, “Adaptive waveform design for sepa-rated transmit/receive ULA-MIMO radar,” IEEE Transactions on Sig-nal Processing, vol. 58, no. 9, pp. 4936–4942, 2010.
[2]W. Book, “85] B. Widrow and SD Stearns, Adaptive Signal Processing, Engelwood Cli s,” 1985.
[3]V. Varadarajan and J. Krolik, “Array shape estimation tracking using active sonar reverberation,” IEEE Transactions on Aerospace and Elec-tronic Systems, vol. 40, no. 3, pp. 1073–1086, 2004.
[4]X. Liu and G. Liao, “Direction finding and mutual coupling estimation for bistatic MIMO radar,” Signal Processing, vol. 92, no. 2, pp. 517–522, 2012.
[5]J. Tsui, “Digital Techniques for Wideband Receivers, chapter 12,” Artech House, Norwood, Mass, USA,, 2001.
[6]R. Klemm, “Space-Time Adaptive Processing: Principles and Applica-tions, vol. 9 of,” IEE Radar, Sonar, Navigation and Avionics, 2000.
[7]J. R. Guerci, Space-time adaptive processing for radar. Artech House, 2014.
[8]J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proceedings of the IEEE, vol. 57, no. 8, pp. 1408–1418, 1969.
[9]R. Schmidt, “Multiple emitter location and signal parameter estima-tion,” IEEE transactions on antennas and propagation, vol. 34, no. 3, pp. 276–280, 1986.
[10]R. Roy and T. Kailath, “ESPRIT-estimation of signal parameters via ro-tational invariance techniques,” IEEE Transactions on acoustics, speech, and signal processing, vol. 37, no. 7, pp. 984–995, 1989.
[11]C. Zhou and J. Zhou, “Direction-of-arrival estimation with coarray ES-PRIT for coprime array,” Sensors, vol. 17, no. 8, p. 1779, 2017.
[12]P. Pal and P. P. Vaidyanathan, “Nested arrays: A novel approach to array processing with enhanced degrees of freedom,” IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4167–4181, 2010.
[13]P. Pal and P. Vaidyanathan, “Nested arrays in two dimensions, Part II: Application in two dimensional array processing,” IEEE Transactions on Signal Processing, vol. 60, no. 9, pp. 4706–4718, 2012.
[14]C.-L. Liu and P. P. Vaidyanathan, “Coprime arrays and samplers for space-time adaptive processing,” in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2015, pp. 2364–2368.
[15]T.-J. Shan, M. Wax, and T. Kailath, “On spatial smoothing for direction-of-arrival estimation of coherent signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, no. 4, pp. 806–811, 1985.
[16] W. Xudong, X. Zhang, J. Li, and J. Bai, “Improved ESPRIT method for joint direction-of-arrival and frequency estimation using multiple-delay output,” International Journal of Antennas and Propagation, vol. 2012, 2012.