於交織正交分頻多工存取上行系統中基於子空間處理方式之具有計算效率載波頻率偏移估測

Computationally Efficient CFO Estimation Based on Subspace Approaches for Interleaved OFDMA Uplink Systems

張威(Wei Zhang)

指導教授 ： 張安成

嶺東科技大學/資訊學院/資訊科技系碩士班/碩士(2017年)

摘要

本論文於交織正交分頻多工接取(Orthogonal Frequency Division Multiple Access, OFDMA)上行系統下研究具有計算效率的基於子空間處理方式之載波頻率偏移(Carrier Frequency Offset, CFO)估測問題且無需使用特定的訓練序列，不像傳統的基於子空間CFO估測器，本論文所提出的處理方式僅需要計算取樣自相關矩陣的兩個子矩陣；同時，採用基於 方法來正確的計算訊號子空間，從而避免直接計算完整的取樣自相關矩陣和它的特徵值分解，並利用完整特徵空間具有單一(Unitary)的特性求得基於雜訊子空間的投影矩陣。因此，所提出的子空間估測方法具有計算吸引力的優勢，特別是在子載波數目或子通道數目相當大的情形下；經結合中央對稱調整的自相關矩陣和所提出的子空間估測方法，可以獲得較正確估測的訊號子空間和基於雜訊子空間的投影矩陣。由於基於頻譜搜尋的估測器是相當耗費計算量，且其計算複雜度和估測精準度是與搜尋格柵的尺寸大小和搜尋範圍的大小有很嚴重的關係，故相當耗時且適當之格柵大小是不明確的；因此，為了達成有效估測之目的，本論文包含二個相關的研究課題。第一個研究課題將先提出兩個簡單而有效的透過多項式求根方法用以取代頻譜搜尋，一個是基於估測的訊號子空間和另一個是基於估測的雜訊子空間之投影矩陣，因為這些多項式求根方法是直接從目標函數來計算根值的解，在有限取樣數目、低訊號雜訊比和多重存取干擾時所得到的根並不是最大相似性估測。因此，本課題還提出了一種可以提高CFO估測精準度之有效的微分多項式求根方法，其主要的想法是對目標函數的一階導函數求根來代替直接對目標函數求根。第二個研究課題將透過單一轉換前處理技術，使得這些估測器處理實數值計算，除此之外資料的前處理並不增加相對應的矩陣的維度，故將擁有高的計算效率。同時，順向-逆向自相關矩陣在CFO估測上被用以代替傳統之僅使用順向自相關矩陣，此一作法可以形成雙倍的資料區塊，並可增進CFO估測精準度。最後，藉由模擬結果將可以驗證這些所提出之盲目估測處理方式的有效性。

關鍵字

載波頻率偏移 ； 交織正交分頻多工存取 ； 上行 ； 訊號子空間 ； 雜訊子空間 ； 正交投影 ； 特徵值分解 ； 多項式求根 ； 單一轉換

並列摘要

This thesis deals with blind carrier frequency offsets (CFO) estimation based on computational efficiency subspace-based approaches without using specific training sequences for interleaved orthogonal frequency division multiple access (OFDMA) uplink systems. Unlike the conventional subspace-based CFO estimators, the proposed approaches only need to calculate two sub-matrices of the sample autocorrelation matrix. In particular, we employ an approach that is based on the method to correctly find the signal subspace, avoiding the direct computation of sample autocorrelation matrix and its eigenvalue decomposition (EVD). Meanwhile, the unitary property of the complete eigenspace is utilized to correctly compute the orthogonal projection matrix of noise subspace. Thus, the proposed subspace estimation method has the advantage of computational attractiveness, particularly when the number of subcarriers or the number of subcannels is large. With the centro-symmetric trimmed autocorrelation matrix and the proposed subspace estimation method, the estimate signal subspace and projection matrix of noise subspace can be obtained. For the searching-based estimators, they are computationally expensive. Moreover, the complexity and estimation accuracy strictly depend on the grid size used during the search. It is time consuming and the search grid is not clear. For the purpose of efficient estimation, this thesis includes two topics. Firstly, two simple and efficient approaches implemented by polynomial rooting will be proposed instead of by spectral searching in the first topic. One is based on estimate signal subspace and the other one is based on estimate projection matrix of noise subspace. Since these polynomial rooting methods compute the roots directly from the object function, the resulting solutions are not the maximum likelihood estimate in finite samples, low signal-to-noise ratio, and multiple access interference. Therefore, this topic also proposes an efficient derivative polynomial rooting method, which can improve the CFO estimate accuracy. The main idea behind is to root the first-order derivative of the object function instead of rooting the object function directly. In the second topic, via the unitary transformation preprocessing technique, these estimators deal with real-valued computation except the data preprocessing without increasing the dimension of corresponding matrices, which leads to high computational efficiency. Meanwhile, the forward-backward correlation matrix is used in CFO estimation instead of conventional forward only correlation matrix, which can be double the data blocks and result in an improved CFO estimation accuracy. Finally, several computer simulation results are provided for illustrating the effectiveness of the proposed blind estimate approaches.

並列關鍵字

carrier frequency offset ； interleaved orthogonal frequency division multiple access ； uplink ； signal subspace ； noise subspace ； orthogonal projection ； eigenvalue decomposition ； polynomial rooting ； unitary transformation

參考文獻

[1] H.T. Hsieh and W.R. Wu, “Blind maximum-likelihood carrier-frequency-offset estimation for interleaved OFDMA uplink systems,” IEEE Trans. Vehicular Technology, vol. 60, no. 1, pp. 160-173, January 2011.

[2] S.H. Song, G.L. Chen, and K.B. Letaief, “Localized or interleaved A tradeoff between diversity and CFO interference in multipath channels,” IEEE Trans. wireless communications, vol. 10, no. 9, pp. 2829-2834, September 2011.

[3] W.C. Huang, Y.S. Yang, and C.P. Li, “A new pilot architecture for sub-band uplink OFDMA systems,” IEEE Trans. Broadcasting, vol. 59, no. 3, pp. 461-470, September 2013.

[4] M.D. Pun, M. Morelli, and C.C. J. Kuo, “Maximum-likelihood synchronization and channel estimation for OFDMA uplink transmissions,” IEEE Trans. Communications, vol. 54, no. 4, pp. 726-736, April 2009.

[5] W. Zhang and Q. Yin, “Blind carrier frequency offset estimation for tile-based orthogonal frequency division multiple access uplink with multi-antenna receiver,” IET Communications, vol. 8, no. 8, pp.1309-1316, May 2014.