藉由峰度最大化的盲蔽信號源分離演算法與其在無線通訊之應用

Blind Source Separation Algorthms by Kurtosis Maximization with Applications to Wireless Communications

彭俊賢(Chun-Hsien Peng)

指導教授 ： 祁忠勇

國立清華大學/電機資訊學院/通訊工程研究所/博士(2006年)

https://doi.org/10.6843/NTHU.2006.00658

摘要

給定一組瞬間多重輸入多重輸出(multiple-input multiple-output, MIMO)系統之有雜訊的輸出量測資料，峰度(四階統計量)最大化準則已被有效地使用於未知非高斯且有色輸入(colored inputs)(信號源)及MIMO系統之估計。從效能及運算複雜度之觀點，祁等人所提出的快速峰度最大化演算法(fast kurtosis maximization algorithm, FKMA)已經是一個有效的演算法，並且已被成功地應用於統計信號處理及無線通訊，例如：盲蔽信號源分離、盲蔽波束成型以及盲蔽多用戶檢測。然而，當系統輸入的峰度很小，FKMA的效能可能會嚴重地下降。FKMA於先進的無線通訊系統之應用仍然是開放的研究領域，例如：多載波-分碼多工接取(multicarrier code division multiple access, MC-CDMA)系統、多重速率直接序列/分碼多工接取(direct sequence/code division multiple access, DS/CDMA)系統以及多用戶正交分頻多工(orthogonal frequency division multiplexing, OFDM)系統。
FKMA在第二章介紹之後，第三章提出一個嶄新的盲蔽信號源抽取演算法，稱為渦輪信號源抽取演算法(turbo source extraction algorithm, TSEA)，此演算法利用信號的時間特性以增加正規化的峰度大小值，並且以循環之方式使用空間及時間處理，進而改善抽取效能。此外，提出兩個非消除多階段演算法，而這兩個演算法從階段到階段免於錯誤增殖之影響。
第四章提出FKMA的應用於配備單一接收天線或多接收天線之準同步改良式MC-CDMA系統的盲蔽多用戶檢測。在第五章，針對空-時編碼MC-CDMA系統之下傳模式，提出一個使用FKMA的嶄新盲蔽空-時解碼演算法。接著，針對配備單一接收天線(或多接收天線)之非同步多重速率DS/CDMA系統(可改變的處理增益系統和多碼系統)，兩個多重速率盲蔽多用戶檢測演算法於第六章提出，一個是基於迴積的MIMO信號模型，而另一個則是基於瞬時的MIMO信號模型。
為了同通道干擾及符碼干擾之抑制，第七章提出兩個峰度最大化的盲蔽空-時接收機，一個是盲蔽串聯空-時接收機(cascade space-time receiver, CSTR)(是一個傳統的空-時架構)，而另一個則是盲蔽渦輪空-時接收機(turbo space-time receiver, TSTR)(是一個循環耦合式的空-時架構)。在效能上，盲蔽TSTR明顯地勝過盲蔽CSTR，而TSTR基本上與第三章中的TSEA是相同的。
第八章描述FKMA於OFDM系統之盲蔽波束成型的應用。在此章中，針對後置傅立葉轉換波束成型架構，基於子載波平均且藉由峰度最大化，我們提出一個全新、盲蔽且單一區塊的波束成型演算法。對於所有子載波而言，所設計的波束成型器皆相同並有效地利用多路徑分集以獲得效能增益，同時也對彼此具相關性的信號源的效能有強健的抵抗力。
第三至第八章中的每一章，皆提供一些模擬結果以證實提出的演算法之功效以及與現存演算法效能的比較。最後，第九章做一些結論及提供一些未來值得進行的研究。

關鍵字

盲蔽信號源分離演算法 ； 峰度最大化 ； 多重輸入多重輸出 ； 渦輪信號源抽取演算法 ； 多階段連續消除 ； 非消除多階段演算法 ； 多載波-分碼多工接取系統 ； 多重速率直接序列/分碼多工接取系統 ； 正交分頻多工系統 ； 盲蔽多用戶檢測演算法 ； 盲蔽空-時解碼演算法 ； 盲蔽串聯空-時接收機 ； 盲蔽渦輪空-時接收機 ； 盲蔽波束成型演算法

並列摘要

The kurtosis maximization criterion has been effectively
used for blind spatial extraction of one source from an
instantaneous mixture of multiple non-Gaussian sources, such as the kurtosis maximization algorithm proposed by Ding and Nguyen, and the fast kurtosis maximization algorithm (FKMA) proposed by Chi et al. By empirical studies we found that the smaller the normalized kurtosis magnitude of the extracted source signal, the worst the performance of these algorithms. In this thesis, with the assumption that each source is a non-Gaussian linear process, a novel blind source extraction algorithm, called turbo source extraction algorithm (TSEA), is proposed. The ideas of the TSEA are to exploit signal temporal properties for increasing the normalized kurtosis magnitude, and to apply spatial and temporal processing in a cyclic fashion to improve the signal extraction performance. The proposed TSEA not only outperforms the FKMA, but also shares the convergence and computation advantages enjoyed by the latter.

This thesis also considers the extraction of multiple sources, also known as source separation, by incorporating the proposed TSEA into the widely used multistage successive cancellation (MSC) procedure. A problem with the MSC procedure is its susceptibility to error propagation accumulated at each stage. Therefore, we propose two noncancellation multistage (NCMS) algorithms, referred
to as NCMS-FKMA and NCMS-TSEA, that are free from the error
propagation effects.

In this thesis, the FKMA is further applied to blind multiuser detection and blind space-time decoding (BSTD) for multicarrier code-division multiple access (MC-CDMA) systems. Assuming that all the users' spreading sequences are given emph{a priori}, a blind multiuser detection algorithm (BMDA), which comprises FKMA and a user identification algorithm, for the uplink of a quasi-synchronous modified MC-CDMA system (with multiple receive
antennas) and a BSTD algorithm, which comprises FKMA and blind maximum ratio combining (BMRC), for the down-link of a space-time coded MC-CDMA system (with multiple transmit and receive antennas used) are proposed.

Moreover, the FKMA is applied to blind multiuser detection for asynchronous multi-rate direct sequence/code division multiple access (DS/CDMA) systems. The ideas are to properly formulate discrete-time multiple-input multiple-output (MIMO) signal models by converting real multi-rate users into single-rate virtual users, followed by the use of FKMA for extraction of virtual users' data sequences associated with the desired user, and recovery of the data sequence of the desired user from estimated virtual users' data sequences. Therefore, two multi-rate BMDAs (with either a single receive antenna or multiple receive antennas), which also enjoy the merits of super-exponential
convergence rate and guaranteed convergence of the FKMA, are
proposed in the thesis, one based on a convolutional MIMO signal model and the other based on an instantaneous MIMO signal model.

For blind co-channel interference and intersymbol interference (ISI) reduction in cellular wireless communications, the FKMA is applied to the design of the conventional cascade space-time receiver (CSTR) in this thesis. However, the receiver performance is limited as the normalized kurtosis magnitude of the ISI-distorted signal of interest is small. Then a blind turbo space-time receiver (TSTR) is further proposed that applies spatial and temporal processing using FKMA in a cyclic fashion to
estimate the desired data sequence. The performance of the
proposed blind TSTR is insensitive to the value of the normalized kurtosis magnitude of the ISI-distorted signal of interest, and therefore is superior to that of the blind CSTR.

This thesis also considers blind beamforming of multiuser
orthogonal frequency division multiplexing (OFDM) systems.
Assuming that the channel is static within one OFDM block, a blind beamforming algorithm by kurtosis maximization based on subcarrier averaging over one OFDM block is proposed, which basically comprises source extraction, time delay estimation and compensation, classification, and BMRC. The designed beamformer is exactly the same for all the subcarriers, effectively utilizes multipath diversity for performance gain, and is robust against the effects of correlated sources. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed blind source separation algorithms, BMDAs, BSTD algorithm, blind CSTR and TSTR, and blind beamforming algorithm.

並列關鍵字

blind source separation ； kurtosis maximization ； multiple-input multiple-output (MIMO) ； turbo source extraction algorithm (TSEA) ； multistage successive cancellation (MSC) ； noncancellation multistage (NCMS) algorithms ； multicarrier code-division multiple access (MC-CDMA) systems ； multi-rate direct sequence/code division multiple access (DS/CDMA) systems ； orthogonal frequency division multiplexing (OFDM) systems ； blind multiuser detection algorithm (BMDA) ； blind space-time decoding (BSTD) algorithm ； blind cascade space-time receiver (CSTR) ； blind turbo space-time receiver (TSTR) ； blind beamforming algorithm

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