從過去的研究結果顯示，很多目前使用的通訊系統是可以單用一個整合型的多重速率濾波器組傳收機模型建置完成。在文獻上，利用這個整合型的多重速率濾波器組傳收機模型來實現一個具冗餘資料量的區塊傳輸系統，我們通常稱為多重輸入多重輸出(Multiple-Input-Multiple-Output, MIMO)系統。本篇論文將利用所提出的斜投影架構，針對多輸入多輸出系統在具完美重建(Perfect Reconstruction, PR)通道下，設計一個最佳的單區塊基底的前置編碼器及其相對應的等化器。我們特別探討在一個有限傳送功率的數位通訊系統鏈結中最感興趣的兩個衡量標準，即平均位元錯誤率的最小化與相互資訊量的最大化。本篇論文的研究架構發展如下。
首先，針對一個使用單區塊基底前置編碼器的系統，我們將建立一個接收訊號模型能相容於堆零(Trailing Zeros, TZ)與循環前置(Cyclic-Prefix, CP)兩種冗餘資料形式。然後，針對區塊傳輸系統(即多輸入多輸出系統)，我們利用斜投影的特性，提出一個串接式等化器(Cascaded equalizer)。在這個串接式等化器的實現機制中，區塊間干擾將可以先被斜投影完整地消除，爾後伴隨提供一具自由度矩陣來等化區塊內的符碼間干擾。當傳送端具有完整通道資訊，且在無符碼間干擾與有限傳送功率的條件限制下，我們將利用所提出串接式等化器中的自由度矩陣，設計一個能滿足最低平均位元錯誤率(或最大相互資訊量)的最佳單區塊基底前置編碼器。於是，這個能滿足無符碼間干擾條件的串接式等化器變成一個串接式迫零(Zero-forcing, ZF)等化器。藉由理論的推導證實與模擬的結果顯示，本篇論文所提出的設計架構，不但在具充份冗餘資料量的環境下可以與過去文獻結果保持相同的錯誤率及相互資訊量，並且可以將文獻上的結果延伸至不具充份冗餘資料量的區塊傳輸環境。

Previous studies have demonstrated that many existing communication systems can be formulated within a unified multirate filterbank transceiver model. A redundant block transmission system implemented via this unified multirate filterbank transceiver model is usually known as a multiple-input-multiple-output (MIMO) system in literature. This dissertation devises an optimum linear block-based precoder and the corresponding equalizer for MIMO systems over perfect reconstruction (PR) channels by exploiting the proposed oblique projection framework. Particularly, two main criteria of interest in a digital communication link with limited transmission power are investigated, namely, average bit error rate (BER) minimization and mutual information rate maximization. The study framework is developed as follows. For a block-based precoder, a received signal model is formulated for the two redundancy schemes, viz., trailing-zeros (TZ) and cyclic-prefix (CP). By exploiting the property of oblique projection, a cascaded equalizer for block transmission systems (i.e., MIMO systems) is proposed and implemented with a scheme, in which the inter-block interference (IBI) is completely eliminated by the oblique projection and followed by a matrix degree of freedom for inter-symbol interference (ISI) equalization. With the available channel state information at the transmitter side, the matrix for ISI equalization of the cascaded equalizer is utilized to design an optimum linear block-based precoder, such that the BER is minimized (or the mutual information rate is maximized), subject to the ISI-free and the transmission power constraints. Accordingly, the cascaded equalizer with the ISI-free constraint yields a cascaded ZF equalizer. Theoretical derivations and simulation results confirm that the proposed framework not only retains identical BER and information rate performances to previous works for cases with sufficient redundancy, but also allows their results to be extended to the cases of insufficient redundancy.

Chapter 1 Introduction ..1
1.1 Literature survey ..2
1.2 Problem statement and objective of this dissertation ..7
1.3 Organization of this dissertation ..9
Chapter 2 Zero-Forcing Equalizer for Redundant Block Transmissions ..12
2.1 Introduction ..12
2.2 Signal model for redundant block transmissions ..13
2.2.1 General block transmission signal model ..13
2.2.2 Signal model for block-based precoding ..15
2.3 Zero-forcing equalizer with oblique projection ..18
2.3.1 Oblique projections ..18
2.3.2 The zero-forcing equalizer for block transmission systems ..18
2.4 Decomposition of the zero-forcing equalizer ..22
2.5 Remarks ..23
2.6 Computer simulations ..26
2.7 Summary ..30
Chapter 3 Minimum BER Block-Based Precoder Design for Zero-Forcing Equalization ..38
3.1 Introduction ..38
3.2 New equalizing scheme and minimum BER precoder design ..39
3.2.1 A new equalizing scheme ..39
3.2.2 Minimum BER precoder ..41
3.3 Remarks ..47
3.4 Computer simulations ..48
3.5 Summary ..51
Chapter 4 Maximum Information Rate Block-Based Precoder Design with Cascaded Equalizer ..59
4.1 Introduction ..59
4.2 Maximum information rate precoder design ..60
4.2.1 Lemma of maximum information rate for block transmissions ..60
4.2.2 Maximum information rate precoder ..61
4.3 Remarks ..63
4.4 Computer simulations ..64
4.5 Summary ..67
Chapter 5 Concluding Remarks ..77
Appendix A Derivation of the equivalency of the BER performance indicated in Fig. 3.2(b) and Fig. 3.2(c) 81
Appendix B Proof of Theorem 3 ..83
Bibliography ..84

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