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作者(中文):林釗翬
作者(外文):Lin, Chao-Hui
論文名稱(中文):基於半正定放寬輔以晶格正交化之多輸入多輸出檢測
論文名稱(外文):Lattice-Reduction-aided Semidefinite Relaxation Approach to MIMO Detection
指導教授(中文):吳仁銘
指導教授(外文):Wu, Jen-Ming
學位類別:碩士
校院名稱:國立清華大學
系所名稱:電機工程學系
學號:9761516
出版年(民國):99
畢業學年度:98
語文別:英文
論文頁數:45
中文關鍵詞:半正定放寬晶格正交化多輸入多輸出系統
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經由觀察得知基於半正定放寬(semidefinite relaxation)方法運用於高階正交振幅調變(quadrature amplitude modulation)之多輸入多輸出(multiple-input multiple-output)檢測法存在多樣性不足的問題,特別是在接收天線數目不夠大(小於八根)的時候情況特別明顯。另一方面,輔以晶格正交化(lattice reduction)的多輸入多輸出系統檢測方法被證實可以達到最大的接收多樣性(receive diversity)。因此,這裡提出了一個不一樣的半正定放寬輔以Lenstra, Lenstra, and Lovasz (LLL) 晶格正交方法去獲得系統檢測上的多樣性。由於使用一般常見的解半正定程式軟體去解半正定放寬輔以晶格正交問題的計算複雜度太高,所以我們提出了一個特殊的內點演算法(interior-point)去解此特定問題。除此之外,我們將基於通道特性的終止機制應用到此特殊內點演算法裡,不同的是,這是一個針對高階正交振幅調變延伸而得的機制。結果顯示,此機制亦可以減少內點演算法的重複次數使得整體的運算時間更加減少而不影響其錯誤機率的表現。
Abstract i
Contents ii

1 Introduction 1
1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 System Model 4

3 Lattice-Reduction-Aided Detection 6
3.1 Lattice Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Lattice-Reduction-Aided Linear Detection . . . . . . . . . . . . . . . . . . . 7

4 Semidefinite Relaxation Approaches and Interior-Point Algorithm 10
4.1 Semidefinite Relaxation Approaches . . . . . . . . . . . . . . . . . . . . . . . 10
4.1.1 Polynomial Inspired SDR (PI-SDR) . . . . . . . . . . . . . . . . . . . 10
4.1.2 Bound Constrained SDR (BC-SDR) . . . . . . . . . . . . . . . . . . . 12
4.1.3 Other SDR detectors and Relations . . . . . . . . . . . . . . . . . . . 12
4.2 Interior-Point Method (IPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.1 Helmberg-Kojima-Monteiro (HKM) Interior-Point Method . . . . . . 14
4.2.2 Specialized IPM for BC-SDR . . . . . . . . . . . . . . . . . . . . . . 17
4.2.3 Channel Dependent Termination of the SDR . . . . . . . . . . . . . . 18

5 Lattice-Reduction-aided Semidefinite Relaxation approach to MIMO detection
21
5.1 Lattice-Reduction-aided Semidefinite Relaxation . . . . . . . . . . . . . . . . 21
5.2 Specialized IPM for LR-aided SDR . . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Channel dependent adaptive approach . . . . . . . . . . . . . . . . . . . . . 24

6 Simulation Results 28
6.1 SER performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Computational complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7 Conclusion 36

A Unconstrained element-wise quantization 37
B Derivation of specilaized IPM for the LR-aided SDR 38
C Derivation of channel dependent termination for the LR-aided SDR 40
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