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研究生：	賈鈞傑 Jia, Jiun-Jie
論文名稱：	應用於單載波區塊傳送系統和空間多工系統之樹狀搜尋訊號偵測演算法 Tree Search Detection Algorithms for Equalizing Single-Carrier Block Transmission Signals and Separating Spatially Multiplexed Signals
指導教授：	賴癸江 Lai, Kuei-Chiang
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 電腦與通信工程研究所 Institute of Computer & Communication Engineering
論文出版年：	2016
畢業學年度：	105
語文別：	英文
論文頁數：	115
中文關鍵詞：	單載波區塊傳送系統、混域式序列偵測器、頻域前置濾波器、樹狀搜尋演算法、平行混域式決策回授等化器、多輸入多輸出偵測器、球體解碼
外文關鍵詞：	single-carrier block transmission, hybrid-domain sequence detector, frequency-domain pre-filtering, tree search, parallel hybrid decision feedback equalizer, MIMO detection, sphere decoding
相關次數：	點閱：238 下載：5
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在本論文中，我們提出有效率的樹狀搜尋偵測演算法來消除下列兩種在無線通訊系統中常見的信號間干擾：(1)在單載波區塊傳送系統中，由多路徑通道造成的符元間干擾，以及(2)在多輸入多輸出系統中，由空間多工信號傳輸造成的天線間干擾。
在單載波區塊傳送系統中常使用頻域等化器處理符元間干擾，因其整體複雜度較時域等化器低。然而，在文獻中之頻域等化器僅限於非序列信號偵測器；例如，頻域線性等化器、迭代區塊回授等化器、與結合頻域前饋濾波器和時域回授等化器的混域式決策回授等化器。雖然上述之頻域等化器整體複雜度較低，但在偵測效能的表現上，與效能最佳但複雜度亦最高的最大概似偵測器相比仍有一段不小的差距。為了提升偵測效能並且保有頻域等化器低複雜度的優點，在本論文中我們提出下列兩種適用在單載波區塊傳送系統之混域式序列偵測演算法。
我們所提出之第一個混域式序列偵測演算法稱作FDF-M演算法，其結合頻域前置濾波器和使用M-演算法的時域樹狀搜尋偵測器。FDF-M演算法與傳統之全時域樹狀搜尋偵測器(例如QRD-M演算法和球狀解碼演算法)有相近的偵測效能，但整體複雜度降低甚多。由於FDF-M演算法在樹狀搜尋中使用M演算法，使得在使用高階調變時，FDF-M演算法的複雜度仍頗高，並且M演算法在硬體執行上無法完全地平行處理。為了解決上述問題，我們提出第二個混域式序列偵測演算法，稱之平行混域式決策回授等化器。平行混域式決策回授等化器是根據決策變數的可靠度，適當地決定其運作模式是使用一組決策回授等化器還是多組平行的決策回授等化器來做決策。模擬結果顯示在適度的訊雜比下，平行混域式決策回授等化器僅需較混域式決策回授等化器增加少量的複雜度，即可有效提升偵測效能。另外，在高訊雜比和靜態通道的條件下，使用四位元相位偏移為調變信號時，我們分析了平行混域式決策回授等化器之符元錯誤率，其考慮因素包含錯誤蔓延和殘餘信號間干擾的效應。模擬結果顯示我們所做的理論錯誤率分析與模擬結果相近。
對於多輸入多輸出系統，我們提出具有最大概似偵測器效能之混合式樹狀搜尋演算法。為了降低樹狀搜尋的複雜度，混合式樹狀搜尋演算法的作法是先以廣度優先的搜尋方法逐層向下搜尋，直到最可能之路徑的正確性超過預先設定之門檻，才使用深度優先的搜尋方法搜尋剩餘之可能路徑。因此，相較於球狀解碼演算法一開始即採用深度優先的搜尋方法向下搜尋，混合式樹狀搜尋演算法利用廣度優先的搜尋方法來增加深度優先搜尋方法向下搜尋方向的正確性。模擬結果顯示我們所提出之混合式樹狀搜尋演算，與球狀解碼演算法相比，僅需增加適當的記憶量下，即可以較低之複雜度達成相同之偵測效能。

In this dissertation, we propose efficient tree search detection algorithms to combat two types of interference that commonly arises in wireless communication systems: (i) inter-symbol interference (ISI) in the single-carrier block transmission (SCBT) systems in frequency-selective channels, and (ii) inter-antenna interference (IAI) in spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems.
For SCBT systems, a conventional, low-complexity approach to ISI mitigation is to use frequency-domain equalization (FDE). However, FDE in the literature is limited to symbol-by-symbol detection only, such as the frequency-domain linear equalizer, iterative block decision feedback equalizer (IBDFE), as well as the hybrid decision feedback equalizer (HDFE) that combines a frequency-domain feedforward filter and a time-domain feedback filter. Although with a low complexity, the performance of these detectors considerably lag behind that of the optimal maximum-likelihood sequence detector (MLSD). To improve the performance of symbol-by-symbol detectors while preserving the implementation advantages of FDE, we propose in this dissertation two hybrid-domain sequence detectors.
The first one, referred to as the FDF-M algorithm, combines FD prefiltering with time-domain tree search using the M-algorithm. The proposed FDF-M algorithm achieves a detection performance that is very close to that of the conventional time-domain sequence detectors (which employ the QRD-M or sphere decoding algorithm), but with a much lower complexity. Due to running the M-algorithm, however, the complexity of FDF-M is still quite high (with respect to that of HDFE) for high-order modulation, and the tree search stage does not exhibit a high degree of parallelism. To address these issues, we propose the second hybrid-domain sequence detector, referred to as the parallel HDFE (P-HDFE) algorithm. It adaptively operates, based on the reliability of the decision variable, as an ordinary HDFE or a tree search detector constructed by multiple HDFEs that run in parallel. Our study shows that, at moderate to high signal-to-noise ratios (SNRs), P-HDFE significantly outperforms HDFE with little increase in complexity. We analyze the symbol-error rate of P-HDFE at high SNRs for the case of quaternary phase-shift keying and static ISI channels, accounting for error propagation and residual ISI. Simulations demonstrate the accuracy of the analysis.
For MIMO systems, hybrid tree search algorithms for maximum likelihood symbol detection are described. Essentially, the search tree is iteratively expanded in the breadth-first (BF) manner until the probability that the current most likely path is correct exceeds the specified threshold, at which point the depth-first (DF) stage is initiated to traverse the rest of the tree.
In contrast to the sphere decoding algorithm (SDA), which starts off with the DF search, the proposed algorithms use the BF stage to enhance the accuracy of the initial DF search direction, by exploiting the diversity inherent in the SM scheme. Simulation results demonstrate that, with a moderate increase in the memory requirement, the proposed algorithms achieve a significantly lower complexity than the SDA in many scenarios.

Introduction 1
1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Equalization of SCBT Signals . . . . . . . . . . . . . . . . . . 1
1.1.1 Overview of SCBT Signals . . . . . . . . . . . . . . . 2
1.1.2 Motivation of Proposed Research in SCBT Equalization. . . . . . . . . 2
1.2 Separation of Spatially Multiplexed Signals . . . . . . . . . . . 4
1.2.1 Motivation of Proposed Research in MIMO Detection . . . . 4
2 Organization and Contributions of the Dissertation . . . . . . . . . . 5
SCBT Signal Model and Related Works in Equalization 8
1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Symbol-by-symbol Detector for SCBT . . . . . . . . . . . . . . . . . 10
2.1 Review of FD-LE . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Review of HDFE . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 ZF-HDFE . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 MMSE-HDFE . . . . . . . . . . . . . . . . . . . . . 14
3 Sequence Detector for SCBT . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 ML Detection via Tree Search . . . . . . . . . . . . . . . . . . 14
3.2 Review of MLSD-SDA Algorithm . . . . . . . . . . . . . . . . 16
3.3 Review of QRD-M-based Algorithms . . . . . . . . . . . . . . 18
3.3.1 QRD-M Algorithm [1], [2] . . . . . . . . . . . . . . . 18
3.3.2 Combining QRD-M with Lattice Reduction-Aided
(LRA) Linear Detector [3] . . . . . . . . . . . . . . . 18
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Hybrid-Domain Sequence Detector: FDF-M Algorithm 20
1 Proposed FDF-M Algorithm . . . . . . . . . . . . . . . . . . . . . . . 20
1.1 Motivation: Tree Search without QRD . . . . . . . . . . . . . 20
1.1.1 Cause of Performance Loss in DM Algorithm . . . . 21
1.2 FDF-M Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 24
1.2.1 Derivation of Prefilter . . . . . . . . . . . . . . . . . 27
1.2.2 FD Implementation of the Prefilter . . . . . . . . . . 29
1.3 Summary of Proposed FDF-M Algorithm (to Equalize a Single
Block) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.4.1 Effect of Non-white Prefiltered Noise . . . . . . . . . 31
1.4.2 Effect of Lu on the Maximum Value of CSNR . . . . 32
1.4.3 Special Case of Prefilter for Lu=1 . . . . . . . . . . . 32
1.4.4 Feasibility of Other Possible Structures of U . . . . . 33
1.5 Relation to Other Known Schemes . . . . . . . . . . . . . . . 33
1.5.1 Comparison with [4] . . . . . . . . . . . . . . . . . . 33
1.5.2 Comparison with ZF-HDFE [5] . . . . . . . . . . . . 34
2 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1 QRD-M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2 FDF-M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 MMSE-HDFE . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1 Channel I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Detection Performance . . . . . . . . . . . . . . . . . 39
3.1.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.3 The Effect of Lu on BER and Complexity . . . . . . 44
3.2 Channel II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Hybrid-Domain Parallel Decision Feedback Equalization 47
1 Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.1 Operations in the Erasure Mode . . . . . . . . . . . . . . . . . 50
2 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.1 Signal Model of Decision Variable ˜xi . . . . . . . . . . . . . . 53
2.1.1 Interpretation of Error Energy as Path Metric in
Tree Search Detector . . . . . . . . . . . . . . . . . . 55
2.2 SER Analysis for MMSE-P-HDFE . . . . . . . . . . . . . . . 56
2.2.1 Derivation of P(e|NEZ) . . . . . . . . . . . . . . . . 57
2.2.2 Derivation of P(e|	, EZ) and P(e|¯	, EZ) . . . . . . . 58
2.2.3 Derivation of P(¯	 |EZ) and P(	|EZ) . . . . . . . . . 59
2.2.4 Derivation of β . . . . . . . . . . . . . . . . . . . . . 60
2.3 SER Analysis for ZF-P-HDFE . . . . . . . . . . . . . . . . . . 60
2.3.1 Derivation of P(e|NEZ) . . . . . . . . . . . . . . . . 61
2.3.2 Derivation of P(e|	, EZ) and P(e|¯	, EZ) . . . . . . . 61
2.3.3 Derivation of P(¯	 |EZ) and P(	|EZ) . . . . . . . . . 62
2.3.4 Derivation of β . . . . . . . . . . . . . . . . . . . . . 62
3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.1 HDFE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 P-HDFE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1 Channel 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.1 Accuracy of SER Analysis . . . . . . . . . . . . . . . 65
4.1.2 Detection Performance . . . . . . . . . . . . . . . . . 68
4.1.3 Complexity . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Channel 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Hybrid Tree Search Algorithms for Detection in Spatial Multiplexing
Systems 75
1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2 Review of Search Tree Representation and SDA . . . . . . . . . . . . 76
2.1 Brute-Force ML Detection via Tree Search . . . . . . . . . . . 76
2.2 SDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3 Proposed Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.1 FBF-SDF: Prototype . . . . . . . . . . . . . . . . . . . . . . . 79
3.1.1 Conceptual Description . . . . . . . . . . . . . . . . 79
3.1.2 Sort-Free Implementation . . . . . . . . . . . . . . . 80
3.1.3 Memory Requirement . . . . . . . . . . . . . . . . . 81
3.1.4 Brief Theoretical Justification . . . . . . . . . . . . . 82
3.2 AFBF-SDF: Adapting FBF-SDF . . . . . . . . . . . . . . . . 83
3.2.1 Conceptual Description . . . . . . . . . . . . . . . . 83
3.2.2 Derivation of the Reliability Index . . . . . . . . . . 83
3.2.3 Approximation of the Reliability Index . . . . . . . . 84
3.2.4 Sort-Free Implementation and Memory Requirement 85
3.3 ARBF-SDF: Trading ML Performance for Further Complexity
Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.1 Complexity Comparison at High SNRs . . . . . . . . . . . . . 87
4.2 Performance and Average Complexity versus SNR . . . . . . . 94
5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Conclusions and Future Works 95
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A Derivation of (3.16) 99
B 101
B.1 Proof of (4.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B.2 SER expression in (4.2) . . . . . . . . . . . . . . . . . . . . . . . . . . 102
B.3 Derivation of P(ǫIi|ǫi) and P(ǫQi |ǫi) for the non-erasure mode . . . . . 103
B.4 Derivation of (4.24) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
B.5 Derivation of Pez for MMSE-P-HDFE . . . . . . . . . . . . . . . . . . 105
B.6 Derivation of Pez for ZF-P-HDFE . . . . . . . . . . . . . . . . . . . . 106
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