本篇論文提出在高都普勒頻移影響下對於正交時頻空間調變(OTFS)架構的壓縮感知通道估計方法。在高移動性通訊下，接收端為了降低延遲並維持負載平衡，除了要求方法的估計性能之外，我們還更進一步減少執行時間。使得提出的方法只需要大幅降低的執行時間，但是仍然有著幾乎相等的誤碼率表現。除此之外，我們還說明了在高都普勒頻移環境之下，例如低軌道衛星通訊，透過將接收訊號補償已知的通道中所有路徑的共同高都普勒頻移之後，我們可以直接使用本論文提出的方法對剩下的訊號做通道估計。
對於第六代行動通訊系統(6G)而言，高移動性通訊是發展的重點之一。在高移動性場景中，處理因為物體間的高速相對運動而造成的高都普勒頻移是通訊系統要面臨的挑戰。對於不適合高移動性通訊的傳統正交分頻多工調變(OFDM)來說，因為高都普勒頻移造成的強大載波間干擾(ICI)是需要額外處理的問題。因此，在這個環境下需要採用一個適合於高移動性通訊的調變技術來進行通訊。正交時頻空間調變(OTFS)是一個在延遲都普勒域放置符元訊號的二維調變，因為每個符元都載在擴散於整個二維時間頻率域的基底上，這讓每個符元都享受著完全通道多樣性，使得其在高移動性場景下有著優秀的表現。另外，因為通道在延遲都普勒域上反映的是物理環境中傳送端、接收端與反射體之間的關係，而反射體通常稀少，使得在延遲都普勒域上的通道響應有著稀疏的特性。然而，因為傳送訊框是有限的長度，這讓通道的都普勒數值可能會被取樣成分數都普勒，使得取樣通道在都普勒軸上有通道擴散的現象。分數都普勒定義為一個路徑的都普勒索引值是由整數部分與分數部分所組成。這讓原先依靠延遲都普勒通道響應在原本整數都普勒下有的稀疏性的通道估計方法面臨挑戰。
壓縮感知是一個用於重新建構稀疏訊號的技術。此技術利用訊號稀疏的特性，得以從較少的觀測訊號還原出整個欲知的訊號。雖然因為在分數都普勒的影響下使得取樣通道在都普勒軸上有通道擴散的現象，但其背後還是一個稀疏的通道。既然通道依舊是稀疏的，透過提升都普勒軸的數值解析度，壓縮感知技術還是能夠被使用。
經由模擬結果得知，在只有一個主導路徑的通道狀況下，基本的正交匹配追蹤(OMP)透過提高都普勒軸的數值解析度就得以達到完美通道資訊下的誤碼率表現。然而，在多個主導路徑的通道狀況下，提高都普勒軸的數值解析度造成壓縮感知中感知矩陣許多行向量(column vector)之間有著高相關性，降低準確分辨出多路徑的感知表現，造成正交匹配追蹤(OMP)的表現不好。為此我們採用多重路徑匹配追蹤(MMP)來達到完美通道資訊下的誤碼率表現。然而，多重路徑匹配追蹤(MMP)的複雜度過高，使得方法難以實用。因此，我們採用已有的降低複雜度的方法-正則化多重路徑匹配追蹤(RMMP)，評估其在執行時間上的改善結果。最後，我們提出改良的方法(Attenuated-RMMP)進一步地減少執行時間。

In this thesis, we propose a compressed sensing channel estimation method for orthogonal time frequency space (OTFS) modulation architecture with high Doppler shift. In order to reduce the latency and maintain the loading balance at the receiver under high mobility communication, we not only require the estimation performance of the method, but also further reduce the running time. Therefore, the proposed method reduces the running time, but still has near bit error rate (BER) performance. In addition, we also show that in the high Doppler shift environment, such as low Earth orbit (LEO) satellite communication, after compensating the known common high Doppler shift of all path in channel to the received signal, we can directly use the proposed method in this thesis to do channel estimation of the remaining signal.
For the sixth generation wireless systems (6G), high mobility communication is one of the key points of development. In high mobility scenario, dealing with the high Doppler shift caused by the high-speed relative motion between physical objects is a challenge to the communication system. For conventional orthogonal frequency division multiplexing (OFDM) which is not suitable for high mobility communication, the strong intercarrier interference (ICI) caused by the high Doppler shift is a problem that needs to be dealt with. Therefore, in this environment, it is necessary to use a modulation technique that is suitable for high mobility communication. Orthogonal time frequency space (OTFS) modulation is a 2D modulation technique that multiplexs data symbols in the delay-Doppler (DD) domain, because each DD domain symbol spreads onto the entire time-frequency (TF) domain, which allows each symbol to enjoy full diversity, making it perform well in high mobility scenario. In addition, because the channel in the DD domain reflects the relationship between the transmitter, the receiver and the reflectors in the physical environment, and the reflectors are usually rare, the channel in the DD domain is usually sparse. However, due to the limited length of the transmission frame, the Doppler value of the channel may be sampled into fractional value, which makes the sampled channel spread along the Doppler axis. The fractional Doppler is defined as the Doppler index of a path, which is composed of the integer part and the fractional part. This challenges the previous channel estimation methods that rely on the sparsity of the DD channel under the original integer Doppler.
Compressed sensing is a technique used to reconstruct a signal that is sparse in some domain. This technique takes advantage of the sparsity of the signal to recover the entire desired signal from fewer samples. Although, under the case of the fractional Doppler, the sampled channel spreads along the Doppler axis, there is still a sparse channel behind it. Since the channel is still sparse, compressed sensing technique can still be used by increasing the resolution of the Doppler value.
According to the results we simulate, under the channel condition that there is only one dominant path, basic orthogonal matching pursuit (OMP) can achieve BER performance of perfect CSI by increasing the resolution of the Doppler value. However, under the channel condition of multiple dominant paths, increasing the resolution of the Doppler value leads to high correlation between many column vectors of the sensing matrix, which reduces the sensing performance of discrimination of multipath, resulting in the poor performance of OMP. Hence, we use multipath matching pursuit (MMP) to achieve BER performance of perfect CSI. However, the computational complexity of MMP is too high, which makes the method impractical. Therefore, we use the existing method to reduce computational complexity which is regularized multipath matching pursuit (RMMP), and evaluate the results of improvement in running time. Finally, we propose a modified version of RMMP (Attenuated-RMMP) to further reduce running time.

Chinese Abstract i
English Abstract iii
Contents vi
1 INTRODUCTION 1
1.1 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Research Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Contribution and Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 BACKGROUNDS 6
2.1 Orthogonal Time Frequency Space (OTFS) Modulation . . . . . . . . . . . . 6
2.1.1 Basic Concept of OTFS . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 OTFS Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Time-varying Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 OTFS Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.5 Characteristic of OTFS . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 OTFS in Presence of the Fractional Doppler . . . . . . . . . . . . . . . . . . 9
2.2.1 OTFS with/without the Fractional Doppler . . . . . . . . . . . . . . 10
2.2.2 Example of the Channel Spreading due to the Fractional Doppler . . 11
2.3 Reduced Cyclic Prefix OTFS (RCP-OTFS) . . . . . . . . . . . . . . . . . . . 12
2.3.1 RCP-OTFS Modulation . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Time-varying Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 RCP-OTFS Demodulation . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.4 Characteristic of RCP-OTFS . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Compensating High Doppler Shift to the Received Signal for RCP-OTFS . . 16
3 COMPRESSED SENSING CHANNEL ESTIMATION 18
3.1 Basic Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 System Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.2 Dictionary of the Delay-Doppler Domain Value and Super-resolution 19
3.1.3 Dictionary of the Effective Channel Matrix . . . . . . . . . . . . . . . 20
3.1.4 Sensing Matrix in Compressed Sensing for RCP-OTFS . . . . . . . . 21
3.2 Orthogonal Matching Pursuit (OMP) . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Multipath Matching Pursuit (MMP) . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Regularized Multipath Matching Pursuit (RMMP) and its Modified Version 25
3.4.1 Regularized Multipath Matching Pursuit (RMMP) . . . . . . . . . . 25
3.4.2 Attenuated-RMMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 SIMULATION RESULTS 32
4.1 Basic Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Single Dominant Path Channel . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Performance of OMP . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Multiple Dominant Paths Channel . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.1 Problem of the Sensing Matrix by using the Doppler Super-resolution 36
4.3.2 Performance of OMP and MMP . . . . . . . . . . . . . . . . . . . . . 37
4.3.3 Performance of OMP, MMP and RMMP . . . . . . . . . . . . . . . . 40
4.3.4 Performance of RMMP and Attenuated-RMMP . . . . . . . . . . . . 42
4.3.5 Performance of Attenuated-RMMP without setting the Iteration Number 44
4.3.6 Performance of MMP, RMMP and Attenuated-RMMP with different Super-resolution Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.7 Tradeoff between BER and Running Time . . . . . . . . . . . . . . . 48
5 CONCLUSION 49
Bibliography 50

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