下個世代的行動通訊將會使用到毫米波段的頻譜，在此波段的資料傳輸量將能大幅提升，在如此高的頻段裡，電磁波的波長會變得較短，這也讓我們能在同一個空間內擺入更多天線，然而在如此高頻的環境中要達到足夠的連結增益是一個主要的挑戰，為了要補償在這個頻段裡能量巨大的損失，我們可以在傳送端極接收端裝置大型的天線陣列並使用方向性波束成型，為了要建立一個可靠的通訊行為，我們可以使用波束找尋的技術，此技術是為了達到最佳雜訊比而在傳送及接收端找到最佳的波束配對，然而要找到最佳的波束配對是一件花時間的操作，所以如何用低複雜度做波束配對將會是一個重要的課題，在這邊論文中，我們主要關注於在毫米波段的多輸入多輸出(MIMO)系統中，如何追蹤天線陣列的出射角度與入射角度，在電機電子工程師協會(IEEE)裡的標準及一些學術文獻裡，廣為提到的訓練波束方法是窮盡搜尋法，這個方法是將所有出射角與入射角都進行一次配對，然而此種方法的搜尋時間過長，複雜度也較高，因此又有些資料文獻提出使用適應性的演算法來估測毫米波段通道以緩和此問題，在這篇論文中，我們透過邏輯拼圖的概念，進而提出一種新的波束追蹤法，名為平衡拼圖追蹤法，在這個方法裡有使用到一種分層多解析度的編碼簿，內含不同寬度的波束成型向量，模擬指出，此篇論文中所提到的通道估測法，在高雜訊比的情況下，能降低複雜度，並達到能與二分通道估測法相比較的通道容量，而所需付出的代價為在每次波束訓練的階段裡需多回傳一個位元。

Next generation cellular standards may leverage the large bandwidth available at millimeter wave (mm Wave) frequencies to provide large data rate in outdoor wireless systems. In this high frequency band, the electromagnetic wavelength is much shorter which enable us to pack lots of antennas in a certain area. However, to achieve high link margin is a main challenge. In order to compensate the high path loss, directional beamforming with large antenna arrays can be applied at both transmitter and receiver. To establish a reliable communication, the beam search technique is adopted to identify the optimal transmit-receive beam pair that maximizes the signal-to-noise ratio. Nevertheless, the alignment of transmitter and receiver beams is a time consuming operation so it is important to develop a beam search method which requires less complexity. In this thesis, we focus on the angle of departure (AoD) and angle of arrival (AoA) tracking problem for millimeter wave MIMO channel. In the IEEE standards and the academic literature, the beam training protocol exhaustive search is generally considered. This method search over all possible beam directions for both the transmitter and the receiver. However, this operation requires a long time and high complexity. Another beam training method proposed by some papers uses an adaptive algorithm to estimate the mm wave channel called bisection method has alleviate the problem mentioned above. This thesis has proposed a new beam training method called the balance puzzle method which mimics the concepts of the logic puzzle problem. In this method a novel hierarchical multi-resolution codebook which contains beamforming vectors with different beamwidths is used. Simulation results show that the proposed channel estimation algorithm achieves comparable spectral efficiency compared to the bisection channel training in the high SNR region and can also reduce the complexity with only one more feedback bits in each stage.

摘要 i
Abstract i
Contents iii
1 Introduction 1
2 Background 4
2.1 MIMO and Spatial Multiplexing [1] . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Physical modeling of MIMO channels [1] . . . . . . . . . . . . . . . . . . . . 7
2.3 System Model [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Design of the Codebook Beamforming Vectors for Diffrent Schemes . . . . . 12
2.4.1 The Bisection Beam Search Method 1 [2] . . . . . . . . . . . . . . . . 12
2.4.2 The Bisection Beam Search Method 2 [3] . . . . . . . . . . . . . . . . 17
2.4.3 The Exhaustive Beam Search Method . . . . . . . . . . . . . . . . . 20
3 Proposed Beam Search Scheme 22
iii
3.1 The Balance Puzzle Method Concepts . . . . . . . . . . . . . . . . . . . . . 22
3.2 Generalized to the Power of Two . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 The Balance Puzzle Searching Method . . . . . . . . . . . . . . . . . . . . . 27
3.4 The Equal Threshold & Error cases . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 Comparisons among Diffrent Schemes . . . . . . . . . . . . . . . . . . . . . 34
4 Simulations 36
4.1 The Comparisons of Spectral Effiency and Correct Probability with Diffrent Scheme and Diffrent Threshold . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 The Comparisons of Complexity and Feedback bits with Diffrent Scheme . 40
5 Conclusions 43

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