由於巨量天線多輸入多輸出系統(Massive MIMO)為下一代通訊系統之關鍵技術，資料串流數也會大幅提升。傳統全類比前編碼架構僅支援單一資料串流數，無法應用於下一代通訊系統。而若使用全數位前編碼架構，在數位端的運算複雜度將會因為資料串流數的上升而大幅上升，因此有混合式前編碼架構的提出，將前編碼兩部分，類比端以數位控制相移器(phase shifter, PS)在射頻(radio frequency)來分擔數位在基頻的運算複雜度。本論文中首先參考單一使用者混合式前編碼系統之參考文獻後進行改良，進而在效能評估與硬體複雜度上做取捨。而針對多使用者混合式前編碼系統，在本論文中分別則提出考量數位前編碼運算的遞迴演算法，同時以特徵值分解取得類比前編碼區塊所需之相位以及以訓練碼簿(codebook)的方式來實現。而數位前編碼區塊則採用奇異值分解之區塊對角化來消除使用者間的通道干擾。 而由於頻寬需求，下世代系統載波波段朝向毫米波(millimeter wave)移動，毫米波通道在巨量天線下，通道矩陣會擁有低秩數(low-rank)的特性，而造成矩陣缺陷。我們利用QR分解與Hessenberg分解來找尋缺陷矩陣的特徵向量。利用零特徵值對應的特徵向量來消除通道對於不同使用者的干擾，並找尋最大特徵值所對應的特徵向量來計算類比前編碼矩陣所需之相位。預計設計一套硬體來處理缺陷矩陣，可視需要計算零特徵值與最大特徵值所對應之特徵向量，主要利用CORDIC來實現QR分解與Hessenberg reduction來，並以Matlab模擬硬體行為，針對16×16的複數矩陣，操作1次Hessberg分解以及3次的QR分解獲取3組最大特徵值所對應之特徵向量，所需的操作時脈約為3580個週期。 ;Massive multiple-input multiple-output (Massive MIMO) is a key technique in the next-generation communication systems. The number of data streams will increase greatly. Traditional full analog precoding architecture supports only one data stream and thus it can not meet the requirements. However, the complexity and power consumption of full digital precoding is too high to be afforded. Consequently, the hybrid beamforming architecture that combines analog precoding and digital precoding has been proposed. In this thesis, we combine two algorithms in literature to support single-user hybrid beamforming and to tradeoff performance and complexity. For multi-user hybrid beamforming, an iterative algorithm that considers digital precoding inside the loop is proposed. Both eigenvalue decomposition and codebook are used to set the phases of the analog precoder. The block diagonalization is adopted for digital precoder to cancel the interference among users. The millimeter wave channel matrix has the low-rank property, namely the rank-deficient matrix. We combine QR decomposition and Hessenberg reduction to find either eigenvectors corresponding to zero eigenvalues or eigenvectors corresponding to the largest eigenvalues. A hardware is designed to handle rank-deficient matrix and to support these two functions simultaneously based on CORDIC modules. For a 16×16 channel matrix, it takes about 3580 clock cycles to compute one Hessenberg reduction and QR decomposition for three times.
