在多天線的系統中，為了減少射頻鏈的使用數，我們採用混合式波束成型的系統架構，並且套用了正交分頻多工來使頻帶的使用更有效率。而在此系統中的通道估測可以表示為一個張量分解的問題。張量為一個高維度下的資料表示型態，我們可以利用Tucker分解法與CANDECOMP/PARAFAC(CP)分解法來將高維度張量做分解，與一般單一維度的向量相比較，使用張量是可以將計算量簡化，因此我們將採用張量的系統模型來完成通道估測。在本論文中，我們比較了4種演算法，分別為tensor-orthogonal matching pursuit with joint search(T-OMP-JS)、tensor-orthogonal matching pursuit with sequential search(T-OMP-SS)、CP分解法與我們所提出的tensor-orthogonal matching pursuit with rotation (T-OMP-R)，在T-OMP-JS與T-OMP-SS中，它們使用的是Tucker分解法，將原始通道張量投影在各維度上的因子矩陣，利用相關性找索引值。CP分解法，則是定義出各維度上的因子矩陣然後將原始通道張量拆解成多個單秩張量，接著使用交替最小平方法估測通道參數，而本論文提出了T-OMP-R與張量融合演算法，使用的是Tucker分解法，此方法中，我們將使用4種相移器組合來估測通道，這些組合分別是為了估測特定方向的通道所設計的，在計算OMP的過程中為了利用通道的稀疏性，我們加入了旋轉矩陣來調整碼簿，並在加入了通道估測結果融合的機制，此機制可以將錯誤的索引值進行修正，進而提升我們估測的效能，在角度解析度2-10下，通道估測誤差的NMSE可達10-4。最後，我們比較了各個演算法所需要的乘法運算量以及估測結果誤差，由這些模擬結果我們可以知道T-OMP-R不但能夠節省計算所需要的複雜度，是T-OMP-SS的33%，是CP分解法的42%，同時也有相當優異的估測結果。;In order to reduce the number of RF chains, hybrid beamforming systems are widely regarded as a promising solution. Orthogonal frequency division multiplexing (OFDM) is also efficient for frequency band utilization. Channel estimation in MIMO-OFDM hybrid beamforming systems can be formulated as a tensor decompo-sition problem where tensor is a high-dimensional data representation. Tucker de-composition and CANDECOMP/PARAFAC(CP) decomposition are often used to de-compose the high-dimensional tensors and simplify the computations by exploiting the channel sparsity. In this paper, we compare 4 algorithms, namely ten-sor-orthogonal matching pursuit (T-OMP) with joint search (T-OMP-JS), T-OMP with sequential search(T-OMP-SS), CP decomposition-based method and our proposed T-OMP with rotation(T-OMP-R). The proposed T-OMP-R uses Tucker decomposition method and we adopt the rotation matrix to adjust the codebook so that we can take advantage of the channel sparsity to reduce complexity. Tensor fusion mechanism is also proposed as the last step to correct the wrong index pairs and to enhance the estimation performance. From the simulation results, the channel estimation NMSE of the proposed T-OMP-R with tensor fusion can achieve 10-4 with a resolution of 2-10 in AOA and AOD. The complexity of the algorithms are evaluated and compared in terms of the number of multiplications required by these algorithms. We show that the complexity of T-OMP-R is only 33% of T-OMP-SS and 42% of the CP algorithm. Hence, the proposed T-OMP-R not only saves the complexity of the calculations, but also has a good estimated result.
