本論文將排列陣列應用在物理層和跨層通訊，並提出低複雜度的解碼器。在物理層，我們將排列陣列對應到天線，進而傳送位元，稱為排列空間調變。在跨層通訊，我們將排列陣列對應到網路層的傳輸路徑，進而傳送資料，稱為路徑排列編碼。
本論文首先分析排列空間調變在使用單一天線情況，以及在開啟多根天線的情況，並分析了不同開啟天線下的排列空間調變的最大似然解碼，並提出適用於排列空間調變的球形解碼，以降低解碼時複雜度，在同樣的位元錯誤率下球形解碼相較於最大似然解碼省了近75%的拜訪節點。
在路徑排列編碼的部分，我們分析了在快通道下使用多條路徑的情形。我們分析了路徑排列編碼在使用最大後置機率判定法則與對數化最大後置機率判定法則的複雜度，並提出適用於路徑排列編碼的球形解碼，以降低解碼時複雜度。分析的結果，球形解碼與使用最大後置機率判定法則與對數化最大後置機率判定法則的解碼相比，在同樣的位元錯誤率下球形解碼相較於兩者節省了近30%的拜訪節點。
除此之外我們也提出旋轉保護可以進一步的改善排列傳輸在排列空間調變及路徑排列編碼之間的效能。對於排列陣列，我們提出排列陣列的設計與編碼，並有效降低空間相關性對系統的影響，提供了更好的效能。

This thesis applies the permutation array to the physical layer and cross-layer communication, and proposes a low-complexity decoder. At the physical layer, we associate the permutation array with the antenna, and then transmit bits, which is called spatial permutation modulation. In cross-layer communication, we will arrange the array to correspond to the transmission path of the network layer, and then transmit data, which is called path permutation code.
The thesis is first to analyze the fast fading physical layer communication which activate only one transmit antenna. We analyzed the maximum likelihood decoding of spatial permutation modulation and proposed sphere decoding to reduce the complexity of decoding. Under the same bit error rate, the sphere decoding is compared with the maximum likelihood decoding. It saves nearly 75% of visited nodes.
In the part of path permutation coding, we analyzed the situation of using multiple paths in the fast fading. We analyzed the complexity of path permutation code using the maximum a posterior probability criterion and logarithmic maximum a posterior probability criterion, and proposed a sphere decoding suitable for path permutation coding to reduce the complexity of decoding. As a result of the analysis, the sphere decoding saves nearly 33% compared at the same bit error rate.
In addition, we also propose that rotation protection to improve the performance. Mapping and permutation set design for spatial permutation modulation, which can effectively reduce the impact of spatial correlation on the system and provide better performance.

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