最大化稀疏碼多重接取星座點之最小歐幾里得距離之碼書設計

Abstract

稀疏碼多重接取是一種基於碼書架構下的非正交多重接取技術，近年來受到了研究的關注。因為碼書的選擇高度影響著系統的性能，有關於稀疏碼多重接取碼書設計的問題也已經得到了一定程度上研究。儘管能預期隨著具有更大的最小歐幾里德距離，稀疏碼多重接取碼書可以獲得更好的位元錯誤率性能表現，但根據作者所知的稀疏碼多重接取文獻中，至今仍然沒有針對最小歐幾里德距離最大化來設計的最佳化稀疏碼多重接取碼書。 在這篇論文當中，為了解決這個問題，我們首先推導出來最小歐幾里德距離最大化問題的拉格朗日偶題，藉此來得到原始問題的最佳值之上限。其次，我們提出了一種基於凸迭代的演算法，該演算法至少在某些特殊情況下證明了，所設計出來的最佳化碼書與其拉格朗日偶題，兩者的最佳值是匹配的。 在模擬結果中更加確認了本論文所提出的碼書，其最小歐幾里德距離確實達到了最佳值，並且在現有存在的碼書中，有著最佳的位元錯誤率性能表現。 然而，在一般情況下，尋找最佳密碼本仍然是一個懸而未決的問題，需要進一步的研究。

Sparse code multiple access (SCMA), as a codebook-based non-orthogonal multiple access (NOMA) technique, has received research attention in recent years. The codebook design problem for SCMA has also been studied to some extent since codebook choices are highly related to system performance. While an SCMA codebook with a larger minimum Euclidean distance (MED) is expected to obtain a better BER performance, no optimal SCMA codebook in terms of MED maximization, to the authors' best knowledge, has been reported in the SCMA literature yet. In this thesis, we approach this problem by first deriving the Lagrange dual of the MED maximization problem to get the upper bound of the optimal value for the primal problem. Secondly, we proposed a convex iteration-based algorithm that proves, at least in some special cases, to obtain an optimal codebook design whose optimal value matches that of the dual problem. Simulation results confirm that the proposed codebook indeed reaches the optimal value and has the best BER performance among all existing codebook designs. The search for optimal codebook in the general case, however, is still an open question that requires future investigations.