在非同步的直接序列分碼多路進接系統中（DS-CDMA）系統中，使用者們因其展頻碼非正交且延遲時間不同而相互干擾（multiple access interference）。Verdu於1986年提出以Viterbi演算法進行最佳序列多使用者偵測（sequence-optimum detection），以及用backward-forward dynamic programming來進行最佳符元多使用者偵測（symbol-optimum detection）。其中最佳符元多使用者偵測雖然運算量龐大，但可以達成最小符元錯誤率（symbol error rate）。
著眼於以backward-forward dynamic programming進行的最佳符元多使用者偵測法無法對極長的訊框（frame）做即時性偵測，我們採取滑動窗（sliding window）的觀點，在每個以目標符元為中心的窗內進行最佳符元偵測，並對其時程加以調整簡化，得到我們所提出的縮短式最佳符元多使用者偵測法（truncated symbol-optimum detection）。此一改良演算法使我們可以犧牲一些幾可忽略的位元錯誤率來換取較短的延遲時間和較低的運算量。為了更確信改良演算法之表現與原本最佳符元多使用者偵測幾乎沒有差別，我們對兩個使用者及四個使用者的系統進行模擬，並發現在很短的延遲時間下，即可達成與最佳符元偵測相同的表現。

我們以因子圖（factor graph）的語言來描述以上演算法，並發現其結構及訊息流通方式與心臟收縮式陣列（systolic array）的設計準則有許多相符之處。因此我們以心臟收縮式陣列來實現我們的改良演算法，以發揮其適於平行處理的特性。我們先以較直覺的方式得到一維的陣列型態，並以較正式的心臟收縮式演算法（systolic algorithm）來檢視其最佳性。

A real-time symbol-optimum detection algorithm for a CDMA system is developed in this paper by a truncation in the backward schedule. Simulations are present to show that the proposed truncated symbol-optimum detection provides negligible
performance loss compared to the original symbol-optimum detection. It allows a tradeoff between the latency, the computation load, and the performance. A systolic array implementation of the algorithm is derived to exploit the suitability of the algorithm for parallel processing. With such an implementation, the processing speed is greatly improved.

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