正交分頻多工在目前的通訊系統中是非常熱門的，它擁有高傳輸的效率且能有效對抗衰減通道。但它其中有一個很顯著的問題是過高的尖峰平均值功率比，它會造成訊號進入功率放大器的時候有可能運作在非線性區域，並且導致輸出訊號產生失真。因此，對於這個問題已經有很多解決方法被提出來了，這其中包括選擇映射（Selective Mapping），部分傳輸序列（Partial Transmit Sequence）。在這兩個方法中，又以選擇映射有較佳的性能，但這方法的缺點在於所需要的運算複雜度太高，因為它需要大量的IFFT硬體元件。因此Wang就提出一個用簡單的轉換矩陣代替IFFT硬體元件的概念，由於Wang的方法找到的可用傳送訊號並不多，因此我們在不比Wang複雜度高的情況下提出利用時域次轉換矩陣之低複雜度的選擇映射方法，去解決可用的傳送訊號太少這個問題。也就是說用多個更簡單的轉換矩陣代替Wang方法裡簡單的轉換矩陣。首先我們會把訊號分成多個群組且每個群組所分到的訊號都是等間隔，然後再經過我們所設計低複雜度運算的時域次轉換矩陣，最後再把每個群組經過時域次轉換矩陣的輸出全部加起來，就是我們所產生的其中一組要傳送的訊號。我們再由這些訊號裡面找出一組尖峰平均值功率比最低的去傳送。因此我們可以大量減少其運算複雜度且達到降低尖峰平均值功率比的目的，而且也可以找到更多可用的傳送訊號。
In orthogonal frequency division multiplexing (OFDM) systems, peak-to-average power ratio (PAPR) is one of the major problems. High PAPR could bring serious impact on hardware implementation. Therefore, many solutions for PAPR reduction have been proposed, including the selective mapping (SLM) approach. However, in SLM approach, the computational complexity due to an amount of IFFT operations is considerable. In this work, we proposed a modified SLM approach based on time-domain conversion sub-matrices. First, we divide the OFDM signal into several sub-blocks by grouping the subcarriers with equally-spaced indices. Afterwards, we find out the conversion matrices for each sub-block and obtain the candidate signals by summing up the conversed signals of all sub-blocks. Based on the time-domain conversion sub-matrices, we can reduce the computational complexity significantly. From the simulation results, the performance by the proposed scheme approaches to that by conventional SLM with the computational complexity much less than conventional SLM.

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