由於無線網路對於高速率資料傳輸以及可靠性資料傳輸的需求,使得正交分頻多工(orthogonal frequency-division multiplexing，簡稱OFDM)在通訊系統中成為非常具有吸引力的一種技術。OFDM系統不僅提供非常高的傳輸速率，另外還能夠有效的對抗多重路徑通道效應。然而在OFDM系統中一個主要的缺點是其輸出信號會產生相當高的峰值對平均功率比(peak-to-average power ratio，簡稱PAPR)。當具有高PAPR比值的傳輸信號經過功率放大器時會產生非線性失真。為了解決這個問題，發展出許多的峰值對平均功率比降低技術。如選擇性映射式(selective mapping，簡稱SLM)以及星座擴張(constellation extension，簡稱CE)。SLM技術可以提供很好的PAPR效能，但是這方法卻需要傳送額外訊息 (side information)。另外CE技術也可以提供好的PAPR效能但卻會增加傳輸信號的平均功率以及傳輸端的運算複雜度。
在這篇論文中，我們提出使用星座擴張之低複雜度峰值對平均功率比降低技術。我們提出的方法是結合SLM以及CE技術的概念，並且控制住增加的平均功率以及信號的錯誤率(bit-error-rate，簡稱BER)在可接受的合理範圍之內。藉由使用一些低複雜度的轉換矩陣T來產生多個候選信號，並且選出具有最低PAPR值的信號作為傳輸信號。除此之外，我們提出的方法是不需要傳送額外訊息(side information)。經由模擬和比較結果我們可看出；相比於傳統SLM技術以及星座擴張CE技術時，所提出的低複雜度技術可以達到不錯的PAPR以及BER的效能並且具有相當低的運算複雜度。

Due to the demand of high data-rate and reliable data transmission over wireless networks, orthogonal frequency-division multiplexing (OFDM) becomes one of the attractive technologies for communication systems. The OFDM systems can offer not only high data-rate services but also robustness to frequency selective fading channels. One of the major drawbacks of OFDM signals is the high peak-to-average power ratio (PAPR). When a high PAPR signal passes through a power amplifier, it may cause nonlinear distortion. Numerous techniques have been proposed to reduce the PAPR of OFDM signals, such as selected mapping (SLM) and constellation extension (CE). The SLM method can provide good performance on PAPR reduction, but it needs to transmit side information to the receiver. The CE method can also provide good PAPR reduction performance by appropriately extending the modulation constellation of input data symbols; however, it will increase the transmit power and the computation complexity at the transmitter.
In this thesis, we propose a low-complexity constellation extension scheme to reduce the PAPR of OFDM signals. The proposed method combines the concept of the conventional SLM and CE schemes, where the average increasing power and the bit-error-rate (BER) due to the extended constellations are limited to an acceptable region. By using some low-complexity conversion matrices T, the proposed scheme generates multiple candidate signals and the signal with the lowest PAPR is selected for transmission. Moreover, the proposed scheme does not need to transmit side information. As compared with the conventional SLM and CE schemes, the proposed one achieves close PAPR reduction and BER performances with much lower computational complexity.

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