在這篇論文中，我們提出了在正交分頻多工(orthogonal frequency-division multiplexing)的系統中，在星座擴充的技術上使用凸優化的方法來降低傳送信號的錯誤率(bit-error-rate，簡稱BER)。傳統的星座擴充技術通常都是用來降低功率峰均比(peak-to-average power ratio，簡稱PAPR)，在這篇論文中我們提出了三種方式來降低信號的錯誤率。與傳統的技術相比較，雖然所提出方式的功率峰均比會略微提高，但若能有效地降低傳送信號的錯誤率，這對整體的系統分析來說，是個比較好的方式。我們的方式是先將訊號做星座擴充的技術，然後再利用凸優化的方式去求解，進而將低傳送訊號的錯誤率。我們是使用第二代數位地面電視傳輸(Digital Video Broadcasting-Second Generation Terrestrial，簡稱DVB-T2)標準中星座擴充技術。模擬結果可看出，與DVB-T2相比較，我們所提出方式可以達到較好BER的表現。

In this thesis, we propose a novel constellation extension (CE) scheme for peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems. Traditionally, most PAPR reduction schemes are designed to minimize the peak value of the transmitted time-domain OFDM signal as low as possible; however, it has been shown in [1] that maximization of the signal-to-distortion ratio (SDR) is a better criterion than minimization of the PAPR because it can achieve better bit error rate (BER) performance. In the proposed CE scheme, different from the most previous CE schemes, all the constellation points are allowed to be shrunk as well as to be extended for maximizing the SDR via solving a convex optimization problem. Furthermore, we separately consider the extension or shrinking of the real and imaginary parts of a constellation point since their contributions to the time-domain peak samples are different. These features result in an improvement in terms of both BER and PAPR with a slightly increase in the computational complexity as compared to the state of the art scheme in [1].

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