以Reed-Muller碼降低正交分頻多工訊號之功率峰均比

Abstract

正交分頻多工(orthogonal frequency-division multiplexed, OFDM)傳輸的功率峰均比(peak to average power ratio, PAPR)過高，一直是一個重要的問題。在實際應用上將導致信號失真及頻譜外溢。格雷互補序列(Golay complementary sequences)可以將相位鍵移(H-ary PSK)調變的正交分頻多工之功率峰均比限制在2之下。而格雷互補序列又可以由Reed-Muller碼所產生。本文首先探討的是Reed-Muller碼編碼前的訊息(message)中有某些元素，並不會影響整體的功率峰均比，以利我們降低計算功率峰均比的計算量。而後提出二階與三階的Reed-Muller碼中，擁有較低的功率峰均比的序列結構。

Controlling the peak to average power ratio (PAPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a very important problem. Golay complementary sequences are well suited for use as codewords in OFDM, since their PAPR in -ary phase shift keying(PSK) modulation is at most 2. It is know that a family of polyphase Golay complementary sequences of length organized in cosets of a -ary generalization of the first-order Reed-Muller code, . In this thesis, we will discuss some PAPR equivalence property on the Reed-Muller codes. And some construction technique for cosets of with low PAPR is established.