以格雷序列與非格雷序列降低OFDM訊號之峰均比

PAPR Reduction for OFDM Signals with Golay and Non Golay Sequences

儲文彬(Wen-Pin Chu)

指導教授 ： 李穎

元智大學/工程學院/通訊工程學系/碩士(2004年)

摘要

格雷序列(Golay sequence)用於OFDM訊號編碼具有低功率峰均比(Low PAPR)的特性，可將PAPR限制在2之內。Davis和Jedwab提出目前所知可產生最多格雷序列的方法，其格雷序列是Reed-Muller碼字，因此有較佳編解碼結構。但即使用了所有已知格雷序列進行降PAPR編碼仍有碼率(Code Rate)太低的問題。
本論文研究提升碼率的方法，及在802.11a系統實現的方式與效能。我們用「窮盡搜尋法」找出其他低PAPR(不大於2)的序列，包含非格雷序列。結果發現在長度較長時，其他序列佔全部低PAPR序列超過85%，遠多於過去使用的格雷序列。因此把這些序列與過去使用的格雷序列共同作為碼字可有效的提升碼率。對802.11a OFDM訊號編碼時，若避開「前導位元(Pilot tone)」會造成編碼區塊過多，無法發揮降低PAPR性能。本文提出將前導位元編入碼字的方法。並以電腦模擬評估其性能。觀察的指標包括，PAPR、編碼率、位元錯誤率、及OBO mask。
過去學者研究認為Davis和Jedwab提出的方法可能已產生所有的格雷序列。本研究搜尋結果顯示，長度16的QPSK-OFDM序列中存在「1024」個非Reed-Muller碼字的格雷序列，其存在推翻了「所有格雷序列皆可由Davis和Jedwab方式產生」的假說。

關鍵字

格雷序列 ； OFDM ； Reed-Muller ； 802.11a ； Pilot tone ； PAPR

並列摘要

Golay sequences can be used as codewords for OFDM signals to limit the PAPR to 2. Davis and Jedwab propose a construction that produces the largest number of Golay sequences known previously. These Golay sequences have better structure for coding and decoding because they are Reed-Muller codewords. Even when all these Golay sequences are used as codewords, the code rate is still very low.
The purpose of this research is to explore methods to increase the code rate and to realize these methods in 802.11a. We use exhaustive search to find all low PAPR (no more than 2) sequences, including non-Golay sequences, and more than 85% of all low PAPR sequences are not Golay sequences. Therefore using both Golay and non-Golay sequences as codewords can increase the code rate. When coding 802.11a signals, avoiding pilot tones increases the numebr of coding blocks and degrades PAPR reduction performance. A new idea is introduced to include pilot tones in the codewords. Computer simulations are conducted and performance is evaluated through PAPR, code rate, bit error rate, and OBO mask.
Davis and Jedwab’s construction was previously believed to possibly generate all binary and quaternary Golay sequences of length 2m . Our exhaustive search reveals that there are “1024” new Golay sequences in 16 subcarrier QPSK-OFDM that are not Reed-Muller codewords. The hypothesis that “all Golay sequences can be generated form Davis and Jedwab’s construction ” is thus not true.

並列關鍵字

Golay sequence ； OFDM ； Reed-Muller ； 802.11a ； Pilot tone ； PAPR

參考文獻

information technology - telecommunications and

metropolitan area networks - specific requirements.

Part 11: wireless LAN Medium Access Control (MAC)

and Physical Layer (PHY) specifications: high-speed

802.11a-1999, Sept. 1999.