TWI255105B - Method and apparatus for papr reduction of an ofdm signal - Google Patents

Method and apparatus for papr reduction of an ofdm signal Download PDF

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TWI255105B
TWI255105B TW93114259A TW93114259A TWI255105B TW I255105 B TWI255105 B TW I255105B TW 93114259 A TW93114259 A TW 93114259A TW 93114259 A TW93114259 A TW 93114259A TW I255105 B TWI255105 B TW I255105B
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sub
division multiplexing
frequency division
length
peak
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TW93114259A
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Chinese (zh)
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TW200539601A (en
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Chih-Chun Feng
Chih-Yaw Wang
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Ind Tech Res Inst
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Abstract

An apparatus and method for peak-to-average power ratio reduction of an OFDM signal are disclosed. The method uses the interleaved characteristics of partial transmit sequences to partition input data x[n] of length N into several disjoint sub-blocks in time domain, and a complete N-point signal x[n] is composed after phase optimization, where N is the length of an OFDM signal and n=0, 1, ..., N-1. Accordingly, the apparatus comprises an N-point inverse fast Fourier transform (N-IFFT), a de-multiplexer, a combiner, a set of memory and an adder. This invention uses only one M-IFFT, whereby it can achieve significant computation reduction. This invention requires (N/2)log2N complex multiplications and N memory units. It also preserves the inherent property as well as advantages of an OFDM system.

Description

1255105 政、發明說明: 【發明所屬之技術領域】 本發明是關於解決正交分頻多工系統(Orthogonal Frequency Division Multiplexing,OFDM)發射端之高峰 均值(Peak-to-Average Power Ratio,PAPR)的技術, 特別是一種降低OFDM信號PAPR值的方法與裝置。 【先前技術】 常使用的離散多載波轉換(Discrete Multitone,DMT) 及OFDM之多載波通訊系統在高速通訊應用中吸引了廣 大的注意,這些高速通訊應用諸如:數位用戶迴路(Digital Subscriber Line,DSL)、數位地面廣播(digital terrestrial broadcasting)、無線區域網路(Wireless Local Area Network,WLAN)、無線都會網路(Wireless Metropolitan Area Network,WMAN)、專用短距離通信系統(Dedicated Short Range Communication,DSRC)以及電源線通訊(p0wer line communication)等等。它們也可望成為下一世代行動通 訊的主流。多載波通訊系統的優點來自於將一高速資料流 (datastream)分隔成為多重平行的資料流,而這些多重平行 的資料流是藉由個別副載波(subcarrier)來傳送。因此,每 一部分資料流是以低速傳輸,具有較強的抗多路徑通道 (multipath channel)效應及窄頻干擾(narrowband interference) 的能力。 1255105 第一圖為傳統多載波通訊系統有關OFDM發射機的 系統方塊圖。在OFDM發射機中,輸入資料;^],灸=〇, L , ΛΜ ’係傳送於一 OFDM符元(symbol)週期之内,經串/並 (Serial/Parallel,S/P)轉換後,藉由#點反向快速傅立葉轉 換(Appoint Inverse Fast Fourier Transform,7V-IFFT),再經並 /串(Parallel/Seria卜P/S)轉換成為以下的離散時間序列: 对打]=η=0, h …,W 一1 ⑴1255105 Administration, Invention Description: [Technical Field] The present invention relates to solving the Peak-to-Average Power Ratio (PAPR) of the Orthogonal Frequency Division Multiplexing (OFDM) transmitting end Techniques, and in particular, a method and apparatus for reducing the PAPR value of an OFDM signal. [Prior Art] Discrete Multitone (DMT) and OFDM multi-carrier communication systems often attract great attention in high-speed communication applications such as Digital Subscriber Line (DSL). ), digital terrestrial broadcasting, Wireless Local Area Network (WLAN), Wireless Metropolitan Area Network (WMAN), Dedicated Short Range Communication (DSRC) And power line communication (p0wer line communication) and so on. They are also expected to become the mainstream of next generations of mobile communications. The advantage of a multi-carrier communication system is that it separates a high-speed data stream into multiple parallel data streams that are transmitted by individual subcarriers. Therefore, each part of the data stream is transmitted at a low speed, and has strong anti-multipath channel effect and narrowband interference capability. 1255105 The first figure is a system block diagram of a conventional multi-carrier communication system related to an OFDM transmitter. In an OFDM transmitter, input data; ^], moxibustion = 〇, L, ΛΜ ' is transmitted within an OFDM symbol period, after serial/parallel (S/P) conversion, It is converted into the following discrete time series by the Appoint Inverse Fast Fourier Transform (7V-IFFT) and then converted to Parallel/Seria (P/S): , h ..., W a 1 (1)

ViV jt=o 其中 · wy (2) 為轉動因子(twiddle factor)。由(1)式獲得的離散時間序列 接著經過循環前置***(cyclic prefix insertion)後,進行 數位/類比轉換獲得一類比信號X⑺。產生的類比信號χ⑺ 再被傳送到RF前端作進一步處理,包含iq調變(jQ modulation)、升頻轉換(up conversion)和功率放大(p0wer amplification)等。類比信號x⑺的PAPR值較高於對應的離 鲁 散時間信號x[«]之PAPR值數個dB,且大約近似Χ[Μ]之 PAPR值。此x[n/7?]表示由:φ]之Λ倍超取樣(oversampiing) 所取得的序列。因此,由可得χ(ί)之近似PAPR值為 max \x[n/R]\2 PAPR = ^n<RNJ Jl ^{\x[n/R]\2} 其中五{·}表示期望值的運算。一般在Λ之4時,此近 似值是相當準確。然而,此類習知多載波通訊系統主要缺 8 1255105 點之為調變化號的高pApR值。當高pApR值的調變信 號經過RF前端時,此信號會因為一般处功率放大器的非 線性特性:敎真,此非線性雜不僅會造成頻帶中 (in-band)信號失真而導致誤碼率(册Err〇r如把,BER)升 同’而且會引起該頻帶外能量散逸(〇ut-〇f:band (或 頻譜再生)而導致相鄰的頻道干擾及違***頻譜規定。此 問題常見的解決方法是簡單地利用具有較大線性範圍的功 率放大器,但會導致功率效能降低、較高的功率消耗量和 較高的製造成本。 春 解決此問題已經有許多習知的方法。這些方法包括區 塊編碼(block coding)、截掉(dipping)、部分傳輸序列 T麵mit Sequences,PTS)、選擇性對應(Sdective Mapping, SLM)、載波保留(Tone Reservation,TR)、載波注入(ToneViV jt=o where · wy (2) is the twiddle factor. The discrete time series obtained by equation (1) is then subjected to digital/analog conversion to obtain an analog signal X(7) after cyclic prefix insertion. The resulting analog signal χ(7) is then passed to the RF front end for further processing, including iq modulation, up conversion, and power amplification (p0wer amplification). The PAPR value of the analog signal x(7) is higher than the PAPR value of the corresponding discrete time signal x[«] by several dB, and is approximately equal to the PAPR value of Χ[Μ]. This x[n/7?] represents the sequence obtained by the oversampling of φ]. Therefore, the approximate PAPR value of the available χ(ί) is max \x[n/R]\2 PAPR = ^n<RNJ Jl ^{\x[n/R]\2} where five {·} represents the expected value The operation. This approximate value is generally quite accurate at 4 o'clock. However, such conventional multi-carrier communication systems mainly lack the high pApR value of 8 1255105. When the modulated signal with high pApR value passes through the RF front end, this signal will be due to the nonlinear characteristics of the power amplifier in general: true, this nonlinear impurity will not only cause distortion of the in-band signal, but also cause bit error rate. (Err〇r, BER) is equal to 'and will cause the out-of-band energy to escape (〇ut-〇f: band (or spectrum regeneration) resulting in adjacent channel interference and violation of government spectrum regulations. This problem is common The solution is to simply use a power amplifier with a large linear range, but it will result in reduced power efficiency, higher power consumption and higher manufacturing costs. There are many well-known methods for solving this problem in spring. Including block coding, dipping, partial transmission sequence T-mit mit Sequences (PTS), selective correspondence (SLM), carrier reservation (Tone Reservation, TR), carrier injection (Tone

Injection,Ή)及脈衝重疊(pUlse superp0siti〇n)等方法。在這 些方法中,PTS方法在實施複雜度與PAPR降低性能上最 具有吸引力,Ericsson公司在美國專利6,125,1〇3中揭露了 一種使用PTS方法解決OFDM發射端信號之高PAPR值的 問題,其方塊圖如第二圖所示,說明如下。 首先將長度#的輸入資料在頻域(frequency domain)上劃分為Μ個分離的子區塊(或組),表示為不闲、 石闲、…、不#],灸=〇, 1,···,τν-ι。該劃分方式可以是交 錯(interleaved)、鄰接(adjacent)和不規貝ij(irregular)等方式, 9 1255105 如第三圖所示(以4為例)。此Μ個分離的子區塊接著 被相位旋轉且相加在一起以形成下列信號: 卜 [fc],fc = 〇, 1,…,W -1 (4) m=l 其中&是有關於第w個子區塊(me {1,2,…,Μ})的相位旋 轉參數(註,|\| = 1)。 (4)式經ΛΓ-IFFT產生:Injection, Ή) and pulse overlap (pUlse superp0siti〇n) and other methods. Among these methods, the PTS method is most attractive in terms of implementation complexity and PAPR reduction performance, and Ericsson discloses a high PAPR value for the OFDM transmitter signal using the PTS method in U.S. Patent No. 6,125,1. The problem is shown in the block diagram as shown in the second figure. First, the input data of length # is divided into two separate sub-blocks (or groups) in the frequency domain, which are represented as not idle, stone idle, ..., not #], moxibustion = 〇, 1, ··, τν-ι. The division method may be an interleaved, an adjacent, and an irregular irregular, and 9 1255105 is as shown in the third figure (taking 4 as an example). The two separated sub-blocks are then phase rotated and added together to form the following signals: 卜[fc], fc = 〇, 1,..., W -1 (4) m=l where & is relevant The phase rotation parameter of the wth sub-block (me {1, 2, ..., Μ}) (Note, |\| = 1). (4) Type ΛΓ-IFFT generation:

又[叮]=[bmxm [η],η = 0,1,…,JV -1 (5) m=l 其中表示對忍闲作7V-IFFT運算之結果。在PAPR降 低演算法中,PTS方法的目標是相位最佳化,亦即尋找最 理想的組合序列{卜,,…,,使得對應的發射信號的 PAPR值為最小。在實際應用上,心的相位通常會限制為 最多只有四種可能的數值{+1,-1,+»},如此相位旋轉動作 便不需要任何乘法運算。Also [叮]=[bmxm [η], η = 0,1,..., JV -1 (5) m=l which represents the result of the 7V-IFFT operation for the idle. In the PAPR reduction algorithm, the goal of the PTS method is to optimize the phase, that is, to find the most ideal combination sequence {b,,..., so that the PAPR value of the corresponding transmitted signal is the smallest. In practice, the phase of the heart is usually limited to a maximum of four possible values {+1, -1, +»}, so that the phase rotation does not require any multiplication.

從第二圖的PTS實現方法中可窺知一個ΛΓ點的OFDM 符元需要做Μ次iV-IFFT運算,亦即需要固複 數乘法運鼻’因此Kang,Kim與J〇〇以及Samsung公司都 提出了降低PTS運算量的實現方法。Kang,Kim與Joo論 文今(A novel subblock partition scheme for partial transmit sequence OFDM,” IEEE Trans· Broadcasting,vol. 45, no· 3, 10 1255105 ρρ· 7999)提到的方法可用第四圖來表示(以 Μ=8為例),其原理為利用PTS的交錯劃分區塊特性,在 頻域上每一個子區塊共有7V點,但只有£點有值(ζ二#/ 的’其餘為〇,因此將此#點子區塊信號心间做尽IFFT 運算,相當於對一個Z點子區塊⑶中不為〇值的資料) k號經過L-IFFT ’並在時域(time domain)上重覆Λ/次形成 #點的信號,再將此7V點信號乘以7V點的複數係數 (1/M).e^-, m = 09l,...9M-l9 η = 0Λ^Ν^ 此方法的運异量為Af.(%)l〇g2 L +腑個乘法數目,所需要的 記憶體為胃個單元。From the PTS implementation method in the second figure, we can see that an OFDM symbol of a defect needs to be used for iV-IFFT operation, that is, it requires a solid complex multiplication method. Therefore, Kang, Kim and J〇〇, and Samsung have proposed An implementation method for reducing the amount of PTS operations. The method mentioned in Kang, Kim and Joo (A novel subblock partition scheme for partial transmit sequence OFDM, IEEE Direct Broadcasting, vol. 45, no. 3, 10 1255105 ρρ· 7999) can be represented by the fourth figure ( Taking Μ=8 as an example), the principle is to use the interleaving block feature of PTS. In the frequency domain, each sub-block has a total of 7V points, but only the point has a value (ζ二#/'s the rest is 〇, Therefore, the #point sub-block signal is done by the IFFT operation, which is equivalent to the data that is not depreciated in a Z-point sub-block (3). The k-number is over the L-IFFT' and is repeated in the time domain. / Times forming the signal of #点, and multiplying this 7V point signal by the complex coefficient of 7V point (1/M).e^-, m = 09l,...9M-l9 η = 0Λ^Ν^ The amount of transport is Af. (%) l 〇 g2 L + 乘 a multiplicative number, the required memory is the stomach unit.

Samsung公司在美國專利申請案us 2〇〇3/〇〇67866也 提出類似的觀念,如第五圖所示。和前述方法不同的是每 一個I點子區塊經過LIFFT後不再重覆,直接在時域乘上 Z點的複數係數使形成的時域子區塊資料彼此正交,以方 便接收端分離出各個子區塊資料。由於各個時域子區塊只 有Z點,其PAPR值較低,所以經過相位旋轉後加總所得 的發射信號的PAPR值也較低。雖然此方法所需的乘法數 目為M.(%)l〇g2L + W,所需要的記憶體為#個單元,但是 此方法將原本長度#的OFDM發射信號縮短為長度z的 發射L號,思明者此系統對抗多路控通道效應的能力也會 隨之降低許多。而且在許多情況下根本無法設計出z點的 複數係數乘法器來使得發射端形成的時域子區塊資料彼此 11 1255105 正父,如此將造成接收端不易還原出原本傳送的資料。 【發明内容】 為克服上述傳統OFDM發射端降低papr值之 PTS實現方法的缺點,本發明主要目的為提供一種降低 〇FE)M信號PAPR值的方法與裝置。本方法利用pTS 交錯劃分區塊的特性,在時域上直接將長度#的一離散時 間序列x[«]劃分為複數個不互相重疊的子區塊後,再經轉 換組合及一相位最佳化處理而合成一完整的#點信號 修 4…,其中#為一正交分頻多工信號的長度且” =〇, I •••,ΑΜ 〇 本發明只需用到一個#_IFFT,可大幅降低運算量,所 需複數乘法數目為(M2)log2iV,所需要的記憶體為#個單 疋,更重要的是本發明仍保有0FDM原本具有的抗多路徑 通道效應之能力。 • 本方法更包含下列步驟:首先將長度#(#:> 1的整數) 的一離散時間序列X[«]劃分為Μ個不互相重疊(disj〇int)的 子區塊(或組),每一子區塊的長度為八,Μ為2的次冪 (power) ’且7V/M為大於1的整數。接著,再利用一個組合 器(combiner)將此Μ個不互相重疊的子區塊合成另外μ個 長度Λ//Μ的序列少办],其中^2,,从且w = 〇, l , (AWk〇-l。最後,運用對稱性質,將此μ個序列經相位 12 1255105 旋轉且相加在一起,形成一完整的#點傳送信號対八]。 本方法中,第一和第二較佳實施例分別以从=2和从 -4的情況來說明上述之時域實現方法的步驟。 依此’本發明之降低OFDM信號PAPR值的裝置 主要包含一#點反向快速傅立葉轉換、一解多工器 (de-multiplexer)、一組合器、一組記憶體、和一個加法 器。#點反向快速傅立葉轉換將輸入的頻域信號;轉換 鲁 成時域信號χΜ,解多工器將x|>]依鄰接方式劃分為从個 不互相重疊且長度相等的子區塊。組合器將此从個不互相 重疊的子區塊合成另外Μ個長度皆為JV/Μ的離散時間序 列λΜ。運用對稱性質,將此Μ個序列經相位旋轉 後,經由加法器相加而形成一完整的#點信號办]。在此 Μ個不互相重疊且長度相等的子區塊和从個序列則 先後儲存在這一組記憶體裡。 以Μ=4的情況,本發明與其他三種PTS實現方法的 運算量與記憶體需求相比較。結果顯示,相較於原來及 Kang、Kim與Joo之PTS實現方法,本發明與Samsung之 PTS實現方法所需的乘法數相同且為最少,並且其記憶體 需求單元相同且為最少。而本發明不需要將OFDM的信號 長度縮短,因此仍保有OFDM系統原本具有的特性和優 Mk 〇 13 1255105 茲配合下列圖式、實施例之詳細說明及申請專利範 圍,將上述及本發明之其他目的與優點詳述於後。 【實施方式】 第六圖為本發明之降低OFDM信號PAPR值的方 法的示意圖。首先,將長度#的頻域信號义闲做尽iFFT 601運鼻得到長度7V的時域信號:φ2],再將x[w]依鄰接方 式劃分為Μ個不互相重疊的子區塊,如步驟6〇3所示,其 中每一子區塊的長度為AWkf,Μ為2的次冪,且iV/Μ為大 於1的整數。接著,此Μ個不互相重疊的子區塊經組合器 605形成Μ個長度為#的離散時間序列μ㈤,乃间,_, 。最後,此Μ個離散時間序列外|>2]經步驟607之相 位旋轉且相加在一起,形成一完整的#點傳送信號3?[n]: x[n] = bxyx [n] γΜ [n] ⑹ 由於序列具備對稱性質,因此組合器605只需形成長 度 7V/M的序列{^[0],:^[1],···αΚΜΛ^-Ι]}即可。 依此,第七圖說明了本發明之降低OFDM信號PAPR 值的裝置的一個結構示意圖。此降低OFDM信號 PAPR值的裝置主要包含一 W-IFFT 601、一解多工器 70卜一組合器703、一組記憶體705、和一個加法器707。 7V-IFFT 601將輸入的頻域信號义[幻轉換成時域信號, 14 1255105 解多工器701將对《]依鄰接方式劃分為Μ個不互相重疊且 長度相等的子區塊。組合器703將此Μ個不互相重疊的子 區塊組合而成Μ個長度TV/Μ的序列外问,其中yfc=l,2,…, Μ且《 = 0, 1,···,π/Λ/Η。此Μ個序列乃[/7]經相位旋轉後, 經由加法器707相加而形成一段長度λγ/Μ的傳送信號{对〇], 印],…,Ϊΐ(#/Μ)-1]}。藉由更換不同的相位旋轉參數民, 可再由此Μ個的序列外Μ求得下一段傳送信號{?|W/M], x[(iV/M) + l],···,对(2#/A〇-1]}。依此方式,最後可求得全 部的傳送訊號?[«]。其中,Μ個不互相重疊的子區塊和M # 個序列則先後儲存在記憶體705裡。 以Μ=2為例來作說明,如第八圖所示。序列χ问,w== 〇, 1,…,胸經解多工器701分成長度搬的兩個子區塊 W〇Lx[1]5-^χ[(Ν/2)^\]}^{χ[Ν/21χ[(Ν/2)+11 ...9χ[Ν^ 1]},儲存於記憶體705。組合器803將這兩個長度#/2 的子區塊組合形成下列兩個長度#的離散時間序列: 鲁 yx [«] = χ[η] + χ[((η - Ν/2))ν] 少2 Μ = φί] - χ[((« — #/2)\ ] ’ (7) 其中((·)V表示循環位移(circular shift) Ί w = ο i (搬)-卜、组合器8〇3的結構相當簡單以兩個加法器,8㈤& 和803b,來實現第⑺式,其結構與2 IFFT兩相同。可以 證明⑺式中所得的離散時間序列川”]與咖]是等同於第 二圖中原本PTS方法所產生的離散時間序列,與咖。 由⑺式可推得 15 1255105 [((« + f)) ^ 1 = yi [((w ~τ))ν] = x[((n ~ N/2))n] + x[n] = y, [n] 少2[((« + 号))#卜 h[((” -f))v] = x[(〇2 — #/2)) j_刺=—a[„]⑻ 換言之, 乃[I]= -少2 [〇],h [号+U = -少2 [l],· · ·,少2 [jv -1] = ->;2 [f -1] (9) 因此組合器803只需形成長度7V/2的序列(^[ο],^[η,· ·, 乃[(#/2) · 1]}和(ν2[0],>;2[ΐ],-川即可。由於 {χ[0],41],"·,χ[7ν- 1]}不再需要,因此記憶體705可釋 _ 放出來供(^肌乃⑴,- 1]}和[y2[0],j;2[l],···, /2) - 1]}使用。換句話說,所需要的記憶體為#個單 元。最後由⑹式及⑼式可得 x[n^bxyx[n\ + b2y2[ri\ x[n^^] = biyi[n]^b2y2[n] (1〇) 其中《 = 0, 1,"·,(Μ2)-1。將(1〇)式進一步表示成 7|>+年]= + ¾少2[«],/? = 0,1,Λ = 0,1,···,|一 1 (11) 其中相位旋轉參數h及民如第九圖所示。由第八圖可看 出,當尾為+1,-1,+j或-j時,本發明總共所需的乘法運算 量來自於7V-IFFT,即需要(M2)log2iV個複數乘法運算,所 需記憶體為#個單元。當M=4的情況時,其實施示意圖 如第十圖所示。序列^φ?],《 = 0,1,···,ΑΜ經解多工器7〇1 分成長度#/4的四個子區塊,{χ[〇],…,χ[〇/4)- 1]丨、丨 16 1255105 /4],··.,4(#/2)- 1] }、Μ#/2],···,4(3#/4)- 1] }、和{jc[3# /4],...,jc[iV- 1] }。組合器1003將這四個長度7V/4的子區塊 組合形成下列四個長度#的離散時間序列: [n] = x[n] + x[((n - N/2))n] + x[((n - N/4))n ] + x[((n ^ 3N/4))n ] y3 [n] = x[n] + x[((n - N/2))n ] - x[((n - N/4))n ] - x[((n - 3N/4))n ] y2 [n] = x[n] - x[((n - N/2)) N ] + jx[((n - N/4))n] - jx[((n - 3N/4))n] γ4 [n] = x[n] - x[((n - N/2)) N ] - jx[((n - N/4))n ] + jx[((n - 3N/4))n ] (12) 組合器1003以八個加法器及一個虛數j的乘法器來實 現第(I2)式,其結構與4_IFFT兩相同。可以證明(12)式中 所得的離散時間序列乃㈣,乃[«],乃㈣,为㈣是等同於第二 圖中原本pts方法所產生的離散時間序列ΧιΜ,々Μ,Χ3Μ, αΜ。類似地,運用對稱性質,可得 其中0, 1,,而相位旋轉參數&則如第^«一圖 所示。由第十圖可看出,當4為+1,],+j或_】時,本發明 總共需要(iV/2)log27V個複數乘法運算,所需記憶體為#個 〇〇 一 早兀。 第十二圖為本發明與其他三種pTS實現方法的運算量 與記憶體需求之比較,其中M=4,N的大小分別為64、 256、1024和2048。可以看出,運算量與記憶體需求皆 隨著N的遞增而增加。相較於原來及〖聊、^與j〇〇 之pts實現方法,本發日月與8_卿之pTS實現方法中, 17 1255105 所需的乘法數為最少,記憶體需求單it也是最少。兩者所 需的乘法數相同,分別為192、1024、5120和11264· 记憶體需求單元也是相同,分別為64、256、和 2048。惟,本發明之m實現方法中,不需將〇f购的 信號Μ縮短,因此仍做〇FDM縣具有的特性和優 點。 綜上所述,本發明利用PTS交錯劃分區塊的特性, 且只需_ 一個娜FT,提供了一種有效降低正交分頻 多工‘號峰均值的方法與裝置。大幅降低運算量,所 需複數乘法數為_1〇心,所需要的記憶體為則固單元, 甚且仍保有GFDM縣具有的雜和優點。 准’以上所述者,鶴本發明之較佳實施例而已,當 不能以此限定轉明實狀細。即大凡依本發明申請專 利範圍所作之均等變化與修飾,皆應仍屬本剌專利涵蓋 之範圍内。 【圖式簡單說明】 第一圖說明一個傳統多載波通訊系統有關0FDM發射機 的系統方塊圖。 第二圖說明一種使用pTS方法解決OFDM發射端信號之 南PAPR的技術。 第三圖說明將輸入資料別A:]在頻域上劃分為子區塊(或組) 之交錯、鄰接和不規則的三種方式。 第四圖說明Kang、Kim與J〇〇提出之降低pts運算量的實 現方法。 第五圖說明Samsung公司提出之降低PTS運算量與記憶體 的實現方法。 第六圖為本發明之降低OFDM信號PAPR值的方法的 示意圖。 第七圖說明本發明之降低OFDM信號PAPR值的裝置 的一個結構示意圖。 第八圖為根據第七圖之本發明的第一較佳實施例。 第九圖說明M=2時,第八圖中的相位旋轉參數之設定。 第十圖為根據第七圖之本發明的第二較佳實施例。 第Η• —圖說明Μ=4時,第十圖中的相位旋轉參數之設定。 第十二圖為本發明與其他三種PTS實現方法的複數乘法運 算量與記憶體需求之比較。 圖號說明: 601 #點反向快速傅立葉轉換 1255105 603時域信號分割 605組合器 607相位最佳化處理和合成 701解多工器 705記憶體 803組合器 1003組合器 703組合器 707加法器 803a、803b加法器A similar concept is also proposed by Samsung in US Patent Application No. 2〇〇3/〇〇67866, as shown in the fifth figure. Different from the foregoing method, each I-point sub-block does not repeat after LIFFT, and multiplies the complex coefficient of the Z-point directly in the time domain to make the formed time-domain sub-block data orthogonal to each other, so as to facilitate the separation of the receiving end. Each sub-block data. Since each time domain sub-block has only Z points and its PAPR value is low, the PAPR value of the transmitted signal after the phase rotation is also low. Although the number of multiplications required for this method is M.(%)l〇g2L + W, the required memory is #units, but this method shortens the original length # OFDM transmission signal to the length z transmission L number, The ability of the system to counter the effects of multi-channels is also reduced. Moreover, in many cases, it is impossible to design a z-point complex coefficient multiplier to make the time domain sub-block data formed by the transmitting end of each other 11 1255105, which will make it difficult for the receiving end to restore the originally transmitted data. SUMMARY OF THE INVENTION In order to overcome the shortcomings of the PTS implementation method for reducing the papr value of the conventional OFDM transmitting end, the main object of the present invention is to provide a method and apparatus for reducing the PAPR value of the 〇FE)M signal. The method utilizes the characteristics of pTS interleaving blocks, and directly divides a discrete time series x[«] of length # into a plurality of sub-blocks that do not overlap each other in the time domain, and then converts the combination and the best one phase. A complete #点信号修4..., where # is the length of an orthogonal frequency division multiplexing signal and "=〇, I •••,ΑΜ 〇 〇 The invention only needs one #_IFFT, To greatly reduce the amount of computation, the number of complex multiplications required is (M2)log2iV, the required memory is # single 疋, and more importantly, the present invention still retains the ability of OFDM to have multi-path channel effects. It further includes the following steps: first, a discrete time series X[«] of length #(#:> 1 integer) is divided into sub-blocks (or groups) that do not overlap each other (disj〇int), each The length of the sub-block is eight, Μ is the power of 2 ' and 7V/M is an integer greater than 1. Then, a comber is used to synthesize the sub-blocks that do not overlap each other. In addition, the sequence of μ length Λ//Μ is less], where ^2,, and w = 〇, l , (AWk〇-l. Then, using the symmetry property, the μ sequences are rotated and added together by the phase 12 1255105 to form a complete #point transmission signal 。8. In the method, the first and second preferred embodiments respectively The steps of the time domain implementation method described above are explained by the case of =2 and -4. Accordingly, the apparatus for reducing the PAPR value of the OFDM signal of the present invention mainly comprises a #point reverse fast Fourier transform, a demultiplexer (de -multiplexer), a combiner, a set of memory, and an adder. The #point reverse fast Fourier transform converts the input frequency domain signal; converts the Lu time domain signal χΜ, and the multiplexer converts x|>] It is divided into sub-blocks that do not overlap each other and have the same length according to the adjacent mode. The combiner combines the sub-blocks that do not overlap each other into another discrete time series λΜ whose length is JV/Μ. After the phases are rotated by the phase, they are added by the adder to form a complete #point signal. Here, the sub-blocks and the sub-sequences that are not overlapping each other and are of equal length are stored in this order. In a set of memory. Take Μ=4 In the case, the calculation amount of the present invention and the other three PTS implementation methods are compared with the memory requirements. The results show that the multiplication required by the present invention and Samsung's PTS implementation method is compared with the original PK implementation method of Kang, Kim and Joo. The numbers are the same and the least, and the memory demand units are the same and the least. However, the present invention does not need to shorten the signal length of the OFDM, and therefore still retains the original characteristics of the OFDM system and the excellent Mk 〇 13 1255105. The above and other objects and advantages of the present invention will be described in detail below. [Embodiment] Fig. 6 is a schematic diagram showing a method of reducing the PAPR value of an OFDM signal according to the present invention. First, the frequency domain signal of length # is used as the iFFT 601 to obtain the time domain signal of length 7V: φ2], and then x[w] is divided into two sub-blocks that do not overlap each other according to the adjacent mode, such as Step 6〇3, wherein each sub-block has a length of AWkf, Μ is a power of 2, and iV/Μ is an integer greater than 1. Then, the sub-blocks that do not overlap each other are combined by the combiner 605 to form a discrete time series μ (five) of length #, Between, _, . Finally, the outer discrete time series > 2] is rotated by the phase of step 607 and added together to form a complete #point transmission signal 3?[n]: x[n] = bxyx [n] γΜ [n] (6) Since the sequence has a symmetrical nature, the combiner 605 only needs to form a sequence of length 7V/M {^[0], :^[1], ···αΚΜΛ^-Ι]}. Accordingly, the seventh diagram illustrates a structural diagram of the apparatus for reducing the PAPR value of the OFDM signal of the present invention. The apparatus for reducing the PAPR value of the OFDM signal mainly comprises a W-IFFT 601, a demultiplexer 70, a combiner 703, a set of memory 705, and an adder 707. The 7V-IFFT 601 converts the input frequency domain signal meaning into a time domain signal, and the 14 1255105 demultiplexer 701 divides the "adjacent" into sub-blocks that are not overlapping each other and of equal length. The combiner 703 combines the sub-blocks that do not overlap each other into a sequence of length TV/Μ, where yfc=l, 2, ..., and = = 0, 1,···, π /Λ/Η. The sequence is [/7] after phase rotation, and is added by the adder 707 to form a transmission signal of length λγ/Μ {opposite], imprinted, ..., Ϊΐ(#/Μ)-1]} . By replacing the different phase rotation parameters, the next transmission sequence can be obtained from the sequence of {?|W/M], x[(iV/M) + l],···, (2#/A〇-1]}. In this way, all the transmitted signals can be obtained in the end [[], where one sub-block and M # sequences that are not overlapping each other are stored in the memory. 705. Take Μ=2 as an example, as shown in the eighth figure. Sequence χ, w== 〇, 1,..., the thoracic solution multiplexer 701 is divided into two sub-blocks of length W〇Lx[1]5-^χ[(Ν/2)^\]}^{χ[Ν/21χ[(Ν/2)+11 ...9χ[Ν^ 1]}, stored in memory 705. The combiner 803 combines the two sub-blocks of length #/2 to form the following two discrete time series of length #: yx [«] = χ[η] + χ[((η - Ν/2) )ν] less 2 Μ = φί] - χ[((« — #/2)\ ] ' (7) where ((··V) means circular shift Ί w = ο i (move)-b, The structure of the combiner 8〇3 is quite simple. The two equations, 8(5)& and 803b, are used to implement the equation (7), and the structure is the same as that of the 2 IFFT. The discrete time series obtained in the equation (7) can be proved. It is equivalent to the discrete time series generated by the original PTS method in the second figure, and can be derived from (7): 15 1255105 [((« + f)) ^ 1 = yi [((w ~τ)) ν] = x[(( n ~ N/2))n] + x[n] = y, [n] less 2[((« +))#卜[[((-f))v] = x[ (〇2 — #/2)) j_刺=—a[„](8) In other words, is [I]= - less 2 [〇], h [number + U = - less 2 [l], · · ·, Less 2 [jv -1] = ->;2 [f -1] (9) Therefore, the combiner 803 only needs to form a sequence of length 7V/2 (^[ο], ^[η,··, is [( #/2) · 1]} and (ν2[0],>;2[ΐ],-川川. Since {χ[0],41],"·,χ[7ν-1]} Needed again, so the memory 705 can be released for (^ muscle is (1), -1]} and [y2[0], j; 2[l], ···, /2) - 1]}. In other words, the required memory is #units. Finally, (6) and (9) can be obtained x[n^bxyx[n\ + b2y2[ri\ x[n^^] = biyi[n]^b2y2[ n] (1〇) where " = 0, 1, "·, (Μ2)-1. Further express (1〇) as 7|>+year]= + 3⁄4 less 2[«], /? = 0,1,Λ = 0,1,···,|一一 (11) where phase The rotation parameter h and the people are as shown in the ninth figure. As can be seen from the eighth figure, when the tail is +1, -1, +j or -j, the total amount of multiplication required by the present invention comes from 7V-IFFT, that is, (M2) log2iV complex multiplication operations are required. The required memory is #units. When M=4, the implementation diagram is as shown in the tenth figure. The sequence ^φ?], " = 0,1,···, the 解 multiplexer 7〇1 is divided into four sub-blocks of length #/4, {χ[〇],...,χ[〇/4 )- 1]丨,丨16 1255105 /4],··.,4(#/2)- 1] },Μ#/2],···,4(3#/4)-1] }, And {jc[3# /4],...,jc[iV- 1] }. The combiner 1003 combines the four sub-blocks of length 7V/4 to form a discrete time series of the following four lengths: [n] = x[n] + x[((n - N/2))n] + x[((n - N/4)) n ] + x[((n ^ 3N/4))] ] y3 [n] = x[n] + x[((n - N/2))n ] - x[(( n - N/4)) n ] - x[((n - 3N/4))n ] y2 [n] = x[n] - x[(( n - N/2)) N ] + jx[((n - N/4))n] - jx[((n - 3N/4))n] γ4 [n] = x[n] - x[(( n - N/2)) N ] - jx[(( n - N / 4)) n ] + jx[((n - 3N / 4)) n ] (12) Combiner 1003 is implemented with eight adders and a multiplier of imaginary number j The formula (I2) has the same structure as the 4_IFFT. It can be proved that the discrete time series obtained in (12) is (4), is [«], is (4), and (4) is equivalent to the discrete time series ΧιΜ, 々Μ, Χ3Μ, αΜ generated by the original pts method in the second figure. Similarly, using the symmetry property, 0, 1, and the phase rotation parameter & is shown in Fig. As can be seen from the tenth figure, when 4 is +1,], +j or _], the present invention requires a total of (iV/2) log 27V complex multiplication operations, and the required memory is #一〇〇早早兀. Figure 12 is a comparison of the amount of computation and memory requirements of the present invention with the other three pTS implementation methods, where M = 4 and the sizes of N are 64, 256, 1024, and 2048, respectively. It can be seen that both the amount of computation and the memory requirement increase as N increases. Compared with the pts implementation method of the original and 〖, ^ and j〇〇, the number of multiplications required by 17 1255105 is the least in the pTS implementation method of the present day and month, and the memory requirement list is also the least. The number of multiplications required by the two is the same, 192, 1024, 5120, and 11264. The memory requirement units are also the same, 64, 256, and 2048, respectively. However, in the m implementation method of the present invention, the signal Μ purchased by 〇f is not required to be shortened, so that the characteristics and advantages of the FDM county are still achieved. In summary, the present invention utilizes the characteristics of PTS interleaving blocks, and only provides a method and apparatus for effectively reducing the mean value of the orthogonal frequency division multiplexing. Significantly reduce the amount of calculation, the number of complex multiplications is _1, and the required memory is a solid unit, and still retains the advantages and advantages of GFDM County. In the above description, the preferred embodiment of the invention of the present invention is not limited to the actual shape. That is, the equivalent changes and modifications made by the applicant in accordance with the scope of the patent application of the present invention should remain within the scope of this patent. [Simple description of the diagram] The first figure illustrates a system block diagram of a conventional multi-carrier communication system for an OFDM transmitter. The second figure illustrates a technique for resolving the south PAPR of an OFDM transmitter signal using the pTS method. The third figure illustrates three ways of dividing the input data A:] into sub-blocks (contiguous and irregular) of sub-blocks (or groups) in the frequency domain. The fourth figure illustrates the implementation method proposed by Kang, Kim, and J〇〇 to reduce the amount of pts. The fifth figure illustrates the implementation of the reduced PTS computation and memory proposed by Samsung. Figure 6 is a schematic diagram of a method of reducing the PAPR value of an OFDM signal of the present invention. Figure 7 is a block diagram showing the structure of an apparatus for reducing the PAPR value of an OFDM signal of the present invention. The eighth figure is a first preferred embodiment of the present invention according to the seventh drawing. The ninth figure illustrates the setting of the phase rotation parameter in the eighth figure when M=2. The tenth embodiment is a second preferred embodiment of the present invention according to the seventh drawing. Dimensional • Figure shows the setting of the phase rotation parameter in the tenth figure when Μ=4. The twelfth figure is a comparison of the complex multiplication operation amount and the memory requirement of the present invention and the other three PTS implementation methods. Description of the figure: 601 #点反逆傅 Fourier transform 1255105 603 time domain signal segmentation 605 combiner 607 phase optimization processing and synthesis 701 solution multiplexer 705 memory 803 combiner 1003 combiner 703 combiner 707 adder 803a , 803b adder

2020

Claims (1)

曰修(更)正替換頁 12輒 拾、申請專利範圍: 1 · 一種降低正交分頻多工信號峰均值、 、J万法,包括 下面步驟:在時域上將長度y的一離散時間序列/ 劃分為Μ個不互相重疊的子區塊,从糸 巧ζ的次冪,每 一子區塊的長度為,且ΑΓ/Μ為大於] 、丄的整數;再曰修(more) is replacing page 12, patent application scope: 1 · A method for reducing the peak-to-average value of the orthogonal frequency division multiplexing signal, and the J-method, including the following steps: a discrete time of length y in the time domain The sequence / is divided into sub-blocks that do not overlap each other. From the power of 糸巧ζ, the length of each sub-block is, and ΑΓ/Μ is an integer greater than , 丄; 將上述Μ個不互相重疊的子區塊經一轉換組合將該# 個不互相重疊的子區塊經-組合H,形成另外則固長 度皆為Λ7Μ的子序列八[π],其中hi,2,· ·,从且” =〇 1,…,(A「/W>1;以及一相位最佳化處理將該从個子序列 ΛΙΧ1經相位旋轉且相加在一起,以形成一完整的#點傳 送<3號对η],其中#為一正交分頻多工信號的長度 且《 = 1,."’AM。 2·如申請專利範圍第1項所述之降低正交分頻多工信 號峰均值的方法,其中該轉換組合等同一個反向快速 傅立葉轉換。Subdividing the above-mentioned sub-blocks that do not overlap each other by a combination of the two non-overlapping sub-blocks by - combining H to form a sub-sequence of eight [π] whose solid length is Λ7Μ, where hi, 2, · ·, from and "= 〇1,...,(A"/W>1; and a phase optimization process that rotates the subsequences ΛΙΧ1 by phase and adds them together to form a complete # Point transmission <3nd pair η], where # is the length of an orthogonal frequency division multiplexing signal and "= 1,."'AM. 2. Reduce the orthogonality as described in claim 1 A method of frequency multiplexed signal peak mean, wherein the transform combination is equivalent to an inverse fast Fourier transform. 3·如申請專利範圍第丨項所述之降低正交分頻多工信 號峰均值的方法,其中該Μ值為2。 4·如申請專利範圍第1項所述之降低正交分頻多工信 號峰均值的方法,其中該Μ值為4。 5·如申請專利範圍第3項所述之降低正交分頻多工信 號峰均值的方法,其中,該子序列Λ[η]由以下的兩 個長度皆為iV/2的子區塊組合而成: 213. The method for reducing the peak-to-average value of the orthogonal frequency division multiplexing signal as described in the scope of the patent application, wherein the threshold value is 2. 4. The method of reducing the peak-to-average value of the orthogonal frequency division multiplexing signal as described in claim 1 of the patent application, wherein the threshold value is 4. 5. The method for reducing the peak mean value of the orthogonal frequency division multiplexing signal as described in claim 3, wherein the sub-sequence Λ[η] consists of the following two sub-block combinations each having an iV/2 length Made of: 21 yM^x[n]^x[{{n-Nl2))N] y2[n}^x[n}-x[{{n-Nl2))N] 其中 ’((·))^γ 表示循環位移 #點,77 =: 0, 1,...,。 6·如申凊專利範圍第4項所述之降低正交分頻多工信 號峰均值的方法,其中,該子序列八㈤由以下的四 個長度皆為iV/4的子區塊組合而成: [«] = x[n] + x[((n ^ N/2))Ν] + χ[((η - Ν/4))ν] + χ[((η -3Ν/4))ν] y3 [η] = χ[η] + χ[((η - Ν/2))ν ] - χ[((η ~ Ν/4))ν ] - χ[((η ^ 3Ν/4))ν ] 3^2 [η] = x[n] - χ[((η - Ν/2))ν ] + jx[((n - Ν/4))ν ] - jx[((n ^ 3Ν/4))ν ] y4 [«] = χ[η] - χ[((η - Ν/2))ν ] - jx[((n - Ν/4))ν ] + jx[((n - 3Ν/4))ν ] 其中’((·))#表示循環位移見點,π = 〇, 1,. .,。 7·如申凊專利範圍第3項所述之降低正交分頻多工信 號峰均值的方法,其中,該相位旋轉參數為可能的數 值{+1,-1}。 8.如申請專利範圍第4項所述之降低正交分頻多工信 號峰均值的方法,其中,該相位旋轉參數為可能的數 值{+1,-1,+»}。 9· 一種降低正交分頻多工信號峰均值的裝置,包含 有: 一解多工器,將長度ΛΓ的一輸入的離散時間序列对y 劃分為Μ個不互相重疊且長度相等的子區塊,其中打= 0,1,…,AM ’ W為大於1的整數,从為2的次幕,且 Λ7Μ為大於1的整數; 一組合器,將該Μ個不互相重疊的子區塊形成另外从 22 is^+05--η 言年?月5日修(更.)正替换頁 個長度皆為撕^的子序列八[XI,其中hi,2,...,M且π —Ο, 1, ... ? (Λ7Λ/)-1 * 一加法器,該Μ個子序列八㈤經相位旋轉後,經由該 加法器相加在一起,以形成一完整的#點傳送信號 χ|>ι];以及 一組記憶體,先後儲存該Μ個不互相重疊的子區塊和 該Μ個子序列八[n]。 10.如申請專利範圍第9項所述之降低正交分頻多工信 號峰均值的裝置,其中Μ為4,且該組合器以八個 加法器和一個虛數j的乘法器來實現。 11·如申請專利範圍第9項所述之降低正交分頻多工信 號峰均值的裝置,其中Μ為2,且該組合器以兩個 加法器來實現。 12·如申請專利範圍第9項所述之降低正交分頻多工信 號峰均值的裝置,其中該裝置只需用到一個y點反 向快速傅立葉轉換。 13 ·如申請專利範圍第11項所述之降低正交分頻多工信 號峰均值的裝置’其中’該子序列八[/7]由以下的兩 個長度皆為7V/2的子區塊組合而成: y^n]^x[n]^x[((n-N/2))N] y2[«] = x[«]-x[({n - Ν/2))Ν] 其中,((.瓜表示循環位移#點1 = 0,1,...,〇^/2)-1。 14.如申請專利範圍第ι〇項所述之降低正交分頻多工信 號峰均值的裝置,其中,該子序列八间由以下的四 23yM^x[n]^x[{{n-Nl2))N] y2[n}^x[n}-x[{{n-Nl2))N] where '((·))^γ denotes a loop Displacement #point, 77 =: 0, 1,...,. 6. The method for reducing the peak mean value of the orthogonal frequency division multiplexing signal according to item 4 of the claim patent scope, wherein the sub-sequence eight (five) is composed of the following four sub-block combinations each having an iV/4 length; Cheng: [«] = x[n] + x[((n ^ N/2))Ν] + χ[((η - Ν/4))ν] + χ[((η -3Ν/4)) ν] y3 [η] = χ[η] + χ[((η - Ν/2))ν ] - χ[((η ~ Ν/4))ν ] - χ[((η ^ 3Ν/4) )ν ] 3^2 [η] = x[n] - χ[((η - Ν/2))ν ] + jx[((n - Ν/4))ν ] - jx[((n ^ 3Ν /4))ν ] y4 [«] = χ[η] - χ[((η - Ν/2))ν ] - jx[((n - Ν/4))ν ] + jx[((( 3Ν/4))ν ] where '((·))# indicates that the cyclic displacement is seen, π = 〇, 1, . 7. The method of reducing the peak-to-average value of the orthogonal frequency division multiplexing signal as described in claim 3, wherein the phase rotation parameter is a possible value {+1, -1}. 8. The method of reducing the peak mean value of an orthogonal frequency division multiplexing signal as described in claim 4, wherein the phase rotation parameter is a possible value {+1, -1, +»}. 9. A device for reducing a peak-to-average value of an orthogonal frequency division multiplexing signal, comprising: a demultiplexer, dividing a length time series y of an input of length ΛΓ into two sub-regions that are not overlapping each other and of equal length Block, where hit = 0,1,...,AM 'W is an integer greater than 1, from the second curtain of 2, and Λ7Μ is an integer greater than 1; a combiner, the sub-blocks that do not overlap each other Forming another from 22 is^+05--η years? On the 5th of the month, the repair (more.) is replacing the sub-sequences of the page length [X, where hi, 2, ..., M and π - Ο, 1, ... ? (Λ7Λ/)- 1 * an adder, the sub-sequences of eight (f) are phase-rotated, added together via the adder to form a complete #dot transmission signal &|>ι]; and a set of memory, sequentially stored The sub-blocks that do not overlap each other and the sub-sequences are eight [n]. 10. Apparatus for reducing the peak-to-average value of an orthogonal frequency division multiplexing signal as recited in claim 9 wherein Μ is 4 and the combiner is implemented with a multiplier of eight adders and an imaginary number j. 11. The apparatus for reducing the peak-to-average value of the orthogonal frequency division multiplexing signal as recited in claim 9, wherein Μ is 2, and the combiner is implemented by two adders. 12. A device for reducing the peak-to-average value of an orthogonal frequency division multiplexing signal as described in claim 9 wherein only one y-point inverse fast Fourier transform is used. 13 · The device for reducing the peak mean value of the orthogonal frequency division multiplexing signal as described in claim 11 of the patent scope 'where' the subsequence eight [/7] consists of the following two sub-blocks each having a length of 7V/2 Combined: y^n]^x[n]^x[((nN/2))N] y2[«] = x[«]-x[({n - Ν/2))Ν] where, ((. melon represents cyclic displacement #点1 = 0,1,...,〇^/2)-1. 14. Reduce the peak mean value of orthogonal frequency division multiplexing signal as described in the application scope Device, wherein the subsequence is eight by the following four 23 個長度皆為#/4的子區塊組合而成: [«] = + x[((^ - N/2)), ] + x[((az - iV/4))^ ] + x[((« - 3N/4))n] y3[^] = x[n] + x[{{n - N/2))n] - x[((^ - N/4))n] - x[((^ - 3N/4))n] [^] = An\ - - N/2))n ] + jx[((n - N/4))n ] - jx[((n - 3N/4))n ] [n] = x[n] - x[((n - N/2))n] - jx[{{n - N/A))n] + jx[((n - 3N/4))n] 其中,((·瓜表示循環位移見點,"=〇, 1,...,(///4)4。 15.如申請專利範圍第11項所述之降低正交分頻多工信 號峰均值的裝置,其中,該相位旋轉參數為可能的數 值{+1,-1}。 16 ·如申請專利範圍第10項所述之降低正交分頻多工信 號峰均值的裝置,其中,該相位旋轉參數為可能的數 值{+1,-1,+/-7} 〇 24Sub-blocks of length #/4 are combined: [«] = + x[((^ - N/2)), ] + x[((az - iV/4))^ ] + x[ ((« - 3N/4))n] y3[^] = x[n] + x[{{n - N/2))n] - x[((^ - N/4))n] - x [((^ - 3N/4))n] [^] = An\ - - N/2))n ] + jx[((n - N/4))n ] - jx[((n - 3N/ 4))n ] [n] = x[n] - x[((n - N/2))n] - jx[{{n - N/A))n] + jx[((n - 3N/ 4))n] where ((·· melon indicates the cyclic displacement see point, "=〇, 1,...,(///4)4. 15. Reduce the positive as described in claim 11 A device for intersecting a peak value of a frequency division multiplexing signal, wherein the phase rotation parameter is a possible value {+1, -1}. 16 - reducing the orthogonal frequency division multiplexing signal peak as described in claim 10 Mean value device, wherein the phase rotation parameter is a possible value {+1, -1, +/- 7} 〇 24 拾壹、圖式: 附加第一圖〜第十二圖,共12頁。 25Pick up, schema: Attach the first map ~ twelfth map, a total of 12 pages. 25
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