Asymmetrically clipped optical OFDM with generalized index modulation for atmospheric turbulent channel

大气湍流信道中的广义索引调制非对称限幅光OFDM Asymmetrically clipped optical OFDM with generalized index modulation for atmospheric turbulent channel corresp first-author E-mail： Whq1222@lut.edu.cn E-mail： Whq1222@lut.edu.cn 王惠琴（1971-），女，甘肃渭源人，教授，博士生导师，2011年于西安理工大学获得博士学位，主要从事无线光通信理论与与技术研究。E-mail：Whq1222@lut.edu.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935645&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935648&type= 22.01332855 32.00399780 王惠琴 （1971-），女，甘肃渭源人，教授，博士生导师，2011年于西安理工大学获得博士学位，主要从事无线光通信理论与与技术研究。E-mail： Whq1222@lut.edu.cn Whq1222@lut.edu.cn 豆红霞（1996-），女，甘肃张掖人，硕士研究生，主要从事无线光通信方面的研究。E-mail：Dou_hongxia @126.com豆红霞（1996-），女，甘肃张掖人，硕士研究生，主要从事无线光通信方面的研究。E-mail：Dou_hongxia @126.com http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935653&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935656&type= 22.01332855 32.00399780 豆红霞 （1996-），女，甘肃张掖人，硕士研究生，主要从事无线光通信方面的研究。E-mail：Dou_hongxia @126.com 豆红霞 （1996-），女，甘肃张掖人，硕士研究生，主要从事无线光通信方面的研究。E-mail：Dou_hongxia @126.com 兰州理工大学计算机与通信学院，甘肃 兰州 730050 兰州理工大学计算机与通信学院，甘肃 兰州 730050 School of Computer and Communication， Lanzhou University of Technology， Lanzhou， Gansu 730050， China School of Computer and Communication， Lanzhou University of Technology， Lanzhou， Gansu 730050， China 索引调制光OFDM虽可实现高频谱效率，但其误码性能还不够理想。为此，本文结合非对称限幅光OFDM技术，通过每组激活数目不等的子载波，提出了一种广义索引调制非对称限幅光OFDM（Asymmetrically Clipped Optical OFDM with Generalized Index Modulation， ACO-OFDM-GIM）方案。每个子载波块中选择激活数目不唯一的子载波，同时引入子载波分配算法进一步提升了系统的误码性能。文中详细介绍了ACO-OFDM-GIM调制映射原理，推导了其在湍流信道下的理论误码率，并采用仿真实验进一步验证了其性能。结果表明，与ACO-OFDM、ACO-OFDM-IM等系统对比，ACO-OFDM-GIM系统的传输速率和误码性能都有明显改善。在频谱效率相同的情况下，ACO-OFDM-GIM系统在大信噪比时能够获得比ACO -OFDM和ACO-OFDM-IM系统更好的误码性能。当误码率为 <math id="M1"><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935667&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935662&type= 11.59933376 3.38666677 时，强湍流条件下（4，［1，2］）ACO-OFDM-GIM系统的信噪比相对于（4，2）ACO-OFDM-IM和ACO-OFDM系统分别改善了约 <math id="M2"><mn mathvariant="normal">2.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935673&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935670&type= 8.38199997 2.37066650 和 <math id="M3"><mn mathvariant="normal">4.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935679&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935675&type= 8.38199997 2.37066650 。ACO-OFDM-GIM方案为未来大气激光通信传输速率的提高提供了一种有效手段。 Optical orthogonal frequency division multiplexing （OFDM） with index modulation has the advantage of high spectral efficiency （SE）； however， the error performance is not optimal. In this paper， a scheme of asymmetrically clipped optical OFDM with generalized index modulation （ACO-OFDM-GIM） is proposed. In this scheme， the number of active subcarriers in each sub-block can be one or more， and these subcarriers extend the frequency domain modulation. Furthermore， a subcarrier allocation algorithm is adopted to eliminate the correlation between adjacent subcarriers. In this way， a better error performance may be achieved. Taking asymmetrically clipped O-OFDM-GIM （ACO-OFDM-GIM） as an example， the modulation mapping principle of O-OFDM-GIM has been introduced in detail. In addition， the asymptotic bit error probability of the ACO-OFDM-GIM scheme for the turbulence channel is derived and the correctness is verified via simulation. Furthermore， the performance of the ACO-OFDM-GIM system is compared with that of ACO-OFDM and ACO-OFDM-IM systems. The results showed that the transmission rate and the error performance of the ACO-OFDM-GIM scheme are improved compared with the ACO-OFDM-IM and ACO-OFDM schemes. When the SE is indifferent， the error performance of the proposed scheme is greater than ACO-OFDM and ACO-OFDM-IM systems at a large signal noise ratio （SNR）. When the bit error rate is 1×10 - 4 ， the SNR of （4，［1，2］） ACO-OFDM-GIM scheme outperforms that of （4，2） ACO-OFDM-IM and ACO-OFDM schemes nearly 2.5 dB and 4.5 dB， under a strong turbulence channel， respectively. Therefore， the ACO-OFDM-GIM scheme is expected to effectively improve the transmission rate of atmospheric laser communication in the future. 广义索引调制 光OFDM 子载波分配算法 误码性能 generalized index modulation optical OFDM subcarrier allocation algorithm error performance 1 引　言 1 光正交频分复用（Optical Orthogonal Frequency Division Multiplexing，O-OFDM） ［ 1 1 - 5 5 1-5 ］ 作为一种多载波调制技术，能够以较高的频谱利用率提升无线光通信（Wireless Optical Communication， WOC）系统的传输速率，而且其所采用的正交子载波能有效抑制大气湍流和大气散射等干扰，成为当今最具发展前景的一种调制技术。但O-OFDM仍然存在峰均（Peak-to Average Power Ratio，PAPR）比过高、对相位噪声和载波频偏十分敏感等问题。这些缺点使得O-OFDM技术难以满足未来智能时代用户对通信技术的容量和速率提出的全新要求。在这种背景下，如何实现超大容量、超高速率以及更低时延的WOC通信已迫在眉睫。因此，探索并寻找一种具有开创性的调制技术是其关键。近年来，受空间调制技术 ［ 6 6 ］ 思想的启发而出现的索引调制（Index Modulation， IM）技术 ［ 7 7 ］ 为解决该问题提供了一个突破口。它通过扩展空间维度，利用子载波索引号额外携带部分信息实现了传输速率的大幅提高。索引调制技术最早起源于射频通信，目前已经取得了丰硕的成果 ［ 8 8 - 10 10 8-10 ］ ，而有关WOC中索引调制技术的研究才刚刚起步 ［ 11 11 - 18 18 11-18 ］ 。文献［ 11 11 ］首次将索引调制与O-OFDM调制方案相结合，研究了索引调制光OFDM （O-OFDM with Index Modulation， O-OFDM-IM）技术。研究结果表明，O-OFDM-IM系统比传统的O-OFDM系统可获得更高的频谱效率。但是，随着频谱效率的增大，O-OFDM-IM的误码性能逐渐趋于O-OFDM系统甚至比后者差。后来，文献［ 12 12 ］提出了一种双模索引调制直流偏置光OFDM（DC Biased Optical OFDM with Dual-mode Index Modulation， DM-DCO-OFDM）方案。该方案通过传输两种互不重叠的星座符号实现了系统频谱效率的提升。在此基础之上，文献 ［ 13 13 ］ 又将IM与DCO-OFDM方案相结合，提出了索引调制直流偏置光OFDM （DC Biased Optical OFDM with Index Modulation， OIM-DCO-OFDM）调制方案。研究结果表明，在相同的频谱效率下OIM-DCO-OFDM比DM-DCO-OFDM具有更好的误码性能。随后，其他索引技术也相继在WOC领域被提出 ［ 14 14 - 18 18 14-18 ］ 。虽然上述研究已取得了一定的成果，但有关WOC中索引调制技术的研究才刚刚起步，其理论还不够成熟和完善，且其传输速率和误码性能还有待进一步的提升。 为了满足WOC系统超高速率和高可靠性的通信目标，本文结合非对称限幅光OFDM，通过在每个子载波块中激活一到多个数目不等的子载波提出了一种广义索引调制非对称限幅光OFDM（Asymmetrically Clipped Optical OFDM with Generalized Index Modulation， ACO-OFDM-GIM）方案，同时引入子载波分配算法（Subcarrier Allocation Algorithm， SAA） ［ 19 19 ］ 进一步实现了系统误码性能的提升。 2 ACO-OFDM-GIM系统模型 1 对于有N个子载波的ACO-OFDM-GIM系统，其系统模型如 图1 图1 所示。在 图1 图1 中，首先根据每帧OFDM-GIM传输的比特数，将二进制比特流进行分帧，然后将每帧的二进制信息经串/并变换后转换成长度为 z 的组数据流。该组数据流经广义索引调制及合并后生成OFDM-GIM数据块。该数据块经子载波分配算法之后，再利用逆傅里叶变换（IFFT）的厄米特对称性与限幅技术相结合的方法将复数/负数信号转换为正实信号，由激光器经光学发射天线后发送出去。在接收端将接收到的信号经过相反的处理之后，再利用最大似然检测准则（ML）即可恢复出原始比特。假设一帧OFDM-GIM发送的二进制比特和子载波总数分别为 <math id="M4"><mi>m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935685&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935682&type= 2.79399991 2.79399991 和 <math id="M5"><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935691&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935688&type= 2.87866688 2.87866688 ，那么每个子载波块中包含的子载波数和信息比特数分别为 <math id="M6"><mi>n</mi><mo>=</mo><mi>N</mi><mo>/</mo><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936293&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936288&type= 12.78466606 3.30200005 和 <math id="M7"><mi>z</mi><mo>=</mo><mi>m</mi><mo>/</mo><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935698&type= 12.53066730 3.30200005 。由 图1 图1 可见，首先将输入的二进制信息比特流进行分帧，每帧长度为 m 。然后将每帧的数据经过串/并变换转换成长度为 z 的 <math id="M8"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936285&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936281&type= 1.52400005 2.79399991 组数据流。由于每个子载波块有着同样的处理过程，因此以第 <math id="M9"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块为例详细说明信号的映射过程。与传统的索引调制光OFDM（O-OFDM-IM）相比，所提方案在每个子载波块中有一到多个数目不等的子载波被激活，所以第 <math id="M10"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块中待激活子载波数的集合 <math id="M11"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 可定义为 <math id="M12"><mi mathvariant="bold-italic">k</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mi>k</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>,</mo><mi>k</mi><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>k</mi><mo stretchy="false">(</mo><mi>δ</mi><mo stretchy="false">)</mo><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>k</mi><mo stretchy="false">(</mo><mi mathvariant="normal">𝓁</mi><mo stretchy="false">)</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935727&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935723&type= 55.79533768 4.31799984 。其中， <math id="M13"><mi>k</mi><mo stretchy="false">(</mo><mi>δ</mi><mo stretchy="false">)</mo><mo>∈</mo><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935734&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935731&type= 12.19200039 3.55599999 ，（ <math id="M14"><mi>δ</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi mathvariant="normal">𝓁</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935737&type= 17.69533348 3.21733332 ）为每个子载波块待激活的子载波数量， <math id="M15"><mi mathvariant="normal">𝓁</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935747&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935743&type= 1.52400005 2.87866688 （ <math id="M16"><mn mathvariant="normal">1</mn><mo><</mo><mi mathvariant="normal">𝓁</mi><mo><</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935757&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935750&type= 14.56266594 2.87866688 ）为待激活子载波数集合 <math id="M17"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 的长度。当激活 <math id="M18"><mi>k</mi><mo stretchy="false">(</mo><mi>δ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935787&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935783&type= 7.28133297 3.55599999 个子载波时，激活子载波的组合形式有 <math id="M19"><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935790&type= 6.68866634 3.72533321 种，其中， <math id="M20"><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935790&type= 6.68866634 3.72533321 为二项式系数。由于使用的激活子载波索引号的组合数必须是2的整数次幂，所以当激活 <math id="M21"><mi>k</mi><mo stretchy="false">(</mo><mi>δ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935787&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935783&type= 7.28133297 3.55599999 个子载波时，只需从 <math id="M22"><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935790&type= 6.68866634 3.72533321 种组合中选取 <math id="M23"><msubsup><mrow><mi>ϑ</mi></mrow><mrow/><mrow><mi>δ</mi></mrow></msubsup><mo>=</mo><msubsup><mrow><mn mathvariant="normal">2</mn></mrow><mrow/><mrow><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></mrow></mfenced></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935801&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935797&type= 19.38866615 6.09600019 种即可，其中 <math id="M24"><mfenced open="⌊" close="⌋" separators="|"><mrow><mo>·</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935808&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935805&type= 3.30200005 3.97933316 表示向下取整运算。那么，在第 <math id="M25"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块中备用子载波索引号的组合共有 <math id="M26"><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi>k</mi></mrow></munder><mrow><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935823&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935819&type= 13.88533401 7.19666624 种，其中，可用的子载波索引号组合为 <math id="M27"><mi>ϑ</mi><mo>=</mo><msup><mrow><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi>k</mi></mrow></munder><mrow><mi>ϑ</mi></mrow></mrow><mrow><mi>δ</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935832&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935827&type= 18.28800011 7.95866632 种。假设将 <math id="M28"><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936988&type= 6.94266701 3.97933316 个 <math id="M29"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935844&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935841&type= 3.38666677 2.87866688 阶调制符号加载在激活子载波上，那么，第 <math id="M30"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块中备用的调制符号的组合共 <math id="M31"><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935859&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935854&type= 7.53533268 3.30200005 种。由此可得，第 <math id="M32"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块上发送的总比特数为 <math id="M33"><mi>Z</mi><mo>=</mo><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfenced separators="|"><mrow><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi>k</mi></mrow></munder><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></mrow></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935873&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935868&type= 40.89400101 11.51466751 。此时，每个子载波块上OFDM频域信号有 <math id="M34"><msubsup><mrow><mn mathvariant="normal">2</mn></mrow><mrow/><mrow><mi>z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935878&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935876&type= 2.96333337 3.89466691 种实现形式。 在广义索引调制中同样也包含索引映射和调制符号映射，所以首先将输入的 <math id="M35"><mi>z</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935922&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935918&type= 1.69333339 2.79399991 比特二进制信息动态地分为 <math id="M36"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935982&type= 2.79399991 3.72533321 bits和 <math id="M37"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 bits。其中， <math id="M38"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935982&type= 2.79399991 3.72533321 bits被映射为每个子载波块内激活子载波索引号的组合， <math id="M39"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 比特被映射为激活子载波索引号上发送的调制符号。当 <math id="M40"><mi>z</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935922&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935918&type= 1.69333339 2.79399991 固定时， <math id="M41"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mi>z</mi><mo>-</mo><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935929&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935926&type= 17.10266685 3.72533321 随着 <math id="M42"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 的变化而变化。此时 <math id="M43"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 为： <math display="block" id="M44"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>M</mi><mtext>    </mtext><msub><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext>   </mtext><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msubsup><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>M</mi><mtext>    </mtext><msub><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msubsup><mo>,</mo><mtext>   </mtext><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced></mrow></msubsup><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mtext>       </mtext><mo>⋮</mo><mtext>                                              </mtext><mo>⋮</mo></mtd></mtr><mtr><mtd><mi>k</mi><mfenced separators="|"><mrow><mi mathvariant="normal">𝓁</mi></mrow></mfenced><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>M</mi><mtext>     </mtext><msub><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi mathvariant="normal">𝓁</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi mathvariant="normal">𝓁</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msubsup><mo>,</mo><mtext>   </mtext><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi mathvariant="normal">𝓁</mi></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi mathvariant="normal">𝓁</mi></mrow></mfenced></mrow></msubsup><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935945&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935943&type= 86.02133942 24.12999916 ， 其中， <math id="M45"><msub><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936139&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936137&type= 2.96333337 3.72533321 表示每个子载波块传输的二进制字符串的十进制形式。 在ACO-OFDM-GIM系统中，如何将 <math id="M46"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935982&type= 2.79399991 3.72533321 比特的二进制信息映射到子载波索引号上是一个关键。在进行具体的映射之前，首先根据第 <math id="M47"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块确定待激活子载波数集合 <math id="M48"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935969&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935967&type= 1.86266661 2.79399991 ，同时将信息比特分为 <math id="M49"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935982&type= 2.79399991 3.72533321 和 <math id="M50"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 两部分。然后将 <math id="M51"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935982&type= 2.79399991 3.72533321 比特转换成十进制数 <math id="M52"><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935987&type= 3.97933316 4.06400013 ，并将其与每组待激活 <math id="M53"><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936988&type= 6.94266701 3.97933316 个子载波时第一种组合方式所对应的十进制数 <math id="M54"><msubsup><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20935998&type= 3.97933316 4.31799984 相减，即 <math id="M55"><msubsup><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub><mo>-</mo><msubsup><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936005&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936004&type= 21.84399986 4.31799984 。然后依据 <math id="M56"><msubsup><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936010&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936008&type= 3.97933316 4.06400013 的值设定待激活 <math id="M57"><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936988&type= 6.94266701 3.97933316 个子载波索引号的组合，其映射关系可表示为一个 <math id="M58"><mn mathvariant="normal">1</mn><mo>×</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936015&type= 8.38199997 2.79399991 维的矩阵 <math id="M59"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mo>⋯</mo><mo>,</mo><mn mathvariant="normal">0,1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mn mathvariant="normal">0,1</mn><mo>,</mo><mo>⋯</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mtext>                    </mtext><mover><mrow><msubsup><mrow><mi>i</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>ε</mi></mrow></mfenced></mrow><mrow><mo>↑</mo></mrow></mover><mtext>     </mtext><mover><mrow><msubsup><mrow><mi>i</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>o</mi></mrow></mfenced></mrow><mrow><mo>↑</mo></mrow></mover></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936018&type= 41.23266602 12.27666664 。其中，非零元素的位置 <math id="M60"><msubsup><mrow><mi>i</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>ε</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936021&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936020&type= 7.11199999 4.06400013 ， <math id="M61"><msubsup><mrow><mi>i</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>o</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936022&type= 7.53533268 4.06400013 表示激活子载波的索引号。 在完成子载波的索引映射之后，依据调制符号的映射规则完成调制符号映射，并将其加载在激活子载波上。假设采用 M -QAM调制，依据该数字调制方式的映射规则，将 <math id="M62"><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936024&type= 2.79399991 3.72533321 比特的二进制信息映射成 <math id="M63"><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936988&type= 6.94266701 3.97933316 个QAM星座调制符号。假设映射后的星座调制符号集合为 <math id="M64"><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>α</mi></mrow></mfenced></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936032&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936031&type= 62.82266998 5.50333309 。其中， <math id="M65"><mi>k</mi><mfenced separators="|"><mrow><mi>α</mi></mrow></mfenced><mo>∈</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936034&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936033&type= 14.22399998 4.06400013 ， <math id="M66"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936583&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936579&type= 2.87866688 3.97933316 为激活子载波索引号的集合， <math id="M67"><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>α</mi></mrow></mfenced></mrow></mfenced><mo>∈</mo><mi mathvariant="fraktur">R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936040&type= 20.74333191 4.74133301 ， <math id="M68"><mi mathvariant="fraktur">R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936046&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936045&type= 2.87866688 2.79399991 表示 M -QAM的所有星座点集合。将映射后的调制符号加载在第 <math id="M69"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块中的激活子载波上，那么，第 <math id="M70"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块上的OFDM频域信号 <math id="M71"><msubsup><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936051&type= 3.47133350 3.97933316 可表示为： <math display="block" id="M72"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>=</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>δ</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">𝓁</mi></mrow></munderover></mstyle><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936056&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936055&type= 20.82799911 8.46666718 . 为了便于更直观的理解整个广义索引调制的映射过程，我们以 n =4， <math id="M73"><mi mathvariant="bold-italic">k</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">2</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936058&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936057&type= 15.49400043 3.97933316 ，调制阶数 M =4为例详细说明其映射原理。在该系统中，每个子载波块发送 <math id="M74"><mi mathvariant="normal">z</mi><mo>=</mo><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfenced separators="|"><mrow><msubsup><mrow><mn mathvariant="normal">4</mn></mrow><mrow/><mrow><mn mathvariant="normal">1</mn></mrow></msubsup><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mn mathvariant="normal">4</mn></mrow><mrow/><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfenced></mrow></mfenced><mo>=</mo><mn mathvariant="normal">6</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936060&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936059&type= 44.78866577 5.16466665 bits二进制信息，每个子载波块OFDM频域信号有 <math id="M75"><msubsup><mrow><mn mathvariant="normal">2</mn></mrow><mrow/><mrow><mn mathvariant="normal">6</mn></mrow></msubsup><mo>=</mo><mn mathvariant="normal">64</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936065&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936063&type= 11.76866722 3.97933316 种实现形式。其结果如表 1 1 ~ 2 2 所示。 z d z 1 z 2 d' z 1 <math id="M76"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936098&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936096&type= 2.53999996 3.38666677 <math id="M77"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936102&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936100&type= 2.96333337 3.38666677 0 0000* 01 0 <math id="M78"><mo stretchy="false">[</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>,</mo><mn>0,0</mn><mo>,</mo><mn>0</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936077&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936075&type= 19.13466644 4.06400013 1 0000 01 0 <math id="M79"><mo stretchy="false">[</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>,</mo><mn>0,0</mn><mo>,</mo><mn>0</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936081&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936079&type= 19.13466644 4.06400013       14 0011 10 3 [0 0 0 1 1 ] <math id="M80"><mo stretchy="false">[</mo><mn>0,0</mn><mo>,</mo><mn>0</mn><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936085&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936083&type= 19.38866615 4.06400013 15 0011 11 3 [0 0 0 1 1 ] <math id="M81"><mo stretchy="false">[</mo><mn>0,0</mn><mo>,</mo><mn>0</mn><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936090&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936088&type= 19.38866615 4.06400013 z d z 1 z 2 d' z 1 <math id="M82"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936098&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936096&type= 2.53999996 3.38666677 <math id="M83"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936102&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936100&type= 2.96333337 3.38666677 16 01* 0000 0 <math id="M84"><mo stretchy="false">[</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>,</mo><mn>0,0</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936106&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936104&type= 24.38400078 4.06400013 17 01 0001 0 <math id="M85"><mo stretchy="false">[</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>,</mo><mn>0,0</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936111&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936108&type= 24.38400078 4.06400013       62 11 1110 2 [0 0 1 1 ] <math id="M86"><mo stretchy="false">[</mo><mn>0,0</mn><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936115&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936113&type= 24.63800049 4.06400013 63 11 1111 2 [0 0 1 1 ] <math id="M87"><mo stretchy="false">[</mo><mn>0,0</mn><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>,</mo><msubsup><mrow><mi>s</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936120&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936118&type= 24.63800049 4.06400013 其中， 表1 表1 为第 <math id="M88"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块中仅激活一个子载波时的映射表，OFDM频域信号的实现形式有 <math id="M89"><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msubsup><mo>=</mo><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msubsup><mo>=</mo><mn mathvariant="normal">16</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936135&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936133&type= 35.13666534 4.82600021 种。如当 <math id="M90"><msub><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936139&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936137&type= 2.96333337 3.72533321 =2时， <math id="M91"><msubsup><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mn mathvariant="normal">0</mn><mo>-</mo><mn mathvariant="normal">0</mn><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936147&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936143&type= 24.12999916 4.06400013 ，选择激活第1个子载波来传输所对应的调制符号，即 <math id="M92"><mn mathvariant="normal">01</mn><mo>→</mo><mfenced open="{" close="}" separators="|"><mrow><mo>-</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>i</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936153&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936150&type= 23.02933502 3.97933316 ，那么，相应的OFDM频域信号为 <math id="M93"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msubsup><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mo>-</mo><mn mathvariant="normal">1</mn><mo>+</mo><mi>i</mi><mo>,</mo><mn mathvariant="normal">0,0</mn><mo>,</mo><mn mathvariant="normal">0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936156&type= 34.03599930 4.06400013 。 表2 表2 为每组激活两个子载波时的映射表。当激活两个子载波时，OFDM频域信号的备选形式共有 <math id="M94"><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced></mrow></msubsup><mo>=</mo><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>=</mo><msub><mrow><mn mathvariant="normal">96</mn></mrow><mrow/></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936166&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936162&type= 36.06800079 4.82600021 种，此时只需从中随机选取 <math id="M95"><mn mathvariant="normal">64</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></msubsup><mo>=</mo><msub><mrow><mn mathvariant="normal">48</mn></mrow><mrow/></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936174&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936170&type= 32.42733002 4.57200003 种即可。 完成所有子载波块的广义索引调制映射后，合并各子载波块上的OFDM频域信号，生成 <math id="M96"><mi>N</mi><mo>×</mo><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936184&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936177&type= 9.90600014 2.87866688 维的OFDM-GIM频域信号向量，即 <math id="M97"><mover><mrow><mi mathvariant="bold-italic">X</mi></mrow><mrow><mi>˜</mi></mrow></mover><mo>=</mo><msubsup><mrow><mfenced open="[" close="]" separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>,</mo><mo>⋯</mo><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>,</mo><mo>⋯</mo><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow/><mrow><mi mathvariant="normal">T</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936193&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936188&type= 43.68799973 6.09600019 。由于该方案激活不止一个子载波，所以不可避免的会出现同一子载波块内相邻子载波被同时激活的情况，导致信道间的码间干扰（ISI）增大。为了减小ISI，降低接收端的出错概率，本文引入子载波分配算法。子载波分配算法的实质是通过对信道状态信息排序而获得子载波分配变换矩阵 <math id="M98"><mi mathvariant="bold-italic">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936353&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936349&type= 2.96333337 2.79399991 。其具体实现方法如下。 假设收发两端频域信道状态信息为 <math id="M99"><mi mathvariant="bold-italic">H</mi><mo>=</mo><msubsup><mrow><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></mfenced></mrow><mrow/><mrow><mi mathvariant="normal">T</mi></mrow></msubsup><mo>∈</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow/><mrow><mi>N</mi><mo>×</mo><mn mathvariant="normal">1</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936207&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936204&type= 53.50933075 6.18066692 。其中， <math id="M100"><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936522&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936518&type= 3.72533321 3.72533321 是第 <math id="M101"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936221&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936218&type= 1.10066664 2.79399991 个子信道的频域信道信息， <math id="M102"><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936228&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936225&type= 21.92866707 3.21733332 。在信道状态信息 <math id="M103"><mi mathvariant="bold-italic">H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936242&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936238&type= 3.04800010 2.79399991 已知的情况下，首先对 <math id="M104"><mi mathvariant="bold-italic">H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936242&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936238&type= 3.04800010 2.79399991 按升序排列得到新矩阵 <math id="M105"><msup><mrow><mi>H</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936297&type= 3.80999994 3.04800010 。此时： <math display="block" id="M106"><msup><mrow><mi>H</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>=</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936256&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936253&type= 15.83266735 3.97933316 ， 其中， <math id="M107"><msub><mrow><mi>Ω</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936262&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936260&type= 3.64066648 3.72533321 为一个 <math id="M108"><mi>N</mi><mo>×</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936494&type= 10.83733368 2.87866688 维的常数对角矩阵。再将排序后的信道信息 <math id="M109"><msup><mrow><mi>H</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936297&type= 3.80999994 3.04800010 等分成 <math id="M110"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936285&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936281&type= 1.52400005 2.79399991 组，其中每组包含 <math id="M111"><mi>n</mi><mo>=</mo><mi>N</mi><mo>/</mo><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936293&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936288&type= 12.78466606 3.30200005 个参数。为了增大符号间的最小欧式距离，减小码间干扰，将分组后的偶数组数据不变，奇数组数据倒序排列，重新更新信道信息 <math id="M112"><msup><mrow><mi>H</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936297&type= 3.80999994 3.04800010 。同时，将每组第一个系数取出作为第一个子载波块的信道信息，将每组第二个系数取出作为第二个子载波块的信道信息，依次类推，得到更新后的信道信息 <math id="M113"><mi mathvariant="bold-italic">H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936308&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936304&type= 3.04800010 2.79399991 ″。此时， <math id="M114"><mi mathvariant="bold-italic">H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936314&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936311&type= 3.04800010 2.79399991 ″满足： <math display="block" id="M115"><mi>H</mi><mo>″</mo><mo>=</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msup><mrow><mi>H</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936323&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936319&type= 16.84866714 4.40266657 ， 其中， <math id="M116"><msub><mrow><mi mathvariant="bold-italic">Ω</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936331&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936327&type= 4.14866638 3.72533321 也为一个 <math id="M117"><mi>N</mi><mo>×</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936494&type= 10.83733368 2.87866688 维的常数对角矩阵，那么最终的变换矩阵为 <math display="block" id="M118"><msub><mrow><mi mathvariant="bold-italic">Ω</mi></mrow><mrow/></msub><mo>=</mo><msub><mrow><mi mathvariant="bold-italic">Ω</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi mathvariant="bold-italic">Ω</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936346&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936342&type= 17.35666656 3.72533321 . 将变换矩阵 <math id="M119"><mi mathvariant="bold-italic">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936353&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936349&type= 2.96333337 2.79399991 与频域信号 <math id="M120"><mover><mrow><mi mathvariant="bold-italic">X</mi></mrow><mrow><mi>˜</mi></mrow></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936361&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936357&type= 2.70933342 3.38666677 相乘，得到OFDM-GIM频域信号向量为： <math display="block" id="M121"><mi mathvariant="bold-italic">X</mi><mo>=</mo><mi mathvariant="bold-italic">Ω</mi><mover><mrow><mi mathvariant="bold-italic">X</mi></mrow><mrow><mi>˜</mi></mrow></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936368&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936365&type= 13.37733269 3.38666677 ， 由（6）式可见，此时信号 <math id="M122"><mi mathvariant="bold-italic">X</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936378&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936372&type= 2.70933342 2.79399991 为复数/负数信号。在WOC系统中，通常采用强度调制/直接检测方式，这使得复数/负数信号无法直接使用光强度来表示。为此，采用IFFT的厄米特对称性与限幅相结合的方法完成信号的转换，即只利用奇数子载波传输数据，同时使得映射到奇数子载波上的频域信号满足厄米特对称。区别于传统的ACO-OFDM-IM系统，所提方案中 <math id="M123"><mi>E</mi><mo stretchy="false">(</mo><mi>x</mi><msubsup><mrow><mi>x</mi></mrow><mrow/><mrow><mi>H</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936385&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936381&type= 19.38866615 4.65666676 ，所以，IFFT和FFT变换的归一化因子变为 <math id="M124"><mroot><mrow><mi>N</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936393&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936390&type= 6.60400009 4.14866638 和 <math id="M125"><mrow><mrow><mn mathvariant="normal">1</mn></mrow><mo>/</mo><mrow><mroot><mrow><mi>N</mi></mrow><mrow/></mroot></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936401&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936397&type= 10.92199993 4.65666676 ，那么经IFFT的实数信号 <math id="M126"><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936409&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936405&type= 2.03200006 2.79399991 可表示为： <math display="block" id="M127"><mi>x</mi><mo>=</mo><mroot><mrow><mi>N</mi></mrow><mrow/></mroot><mi>I</mi><mi>F</mi><mi>F</mi><mi>T</mi><mfenced open="{" close="}" separators="|"><mrow><mi mathvariant="bold-italic">X</mi></mrow></mfenced><mo>=</mo><mrow><mrow><msubsup><mrow><mi mathvariant="bold-italic">L</mi></mrow><mrow><mi>N</mi></mrow><mrow><mi>H</mi></mrow></msubsup><mi mathvariant="bold-italic">X</mi></mrow><mo>/</mo><mrow><mroot><mrow><mi>N</mi></mrow><mrow/></mroot></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936412&type= 51.47733307 4.65666676 ， 其中， <math id="M128"><msubsup><mrow><mfenced separators="|"><mrow><mo>·</mo></mrow></mfenced></mrow><mrow/><mrow><mi>H</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936423&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936418&type= 5.84200001 5.24933338 表示矩阵共轭转置， <math id="M129"><msub><mrow><mi mathvariant="bold-italic">L</mi></mrow><mrow><mi>N</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936431&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936428&type= 4.06400013 3.72533321 是 <math id="M130"><mi>N</mi><mo>×</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936494&type= 10.83733368 2.87866688 维的离散傅里叶变换矩阵。经过IFFT后，再对该实数信号进行限幅，得到非负实信号后由激光器发送出去。 经大气信道传输后，假设探测器接收到的信号为： <math display="block" id="M131"><mi>y</mi><mo>=</mo><mi>η</mi><mi>h</mi><mo>⊗</mo><mi>x</mi><mo>+</mo><mi>w</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936445&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936441&type= 24.97666740 4.06400013 ， 其中， <math id="M132"><mi>η</mi><mo>∈</mo><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>~</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936452&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936449&type= 15.83266735 3.72533321 是光电转换效率， <math id="M133"><mi>w</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936456&type= 2.96333337 2.79399991 是服从均值为常数 <math id="M134"><mi>c</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936467&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936464&type= 1.52400005 2.79399991 （ <math id="M135"><mi>c</mi><mo>≥</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936476&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936471&type= 8.12800026 3.30200005 ）、方差为 <math id="M136"><msub><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936485&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936480&type= 4.40266657 3.72533321 的加性高斯白噪声。 <math id="M137"><mi>h</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936491&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936487&type= 1.94733346 2.79399991 表示时域信道信息，是一个 <math id="M138"><mi>N</mi><mo>×</mo><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936494&type= 10.83733368 2.87866688 维的对角矩阵，即 <math id="M139"><mi mathvariant="bold-italic">h</mi><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⋯</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></mfenced><mo>∈</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow/><mrow><mi>N</mi><mo>×</mo><mi>N</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936506&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936502&type= 47.58266449 4.91066647 。其中，光强衰落系数 <math id="M140"><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936513&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936509&type= 2.70933342 3.72533321 与 <math id="M141"><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936522&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936518&type= 3.72533321 3.72533321 是一对傅里叶变换对。在湍流大气中，它通常服从指数威布尔分布 ［ 20 20 ］ 。 由于光电检测器输出的电信号是正实数信号，不能直接对其进行索引调制的解映射，需要将其转换为复数/负数信号。为此，采用 N 点的FFT变换，设转化后的频域信号为 <math display="block" id="M142"><mi mathvariant="bold-italic">Y</mi><mo>=</mo><mrow><mrow><mi>F</mi><mi>F</mi><mi>T</mi><mfenced open="{" close="}" separators="|"><mrow><mi>y</mi></mrow></mfenced></mrow><mo>/</mo><mrow><mroot><mrow><mi>N</mi></mrow><mrow/></mroot></mrow></mrow><mo>=</mo><mrow><mrow><msubsup><mrow><mi mathvariant="bold-italic">L</mi></mrow><mrow><mi>N</mi></mrow><mrow/></msubsup><mi>y</mi></mrow><mo>/</mo><mrow><mi>N</mi><mroot><mrow><mi>N</mi></mrow><mrow/></mroot></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936530&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936526&type= 56.30332947 5.41866684 . 在ACO-OFDM-GIM系统中，由于FFT的厄米特对称性使得传输的有效信号仅包含在前 <math id="M143"><mi>r</mi><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936647&type= 5.16466665 3.30200005 组内。因此，从FFT处理后的信号中直接提取前 <math id="M144"><mi>r</mi><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936647&type= 5.16466665 3.30200005 组信号得到 <math id="M145"><msup><mrow><mi>Y</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mrow><mi>Y</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow/></msubsup><mo>,</mo><msubsup><mrow><mi>Y</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow/></msubsup><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msubsup><mrow><mi>Y</mi></mrow><mrow><mfrac bevelled="true"><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow><mrow/></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936552&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936549&type= 34.62866592 5.24933338 ，将其扩大一倍后得到 <math id="M146"><mi>Y</mi><mo>″</mo><mo>=</mo><mn mathvariant="normal">2</mn><msup><mrow><mi>Y</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936560&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936557&type= 14.47799969 3.47133350 。这是因为发射端采用限幅技术后致使接收端信号的幅值仅为原始信号幅值的一半。 在ACO-OFDM-GIM系统中，我们不仅需要检测出子载波索引号，还需检测出QAM调制符号。最大似然检测准则（ML）具有优良的误码性能，它通过遍历所有的信号空间联合估计出激活子载波索引号与调制符号。因此，本文采用最大似然译码算法进行译码，其准则为： <math display="block" id="M147"><mfenced separators="|"><mrow><mover accent="true"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow><mo>̂</mo></mover><mtext> </mtext><mo>,</mo><mtext> </mtext><mover accent="true"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow><mo>̂</mo></mover></mrow></mfenced><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><munder><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mrow><mi>δ</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mo>⋯</mo><mtext> </mtext><mo>,</mo><mi mathvariant="normal">𝓁</mi></mrow></mfenced></mrow></munder><mfenced separators="|"><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mtable columnalign="left"><mtr><mtd><mi>γ</mi><mo>=</mo><mn mathvariant="normal">1</mn></mtd></mtr><mtr><mtd><mi>γ</mi><mo>∉</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mtd></mtr></mtable></mrow><mrow><mi>n</mi></mrow></munderover></mstyle><mrow><msubsup><mrow><mfenced open="|" close="|" separators="|"><mrow><msubsup><mrow><mi>Y</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">'</mi><mi mathvariant="normal">'</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>γ</mi></mrow></mfenced></mrow></mfenced></mrow><mrow/><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>φ</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></munderover></mstyle><mrow><msubsup><mrow><mfenced open="|" close="|" separators="|"><mrow><msubsup><mrow><mi>Y</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">'</mi><mi mathvariant="normal">'</mi></mrow></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>φ</mi></mrow></mfenced></mrow></mfenced><mo>-</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow></msub><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>φ</mi></mrow></mfenced></mrow></mfenced><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>φ</mi></mrow></mfenced></mrow></mfenced></mrow><mrow/><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mrow></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936568&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936564&type= 116.58599854 16.67933464 ， 其中， <math id="M148"><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mo>•</mo></mrow></mfenced></mrow><mrow><mi mathvariant="normal">F</mi></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936572&type= 6.68866634 5.24933338 表示F-范数， <math id="M149"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936583&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936579&type= 2.87866688 3.97933316 和 <math id="M150"><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936591&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936587&type= 3.21733332 4.82600021 分别代表第 <math id="M151"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块内检测到激活子载波的索引号和QAM调制符号， <math id="M152"><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>g</mi><mo>,</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>H</mi></mrow><mrow><mi>g</mi><mo>,</mo><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><mo>⋯</mo><mtext> </mtext><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></mrow></mfenced><mo>∈</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow/><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936605&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936601&type= 59.52066422 4.91066647 和 <math id="M153"><msubsup><mrow><mi mathvariant="normal">Y</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">'</mi><mi mathvariant="normal">'</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>γ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936613&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936610&type= 9.22866726 4.74133301 分别表示频域内第 <math id="M154"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936617&type= 1.94733346 3.64066648 个子载波块相应的信道信息和接收信号矢量。在信号检测完成之后，按照发送端的映射原理进行解映射，并将解映射后的二进制信息 通过并串变换，即可恢复出原始比特信息。 3 误码率分析 1 由ACO-OFDM-GIM系统原理可知，各子载波块间是相互独立的，所以ACO-OFDM-GIM系统的平均误码率可用前 <math id="M155"><mi>r</mi><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936647&type= 5.16466665 3.30200005 个子载波块误码率之和来表示。那么，依据参考文献［ 21 21 ］，采用联合界技术可将ACO-OFDM-GIM 系统的平均误码率表示为： <math display="block" id="M156"><mtable><mtr><mtd><mi>A</mi><mi>B</mi><mi>E</mi><mi>R</mi><mo>≈</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>g</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mrow><mrow><mi>r</mi></mrow><mo>/</mo><mrow><mn mathvariant="normal">2</mn></mrow></mrow></mrow></munderover></mstyle><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>z</mi><msub><mrow><mi>D</mi></mrow><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></msub></mrow></mfrac><munder><mo movablelimits="false">∑</mo><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></munder><mrow><munder><mo movablelimits="false">∑</mo><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></munder><mrow><mi>P</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>→</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow></mrow><mi>e</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936636&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936630&type= 61.63733673 14.64733315 ， 其中： <math id="M157"><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936643&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936639&type= 5.84200001 3.72533321 表示前 <math id="M158"><mi>r</mi><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936647&type= 5.16466665 3.30200005 个子载波块上传输的总比特数， <math id="M159"><msub><mrow><mi>D</mi></mrow><mrow><msubsup><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></msub><mo>=</mo><msubsup><mrow><mi>M</mi></mrow><mrow/><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936657&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936654&type= 15.32466698 5.75733376 表示OFDM频域信号 <math id="M160"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936664&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936661&type= 3.38666677 3.97933316 所有备选向量的个数， <math id="M161"><mi>e</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936671&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936667&type= 13.46199989 5.67266655 表示第 g 个子载波块信号 <math id="M162"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936700&type= 3.38666677 3.97933316 与被错误检测为信号 <math id="M163"><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936685&type= 3.38666677 4.82600021 之间的汉明距离， <math id="M164"><mi>P</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>→</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936691&type= 17.78000069 5.67266655 表示信号 <math id="M165"><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936700&type= 3.38666677 3.97933316 被错误检测为信号 <math id="M166"><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936710&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936706&type= 3.38666677 4.82600021 时的成对错误概率。 从 公式（11） 公式（11） 可以看出，系统总误码率与每个子载波块上的符号成对错误概率有关，我们仍以第 g 个子载波块为例来进行分析。若要得到每个子载波块的成对错误概率，需首先计算出信道状态信息 <math id="M167"><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936766&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936763&type= 4.31799984 3.97933316 已知时第 g 个子载波块的条件成对错误概率，其可表示为： <math display="block" id="M168"><mtable><mtr><mtd><mi>P</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>→</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced open="|" close="" separators="|"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>P</mi><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>η</mi></mrow></mfrac><msubsup><mrow><mfenced separators="|"><mrow><mi>η</mi><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow/><mrow><mi>H</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><mo>></mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>-</mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mi>P</mi><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>η</mi></mrow></mfrac><msubsup><mrow><mi>W</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>H</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><mo>></mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936725&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936721&type= 120.65000153 20.65866661 . 依据信道模型（8），可将（12）式表示为： <math display="block" id="M169"><mtable><mtr><mtd><mi>P</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mi mathvariant="normal">δ</mi></mrow></msubsup><mo>→</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mfenced open="|" close="" separators="|"><mrow><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>P</mi><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>η</mi></mrow></mfrac><msubsup><mrow><mfenced separators="|"><mrow><mi>η</mi><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow/><mrow><mi>H</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><mo>></mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>-</mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mtd></mtr><mtr><mtd><mo>=</mo><mi>P</mi><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>η</mi></mrow></mfrac><msubsup><mrow><mi>W</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>H</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><mo>></mo><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936728&type= 117.77133942 19.55800056 . 令 <math id="M170"><mi>ζ</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>η</mi></mrow></mfrac><msubsup><mrow><mi>W</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>H</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936738&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936735&type= 34.37466812 8.38199997 ，则 <math id="M171"><mi>ζ</mi><mo>∼</mo><mi>C</mi><mi>N</mi><mfenced separators="|"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>ζ</mi></mrow></msub><mo>,</mo><msub><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi>ζ</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936739&type= 23.02933502 4.91066647 。其中， <math id="M172"><msub><mrow><mi>m</mi></mrow><mrow><mi>ζ</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936748&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936745&type= 10.66800022 3.72533321 ， <math id="M173"><msub><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi>ζ</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">4</mn><msubsup><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow><mrow><msubsup><mrow><mi>η</mi></mrow><mrow/><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfrac><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936754&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936751&type= 40.89400101 8.89000034 ，且 <math id="M174"><msubsup><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>=</mo><mrow><mrow><mi>r</mi><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi mathvariant="bold">k</mi></mrow></munder><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>t</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow><mo>/</mo><mrow><mi>N</mi></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936760&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936757&type= 38.26933289 7.70466709 。在信道状态信息 <math id="M175"><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936766&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936763&type= 4.31799984 3.97933316 已知的条件下，对条件成对错误概率求统计平均，从而第 g 个子载波块的成对错误概率可表示为： <math display="block" id="M176"><mtable><mtr><mtd><mi>P</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>→</mo><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><mo>=</mo><mi>Q</mi><mfenced separators="|"><mrow><mfrac><mrow><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>-</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>ζ</mi></mrow></msub></mrow><mrow><mroot><mrow><msub><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi>ζ</mi></mrow></msub></mrow><mrow/></mroot></mrow></mfrac></mrow></mfenced><mo>=</mo></mtd></mtr><mtr><mtd><mi>Q</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>η</mi></mrow><mrow><mn mathvariant="normal">2</mn><msubsup><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></mfrac><msubsup><mrow><mfenced open="‖" close="‖" separators="|"><mrow><mfenced separators="|"><mrow><msubsup><mrow><mover accent="true"><mi>S</mi><mo>̂</mo></mover></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>δ</mi></mrow></msubsup></mrow></mfenced><msubsup><mrow><mi>H</mi></mrow><mrow><mi>g</mi></mrow><mrow/></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow><mrow/></msubsup></mrow></mfenced><mo>.</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936769&type= 68.24134064 28.70199966 4 仿真结果分析 1 为了进一步验证所提方案的正确性，采用蒙特卡洛方法对其进行仿真实验，其结果如图 2 2 ~ 7 7 所示。所有仿真过程中相同的条件为：总子载波数 N =256，光电转换系数 <math id="M177"><mi>η</mi><mo>=</mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936778&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936775&type= 11.34533310 3.64066648 ，光端机发射功率为1，传输距离 <math id="M178"><mi>d</mi><mo>=</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mn mathvariant="normal">000</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936784&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936781&type= 15.07066536 2.79399991 m，发射波长 <math id="M179"><mi>λ</mi><mo>=</mo><mn mathvariant="normal">780</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936790&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936787&type= 11.93799973 2.79399991 nm，采用4QAM调制，指数威布尔信道的参数如 表3 表3 所示 ［ 20 20 ］ 。同时，为了描述方便，用 <math id="M180"><mfenced separators="|"><mrow><mi>n</mi><mtext> </mtext><mo>,</mo><mfenced open="[" close="]" separators="|"><mrow><mi>k</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936791&type= 31.15733528 5.50333309 A-OFDM-GIM表示不同参数的ACO-OFDM-GIM系统， <math id="M181"><mfenced separators="|"><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936800&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936798&type= 7.95866632 3.97933316 A-OFDM-IM表示不同参数的ACO-OFDM-IM系统。 湍流强度 李拓夫方差 形状参数1 形状参数2 尺度 参数 接收孔径 D /mm Weak 0.317 3.67 1.97 0.73 25 Moderate 2.202 5.37 0.81 0.33 25 strong 15.851 5.50 0.74 0.29 25 图2 图2 为ACO-OFDM-GIM系统平均误码率的理论结果与仿真结果。由 图2 图2 可知：①随着信噪比的增大，系统误码率的理论曲线与仿真曲线逐渐趋于吻合，说明了理论推导的正确性。②当调制阶数 M 和 <math id="M184"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 一定时，随着每组子载波数 n 的增加，ACO-OFDM-GIM系统的误码性能得到了较好改善。这是因为每组子载波数的增加，使得符号间的最小欧式距离增大。当 <math id="M185"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936861&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936859&type= 25.82333374 3.97933316 ，（8，［1，2］）ACO-OFDM-GIM系统的信噪比比（4，［1，2］）ACO-OFDM-GIM系统的信噪比改善了约 <math id="M186"><mn mathvariant="normal">1.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936865&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936863&type= 9.82133293 2.79399991 。③随着湍流强度的增大，系统的误码性能逐渐变差。例如，当湍流强度由弱变强时，（4，［1，2］）ACO-OFDM-GIM系统的信噪比在 <math id="M187"><mi>B</mi><mi>E</mi><mi>R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936869&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936867&type= 25.82333374 3.97933316 处损失了约 <math id="M188"><mn mathvariant="normal">2</mn><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936873&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936871&type= 6.85799980 2.79399991 。 除了 图2 图2 中每组子载波数 n 以及湍流强度对系统的误码性能有影响之外，调制阶数 M 和 <math id="M189"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 对ACO-OFDM-GIM系统的误码率也有影响，其结果如 图3 图3 所示。从 图3 图3 可以看出，①当调制阶数 M 一定时，随着 <math id="M190"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 值的增加其频域映射比特数增加，传输速率也随之增大，但会带来一定的误码率损失。这是因为调制阶数 M 一定时，当 <math id="M191"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936885&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936883&type= 1.86266661 2.79399991 值增加时，传输有效信息的子载波数增多，导致接收端检测错误概率将会增大，从而会带来一定的误码性能损失。例如，在 <math id="M192"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936933&type= 25.82333374 3.97933316 时，（4，［1，2，3］）ACO-OFDM-GIM系统的信噪比较（4，［1，2］）ACO-OFDM-GIM系统损失了约 <math id="M193"><mn mathvariant="normal">1</mn><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936893&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936891&type= 6.85799980 2.79399991 。②当 <math id="M194"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 长度一定时，随着调制阶数 M 的增大，信号域映射的比特数随之增加，从而实现了系统传输速率的提升。但此时系统的误码率和成本会相应提高。例如，当QAM的调制阶数 M 从4增大到8时，（4，［1，2，3］）ACO-OFDM-GIM系统每帧发送比特数增加了96 bits。当 <math id="M195"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936933&type= 25.82333374 3.97933316 时，（4，［1，2，3］）ACO-OFDM-GIM系统的信噪比损失了约 <math id="M196"><mn mathvariant="normal">2.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936999&type= 9.82133293 2.79399991 。 图4 图4 为采用子载波分配算法前后ACO-OFDM-GIM系统的误码率。由仿真曲线可见，在强湍流条件下，当 <math id="M197"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936933&type= 25.82333374 3.97933316 时，相对于未采用子载波分配算法的系统，采用分配算法后（4，［1，2］）ACO-OFDM-GIM和（4，［1，2，3］）ACO-OFDM-GIM系统的信噪比分别改善了约 <math id="M198"><mn mathvariant="normal">2</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936912&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936910&type= 6.85799980 2.79399991 和 <math id="M199"><mn mathvariant="normal">2.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936999&type= 9.82133293 2.79399991 。由此可得，加入子载波分配算法后，使得同一子载波块的子载波信道衰落尽可能互不相关，从而增大了符号间的最小欧氏距离，提升了系统的误码性能。 图5 图5 为所提方案与ACO-OFDM-IM、ACO-OFDM系统的误码率。由仿真曲线可见，在小信噪比下，本文所提方案的误码率大于ACO-OFDM-IM和ACO-OFDM系统的误码率。这是因为在小信噪比下，子载波索引号出错的概率增大，从而导致整个系统误码率变大。而在大信噪比下，本文所提方案的误码率明显优于ACO-OFDM-IM和ACO-OFDM系统的误码率，尤其是强湍流条件下，误码性能的改善更加明显。例如，在强湍流、大信噪比（ <math id="M200"><mi mathvariant="normal">S</mi><mi mathvariant="normal">N</mi><mi mathvariant="normal">R</mi><mo>≥</mo><mn mathvariant="normal">6</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936920&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936917&type= 19.30400085 3.30200005 ）下，（4，［1，2］）ACO-OFDM-GIM系统的误码性能明显优于ACO-OFDM系统。当 <math id="M201"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936933&type= 25.82333374 3.97933316 时，相对于前者，后者的信噪比改善了约 <math id="M202"><mn mathvariant="normal">4.5</mn><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936927&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936925&type= 9.82133293 2.79399991 。当SE=0.75 bits/s/Hz时，低信噪比下（4，［1，2］）ACO-OFDM-GIM系统的误码率高于（4，2）ACO-OFDM-IM系统；但是，当 <math id="M203"><mi mathvariant="normal">S</mi><mi mathvariant="normal">N</mi><mi mathvariant="normal">R</mi><mo>≥</mo><mn mathvariant="normal">7</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936931&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936929&type= 19.38866615 3.30200005 时，前者的误码性能逐渐优于后者。在 <math id="M204"><mi mathvariant="normal">B</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936933&type= 25.82333374 3.97933316 时，相对于后者，前者的信噪比改善了约 <math id="M205"><mn mathvariant="normal">2.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936999&type= 9.82133293 2.79399991 。 调制方式 传输速率 频谱效率 计算复杂度 峰均比 ACO-OFDM <math id="M206"><mfrac><mrow><mi>N</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow><mrow><mn>4</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936943&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936941&type= 15.32466698 6.60400009 <math id="M207"><mfrac><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow><mrow><mn>4</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936947&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936945&type= 12.36133385 6.60400009 <math id="M208"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936951&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936949&type= 4.23333359 2.62466669 <math id="M209"><mfrac><mrow><mi>N</mi></mrow><mrow><msubsup><mrow><mi>E</mi></mrow><mrow><mi>a</mi><mi>v</mi><mi>e</mi><mo>_</mo><mi>p</mi></mrow><mrow><mi>Q</mi><mi>A</mi><mi>M</mi></mrow></msubsup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936955&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936953&type= 7.53533268 7.61999989 ACO-OFDM-IM <math id="M210"><mfrac><mrow><mi>r</mi><mfenced separators="|"><mrow><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></mfenced><mo>+</mo><mi>k</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936959&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936957&type= 36.15266418 8.21266651 <math id="M211"><mfrac><mrow><mi>r</mi><mfenced separators="|"><mrow><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></mfenced><mo>+</mo><mi>k</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow></mfenced></mrow><mrow><mn>2</mn><mi>N</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936963&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936961&type= 36.15266418 8.29733276 <math id="M212"><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936965&type= 4.06400013 2.62466669 <math id="M213"><mfrac><mrow><mi>k</mi><mi>N</mi></mrow><mrow><mi>n</mi><msubsup><mrow><mi>E</mi></mrow><mrow><mi>a</mi><mi>v</mi><mi>e</mi><mo>_</mo><mi>p</mi></mrow><mrow><mi>Q</mi><mi>A</mi><mi>M</mi></mrow></msubsup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936971&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936969&type= 9.05933285 7.61999989 ACO-OFDM-GIM <math id="M214"><mfrac><mrow><mi>r</mi><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi mathvariant="bold">k</mi></mrow></munder><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></mrow></mrow></mfenced></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936973&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936972&type= 31.32666588 13.12333298 <math id="M215"><mfrac><mrow><mi>r</mi><mfenced open="⌊" close="⌋" separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi mathvariant="bold">k</mi></mrow></munder><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msup><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msubsup></mrow></mrow></mfenced></mrow></mfenced></mrow><mrow><mn>2</mn><mi>N</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936975&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936974&type= 31.32666588 13.20800018 <math id="M216"><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn>1</mn></mrow></mfenced></mrow></msup><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mn>2</mn></mrow></mfenced></mrow></msup><mo>⋯</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936976&type= 23.45266724 2.87866688 <math id="M217"><mfrac><mrow><munder><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced><mo>∈</mo><mi mathvariant="bold">k</mi></mrow></munder><mrow><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></mrow><mi>N</mi></mrow><mrow><mi>n</mi><msubsup><mrow><mi>E</mi></mrow><mrow><mi>a</mi><mi>v</mi><mi>e</mi><mo>_</mo><mi>p</mi></mrow><mrow><mi>Q</mi><mi>A</mi><mi>M</mi></mrow></msubsup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936979&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936978&type= 16.00200081 10.58333302 除了误码率，传输速率，频谱效率和计算复杂度，峰均比也是衡量ACO-OFDM-GIM系统性能不可或缺的因素。鉴于此， 图7 图7 给出了ACO-OFDM-GIM与ACO-OFDM-IM、ACO-OFDM等系统的峰均比。对比仿真曲线可得，ACO-OFDM-GIM系统的峰均比总是低于ACO-OFDM系统。导致这一现象的原因是所提方案中只激活了部分子载波传输有效信息。当频谱效率为0.75 bits/s/Hz、互补累积分布函数（CCDF）为 <math id="M218"><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936983&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936982&type= 13.37733269 3.97933316 时，（4，［1，2］）ACO-OFDM-GIM系统的峰均比比（4，2）ACO–OFDM-IM系统低 <math id="M219"><mn mathvariant="normal">0.3</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936985&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936984&type= 9.73666668 2.79399991 左右。但随着激活子载波数组合 <math id="M220"><mi mathvariant="bold-italic">k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936986&type= 1.86266661 2.79399991 中 <math id="M221"><mi>k</mi><mfenced separators="|"><mrow><mi>δ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936988&type= 6.94266701 3.97933316 的增大，ACO-OFDM-GIM系统的峰均比也会变高。例如，当 <math id="M222"><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">F</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936993&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936992&type= 28.36333466 3.97933316 时，（4，［1，3］）ACO-OFDM-GIM系统的峰均比比（4，［1，2］）ACO-OFDM-GIM系统高了约 <math id="M223"><mn mathvariant="normal">0.4</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936996&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936995&type= 9.82133293 2.79399991 。 5 结　论 1 针对WOC领域超高速率和高可靠性的通信需求，本文通过在每个子载波块中选择激活数目不唯一的子载波，并结合SAA而提出了一种ACO-OFDM-GIM方案。结果表明，该方案可大幅提升系统的传输速率和误码性能，其性能的改善量与每组总子载波数、激活子载波数目以及调制阶数有关。特别是每组总子载波数的增大会带来ACO-OFDM-GIM系统传输速率和误码性能的大幅提升。与ACO-OFDM、ACO-OFDM-IM系统相比，该系统还可以有效抵御大气湍流，尤其是在强湍流下系统误码性能的改善更为明显。在误码率为 <math id="M224"><mn mathvariant="normal">1</mn><mo>×</mo><msubsup><mrow><mn mathvariant="normal">10</mn></mrow><mrow/><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936998&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936997&type= 13.37733269 3.97933316 时，（4，［1，2］）ACO-OFDM-GIM系统的信噪比较（4，2）ACO-OFDM-IM和ACO-OFDM系统分别改善了约 <math id="M225"><mn mathvariant="normal">2.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20936999&type= 9.82133293 2.79399991 和约 <math id="M226"><mn mathvariant="normal">4.5</mn><mtext> </mtext><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937004&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=20937003&type= 9.82133293 2.79399991 。另外，当激活少量子载波时，该系统还会降低系统的PAPR。因此，ACO-OFDM-GIM有望成为超高速WOC系统的关键技术之一。但是，ACO-OFDM-GIM在实现高速率的同时会伴随着很高的译码复杂度。为了加大ACO-OFDM-GIM系统的推广和应用，在后续研究中，我们将寻找低复杂度的译码算法进一步降低系统的复杂度。 参考文献 ARMSTRONG J . 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