1、基于 Matlab 的 OFDM 设计仿真与分析0目录设计总说明 IThe total designed to show that .V1 绪论 .11.1 课题背景 .11.2 无线通信 11.2.1 无线通信概述 11.2.2 无线信道特性 21.3 OFDM 系统介绍 31.3.1 OFDM 的概述 31.3.2 OFDM 的应用 41.3.3 OFDM 的关键技术 51.3.4 OFDM 系统的优点及缺点 71.4 MATLAB 特点与功能 92 OFDM 系统的基本原理 .112.1 OFDM 技术原理 .112.2 基于 IFFT/FFT 的 OFDM 系统模型 122.3 OFD
2、M 信号的频谱特性 .142.4 串并转换 .153 OFDM 系统在 MATLAB 上的仿真分析 163.1 0FDM 系统调制与解调解析 163.2 加窗 .183.3 AWGNA 信道下的仿真 203.3.1 加入高斯白噪声前后分析对比 203.3.2 BER 性能曲线 214 对系统误码率的改善分析 234.1 循环前缀 23仁 人 教 育14.2 OFDM 系统的峰值平均功率比 .274.3 信道估计 284.3.1 信道估计概述 284.3.2 基于导频的信道估计方法 294.3.3 信道的插值方法 294.3.4 仿真结果及分析 305 总结 325.1 完成的主要工作 325.
3、2 不足与展望 32参考文献 .34附录 .35致谢 .50基于 Matlab 的 OFDM 设计仿真与分析基于 Matlab 的 OFDM 系统设计及分析设计总说明正交频分复用是一种历史悠久的多载波调制技术，最早在 20 世纪中期的时候，在通信领域，研究者们做了大量的卓有成效的研究工作，对多载波调制理论进行了研究，并论证了利用多载波调制技术能够对整体系统性能进行优化。当时许多专家学者对这频域非常密集的多载波调制的 OFDM 系统产生了巨大的关注。然而那个时候的数字信号处理技术还没有得到足够的成长，OFDM 也因此没有得到普遍的关注和使用。在 20 世纪 90 年代，随着数字信号处理技术的日渐
4、成熟，OFDM 技术在告诉数据传输方面得到了人们的重视，已经普遍应用于数字音频广播（如 DAB 和 DBA）、无线局域网、电话上的数字传输（VDSL 和 ADSL）和电力线通信（homeplugav 和 BPL）等领域。2004 年，已经作为 3G 核心之一的 WiMAX 影响力的扩大强烈迫使传统电信领域的标准化组织 3GPP 启动了它的长期演进计划，以 OFDM 为基础的多址接入技术在这次以空中接口技术的较量中，通过下行 OFDMA 和上行 SC-FDMA 奠定巨大优势获得胜利，这也意味着未来的一段时间移动通讯系统中将出现 OFDM 一统天下的局面。 正交频分复用（OFDM）技术能够有效的避
5、免有符号间干扰信道，因为其简易高效，现已成为现今无线高速通讯整体中不可或缺的主要技术之一。本文最开始介绍了无线通信的发展史以及到现在的移动通信系统中的 OFDM 采用多种新技术所以具备更高的带宽利用率和克服符号间干扰与突发噪声的能力，也因其子载波彼此之间存在正交性，能让其频谱互相叠加，对比一般的频分复用，OFDM 能够尽可能地操控频谱资源去扩大系统容量，最主要的是它的灵活开放性能很好地符合多媒体通讯的特点，将包含数据、语音、影像等多种多样的多媒体业务高效完善地传达出去。并简略阐述了仿真必须用到的 MATLAB 的可靠的数值和符号运算功能，简易的符号语言，可视化的特点。文章对 OFDM 系统进行
6、了概述以及当今社会普遍应用的主要原因在于它能够将宽带有符号间干扰信道改造为一系列衰落信道，这也表明，带宽利用率是非常高的，和高速离散傅里叶变换（DFT）技术来实现调制和解调，且选用联合编码技术，使其能够有很强的抗衰减特点及可与多种接入方式结合使用的优势与需要补足的地方，如OFDM 对系统定时和频率偏移敏感和存在较高的峰值平均功率比，同时由于无线信道的不稳定性，且发射端载波和本地振荡器的频率偏差，所以产生的频率存在一定偏差仁 人 教 育I使 OFDM 整体出现问题。同时，就 OFDM 系统的基本原理进行了讨论，事实上，它是用 N 个子载波信道切割成相应的子信道，因为这些子信道调制，实现多个数据的
7、频域并行传输，这点和 OFDM 的原理差不多，唯一的区别就是 OFDM 技术很好的抓住了其控制特点，使其整个体系中每个子信道的载波相互正交，频谱彼此叠加，所以频谱利用率有所提升并减少了每一个子载波之间的影响。得到了 OFDM 为了保证不同子信道上承载的数据在接收端可以正常分离，必须保证自信道之间的“正交性”，也就是说并行传输子信道并不是无限随意划分的。所谓的正交性在时域应体现为： jidtxtji ,01)(*-在频域体现为： jidfXfxj,01()*-i）OFDM 所采用的信号设计形式是满足正交性要求的最佳信号设计，满足频域奈奎斯特采样定律的最密的采样，它的正交性是根据在某一个积分时间内
8、所有子载波都是整周期而且不同载波之间周期个数不同来实现的。这样，就利用了子载波在时域的正交性可以完全屏蔽其他子载波的干扰，恢复了本子载波承载的数据信息。从 OFDM 信号在频域的图像可以看出，每个子载波的频谱实际上就是频域的抽样函数，在频域的最佳采样点无子载波间干扰。其实更本上 OFDM 调制和解调都是在数字基带上进行数字信号处理实现的，因此 t = 为起始时间可以得出 OFDM 的符号表达式：s Tttfijtdnect sssNk ),(2exp)()(s10 然后 OFDM 等效复基带信号通过逆傅里叶变换（IDFT）的定义，能够得到它的 DFT转换： 10),2exp(10 Nikjsd
9、Nki 从而可以得出由 DFT 和 IDFT 来分别代替 OFDM 系统的调制和解调。其中通过上式中 OFDM 符号看出其功率谱的带外衰减速率很慢，我们不妨对其每一个都进行加窗调制，符号周期边的幅值逐渐减小为零，信号的幅度也逐渐减小，即使对信号的误码率有一定的影响。通过以上 OFDM 系统参数数学公式和加窗技术的原理及运用 IDFT 和DFT 完成了基于 IFFT/FFT 的 OFDM 系统设计，即在接收端把时域信号通过快速傅里叶基于 Matlab 的 OFDM 设计仿真与分析II变换(FFT)转化为频域信号，由此我们在程序编码上配置调制解调相关参数和帧结构等相关参数可以得到 OFDM 在 A
10、WGN 信道下的 BER 性能曲线仿真图，并粗略分析系统误码率与信噪比之间的关系，而其代码中也不会包含信道估计，循环前缀等模块。接下来通过上述的 AWGN 信道编写的程序代码的基础上进行添加修改下着重探讨了了理想同步条件下,保护时隙(CP)、循环前缀加入前后和各种信道内插方式在多径瑞利衰落信道下对 OFDM 系统整体性能的影响。其中如果一个符号的长度严格等于 Ts，即 N 个采样点，那么经过符号间干扰信道之后连续的两个符号之间的样点之间必然发生重叠，而且符号之间的干扰还会影响每一个子载波间的正交性，带来严峻的后果。因此，系统中往往需要增添保护时隙在两个 OFDM 符号之间。 一种直接的思路是在
11、两个符号间加上一段时间为 0 的区域，这虽然消除了 ISI，但是这种方法实际上无法克服符号间干扰所带来的子载波干扰。即在 FFT 积分时间的子载波的延迟路径已经不在整个周期中，子载波之间的正交性受其严重的损伤。我们为了解决这一问题，在目前实用化的 OFDM 系统中都采用了添加循环前缀（ CP）的方法。所谓的循环前缀其实是将一个符号的后面若干个(Ncp ）样点按顺序移到这个符号前面，代替保护间隔，其作用是在 FFT 积分时间内，每一条延迟径上的各个子载波都仍然是整周期的，保证了子载波间的正交性。循环前缀的引入虽然对抗了符号间干扰，但是带来了传输效率的下降，因此在 OFDM 系统设计时循环前缀的长
12、度需要适当的选择一个参数，其长度一定要大于最大多径时延时，才能担保子载波间正交性。在添加循环前缀后，很明显，整个系统都会产生功率和信息速率的损耗，但它能够克服符号间干扰和多径产生的符号间干扰，本文也会通过仿真的实际结果重点说明其两面性的长短。同时研究 OFDM 系统峰均功率比更高的原因，主要是该符号是由一个单一的调制的副载波信号。因此，它可能会导致一个非常高的信号峰值功率，具有很高的峰值均匀功率比。因此对比单载波系统，OFDM 系统发射机的发送信号的瞬间时值极度不稳定。这势必要求系统内的如A/D、D/A 转换器等一些器件具备非常大的线性动态范围；然而同时也会由于这些器件的非线性对动态范围较广的
13、信号引起非线性失真，以及彼此之间的干扰信道引起的谐波, 从而降低整个 OFDM 体系的性能。在接收端的同时，由于无线信道的波动范围很广和不可预测性，且随着多种原因的不稳定性，从而致使收到的信号幅值、相位和频率的失真，从而难以解析。这些问题对接收机的设计造成了很大的阻碍，因此在接收机中，信道估计器是一个不可或缺的部分。信道估计器的设计在 OFDM 系统中首要直接就面临着两个困难：一是导频信息的选择，二是要有较低的复杂度。在最新建立于正仁 人 教 育III交频分复用的无线通信系统，因为其传输速率高，它必然运用相干检测技术来得到更高的性能，因此一般选取非盲估计收获很不错的估计结果，使其能够很好的追寻
14、无线信道的改变，提升接收端信号的质量。此课题所研究的基于导频信道估计的信道估计方法也是其中一种很实用的方法。由于其分为常值内插、线性内插和 DFT 插值，其中常值内插是相当容易的方式，但是考虑到达成的困难度，信道估计准则选取 LS 估计准则，简单讨论 LS 算法下不同插值方式下对信道估计的仿真。在基于 IFFT/FFT 的系统的OFDM 系统内加入保护间隔之前之后的模拟和循环前缀等模块后，在完全不一样的信道条件基础上，,对比保护时隙、循环前缀、采用 LS 估计方法对 OFDM 系统误码率影响,得到了自己此次设计中想要的结论。最后对整个毕业设计归纳总结，并提出本文存在的不足的地方和对 OFDM
15、技术将来工作的研究展望。关键词:正交频分复用;系统仿真;误码率影响基于 Matlab 的 OFDM 设计仿真与分析IVMATLAB Simulation and Performance Analysis of OFDM SystemThe total designed to show that Orthogonal frequency division multiplexing is a multi-carrier modulation technology with a long history, as early as the middle of the 20th century, in
16、the field of communication, the researchers have done a lot of fruitful work, studied the multicarrier modulation theory, and demonstrates the use of multicarrier modulation technique to optimize the overall performance of the system. At that time, many experts and scholars on the frequency domain o
17、f very intensive multicarrier modulation OFDM system to produce a great deal of attention. At that time, however the growth of digital signal processing technology has not been enough, OFDM and therefore didnt get the attention and widely used.In the 1990 s, with the maturing of digital signal proce
18、ssing technology, OFDM technology in tell data transmission has got the attention of the people, has been widely applied in the digital audio broadcasting (DAB) and DBA), wireless local area network (LAN), the digital transmission (VDSL and ADSL) on the phone and power line communication (homeplugav
19、 and BPL), etc.In 2004, has been one of the 3 g core WiMAX influence to expand a strong force of traditional telecom organization for standardization in the field of 3 GPP launched its long-term evolution plan, on the basis of OFDM multiple access technology in the air interface technology, through
20、the downlink OFDMA uplink SC - FDMA and lay a huge advantage to win, it also means a period of time in the future mobile communication system will appear OFDM the situation of unify the whole country.Orthogonal frequency division multiplexing (OFDM) technology can effectively avoid the intersymbol i
21、nterference channel, because of its simple and efficient, has now become the indispensable one of the main technology of high-speed wireless communication overall. This paper at first introduced the wireless communication in the history of development, as well as to the present system for mobile com
22、munications OFDM USES the many kinds of new technology so with higher bandwidth utilization, and overcome the intersymbol interference and burst noise strength, also because of its carrier orthogonality between each other, each other can make its spectrum superposition, compared with the general fre
23、quency division 仁 人 教 育Vmultiplexing, OFDM can be as much as possible manipulation of the spectrum resources to expand the system capacity, the mainest is it flexible open performance conforms to the characteristics of multimedia communication, well will contain data, voice, image and so on a variet
24、y of multimedia business effective and perfect pass out. And briefly expounds the simulation must be used in the reliable numerical and symbolic operation function of MATLAB, a simple sign language, the characteristics of the visual.Articles on the OFDM system were summarized, and the main reason fo
25、r general use in todays society is that it can be a broadband has transformed into a series of intersymbol interference channel fading channel, this also shows that the bandwidth utilization rate is very high, and the discrete Fourier transform (DFT) technology to realize the modulation and demodula
26、tion, and selects the joint coding technology, enable it to have a strong resistance attenuation characteristics and can be used with multiple access methods in combination with the advantages and the need to complement, such as OFDM is sensitive to timing and frequency offset and the existing high
27、peak average power ratio, at the same time due to the instability of the wireless channel, the sender and the carrier and the local oscillator frequency deviation, so there is a certain deviation of frequency OFDM the whole problem. At the same time, it discusses the basic principle of OFDM system,
28、in fact, it is the carrier channel cut into corresponding person with N sub-channels, because these sub channel modulation, implement multiple frequency domain parallel data transmission, which is similar to the principle of OFDM, the only difference is the OFDM technology good caught its control ch
29、aracteristic, make the whole system of orthogonal to each other, each channel in the carrier frequency spectrum superposition of each other, so to improve spectrum efficiency and to reduce the influence between each child carrier. In different sub-channels of OFDM in order to ensure the bearing data
30、 can be separated at the receiving end, must ensure the orthogonality between self-confidence, that is to say, parallel transmission is not infinite sub-channels randomly divided. The orthogonality of the so-called time domain should be embodied in:In the frequency domain embodied in:OFDM signal des
31、ign form is adopted by the best signal that could satisfy the requirement of orthogonality design, satisfy the frequency domain Nyquist sampling law is the most dense sampling, its orthogonality is according to all the subcarrier in a certain integral time is the whole cycle and cycle number is diff
32、erent between different carrier. So, it is using the orthogonality of the subcarrier in time domain can be completely shielded other sub-carrier interference, restored the book data information carrier. Can be seen from the OFDM signal in the frequency domain image, each subcarrier frequency spectru
33、m is actually the sample 基于 Matlab 的 OFDM 设计仿真与分析VIfunction of frequency domain, in the frequency domain of the best sampling points without interference between subcarrier. More on the OFDM modulation and demodulation is carried out on the digital baseband digital signal processing, so t = as the s
34、tarting time can be concluded that OFDM symbol expressions:Then OFDM complex equivalent baseband signal by inverse Fourier transform (IDFT) definition, to get its DFT transformation:Thus can draw by DFT and IDFT respectively instead of modulation and demodulation of OFDM system. Among them through t
35、he type on OFDM symbol to see its power spectrum out-of-band attenuation rate is slow, we might as well to each add window modulation, symbol of the periodic boundary amplitude decreases to zero, the signal amplitude decreases, even if the error rate of the signal has the certain influence. OFDM sys
36、tem parameters through the above mathematical formula and the principle of window technology and using IDFT based on IFFT/FFT and DFT of the OFDM system design, namely the time-domain signal at the receiving end through the fast Fourier transform (FFT) is converted into frequency domain signal, thus
37、 we configure modem related parameters on the program code and frame structure parameters can be related to OFDM BER performance under AWGN channel simulation curve graph, and a rough analysis of the relationship between the system bit error rate and signal to noise ratio, and the code will not be i
38、ncluded in channel estimation, cyclic prefix and other modules.Then through the program code written in AWGN channel on the basis of adding modified item is emphatically discussed, under the condition of ideal synchronization protection time slot (CP), and a variety of before and after cyclic prefix
39、 to join channel interpolation method in multipath Rayleigh fading channel in OFDM system under the influence of the overall performance. One if the symbol is equal to the length of the strict Ts, namely N sampling points, then after the intersymbol interference channel between two consecutive symbo
40、l of sample must be overlap, and the interference among the symbols can also affect the orthogonality between each child carrier, serious consequences. Therefore, systems often need to add protection time slot between two OFDM symbol. A direct approach is combined with a period of time between two s
41、ymbols of 0, it eliminates ISI, but this method is actually unable to overcome sub-carrier interference brought by the intersymbol interference. In FFT subcarrier delay path integral time isnt the whole cycle, the subcarrier orthogonality between its serious damage. We have to solve this problem, in
42、 the current practical OFDM systems are adopted the approach of adding cyclic prefix (CP). So-called cyclic prefix is actually a symbol behind a number of sample point (Ncp) moved to the front 仁 人 教 育VIIof the symbol according to the order instead of protection interval, and its role is in the FFT i
43、ntegral time, each delay diameter on each subcarrier is still a whole cycle, ensure the orthogonality between the subcarrier. The introduction of the cyclic prefix although against the intersymbol interference, but lead to a drop in efficiency, so when the length of the cyclic prefix in OFDM system
44、design need to select a proper parameter, when most of its length must be greater than the diameter delay, to guarantee the subcarrier orthogonality between. After adding cyclic prefix, obviously, the whole system will produce loss of power and information rate but it can overcome the intersymbol in
45、terference and multipath intersymbol interference, this paper will through the simulation of the actual results based on the length of the two sides. Research OFDM system peak power is higher than at the same time, is the symbol is dominated by a single modulated subcarrier signal. Therefore, it may
46、 lead to a very high signal peak power, has the very high peak power ratio. So comparing single carrier system, OFDM system transmitter signal instantaneous value extremely unstable. This will inevitably request in the system, such as A/D, D/A converter and some other devices with very large linear
47、dynamic range; But also because of these devices with wider range of nonlinear dynamic nonlinear distortion caused by the signal, and the interference between each channel caused by harmonics, thus reducing the whole performance of the OFDM system. On the receiving end at the same time, because of t
48、he wireless channel fluctuation range is very wide and unpredictability, and as the instability of a variety of reasons, thus received signal amplitude, phase and frequency distortion, which is difficult to parse. These problems to the design of receiver caused great obstacles, so in the receiver, c
49、hannel estimation is an indispensable part. The design of the channel estimator in OFDM systems directly to face two difficulties: first one is the choice of pilot information, 2 it is to have a lower complexity. In the newly established in orthogonal frequency division multiplexing wireless communication system, because of its high transmission rate, it must use coherent detection technology to get a higher performance, therefore generally choose the blind estimation harvest good estimation results, enable it to very good after the change of the wireless channel, im
