【正文】 d DemodulationAbstractOFDM (Orthogonal Frequency Division Multiplexing) is a special multicarrier modulation technique. OFDM is short of Orthogonal Frequency Division Multiplexing. It is a new type of highly efficient multicarrier modulation technique, it can effectively fight against multipath spread and make the signal interference reliably receive. After several decades of development, OFDM / COFDM has been widely used in highspeed digital munications, and has spread to other fields. At the same time, modern digital signal processing technology and ultralargescale application specific integrated circuits (VLSI) also make the development of fast Fourier transform more easily and the cost of the technology more practically, and open the market for OFDM widely used in the field of munication in the future. 　Paper analyzes the basic principles of OFDM technology, OFDM protection interval, cyclic prefix, OFDM modulation and demodulation of the key technologies.　　Keywords：（OFDM ）Orthogonal Frequency Division Multiplexing,Multicarrier modulation,SNR,Modulation mapping.　　　　　　　　　　　　第 1 章 正交頻分復用的來源　　 OFDM 的歷史起源隨著通信技術的不斷成熟和發(fā)展，如今的通信傳輸方式可以說多種多樣，變化日新月異，從最初的有線通信到無線通信，再到現(xiàn)在的光纖通信。但是，一個 OFDM 系統(tǒng)的結構非常復雜，從而限制了其進一步推廣。分組隨機跳頻空閑時間較短，約n個字符時間。跳頻的開銷比特數(shù)量與用戶速率、用戶數(shù)量以及系統(tǒng)是全雙工還是半雙工有關?！　? 多天線　　ODFM由于碼率低和加入了時間保護間隔，因此具有極強的抗多徑干擾能力。使用與信噪比相匹配的調制方式可以提高頻譜利用率。功率控制與自適應調制要取得平衡，也就是說對于一個遠端發(fā)射臺，它有良好的信道，若發(fā)送功率保持不變，可使用較高的調制方案如64QAM；若功率可以減小，調制方案也相應降低，可使用QPSK?！? OFDM 系統(tǒng)的基本原理　　 OFDM 原理簡介　多載波傳輸是把數(shù)據(jù)流分解為若干個獨立的子比特流，這樣每個子數(shù)據(jù)流具有低得多的比特速率，用此比特率形成低速率多狀態(tài)符號再去調制相應的子載波?！≡趥鹘y(tǒng)的并行通信系統(tǒng)中，整個系統(tǒng)頻帶被劃分為N 個互不混疊的子信道，每個子信道被一個獨立的信源符號調制，即N個子信道被頻分復用。盡管還是頻分復用，但己與過去的FDMA有了很大的不同:不再是通過很多帶通濾波器來實現(xiàn)，而是直接在基帶處理，這也是OFDM有別于其他系統(tǒng)的優(yōu)點之一。這樣 和 明顯能夠滿足公式:　??tfjmmetp?2???tfjn?2????tpiqi (22)　?nmTtfjTtfj snsmd???,020?但是 必須滿足關系： ， 。而FFT和IFFT 可以顯著的降低運算復雜度。例如在64點的FFT 中，需要計算96次復數(shù)乘法和384次復數(shù)加2log法，換句話說。這樣的話，在FFT 運算長度內，第一個子載波與帶有時延的第二個子載波之間的周期個數(shù)之差不再是整數(shù)，所以當接收機解調第一個載波時，第二個子載波會對第一個子載波造成干擾?！? OFDM 子載波調制在串行系統(tǒng)中，符號是逐次發(fā)送的，每一個數(shù)據(jù)符號的頻譜允許占用所有的可利用帶寬，這樣的信號極容易受到菲理想頻率傳輸特性的影響而失真。　利用濾波器完全地分開這些子帶。接收時由相應ncf,的濾波器就可以得到某一子帶的數(shù)據(jù)。如圖 ，在一個OFDM 符號內 4 個子載波的具有如下特性：　在給定的時間間隔 T 內每個子載波正好有整數(shù)個周期寬度也就是每個子載波頻率是基本頻率的整數(shù)倍 f1=f0 f2=2*f0 f3=3*f0 等一個符號時間段內兩個相鄰子載波的周期數(shù)嚴格地相差一個周期此特性保證了兩個子載波間的正交性允許每個子載波能被接收并獨立地解調而不會受其它副載波產(chǎn)生的干擾影響?！　　　　　　　　　⒖嘉墨I　[1] J J van de Beek,M Sandell,P O estimation of time and frequency offset in 0FDM Systems[J],IEEE 1997,45(7):18001805　[2] 吳偉陵,移動通信中的關鍵技術[M],11:411[3] Theodore ,Wireless Communication Principles and Practice[M],電子工業(yè)出版社.2022,6:299357[4] John ,張力軍,張宗橙,鄭寶玉譯“Digital Communication (Third Editon)”[M],電子,2:552560[5] Chang ,Synthesis of bandlimited orthogonal signals for multichannel data transmission [J],Bell Syst Tech ,2:17751796　[6] Chang .,Gibbery ,theoretical study of performance of an orthogonal multiplexing data transmission scheme[M],IEEE Trans Communication ,540　[7] 姜丹,信息論與編碼[M],[8] Jean Armstrong,Analysis of New and Existing Methods of Reducing Intercarrier Interference Due to Carrier Frequency Offset in OFDM[M],IEEE 369　　[9] 李建東,楊家瑋,個人通信[M],　　　　　　　　　　　　　　　　　致謝首先，我要感謝我尊敬的導師王華夏老師?！?　　% Basic OFDM system parameters　　% choice of defaults or user selections　%　fprintf (39。 % number of carriers bits_per_symbol = 2。)。SNR = 39。 integers where N = 2^bits_per_symbol　% this defines how many states each symbol can represent　% first, make a matrix with each column representing consecutive bits 　% from the input stream and the number of bits in a column equal to the% number of bits per symbol　% then, for each column, multiply each row value by the power of 2 that 　　% it represents and add all the rows% for example: input 0 1 1 0 0 0 1 1 1 0　　% bits_per_symbol = 2% convert_matrix = 0 1 0 1 1% 1 0 0 1 0　%　% modulo_baseband = 1 2 0 3 2%　convert_matrix = reshape(baseband_out, bits_per_symbol, length(baseband_out)/bits_per_symbol)。　　end　%% Convert the differential coding into a phase　% each phase represents a different state of the symbol% for example:　　% bits_per_symbol = 2 (modulo 4)% symbols = 0 3 2 1　% phases =　　% 0 * 2pi/4 = 0 (0 degrees)　% 3 * 2pi/4 = 3pi/2 (270 degrees)　% 2 * 2pi/4 = pi (180 degrees)　　% 1 * 2pi/4 = pi/2 (90 degrees)　　%　　carrier_matrix = carrier_matrix * ((2*pi)/(2^bits_per_symbol))。)　　%grid on　%axis ([0 IFFT_bin_length ])　　%ylabel(39。)%hold on　%stem(carriers1, (180/pi)*angle(IFFT_modulation(2,carriers)),39。)　%title(39。 symbol due to differential implementation　% second plot strips out each carrier and plots them on the% same graph　% only works for carrier count = 16 due to colors variable (more　% than 16 would really be legible anyway　 　%　　%figure (3)%plot(0:IFFT_bin_length1,time_wave_matrix(2,:))　　%grid on　%ylabel(39。 39。 39。 39。 39。% temp_bins(carriers(f))=IFFT_modulation(2,carriers(f))。)　　%title(39?！?　　% PLOT OFDM SIGNAL (time)　%　　%temp_time = IFFT_bin_length*(symbols_per_carrier+1)?！　?avg_temp_time = IFFT_bin_length*symbols_per_average。rd39?！?　%CHANNEL ======================================================================　%　　% The channel model is Gaussian (AWGN) only 　　% Rayleigh fading would be a useful addition　　%Tx_signal_power = var(Tx_data)。%% PLOT BASIC FREQUENCY DOMAIN REPRESENTATION%%figure (7)　%stem(0:IFFT_bin_length1, abs(Rx_spectrum(1:IFFT_bin_length,2)),39。)　%figure (8)%plot(0:IFFT_bin_length1, (180/pi)*angle(Rx_spectrum(1:IFFT_bin_length,2)), 39。)　 　%xlabel(39。bd39?！?　% Convert phase to symbol　　%