CN101014029A

CN101014029A - Method for generating OFDM synchronous training sequence and synchronizing method based on the training sequence

Info

Publication number: CN101014029A
Application number: CN 200610030331
Authority: CN
Inventors: 丁铭; 吴赟; 罗汉文; 佘锋; 张霆蔚; 张海滨
Original assignee: Shanghai Jiao Tong University; Sharp Corp
Current assignee: Shanghai Jiao Tong University; Sharp Corp
Priority date: 2006-08-24
Filing date: 2006-08-24
Publication date: 2007-08-08
Anticipated expiration: 2026-08-24
Also published as: CN101014029B

Abstract

The invention provides a method for generating an OFDM synchronous training sequence and a synchronization method based on the training sequence, which are used in the technical field of communication. The method for generating the OFDM synchronous training sequence is to generate the OFDM synchronous training sequence by concatenating two OFDM symbols, and the two OFDM symbols are respectively an irregular OFDM symbol S _a and a regular OFDM symbol S _n . The synchronization method based on the training sequence includes the following steps: coarse timing synchronization, fractional frequency offset estimation, integer frequency offset estimation, and fine timing synchronization. Among them, the dual-symbol joint decision algorithm is used to obtain a better coarse timing synchronization estimate, and the remainder theorem algorithm is used to estimate the frequency offset. The invention has the advantages of low computational complexity, large frequency offset estimation range, relatively accurate symbol timing synchronization and frequency synchronization, and the like.

Description

Method for generating OFDM synchronous training sequence and synchronization method based on the training sequence

技术领域technical field

本发明涉及通信技术领域，特别涉及一种OFDM(正交频分复用)同步训练序列的生成方法和基于该训练序列的同步方法。The invention relates to the field of communication technology, in particular to a method for generating an OFDM (orthogonal frequency division multiplexing) synchronous training sequence and a synchronization method based on the training sequence.

背景技术Background technique

目前，OFDM技术在越来越多的有线、无线通信领域得到应用，如：DAB(数字音频广播)、DVB(数字视频广播)、IEEE802.11a、HIPERLAN/2、ADSL(非对称用户环路)等等。这主要由于OFDM技术具有许多优势：有效对抗多径干扰和窄带干扰，频谱利用率高，数据传输速率高等。At present, OFDM technology is applied in more and more wired and wireless communication fields, such as: DAB (Digital Audio Broadcasting), DVB (Digital Video Broadcasting), IEEE802.11a, HIPERLAN/2, ADSL (Asymmetric Subscriber Loop) etc. This is mainly because OFDM technology has many advantages: effectively resisting multipath interference and narrowband interference, high spectrum utilization rate, and high data transmission rate.

OFDM系统对于同步偏差非常敏感。同步偏差主要分为符号定时偏差和频率偏差。符号定时偏差是指解调OFDM符号时，FFT窗口提前或是滞后。如果符号定时偏差过大，使定时的偏移量与最大时延扩展的长度之和小于循环前缀的长度，会产生符号间干扰，破坏OFDM符号的完整性，降低系统的性能。频率偏差fΔ是指接收端的解调载频与发送端的调制载频不一致，这主要由于晶振不稳定或是多普勒频移。频率偏差又分为子载波间隔的小数倍频率偏差f_F和子载波间隔的整数倍频率偏差f_I在下文中分别简称为小数频偏和整数频偏。其中，小数频偏会造成子载波间干扰(ICI)；整数频偏不会引起ICI，但会引起接收数据符号的循环移位，使得解调出来的信息符号的错误概率为50％。因此，有效地估计符号定时偏差和频率偏差，是OFDM系统能否正常工作的关键因素。OFDM systems are very sensitive to synchronization deviations. Synchronization deviation is mainly divided into symbol timing deviation and frequency deviation. The symbol timing deviation refers to whether the FFT window advances or lags when demodulating OFDM symbols. If the symbol timing deviation is too large, the sum of the timing offset and the maximum delay extension length is less than the length of the cyclic prefix, which will cause intersymbol interference, destroy the integrity of OFDM symbols, and reduce system performance. The frequency deviation fΔ means that the demodulation carrier frequency at the receiving end is inconsistent with the modulation carrier frequency at the sending end, which is mainly due to unstable crystal oscillator or Doppler frequency shift. The frequency offset is divided into fractional frequency offset f _F of subcarrier spacing and integer multiple frequency offset f _I of subcarrier spacing, which are referred to as fractional frequency offset and integer frequency offset respectively in the following. Among them, fractional frequency offset will cause inter-carrier interference (ICI); integer frequency offset will not cause ICI, but will cause cyclic shift of received data symbols, so that the error probability of demodulated information symbols is 50%. Therefore, effectively estimating the symbol timing offset and frequency offset is a key factor for the OFDM system to work normally.

图1是一个通用OFDM基带系统的框图。图1中的发送端串并转换、IDFT(傅里叶反变换)、发送端并串转换、插入循环前缀，插入同步信息等模块，代表OFDM基带调制过程；图1中的分离同步信息，去除循环前缀，接收端串并转换，DFT(傅里叶变换)以及频域均衡，接收端并串转换等模块是与之对应的OFDM基带解调过程；图1中的数模转换，发送滤波处理，信道，接收滤波处理，模数转换等模块是模拟发射与信道环节；图1中的同步单元模块即是实现OFDM同步的部件。现结合图1对OFDM系统的调制和解调过程进行简要介绍：Figure 1 is a block diagram of a general OFDM baseband system. The serial-to-parallel conversion at the sending end, IDFT (inverse Fourier transform), parallel-serial conversion at the sending end, insertion of cyclic prefix, and insertion of synchronization information in Figure 1 represent the OFDM baseband modulation process; the separation of synchronization information in Figure 1, remove Cyclic prefix, serial-to-parallel conversion at the receiving end, DFT (Fourier transform) and frequency domain equalization, parallel-serial conversion at the receiving end and other modules are the corresponding OFDM baseband demodulation processes; digital-to-analog conversion in Figure 1, sending filter processing , channel, receiving filter processing, analog-to-digital conversion and other modules are analog transmission and channel links; the synchronization unit module in Figure 1 is the component that realizes OFDM synchronization. The modulation and demodulation process of the OFDM system is briefly introduced in conjunction with Figure 1:

设基带采样时间间隔为T_s，OFDM系统的有效符号点数为N(一般情况下，N＝2^β)，与之对应的有效符号周期为T＝NT；N_u是N个OFDM子载波中有效子载波的数目。在发送端，频域数据{a_i，k|(k＝-N/2，...，0，1，...，N/2-1)}(a_i，k是第i个符号，第k个子载波上加载的数据)被置入图1中的发送端串并转换模块；经过IDFT模块，在发送端并串转换模块的输出端得到时域数据{b_i，l|(l＝0，1，2，...，N-1)}(b_i，j是第i个符号，第l个采样点的数据)；为了对抗符号间干扰(ISI)，添加N_g点的循环前缀(图1中的插入循环前缀模块)，于是，每个OFDM符号含点数为N_sym(N_sym＝N+N_g)；再插入同步训练序列(图1中的插入同步信息模块)，然后整个信号通过信道到达接收端；在接收端，分离出同步训练序列(图1中的分离同步信息模块)送入图1中的同步单元模块；再删去循环前缀(图1中的去除循环前缀模块)，在图1中的接收端串并转换模块的输出端得到时域数据{r_i，m|(m＝0，1，2，...，N-1)}(r_i，m是第i个符号，第m个采样点的数据)；最后经过图1中的DFT和频域均衡模块，在图1中的接收端并串转换模块的输出端得到解调的频域数据{z_i，n|(n＝-N/2，...，0，1，...，N/2-1)}(z_i，n是第i个符号，第n个子载波上解调的数据)。Assuming that the baseband sampling time interval is T _s , the number of effective symbol points in the OFDM system is N (generally, N=2 ^β ), and the corresponding effective symbol period is T=NT; N _u is the effective The number of subcarriers. At the sending end, the frequency domain data {a _{i, k} |(k=-N/2, ..., 0, 1, ..., N/2-1)} (a _{i, k} is the i-th symbol , the data loaded on the kth subcarrier) is put into the serial-to-parallel conversion module at the sending end in Figure 1; after passing through the IDFT module, the time-domain data {b _{i, l} |(l =0, 1, 2,..., N-1)} (b _{i, j} is the i-th symbol, the data of the l-th sampling point); in order to combat inter-symbol interference (ISI), add N _g points Cyclic prefix (insert cyclic prefix module among Fig. 1), so, each OFDM symbol contains point number to be _Nsym ( _Nsym =N+ _Ng ); Insert synchronous training sequence again (insert synchronous information module among Fig. 1), Then the whole signal arrives at the receiving end through the channel; at the receiving end, separate the synchronous training sequence (separate synchronous information module in Fig. 1) and send it into the synchronous unit module among Fig. 1; prefix module), the time domain data {r _{i, m} |(m=0,1,2,...,N-1)}(r _{i, m} is the i-th symbol, the data of the m-th sampling point); finally through the DFT and frequency-domain equalization module in Figure 1, the demodulated frequency-domain data is obtained at the output of the parallel-to-serial conversion module at the receiving end in Figure 1 {z _{i, n} |(n=-N/2, ..., 0, 1, ..., N/2-1)} (z _{i, n} is the i-th symbol, and the solution on the n-th subcarrier tuned data).

常见的OFDM同步方案有两种：There are two common OFDM synchronization schemes:

(1)基于特定频域序列和2等分结构的同步训练序列，该方法通过计算训练符号的半个符号延时的自相关，寻找相关峰值获得符号定时，求相关峰值处的相角估计小数频偏，再对同步训练符号进行小数频偏补偿后，作快速傅里叶变换(FFT)，然后与已知频域序列作循环移位相关，通过寻找相关峰来估计整数频偏。该方法所能估计的频偏范围，随着相关搜索范围的扩大而增大，但是，其计算复杂度也会不断上升。因此，由于计算复杂度的原因，该方法难以应用到实际系统中。参见文献：Schmidl，T.M.等“Low-overhead，low-complexity [burst]synchronization for OFDM”，IEEE International Conference onCommunications，Volume 3，June 1996，Page(s)：1301-1306 (“低数据开销、低复杂度的OFDM同步方法”IEEE国际通信技术会议)。(1) Based on a specific frequency domain sequence and a synchronous training sequence with a bisection structure, this method calculates the autocorrelation of the half-symbol delay of the training symbol, finds the correlation peak to obtain the symbol timing, and calculates the phase angle estimation decimal at the correlation peak Frequency offset, after performing fractional frequency offset compensation on the synchronous training symbols, perform fast Fourier transform (FFT), and then perform cyclic shift correlation with known frequency domain sequences, and estimate integer frequency offset by looking for correlation peaks. The range of frequency offsets that can be estimated by this method increases with the expansion of the correlation search range, but its computational complexity will also continue to increase. Therefore, it is difficult to apply this method to practical systems due to the computational complexity. See literature: Schmidl, T.M. et al. "Low-overhead, low-complexity [burst] synchronization for OFDM", IEEE International Conference on Communications, Volume 3, June 1996, Page(s): 1301-1306 ("Low data overhead, low complexity Degree-based OFDM Synchronization Methods" IEEE International Conference on Communication Technology).

(2)基于L等分(L＝2^v)的OFDM同步训练符号结构，通过计算训练符号的特定延时的自相关，寻找相关峰值获得符号定时，再求相关峰值处的相角来估计频偏。该方法虽然计算复杂度低，但其时间同步性能较差，且频偏估计范围较小，仅为[-L/2，L/2)。在实际中，L的取值一般不能太大。因为过大的L，会造成OFDM系统的峰均功率比过高，并产生较大的频偏估计误差，以及训练符号的频域数据稀疏性导致其抵抗频率选择性衰落的能力下降。参见文献：Heiskala J，Terry J：OFDM Wireless LANs-A Theoretical and Practical Guide.[M].Indianapolis USA：Pearson Education Inc，2002.70-73(《OFDM无线局域网——理论与实践的指导》)。(2) Based on L equal division (L=2 ^v ) OFDM synchronous training symbol structure, by calculating the autocorrelation of the specific delay of the training symbol, finding the correlation peak to obtain the symbol timing, and then calculating the phase angle at the correlation peak to estimate the frequency Partial. Although this method has low computational complexity, its time synchronization performance is poor, and the frequency offset estimation range is small, only [-L/2, L/2). In practice, the value of L generally cannot be too large. Because L is too large, the peak-to-average power ratio of the OFDM system will be too high, and a large frequency offset estimation error will be generated, and the frequency domain data sparsity of the training symbols will reduce its ability to resist frequency selective fading. See literature: Heiskala J, Terry J: OFDM Wireless LANs-A Theoretical and Practical Guide. [M]. Indianapolis USA: Pearson Education Inc, 2002.70-73 ("OFDM Wireless LANs-A Theoretical and Practical Guide").

因此，方法(1)属于频域算法，需要对整个同步训练符号作FFT，其主要缺点是复杂度高；方法(2)属于时域算法，虽然不需要对整个同步训练符号作FFT，具有较低的复杂度，但其主要缺点是性能较差，这使上述两种方法在实际应用中受到限制。Therefore, method (1) belongs to the frequency domain algorithm, and needs to do FFT to the entire synchronous training symbol, and its main disadvantage is that the complexity is high; method (2) belongs to the time domain algorithm, although it does not need to do FFT to the entire synchronous training symbol, it has relatively low complexity, but its main disadvantage is poor performance, which makes the above two methods limited in practical applications.

发明内容Contents of the invention

本发明的目的在于针对现有技术的不足，提供一种OFDM同步训练序列的生成方法和基于该训练序列的同步方法。本发明所述的OFDM同步训练序列的生成方法为由2个OFDM符号级联生成OFDM同步训练序列，所述2个OFDM符号分别是非正则OFDM符号与正则OFDM符号。本发明所述的同步方法基于根据所述OFDM同步训练序列的生成方法生成的OFDM同步训练序列，包括以下步骤：粗定时同步，小数频偏估计，整数频偏估计，细定时同步。其中采用双符号联合判决算法获得较优的粗定时同步估计，又采用余数定理算法对频偏进行估计。相对于现有方案，本发明具有计算复杂度较低、频偏估计范围较大、符号定时同步及频率同步较为准确等优点。The object of the present invention is to provide a method for generating an OFDM synchronous training sequence and a synchronization method based on the training sequence to address the deficiencies in the prior art. The method for generating the OFDM synchronous training sequence of the present invention is to generate the OFDM synchronous training sequence by concatenating two OFDM symbols, and the two OFDM symbols are respectively non-regular OFDM symbols and regular OFDM symbols. The synchronization method of the present invention is based on the OFDM synchronization training sequence generated according to the generation method of the OFDM synchronization training sequence, and includes the following steps: coarse timing synchronization, decimal frequency offset estimation, integer frequency offset estimation, and fine timing synchronization. Among them, the dual-symbol joint decision algorithm is used to obtain a better coarse timing synchronization estimate, and the remainder theorem algorithm is used to estimate the frequency offset. Compared with the existing solutions, the present invention has the advantages of lower computational complexity, larger frequency offset estimation range, more accurate symbol timing synchronization and frequency synchronization, and the like.

本发明是通过以下技术方案实现的：The present invention is achieved through the following technical solutions:

本发明所述的OFDM同步训练序列的生成方法，是由2个OFDM符号级联生成OFDM同步训练序列，而现有的一些同步训练序列结构往往需要更多符号(如无线局域网需要4个OFDM符号)，因此，用本发明的OFDM同步训练序列的生成方法所生成的训练序列具有数据开销低的优点。该序列的构成如下：The generation method of the OFDM synchronous training sequence of the present invention is to generate the OFDM synchronous training sequence by cascading 2 OFDM symbols, and some existing synchronous training sequence structures often need more symbols (as wireless local area network needs 4 OFDM symbols ), therefore, the training sequence generated by the method for generating the OFDM synchronous training sequence of the present invention has the advantage of low data overhead. The sequence is structured as follows:

第1个符号：这是一个非正则符号(irregular symbol)，记为S_a，S_a的有效符号部分的点数为N_a(N_a为整数，且含有奇素数因子q，N_a≠N，N为除非正则符号外，包括正则符号在内的其他OFDM符号的有效符号点数)，其被等分为L_a份(L_a为整数，也含有奇素数因子q)，通常，每一份信号称为一个slot。每一个slot含M_a点(M_a为整数，且M_a＝N_a/L_a)，S_a的循环前缀部分含点数为N_ag(N_ag＝N_sym-N_a)，因此，S_a的总点数仍为N_sym。The first symbol: This is an irregular symbol (irregular symbol), denoted as S _a , the number of points in the effective symbol part of S _a is N _a (N _a is an integer, and contains an odd prime factor q, N _a ≠ N, N is the number of effective symbol points of other OFDM symbols including regular symbols except regular symbols), which is divided into L _a parts (L _a is an integer and also contains an odd prime factor q), usually, each part of the signal Called a slot. Each slot contains M _a points (M _a is an integer, and M _a =N _a /L _a ), the number of points in the cyclic prefix part of S _a is Na _ag (N _ag =N _sym -N _a ), therefore, S _a The total number of points is still N _sym .

第2个符号：这是一个正则符号(regular symbol)，记为S_n，其有效部分的点数为N，其被等分为L份(L为整数，且L＝2^v)，每一个slot含M点(M为整数，且M＝N/L)，L的一些典型值为4、8、16等。The second symbol: This is a regular symbol (regular symbol), denoted as S _n , the number of points in its effective part is N, which is divided into L parts (L is an integer, and L=2 ^v ), each slot Containing M points (M is an integer, and M=N/L), some typical values of L are 4, 8, 16, etc.

以下对本发明的OFDM同步训练序列的生成方法进行进一步的描述：The generation method of OFDM synchronous training sequence of the present invention is further described below:

设S_a、S_n对应的OFDM符号标号分别为1、2。Let the OFDM symbol labels corresponding to S _a and S _n be 1 and 2 respectively.

S_n是一个L等分的正则OFDM同步训练符号，这是一种相当常见的序列结构，经常用于符号定时同步算法和频偏估计算法中。例如，IEEE802.11a标准中取L＝4。其生成方法是首先按照式(1)插入频域数据S _n is an L equally divided regular OFDM synchronous training symbol, which is a fairly common sequence structure and is often used in symbol timing synchronization algorithms and frequency offset estimation algorithms. For example, L=4 in the IEEE802.11a standard. Its generation method is to first insert the frequency domain data according to formula (1)

$\{\begin{matrix} {a a}_{22,, k k} &NotEqual; &NotEqual; 00 & k k ((mod mod L L)) = = 00 \\ {a a}_{22,, k k} = = 00 & k k ((mod mod L L)) &NotEqual; &NotEqual; 00 \end{matrix} ((00 < < | | k k | | \frac{{N N}_{u u}}{22})) - - - - - - ((11))$

然后进行N点傅里叶反变换产生对应的时域信号，之后在时域信号的前端加上循环前缀，即可生成S_n。在L等分的情况下，S_n的每一个slot所含的点数为M(M＝N/ L)。Then perform N-point inverse Fourier transform to generate a corresponding time-domain signal, and then add a cyclic prefix to the front end of the time-domain signal to generate S _n . In the case of L equal division, the number of points contained in each slot of S _n is M (M=N/L).

符号S_a含有L_a个slot，设L_a含有奇素数因子q，且有，2^α-1＜L_a≤2^α，(α为一个正整数)，N_a(mod L_a)＝0以及N(mod L_a)≠0，取N_a为L_a的整数倍数中与N最接近的自然数，即：The symbol S _a contains L _a slots, let L _a contain an odd prime factor q, and have, 2 ^α-1 <L _a ≤2 ^α , (α is a positive integer), N _a (mod L _a )=0 and N(mod L _a )≠0, take N _a as the natural number closest to N among integer multiples of L _a , namely:

${N N}_{a a} = = \underset{μ μ}{arg arg min min} {{| | μ μ - - N N | | | | μ μ ((mod mod {L L}_{a a})) = = 00}} - - - - - - ((22))$

S_a的生成方法是：将L_a和N_u-2^α+1代替式(1)中的L和N_u，得：The generation method of S _a is: replace L and _Nu in formula (1) with L a and _Nu -2 _α ⁺¹ , get:

$\{\begin{matrix} {a a}_{11,, k k} &NotEqual; &NotEqual; 00 & k k ((mod mod {L L}_{a a})) = = 00 \\ {a a}_{11,, k k} = = 00 & k k ((mod mod {L L}_{a a})) &NotEqual; &NotEqual; 00 \end{matrix} ((00 < < | | k k | | \leq \leq \frac{{N N}_{μ μ} 22^{α α + + 11}}{22})) - - - - - - ((33))$

按照式(3)插入频域数据，然后进行N_a点傅里叶反变换后可得b_1，l：According to the formula (3) to insert the frequency domain data, and then perform N _a point inverse Fourier transform to obtain b _1,l :

${b b}_{11,, l l} = = \frac{11}{N N} {Σ Σ}_{k k = = 00}^{{N N}_{a a} - - 11} {a a}_{I I,, k k} exp exp ((j j 22 π π \frac{kl kl}{{N N}_{a a}})) ((l l = = 0,1,2 0,1,2,, . . . . . .,, {N N}_{a a} - - 11)) - - - - - - ((44))$

再添加N_ag点循环前缀，就能得到S_a。需要说明的是，式(3)的N_u，比式(1)少2^α+1个，这是为了补偿式(2)造成的频谱畸变。Then add _Nag point cyclic prefix to get S _a . It should be noted that _Nu in formula (3) is 2 ^α+1 less than formula (1), which is to compensate for the spectrum distortion caused by formula (2).

本发明还提供基于上述同步训练序列的同步方法，具体如下：The present invention also provides a synchronization method based on the above-mentioned synchronization training sequence, specifically as follows:

步骤一：粗定时同步，对S_a作延时为M_a点，窗长为(N_sym-M_a)点的自相关，得P_a(d)。对S_n作延时为M点，窗长为(N_sym- M)点的自相关，得P_n(d)。对S_n作延时为N/2点，窗长为(N_sym-N/2)点的自相关，得P_f(d)，再对P_a(d)、P_n(d)与P_f(d)求能量之和，除以相关窗内的信号总能量，得平均自相关P(d)，寻找P(d)的峰值，初步估计出OFDM符号的起始位置

这一算法称为“双符号联合判决算法”。该算法可以大大提高系统粗定时同步的性能，而且，该算法具有较低的计算复杂度。Step 1: Coarse timing synchronization, the autocorrelation of point _Ma with a window length of (N _sym -M _a ) as the time delay for S _a , to obtain P _a (d). Delay S _n as M points, window length is (N _sym - M) point autocorrelation, get P _n (d). For S _n , the time delay is N/2 points, the window length is (N _sym -N/2) point autocorrelation, and P _f (d) is obtained, and then P _a (d), P _n (d) and P _f (d) Calculate the sum of energy, divide by the total energy of the signal in the correlation window, get the average autocorrelation P(d), find the peak value of P(d), and preliminarily estimate the starting position of the OFDM symbol

This algorithm is called "Double Symbol Joint Decision Algorithm". This algorithm can greatly improve the performance of coarse timing synchronization of the system, and the algorithm has lower computational complexity.

步骤二：小数频偏估计，即根据步骤一得到的P_f(d)，计算其在位置处的相角，从而估计频偏的小数部分

和整数频偏的奇偶性η。Step 2: Fractional frequency offset estimation, that is, according to the P _f (d) obtained in Step 1, calculate its position The phase angle at , thus estimating the fractional part of the frequency offset

and parity η of integer frequency offset.

步骤三：整数频偏估计，即根据步骤一得到的P_a(d)和P_n(d)，计算其在位置

处的相角，利用数论中的余数定理，估计整数频偏该算法称为“余数定理算法”。将步骤二得到的与

相加，得到频偏估计值

其估计范围可以达到[-L_x/2，L_x/2)(L_x是L和L_a的最小公倍数)。该算法同时具有计算复杂度低和频偏估计范围大的优点。Step 3: Integer frequency offset estimation, that is, according to P _a (d) and P _n (d) obtained in step 1, calculate its position

The phase angle at , using the remainder theorem in number theory, to estimate the integer frequency offset This algorithm is called the "remainder theorem algorithm". the obtained in step 2 and

Add up to get the frequency offset estimate

Its estimated range can reach [-L _x /2, L _x /2) (L _x is the least common multiple of L and L _a ). The algorithm has the advantages of low computational complexity and large frequency offset estimation range.

步骤四：细定时同步，即根据步骤一得到的

抽取S_n的第2个slot，然后根据步骤三得到的

对其进行频偏补偿，再把其与本地slot样本作循环移位相关，寻找相关峰，从而估计出OFDM符号的精确起始位置 Step 4: Fine timing synchronization, which is obtained according to Step 1

Extract the second slot of S _n , and then obtain according to step 3

Perform frequency offset compensation on it, and then perform cyclic shift correlation with local slot samples to find correlation peaks, thereby estimating the precise starting position of OFDM symbols

以下对本发明的同步方法进行进一步的描述：The synchronization method of the present invention is further described below:

(1)粗定时同步(1) Coarse timing synchronization

本发明提供的粗定时同步算法称为“双符号联合判决法”。The coarse timing synchronization algorithm provided by the present invention is called "double-symbol joint decision method".

首先，计算P_a(d)、P_n(d)和P_f(d)。如下：First, P _a (d), P _n (d) and P _f (d) are calculated. as follows:

对S_a作延时为M_a点，窗长为(N_sym-M_a)点的自相关，得P_a(d)：Delay S _a as point _Ma , and the window length is (N _sym -M _a ) point autocorrelation, get P _a (d):

${P P}_{a a} ((d d)) = = {Σ Σ}_{m m = = d d}^{{d d + + N N}_{sym sym} - - {M m}_{a a}} {r r}_{11,, m m}^{* *} {r r}_{11,, m m + + {M m}_{a a}} - - - - - - ((55))$

对S_n作延时为M点，窗长为(N_sym-M)点的自相关，得P_n(d)：Delay S _n as M points, and the window length is (N _sym -M) point autocorrelation, get P _n (d):

${P P}_{n no} ((d d)) = = {Σ Σ}_{m m = = d d}^{d d + + {N N}_{sym sym} - - M m} {r r}_{22,, m m}^{* *} {r r}_{22,, m m + + M m} - - - - - - ((66))$

对S_n作延时为N/2点，窗长为(N_sym-N/2)点的自相关，得P_f(d)：The autocorrelation of S _n with a delay of N/2 points and a window length of (N _sym -N/2) points is obtained to obtain P _f (d):

${P P}_{f f} ((d d)) = = {Σ Σ}_{m m = = d d}^{d d + + {N N}_{sym sym} - - N N / / 22} {r r}_{22,, m m}^{* *} {r r}_{22,, m m + + N N / / 22} - - - - - - ((77))$

接着对式(5)、式(6)与式(7)求能量之和，再除以相关窗内的信号总能量，得平均自相关P(d)，Then calculate the energy sum of formula (5), formula (6) and formula (7), and then divide by the total energy of the signal in the correlation window to get the average autocorrelation P(d),

$P P ((d d)) = = \frac{{| | {P P}_{a a} ((d d)) | |}^{22} + + {| | {P P}_{n no} ((d d)) | |}^{22} + + {| | {P P}_{f f} ((d d)) | |}^{22}}{{(({Σ Σ}_{m m = = d d}^{d d + + {N N}_{sym sym} - - {M m}_{a a}} {| | {r r}_{11,, m m + + {M m}_{a a}} | |}^{22}))}^{22} + + {(({Σ Σ}_{m m = = d d}^{d d + + {N N}_{sym sym} - - M m} {| | {r r}_{22,, m m + + M m} | |}^{22}))}^{22} + + {(({Σ Σ}_{m m = = d d}^{d d + + {N N}_{sym sym} - - N N / / 22} {| | {r r}_{22,, m m + + N N / / 22} | |}^{22}))}^{22}} - - - - - - ((88))$

然后寻找P(d)的峰值，从而估计出OFDM符号的粗定时起始点

Then look for the peak value of P(d) to estimate the coarse timing start point of the OFDM symbol

$\overset{^^}{d d} = = \underset{d d}{arg arg max max} {{P P ((d d))}} - - - - - - ((99))$

式(8)中，|P_a(d)|²和|P_n(d)|²的相关峰不尖锐，在低信噪比时具有较强的抗噪性能；|P_f(d)|²的相关峰较尖锐，在高信噪比时可以对符号定时同步作出较为精确的估计。因此，本发明提供的“双符号联合判决法”使用多个相关峰合并，大大提高了系统粗定时同步的性能。而且，式(5)至式(8)的计算可以递归进行，对每个采样点的计算量等效为9次复乘和若干次复数加减。In formula (8), the correlation peaks of |P _a (d)| ² and |P _n (d)| ² are not sharp, and have strong anti-noise performance at low SNR; |P _f (d)| The correlation peak of ² is sharper, and a more accurate estimation of symbol timing synchronization can be made when the signal-to-noise ratio is high. Therefore, the "double-symbol joint decision method" provided by the present invention uses the combination of multiple correlation peaks, which greatly improves the performance of the coarse timing synchronization of the system. Moreover, the calculations of formulas (5) to (8) can be performed recursively, and the calculation amount for each sampling point is equivalent to 9 times of complex multiplication and several times of complex number addition and subtraction.

需要指出的是，“双符号联合判决法”只适用于本发明设计的同步序列结构。如果采用另一个正则符号S_n代替S_a，假设其也被等分为L份，那么，“双符号联合判决法”会在d＝N_sym和d＝-N_sym(假定理想的符号起始位置d＝0)处分别出现了一个相关峰，这会严重干扰符号定时同步的判断。It should be pointed out that the "double-symbol joint decision method" is only applicable to the synchronization sequence structure designed in the present invention. If another regular symbol S _n is used to replace S _a , assuming that it is also equally divided into L parts, then the "double-symbol joint decision method" will be between d=N _sym and d=-N _sym (assuming that the ideal symbol starts A correlation peak appears at position d=0), which will seriously interfere with the judgment of symbol timing synchronization.

(2)小数频偏估计(2) Fractional frequency offset estimation

本发明采用的小数频偏算法是一种传统的小数频偏估计算法。该方法可参见文献：Schmidl，T.M.等“Low-overhead，low-complexity[burst]synchronization for OFDM”，IEEE International Conference onCommunications，Volume 3，June 1996，Page(s)：1301-1306(“低数据开销、低复杂度的OFDM同少方法”，IEEE国际通信技术会议)。具体实现方法是把N点OFDM符号等分为2份，对其作自相关，再求相角，从而估计小数频偏。The fractional frequency offset algorithm adopted in the present invention is a traditional fractional frequency offset estimation algorithm. This method can be found in the literature: Schmidl, T.M. et al. "Low-overhead, low-complexity [burst] synchronization for OFDM", IEEE International Conference on Communications, Volume 3, June 1996, Page(s): 1301-1306 ("Low data overhead , low-complexity OFDM with few methods", IEEE International Conference on Communication Technology). The specific implementation method is to divide the N-point OFDM symbols into two equal parts, make autocorrelation to them, and then calculate the phase angle, so as to estimate the fractional frequency offset.

由于本发明中的S_n是一个正则符号，L为偶数，故S_n也可以视作2等分的OFDM符号，时以利用式(7)中P_f(d)的相角来估计小数频偏：Since S _n in the present invention is a regular symbol and L is an even number, S _n can also be regarded as an OFDM symbol divided into two, and the fractional frequency can be estimated by using the phase angle of P _f (d) in formula (7). Bias:

$ξ ξ = = \frac{11}{π π} angle the angle {{{P P}_{f f} ((\overset{^^}{d d}))}} - - - - - - ((1010))$

ξ的范围是[-1，1)，而小数频偏的范围是[-0.5，0.5)，所以需要分类讨论，得到小数频偏估计值

和整数频偏估计值

的奇偶性η：The range of ξ is [-1, 1), and the range of decimal frequency offset is [-0.5, 0.5), so it needs to be discussed by category to get the estimated value of decimal frequency offset

and an integer frequency offset estimate

The parity η of:

其中，η＝1表示

为奇数；η＝0表示

为偶数。在本方案中，和η是重要的辅助信息，该信息帮助整数频偏估计模块实现大范围的频偏估计。Among them, η=1 means

is an odd number; η=0 means

is an even number. In this scheme, and η are important auxiliary information, which help the integer frequency offset estimation module realize a wide range of frequency offset estimation.

(3)整数频偏估计(3) Integer frequency offset estimation

在未来的OFDM系统中，载频将高达1GHz至100GHz，而子载波的间隔相对较小，只有几kHz至几十kHz，当接收端的晶振不是非常稳定时，就要求OFDM系统的频率同步模块能够纠正较大范围的频偏。以载频为10GHz，晶振频偏为20ppm，子载波间隔为5KHz的系统为例，其最大可能f_Δ为±40。目前，纠正大范围频偏的技术主要有2种：In the future OFDM system, the carrier frequency will be as high as 1GHz to 100GHz, and the interval between subcarriers is relatively small, only a few kHz to tens of kHz. When the crystal oscillator at the receiving end is not very stable, the frequency synchronization module of the OFDM system is required to be able to Corrects a wide range of frequency offsets. Taking a system with a carrier frequency of 10GHz, a crystal oscillator frequency deviation of 20ppm, and a subcarrier spacing of 5KHz as an example, the maximum possible f _Δ is ±40. At present, there are two main technologies for correcting large-scale frequency offset:

●基于特定频域序列的同步训练序列，该方法需要对同步训练符号进行小数频偏补偿，再作FFT，至少需要次复数乘法，然后与已知频域序列作循环移位相关，通过寻找相关峰来估计整数频偏。该方法所能估计的频偏范围，随着相关搜索范围的扩大而增大，但是，其计算复杂度也会不断上升。每搜索一个频点，就需要约

次复乘。因此，由于计算复杂度的原因，该方法难以应用到实际系统中。参见文献：Schmidl，T.M.等“Low-overhead，low-complexity[burst]synchronization for OFDM”，IEEE International Conference onCommunications，Volume 3，June 1996，Page(s)：1301-1306(“低数据开销、低复杂度的OFDM同步方法”IEEE国际通信技术会议)。Based on the synchronization training sequence of a specific frequency domain sequence, this method needs to perform fractional frequency offset compensation on the synchronization training symbols, and then perform FFT, at least Complex multiplication times, and then do cyclic shift correlation with the known frequency domain sequence, and estimate the integer frequency offset by looking for the correlation peak. The range of frequency offsets that can be estimated by this method increases with the expansion of the correlation search range, but its computational complexity will also continue to increase. Every time a frequency point is searched, about

multiple times. Therefore, it is difficult to apply this method to practical systems due to the computational complexity. See literature: Schmidl, TM, etc. "Low-overhead, low-complexity [burst] synchronization for OFDM", IEEE International Conference on Communications, Volume 3, June 1996, Page(s): 1301-1306 ("Low data overhead, low complexity Degree-based OFDM Synchronization Methods" IEEE International Conference on Communication Technology).

●基于L等分(L＝2^v)的OFDM 同步训练符号结构，通过计算训练符号的特定延时的自相关，再求相角来估计整数频偏。该方法的最大估计范围为[-L/2，L/2)，但是，L的实际取值一般不能太大。因为过大的L，会造成OFDM系统的峰均功率比过高，并产生较大的频偏估计误差，以及训练符号的频域数据稀疏性导致其抵抗频率选择性衰落的能力下降。参见文献：Heiskala J，Terry J：OFDM Wireless LANs-A Theoretical and Practical Guide.[M].Indianapolis USA：Pearson Education Inc，2002.70-73(《OFDM无线局域网——理论与实践的指导》)。● Based on the OFDM synchronous training symbol structure of L equal division (L=2 ^v ), the integer frequency offset is estimated by calculating the autocorrelation of the specific time delay of the training symbol and calculating the phase angle. The maximum estimated range of this method is [-L/2, L/2), however, the actual value of L generally cannot be too large. Because L is too large, the peak-to-average power ratio of the OFDM system will be too high, and a large frequency offset estimation error will be generated, and the frequency domain data sparsity of the training symbols will reduce its ability to resist frequency selective fading. See literature: Heiskala J, Terry J: OFDM Wireless LANs-A Theoretical and Practical Guide. [M]. Indianapolis USA: Pearson Education Inc, 2002.70-73 ("OFDM Wireless LANs-A Theoretical and Practical Guide").

基于本发明的OFDM同步训练序列的生成方法生成的OFDM同步训练序列，设计一种频偏估计范围较大，且复杂度较低的整数频偏估计算法，称之为“余数定理算法”。该算法首先利用式(11)得到的和η，求出式(5)中的P_a(d)和式(6)中的P_n(d)在位置处的相角，从而对整数频偏作出2个估计(f_a与f_n)：Based on the OFDM synchronous training sequence generated by the method for generating the OFDM synchronous training sequence of the present invention, an integer frequency offset estimation algorithm with a large frequency offset estimation range and low complexity is designed, which is called "remainder theorem algorithm". The algorithm first uses formula (11) to get and η, find P _a (d) in formula (5) and P _n (d) in formula (6) in position The phase angle at , thus making 2 estimates of the integer frequency offset (f _a and f _n ):

${f f}_{a a} = = \{\begin{matrix} \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | |}} & {L L}_{a a} ((mod mod 22)) = = 11 \\ \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | | | | λ λ ((mod mod 22)) = = η η}} & {L L}_{a a} ((mod mod 22)) = = 00 \end{matrix} - - - - - - ((1212))$

${f f}_{n no} = = \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{n no} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | | | | λ λ ((mod mod 22)) = = η η}} - - - - - - ((1313))$

f_a(mod L_a)有L_a种可能的取值：{0，1，...，L_a-1}；f_n(mod L)有L种可能的取f _a (mod L _a ) has L _a possible values: {0, 1, ..., L _a -1}; f _n (mod L) has L possible values

值：{0，1，...，L-1}。由f_a(mod L_a)和f_n(mod L)，可以导出一个不定方程组：Values: {0, 1, ..., L-1}. From f _a (mod L _a ) and f _n (mod L), a system of indeterminate equations can be derived:

$\{\begin{matrix} {\overset{^^}{f f}}_{I I} ((mod mod {L L}_{a a})) = = {f f}_{a a} ((mod mod {L L}_{a a})) \\ {\overset{^^}{f f}}_{I I} ((mod mod L L)) = = {f f}_{n no} ((mod mod L L)) \end{matrix} - - - - - - ((1414))$

根据数论中的余数定理，由f_a(mod L_a)和f_n(mod L)的不同组合，可以解出其有L_x种可能的整数解：{-L_x/2，-L_x/2+1，...，L_x/2-1}(L_x是L和L_a的最小公倍数)。因此，本发明所能估计的频偏范围达到[-L_x/2，L_x/2)。为了方便硬件实现，可以使用查表法来解方程组(14)：先对L_x个可能解

进行枚举，计算出其对应的

和

并把这两个值作为

的表格的入口地址，再将

填进入口地址对应的存储单元，这样就制成了方程组(14)的求解表。在估计整数频偏过程中，只需用f_a(mod L_a)和f_n(mod L)作为表格索引，查表求出

即可。According to the remainder theorem in number theory, by different combinations of f _a (mod L _a ) and f _n (mod L), we can solve It has L _x possible integer solutions: {-L _x /2, -L _x /2+1, ..., _{L x} /2-1} (L _x is the least common multiple of L and L _a ). Therefore, the frequency offset range that the present invention can estimate reaches [-L _x /2, L _x /2). In order to facilitate hardware implementation, the look-up table method can be used to solve equations (14): first, L _x possible solutions

Enumerate and calculate its corresponding

and

and put these two values as

The entry address of the table, and then the

Fill in the storage unit corresponding to the entry address, so that the solution table of the equation group (14) is made. In the process of estimating the integer frequency offset, it is only necessary to use f _a (mod L _a ) and f _n (mod L) as table indexes, and look up the table to obtain

That's it.

本发明提供的“余数定理算法”同时具有计算复杂度低和频偏估计范围大的优点，具体来讲，本算法的式(12)和式(13)只需要2次求相角的运算，然后可以用查表法解不定方程组(14)，就能完成对整数频偏的估计：The "remainder theorem algorithm" provided by the present invention has the advantages of low computational complexity and large frequency offset estimation range. Specifically, the formula (12) and formula (13) of this algorithm only need two phase angle calculations, Then the indeterminate equations (14) can be solved by the look-up table method, and the estimation of the integer frequency offset can be completed:

${\overset{^^}{f f}}_{I I} = = LUT LUTs (({f f}_{a a} ((mod mod {L L}_{a a})),, {f f}_{n no} ((mod mod L L)))) - - - - - - ((1515))$

式(15)中的函数LUT代表查表函数，其计算复杂度可以忽略不计，然而，本算法的频偏估计范围却非常大。以L_a＝7，L＝8为例，由于L_x＝56，所以频偏估计范围为[-28，28)，再以L_a＝15，L＝8为例，由于L_x＝120，所以频偏估计范围达到[-60，60)，这样大的频偏估计范围可以满足未来OFDM系统的需要。The function LUT in formula (15) represents the look-up table function, and its computational complexity is negligible. However, the frequency offset estimation range of this algorithm is very large. Taking L _a =7, L=8 as an example, since L _x =56, the frequency offset estimation range is [-28, 28), and then taking L _a =15, L=8 as an example, since L _x =120, Therefore, the frequency offset estimation range reaches [-60, 60), and such a large frequency offset estimation range can meet the needs of future OFDM systems.

另外，本发明具有灵活性，选取不同的L_a和L，就能满足不同场合的整数频偏估计的要求。比如，取L_a＝3，L＝2，则L_x＝6，其频偏估计范围只有[-3，3)，可以用于小范围的频偏估计中。而且，方程组(14)所用的求解表是相当简单的，只需一个大小为(L_a×L)Byte的二维数组来存储L_x个整数解即可。以L_a＝7，L＝8为例，方程组(14)的求解表如下表所示：In addition, the present invention has flexibility, and different L _a and L can be selected to meet the requirements of integer frequency offset estimation in different occasions. For example, if L _a =3, L=2, then L _x =6, the frequency offset estimation range is only [-3, 3), which can be used for frequency offset estimation in a small range. Moreover, the solution table used in the equation group (14) is quite simple, only a two-dimensional array with a size of (L _a ×L)Byte is required to store L _x integer solutions. Taking L _a =7, L=8 as an example, the solution table of the equation system (14) is shown in the following table:

不定方程组求解表L_a＝7，L＝8Indeterminate equations solution table L _a = 7, L = 8 f_n(mod 8)f _n (mod 8) 00 11 22 33 44 55 66 77 f_a(mod 7)f _a (mod 7) 0 0 0 0 -7 -7 -14 -14 -21 -twenty one -28 -28 21 twenty one 14 14 7 7 1 1 8 8 1 1 -6 -6 -13 -13 -20 -20 -27 -27 22 twenty two 15 15 22 1616 99 22 -5-5 -12-12 -19-19 -26-26 23twenty three 3 3 24 twenty four 17 17 10 10 3 3 -4 -4 -11 -11 -18 -18 -25 -25 4 4 -24 -twenty four 25 25 18 18 11 11 4 4 -3 -3 -10 -10 -17 -17 55 -16-16 -23-twenty three 2626 1919 1212 55 -2-2 -9-9 6 6 -8 -8 -15 -15 -22 -twenty two 27 27 20 20 13 13 6 6 -1 -1

将式(11)得到的

与式(15)得到的

相加，作出完整的频偏估计：Get the formula (11)

and formula (15) to get

Add together to make a complete frequency offset estimate:

${\overset{^^}{f f}}_{Δ Δ} = = {\overset{^^}{f f}}_{I I} + + {\overset{^^}{f f}}_{F f} - - - - - - ((1616))$

需要特别指出的是，由于S_a的非正则性，式(12)中的

是频偏估计的近似公式。实际上，利用

的相角进行频偏作估计的正确公式如式(17)所示：It needs to be pointed out that due to the non-regularity of S _a , in formula (12)

is an approximate formula for frequency offset estimation. In fact, using

The correct formula for estimating the frequency offset of the phase angle is shown in formula (17):

${ξ ξ}_{a a} = = \frac{N N}{22 π π (({N N}_{a a} / / {L L}_{a a}))} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - - - - - ((1717))$

当式(2)确定的N_a与N非常接近时：When _Na determined by formula (2) is very close to N:

${ξ ξ}_{a a} \approx \approx \frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - - - - - ((1818))$

显然，式(18)的估计范围是[-L_a/2，L_a/2)，满足余数定理的要求，而式(17)的估计范围是[-NL_a/2N_a，NL_a/2N_a)，与余数定理的内在要求不符，因此，本发明中，采用式(18)来代替式(17)，由此引入的误差因子为：Obviously, the estimated range of formula (18) is [-L _a /2, L _a /2), which meets the requirements of the remainder theorem, while the estimated range of formula (17) is [-NL _a /2N _a , NL _a /2N _a ), inconsistent with the intrinsic requirements of the remainder theorem, therefore, in the present invention, formula (18) is adopted to replace formula (17), and the error factor introduced thus is:

$error error (({ξ ξ}_{a a})) = = | | \frac{{N N}_{a a}}{N N} - - 11 | | - - - - - - ((1919))$

由于error(ξ_a)是一个乘性因子，所以其在频偏较大时的影响会略微严重一些，其造成的最大频偏误差为

例如，当N_a＝1022，L_a＝7，N＝1024，L＝8时，error(ξ_a)＝0.00195，

\frac{L_{a}}{2} error (ξ_{a}) = 0.006825 .

考虑到ξ_a只是用于整数频偏估计，因此，error(ξ_a)几乎不会对f_a的估计产生影响。Since error(ξ _a ) is a multiplicative factor, its impact will be slightly more serious when the frequency offset is large, and the maximum frequency offset error caused by it is

For example, when N _a =1022, L _a =7, N=1024, L=8, error(ξ _a )=0.00195,

\frac{L_{a}}{2} error (ξ_{a}) = 0.006825 .

Considering that ξ _a is only used for integer frequency offset estimation, error(ξ _a ) hardly affects the estimation of f _a .

(4)细定时同步(4) fine timing synchronization

为了达到较好的定时同步估计性能，本发明在采用“双符号联合判决法”取得较好的粗定时同步估计

后，再采用细同步算法对符号定时同步作出精细估计，具体方法为：In order to achieve better timing synchronization estimation performance, the present invention obtains better rough timing synchronization estimation by adopting the "double-symbol joint judgment method"

After that, the fine synchronization algorithm is used to make a fine estimation of the symbol timing synchronization. The specific method is as follows:

抽取正则符号S_n中的第2个slot，并用式(16)得到的

对其进行相位补偿，得x＝(x₀，x₁，...，x_m，...，x_M-1)，其中，Extract the second slot in the regular symbol S _n , and use formula (16) to get

Perform phase compensation on it to get x=(x ₀ , x ₁ ,..., x _m ,..., x _M-1 ), where,

${x x}_{m m} = = {r r}_{22,, \overset{^^}{d d} + + M m + + m m} exp exp ((- - j j 22 πm πm {\overset{^^}{f f}}_{Δ Δ} / / N N)) ((m m = = 0,1,2 0,1,2,, . . . . . .,, M m - - 11)) - - - - - - ((2020))$

将x与本地slot样本作时域的循环移位相关，寻找相关峰，从而达到细定时同步的目的：Correlate x with the local slot sample for time-domain cyclic shift, and find the correlation peak, so as to achieve the purpose of fine timing synchronization:

$\overset{^^}{ϵ ϵ} = = \overset{^^}{d d} + + \underset{u u}{arg arg max max} {{R R ((u u)) = = | | {Σ Σ}_{m m = = 00}^{M m - - 11} {b b}_{22,, m m + + u u ((mod mod M m))}^{* *} {x x}_{m m} {| |}^{22} | | u u = = - - \frac{M m}{22},, - - \frac{M m}{22} + + 11,, . . . . . .,, \frac{M m}{22} - - 11}} - - - - - - ((21 twenty one))$

只要

的估计误差在±M/2以内，式(21)可以对OFDM符号的起始时刻作出相当准确的估计，其主要计算量是M(M+1)次复数乘法。if only

The estimation error of is within ±M/2, and the formula (21) can make a fairly accurate estimation of the initial moment of the OFDM symbol, and its main calculation amount is M(M+1) complex number multiplications.

本发明的创新之处在于：设计了非正则OFDM符号S_a与正则OFDM符号S_n级联的同步训练序列的生成方法，并基于该训练序列，提出“双符号联合判决法”，不会出现2个相关峰，防止了对符号定时同步的判断的干扰，改善了粗定时同步的估计性能，同时又提出“余数定理算法”，将频偏估计范围扩大至[-L_x/2，L_x/2)，L_x是S_a的等分数L_a与S_n等分数L的乘积，一些常用的L_a与L的组合参数及其频偏估计范围和误差如下表所示：The innovation of the present invention is: the generation method of the synchronous training sequence concatenated with the non-regular OFDM symbol S _a and the regular OFDM symbol S _n is designed, and based on the training sequence, a "double-symbol joint judgment method" is proposed, which will not appear Two correlation peaks prevent the interference of the judgment of symbol timing synchronization and improve the estimation performance of coarse timing synchronization. At the same time, a "remainder theorem algorithm" is proposed to expand the frequency offset estimation range to [-L _x /2, L _x /2), L _x is the product of the equal fraction L _a of S _a and the equal fraction L of S _n , some commonly used combination parameters of L _a and L and their frequency offset estimation range and error are shown in the following table:

N＝1024 N=1024 N_a _Na M_a M _a L_x _x f_Δ的估计范围Estimated range of f _Δ error(ξ_a)error(ξ _a ) L_a＝3，L＝2L _a = 3, L = 2 1023 1023 341 341 6 6 [-3，3) [-3, 3) 0.00098 0.00098 L_a＝5，L＝2L _a = 5, L = 2 1025 1025 205 205 10 10 [-5，5) [-5, 5) 0.00098 0.00098 L_a＝7，L＝2L _a = 7, L = 2 1022 1022 146 146 14 14 [-7，7) [-7, 7) 0.00195 0.00195 L_a＝9，L＝2L _a = 9, L = 2 1026 1026 114 114 18 18 [-9，9) [-9, 9) 0.00195 0.00195 L_a＝11，L＝2L _a = 11, L = 2 1023 1023 93 93 22 twenty two [-11，11) [-11, 11) 0.00098 0.00098 L_a＝3，L＝4L _a = 3, L = 4 1023 1023 341 341 12 12 [-6，6) [-6, 6) 0.00098 0.00098 L_a＝5，L＝4L _a = 5, L = 4 1025 1025 205 205 20 20 [-10，10) [-10, 10) 0.00098 0.00098 L_a＝7，L＝4L _a = 7, L = 4 1022 1022 146 146 28 28 [-14，14) [-14, 14) 0.00195 0.00195 L_a＝9，L＝4L _a = 9, L = 4 1026 1026 114 114 36 36 [-18，18) [-18, 18) 0.00195 0.00195 L_a＝11，L＝4L _a = 11, L = 4 1023 1023 93 93 44 44 [-22，22) [-22, 22) 0.00098 0.00098 L_a＝3，L＝8L _a = 3, L = 8 1023 1023 341 341 24 twenty four [-12，12) [-12, 12) 0.00098 0.00098 L_a＝5，L＝8L _a = 5, L = 8 1025 1025 205 205 40 40 [-20，20) [-20, 20) 0.00098 0.00098 L_a＝7，L＝8L _a = 7, L = 8 1022 1022 146 146 56 56 [-28，28) [-28, 28) 0.00195 0.00195

L_a＝9，L＝8L _a =9, L =8 1026 1026 114 114 72 72 [-36，36) [-36, 36) 0.00195 0.00195 L_a＝11，L＝8L _a = 11, L = 8 1023 1023 93 93 88 88 [-44，44) [-44, 44) 0.00098 0.00098

特别需要指出的是，本发明的计算复杂度非常低，如下表所示：In particular, it should be pointed out that the computational complexity of the present invention is very low, as shown in the following table:

同步模块 Synchronization module 每一帧内的计算复杂度 Computational complexity within each frame 粗定时同步 Coarse timing synchronization 每个采样点，9次复数乘和若干次复数加减 Each sample point, 9 complex multiplications and several complex additions and subtractions 小数频偏估计 Fractional frequency offset estimation 1次求相角 1 phase angle 整数频偏估计 Integer frequency offset estimation 2次求相角，查一个L_a×L维的整数表格Find the phase angle twice, look up a L _a ×L-dimensional integer table 细定时同步 Fine timing synchronization M(M+1)次复数乘法 M(M+1) times complex multiplication

而且，本发明的符号定时同步错误率和频偏估计错误率较低，因此，本发明在OFDM系统中具有很高的应用价值。Moreover, the symbol timing synchronization error rate and the frequency offset estimation error rate of the present invention are relatively low, so the present invention has high application value in OFDM systems.

附图说明Description of drawings

图1为OFDM基带调制解调框图Figure 1 is a block diagram of OFDM baseband modulation and demodulation

图2为本发明同步训练序列的示意图Fig. 2 is the schematic diagram of synchronous training sequence of the present invention

图3为N_a＝1022，L_a＝7时，符号S_a的生成示意图Figure 3 is _a schematic diagram of the generation of symbol S _a when Na = 1022 and L _a = 7

图4为N＝1024，L＝8时，符号S_n的生成示意图Figure 4 is a schematic diagram of the generation of symbols S _n when N=1024 and L=8

图5为本发明的同步方法框图Fig. 5 is a synchronous method block diagram of the present invention

图6为本发明的同步方法的具体实施流程图Fig. 6 is the specific implementation flowchart of the synchronization method of the present invention

图7为本发明提供的“双符号联合判决算法”在N_a＝1022，L_a＝7，N＝1024，L＝8，N_sym＝1088时，相关运算及合并的示意图Fig. 7 is a schematic diagram of correlation operation and combination when _Na = 1022, L _a = 7, N = 1024, L = 8, N _sym = 1088 of the "Double Symbol Joint Decision Algorithm" provided by the present invention

图8为本发明提供的“双符号联合判决算法”在N_a＝1024，L_a＝8，N＝1024，L＝8，N_sym＝1088时，相关运算及合并的示意图Fig. 8 is a schematic diagram of correlation operation and combination when Na ₌ 1024, L _a = 8, N = 1024, L = 8, N _sym = 1088 of the "Double Symbol Joint Decision Algorithm" provided by the present invention

图9为本发明在0dB高斯白噪声情况下，某一次仿真时P(d)的数值图形Fig. 9 is the numerical graph of P(d) during a certain simulation in the present invention under the condition of 0dB Gaussian white noise

图10为本发明在0dB高斯白噪声情况下，某一次仿真时angle{P_f(d)}/π的数值图形Fig. 10 is the numerical graph of angle{P _f (d)}/π during a certain simulation under the condition of 0dB Gaussian white noise of the present invention

图11为本发明在0dB高斯白噪声情况下，某一次仿真时R(u)的数值图形Fig. 11 is the numerical graph of R (u) during a certain simulation under the condition of 0dB Gaussian white noise of the present invention

图12为本发明与传统的正则符号训练序列在粗定时同步方面的性能比较Fig. 12 is the performance comparison of the present invention and the traditional regular symbol training sequence in coarse timing synchronization

图13为本发明与传统的正则符号训练序列在定时同步估计标准差方面的性能比较Fig. 13 is the performance comparison of the present invention and the traditional regular symbol training sequence in timing synchronization estimation standard deviation

图14为本发明与传统的正则符号训练序列在整数频偏估计错误率方面的性能比较。FIG. 14 is a performance comparison between the present invention and the traditional regular symbol training sequence in terms of integer frequency offset estimation error rate.

图15为本发明与频域估计算法在整数频偏估计错误率方面的性能比较Fig. 15 is the performance comparison between the present invention and the frequency domain estimation algorithm in terms of integer frequency offset estimation error rate

图16为SNR＝2dB，采用本发明的整数频偏估计算法在估计范围内的错误率平坦性Fig. 16 is SNR=2dB, adopts the error rate flatness within the estimated range of the integer frequency offset estimation algorithm of the present invention

具体实施方式Detailed ways

下面给出一个具体的OFDM参数配置实施例，来阐述本发明的实现步骤。需要说明的是，下例中的参数并不影响本发明的一般性。A specific embodiment of OFDM parameter configuration is given below to illustrate the implementation steps of the present invention. It should be noted that the parameters in the following examples do not affect the generality of the present invention.

3GPP组织的文档：TR 25.892 V6.0.0，“Feasibility Study for OrthogonalFrequency Division Multiplexing(OFDM)for UTRAN enhancement (Release 6)”(通用移动通信系统及陆基无线电接入的技术升级中采用OFDM方案的可靠性研究(第6版))，给出的一组OFDM参数，如下：Documents organized by 3GPP: TR 25.892 V6.0.0, "Feasibility Study for Orthogonal Frequency Division Multiplexing (OFDM) for UTRAN enhancement (Release 6)" Research (6th Edition)), a set of OFDM parameters are given, as follows:

载频fc 3.5GHzCarrier frequency fc 3.5GHz

系统带宽B 6.528MHzSystem bandwidth B 6.528MHz

子载波数N 1024Number of subcarriers N 1024

有效子载波数N 705Effective number of subcarriers N 705

有效带宽 4.495MHzEffective Bandwidth 4.495MHz

子载波间隔Δf 6.375kHzSubcarrier spacing Δf 6.375kHz

循环扩展CP 64(9.803us)Cyclic extension CP 64(9.803us)

符号周期Ts 156.85+9.81＝166.66usSymbol period Ts 156.85+9.81＝166.66us

保护载波数 319Number of protected carriers 319

在上述参数条件下，取N_a＝1024，L_a＝7，N＝1024，L＝8，N_sym＝1088，仿真时，设系统频偏f_Δ＝19.3，采用的信道为8路瑞利衰落信道：Under the above parameter conditions, take _Na = 1024, L _a = 7, N = 1024, L = 8, N _sym = 1088. During the simulation, set the system frequency offset f _Δ = 19.3, and use 8 channels of Rayleigh Fading channel:

延时(us) Delay (us) 相对功率(dB) Relative power (dB) 路径1 Path 1 0 0 0 0 路径2 Path 2 153 153 -6.65 -6.65 路径3 Path 3 306 306 -13.31 -13.31 路径4 Path 4 459 459 -19.95 -19.95

路径5 Path 5 612 612 -26.61 -26.61 路径6 Path 6 765 765 -33.26 -33.26 路径7 Path 7 919 919 -39.92 -39.92 路径8 Path 8 1072 1072 -46.57 -46.57

本发明的实现步骤如下：The realization steps of the present invention are as follows:

(1)生成OFDM同步训练符号，图2为由本发明的OFDM同步训练序列的生成方法所生成的同步训练序列的示意图。其具体生成过程如下：依照式(2)得N_a＝1022，根据式(3)在子载波序号为170、177、184、191、198、205、212、219、226、233、240、247、254、261、268、275、282、289、296、303、310、317、324、331、338、345、352、359、366、373、380、387、394、401、408、415、422、429、436、443、450、457、464、471、478、485、492、499、506、520、527、534、541、548、555、562、569、576、583、590、597、604、611、618、625、632、639、646、653、660、667、674、681、688、695、702、709、716、723、730、737、744、751、758、765、772、779、786、793、800、807、814、821、828、835、842、849、856的频率上加载随机生成的恒包络频域数据，在其他子载波上放置零数据，将这些频域数据通过图1的发送端串并转换、IDFT、发送端并串转换、插入循环前缀等模块，得到式(4)所对应的7等分的同步训练符号S_a。图3是N_a＝1022，L_a＝7时，Sa的生成示意图。然后，依照式(1)在子载波序号为160、168、176、184、192、200、208、216、224、232、240、248、256、264、272、280、288、296、304、312、320、328、336、344、352、360、368、376、384、392、400、408、416、424、432、440、448、456、464、472、480、488、496、504、520、528、536、544、552、560、568、576、584、592、600、608、616、624、632、640、648、656、664、672、680、688、696、704、712、720、728、736、744、752、760、768、776、784、792、800、808、816、824、832、840、848、856、864的频率上加载随机生成的恒包络频域数据，其他子载波上放置零数据，将这样的频域数据通过图1的发送端串并转换、IDFT、发送端并串转换、插入循环前缀等模块，就能生成8等分的同步训练符号S_n。图4是N＝1024，L＝8时，S_n的生成示意图。(1) Generate OFDM synchronous training symbols, FIG. 2 is a schematic diagram of a synchronous training sequence generated by the method for generating an OFDM synchronous training sequence of the present invention. The specific generation process is as follows: According to formula (2), _Na = 1022, and according to formula (3), the subcarrier numbers are 170, 177, 184, 191, 198, 205, 212, 219, 226, 233, 240, 247 ,254,261,268,275,282,289,296,303,310,317,324,331,338,345,352,359,366,373,380,387,394,401,408,415,422 ,429,436,443,450,457,464,471,478,485,492,499,506,520,527,534,541,548,555,562,569,576,583,590,597,604 ,611,618,625,632,639,646,653,660,667,674,681,688,695,702,709,716,723,730,737,744,751,758,765,772,779 , 786, 793, 800, 807, 814, 821, 828, 835, 842, 849, and 856 are loaded with randomly generated constant-envelope frequency domain data, and zero data is placed on other subcarriers, and these frequency domain data Through the serial-to-parallel conversion at the sending end, IDFT, parallel-serial conversion at the sending end, cyclic prefix insertion and other modules in Fig. 1, the 7-equalized synchronous training symbol _S a corresponding to formula (4) is obtained. Fig. 3 is _{a schematic diagram of the formation of Sa when Na = 1022 and L a} ₌ 7. Then, according to formula (1) when the subcarrier numbers are 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 520, 528, 536, 544, 552, 560, 568, 576, 584, 592, 600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696, 704, 712, 720, 728, 736, 744, 752, 760, 768, 776, 784, 792, 800, 808, 816, 824, 832, 840, 848, 856, 864 are loaded with randomly generated constant envelope frequency domain data , place zero data on other subcarriers, and pass such frequency-domain data through the serial-to-parallel conversion at the sending end, IDFT, parallel-serial conversion at the sending end, and inserting a cyclic prefix and other modules in Figure 1 to generate 8 equally divided synchronous training symbols S _n . Fig. 4 is a schematic diagram of the generation of S _n when N=1024 and L=8.

(2)运用“双符号联合判决法”进行粗定时同步，该过程位于图5的粗定时同步模块，其详细过程位于图6的粗定时同步模块，即根据式(5)至式(8)，估计出粗定时位置

图7是“双符号联合判决算法”在N_a＝1022，L_a＝7，N＝1024，L＝8，N_sym＝1088时，相关运算及合并的示意图(假定理想的符号起始位置d＝0)。|P_a(d)|²和|P_n(d)|²的相关峰不尖锐，在低信噪比时具有较强的抗噪性能；|P_f(d)|²的相关峰较尖锐，在高信噪比时可以对符号定时同步作出较为精确的估计。因此，本发明提供的“双符号联合判决法”使用多个相关峰合并，大大提高了系统粗定时同步的性能。如果采用另一个正则符号S_n代替S_a，假设其也被等分为L＝8份，那么，“双符号联合判决法”的相关运算及合并的示意图如图8所示，此时，在d＝N_sym和d＝-N_sym处分别出现了一个相关峰，这会严重干扰符号定时同步的判断。图9是本发明在0dB高斯白噪声情况下，某一次仿真时P(d)的数值图形，可见其在正确的定时点附近出现了峰值。在图9中，d＝0是理想的符号起始点，此时根据式(8)得到的的粗同步估计值为

\hat{d} = - 5 .

(2) Use the "double-symbol joint judgment method" for coarse timing synchronization. This process is located in the coarse timing synchronization module in Figure 5, and its detailed process is located in the coarse timing synchronization module in Figure 6, that is, according to formula (5) to formula (8) , to estimate the coarse timing position

Fig. 7 is a schematic diagram of correlation operation and merging when _Na = 1022, L _a = 7, N = 1024, L = 8, N _sym = 1088 in the "Double Symbol Joint Decision Algorithm" (assuming an ideal symbol starting position d =0). The correlation peaks of |P _a (d)| ² and |P _n (d)| ² are not sharp, and they have strong anti-noise performance at low SNR; the correlation peaks of |P _f (d)| ² are sharp , a more accurate estimate of symbol timing synchronization can be made at high SNR. Therefore, the "double-symbol joint decision method" provided by the present invention uses the combination of multiple correlation peaks, which greatly improves the performance of the coarse timing synchronization of the system. If another regular symbol S _n is used to replace S _a , assuming that it is also equally divided into L=8 parts, then the schematic diagram of the related operation and combination of the "double-symbol joint judgment method" is shown in Figure 8. At this time, in A correlation peak appears at d=N _sym and d=-N _sym respectively, which will seriously interfere with the judgment of symbol timing synchronization. Fig. 9 is the numerical graph of P(d) during a certain simulation in the present invention under the condition of 0dB Gaussian white noise, it can be seen that a peak value appears near the correct timing point. In Fig. 9, d=0 is the ideal starting point of the symbol, and the rough synchronization estimate obtained according to formula (8) at this time is

\hat{d} = - 5 .

(3)小数频偏估计，该过程位于图5的小数频偏估计模块，其详细过程位于图6的小数频偏估计模块，即根据式(10)和式(11)，估计出小数频偏

和整数频偏估计值

的奇偶性η。图10是本发明在0dB高斯白噪声情况下，某一次仿真时angle{P_f(d)}/π的数值图形，由式(10)计算得(3) Fractional frequency offset estimation, the process is located in the fractional frequency offset estimation module in Figure 5, and its detailed process is located in the fractional frequency offset estimation module in Figure 6, that is, the fractional frequency offset is estimated according to formula (10) and formula (11).

and an integer frequency offset estimate

The parity η. Fig. 10 is the numerical graph of angle {P _f (d)}/π during a certain simulation under the condition of 0dB Gaussian white noise of the present invention, calculated by formula (10)

$ξ ξ = = angle the angle {{{P P}_{f f} ((\overset{^^}{d d}))}} / / π π = = angle the angle {{{P P}_{f f} ((- - 55))}} / / π π = = - - 0.6772 0.6772$

再由式(11)得Then from formula (11) we get

${\overset{^^}{f f}}_{F f} = = ξ ξ - - ξ ξ / / | | ξ ξ | | = = - - 0.6772 0.6772 - - ((- - 0.6772 0.6772)) / / abs abs ((- - 0.6772 0.6772)) = = 0.3228 0.3228$

$η η {{((ξ ξ - - {\overset{^^}{f f}}_{f f})) ((mod mod 22))}} = = {{((- - 0.6772 0.6772 - - 0.3228 0.3228)) ((mod mod 22))}} = = 11$

(4)运用“余数定理算法”进行整数频偏估计，该过程位于图5的整数频偏估计模块，其详细过程位于图6的整数频偏估计模块，即根据式(12)和式(13)，得到2个整数频偏f_a和f_n，代入式(14)，把f_a(mod 7)和f_n(mod 8)作为入口地址，查询不定方程的求解表，从而对整数频偏作出估计

再由式(16)得到完整的频偏估计值

本发明在0dB高斯白噪声情况下，某一次仿真时，

\hat{d} = - 5,

{\hat{f}}_{F} = 0.3228,

η＝1，由式(12)得f_a＝5，由式(13)得f_n＝3，查询不定方程的求解表，在纵坐标为5，横坐标为3处得到

{\hat{f}}_{I} = 19,

再由式(16)得

{\hat{f}}_{Δ} = {\hat{f}}_{I} + {\hat{f}}_{F} = 19.3228,

频偏仙计误差仅为19.3228-19.3＝0.0228。(4) Use the "remainder theorem algorithm" to estimate the integer frequency offset. This process is located in the integer frequency offset estimation module in Figure 5, and its detailed process is located in the integer frequency offset estimation module in Figure 6, that is, according to formula (12) and formula (13 ), get two integer frequency offsets f _a and f _n , substitute them into formula (14), take f _a (mod 7) and f _n (mod 8) as the entry address, query the solution table of the indeterminate equation, and thus the integer frequency offset make an estimate

Then the complete frequency offset estimate is obtained by formula (16)

In the present invention, under the condition of 0dB Gaussian white noise, during a certain simulation,

\hat{d} = - 5,

{\hat{f}}_{f} = 0.3228,

η = 1, get f _a = 5 by formula (12), get f _n = 3 by formula (13), query the solution table of indefinite equation, and get at 5 in ordinate and 3 in abscissa

{\hat{f}}_{I} = 19,

Then from formula (16) we get

{\hat{f}}_{Δ} = {\hat{f}}_{I} + {\hat{f}}_{f} = 19.3228,

The error of the frequency offset meter is only 19.3228-19.3=0.0228.

(5)细定时同步，该过程位于图5的细定时同步模块，其详细过程位于图6的细定时同步模块，即根据的信息，抽取正则符号S_n中的第2个slot，运用式(20)对其进行频偏补偿，再通过式(21)，对符号定时位置作出精细估计本发明在0dB高斯白噪声情况下，某一次仿真时， $\hat{d} = - 5,$ ${\hat{f}}_{Δ} = 19.3228,$ 运用式(20)对接收到的S_n中第2个slot进行频偏补偿后，再计算式(21)中的R(u)，R(u)的数值图形如图11所示，其在u＝5出现峰值，所以，根据式(21)得(5) fine timing synchronization, this process is positioned at the fine timing synchronization module of Fig. 5, and its detailed process is positioned at the fine timing synchronization module of Fig. 6, promptly according to information, extract the second slot in the regular symbol S _n , use the formula (20) to compensate the frequency offset, and then use the formula (21) to make a fine estimation of the symbol timing position In the present invention, under the condition of 0dB Gaussian white noise, during a certain simulation, $\hat{d} = - 5,$ ${\hat{f}}_{Δ} = 19.3228,$ After using formula (20) to compensate the frequency offset of the second slot in the received S _n , then calculate R(u) in formula (21). The numerical graph of R(u) is shown in Figure 11. It is in There is a peak at u=5, so, according to formula (21), we get

$\overset{^^}{ϵ ϵ} = = \overset{^^}{d d} + + \underset{u u}{arg arg max max} {{R R ((u u))}} = = - - 55 + + 55 = = 00$

可见，此时的定时估计误差为0。It can be seen that the timing estimation error at this time is 0.

以下考察本发明的性能表现：The performance of the present invention is investigated below:

图12是本发明与传统的正则符号训练序列在粗定时同步方面的性能比较。传统的正则符号训练序列的参数为N_a＝1024，L_a＝64，N＝1024，L＝64，N_sym＝1088。定义粗定时同步错误率为概率 $\Pr (| \hat{d} | \leq \frac{M}{2}),$ M＝128。图12表明，本发明的粗定时同步性能优于传统方案超过4dB，这是本发明的“双符号联合判决算法”所产生的效果。Fig. 12 is a performance comparison between the present invention and the traditional regular symbol training sequence in coarse timing synchronization. The parameters of the traditional regular symbol training sequence are N _a =1024, L _a =64, N=1024, L=64, N _sym =1088. Define the coarse timing synchronization error rate as probability $PR (| \hat{d} | \leq \frac{m}{2}),$ M=128. Fig. 12 shows that the coarse timing synchronization performance of the present invention is better than the traditional scheme by more than 4dB, which is the effect produced by the "double-symbol joint decision algorithm" of the present invention.

图13是本发明与传统的正则符号训练序列在定时同步估计标准差方面的性能比较。传统的正则符号训练序列的参数仍为N_a＝1024，L_a＝64，N＝1024，L＝64，N_sym＝1088。其细同步也采用与本发明相同的细同步方法。图13表明，本发明的定时同步性能优于传统方案超过3dB，这主要是本发明的“双符号联合判决算法”使粗同步较为准确所产生的效果。Fig. 13 is a performance comparison between the present invention and the traditional regular symbol training sequence in timing synchronization estimation standard deviation. The parameters of the traditional regular symbol training sequence are still N _a =1024, L _a =64, N=1024, L=64, N _sym =1088. Its fine synchronization also adopts the same fine synchronization method as the present invention. Figure 13 shows that the timing synchronization performance of the present invention is better than the traditional scheme by more than 3dB, which is mainly due to the effect of the "double-symbol joint decision algorithm" of the present invention making the coarse synchronization more accurate.

图14是本发明与传统的正则符号训练序列在整数频偏估计错误率方面的性能比较。传统的正则符号训练序列的参数仍为N_a＝1024，L_a＝64，N＝1024，L＝64，N_sym＝1088，其小数频偏估计算法与本发明完全相同，其整数频偏估计算法也与本发明类似，因而计算复杂度也基本相同，不同之处是传统的正则符号训练序列无法采用“余数定理算法”，其通过式(12)和式(13)得到f_a与f_n之后，形成式(14)的方程组，然后直接将f_a与f_n作平均，得到整数频偏的估计值。图14表明，本发明的整数频偏估计性能优于传统方案超过6dB，这主要是本发明的“余数定理算法”使整数频偏估计较为准确。Fig. 14 is a performance comparison between the present invention and the traditional regular symbol training sequence in terms of integer frequency offset estimation error rate. The parameters of the traditional regular symbol training sequence are still Na = 1024, _{L a} ₌ 64, N = 1024, L = 64, N _sym = 1088, its decimal frequency offset estimation algorithm is exactly the same as the present invention, and its integer frequency offset estimation Algorithm is also similar to the present invention, so computational complexity is also basically the same, and difference is that traditional regular symbol training sequence cannot adopt " remainder theorem algorithm ", and it obtains f _a and f _n by formula (12) and formula (13) Afterwards, the equation group of formula (14) is formed, and f _a and f _n are directly averaged to obtain an estimated value of the integer frequency offset. Figure 14 shows that the performance of the integer frequency offset estimation of the present invention is better than the traditional scheme by more than 6dB, which is mainly because the "remainder theorem algorithm" of the present invention makes the integer frequency offset estimation more accurate.

图15是本发明与频域估计算法在整数频偏估计错误率方面的性能比较。频域估计算法的具体实现方法参见文献：Schmidl，T.M.等“Low-overhead，low-complexity [burst] synchronization for OFDM”，IEEE InternationalConference on Communications，Volume 3，June 1996，Page(s)：1301-1306(“低数据开销、低复杂度的OFDM同步方法”IEEE国际通信技术会议)。由于只考察频偏估计性能，所以，令两种方法的时间同步完全正确，且该频域估计算法中获得小数频偏估计值的方法以及频偏估计范围与本发明完全相同。图15表明，本发明的整数频偏估计性能几乎与频域估计算法相同，而本发明的计算复杂度远远低于该频域估计算法，在当前的参数条件下，本发明的计算复杂度大约只有法频域估计算法的5％。Fig. 15 is a performance comparison between the present invention and the frequency domain estimation algorithm in terms of integer frequency offset estimation error rate. For the specific implementation method of the frequency domain estimation algorithm, please refer to the literature: Schmidl, T.M. et al. "Low-overhead, low-complexity [burst] synchronization for OFDM", IEEE International Conference on Communications, Volume 3, June 1996, Page(s): 1301-1306 ("Low Data Overhead, Low Complexity OFDM Synchronization Methods" IEEE International Conference on Communication Technology). Since only the frequency offset estimation performance is considered, the time synchronization of the two methods is completely correct, and the method of obtaining the fractional frequency offset estimation value and the frequency offset estimation range in the frequency domain estimation algorithm are completely the same as the present invention. Figure 15 shows that the integer frequency offset estimation performance of the present invention is almost the same as the frequency domain estimation algorithm, and the computational complexity of the present invention is far lower than the frequency domain estimation algorithm, under the current parameter conditions, the computational complexity of the present invention Only about 5% of the normal frequency domain estimation algorithm.

图16是本发明在SNR＝2dB时，在频偏估计范围内的错误率平坦性仿真结果，该图表明，尽管非正则符号S_a引入了估计误差error(ξ_a)，但其对整数频偏估计几乎没有影响。Fig. 16 is the simulation _result of error rate flatness within the range of frequency offset estimation in the present invention when SNR= _2dB . Bias estimates have little effect.

仿真结果表明，本发明具有计算复杂度较低，且估计错误率较低的优点，在OFDM系统中具有很高的应用价值。Simulation results show that the present invention has the advantages of low computational complexity and low estimation error rate, and has high application value in OFDM systems.

Claims

1, a kind of generation method of OFDM synchronous training sequence, it is characterized in that: generate OFDM synchronous training sequence by 2 OFDM symbol concatenation, described 2 OFDM symbols are respectively non-regular OFDM symbol S _a and regular OFDM symbol S _n , so The number of points in the effective symbol part of the non-regular symbol S _a is N _a , N _a ≠ N, Na contains an odd prime factor q, the non-regular symbol _{S a} _is divided into equal parts of L _a , and L _a contains an odd prime factor q Prime factor q, said each equal division contains M _a points, wherein M _a =N _a /L _a , and Na _, L _a , M _a are all integers, the number of points contained in the cyclic prefix part of S _a is Na _ag , N _ag = N _sym -N _a , N _sym is the total number of OFDM symbol points; the regular symbol S _n is divided into L equal parts, L=2 ^v , and each equal part contains M points, where M=N /L, N is the number of effective symbol points of other OFDM symbols including regular symbols except regular symbols, and N, L, and M are all integers.

2, the generation method of OFDM synchronous training sequence according to claim 1, it is characterized in that: described non-regular symbol S _a , its generation method is, choose N _a to be the natural number closest to N in the integer multiple of L _a

{N N}_{a a} = = \underset{μ μ}{arg arg min min} {{| | μ μ - - N N | | | | μ μ ((mod mod {L L}_{a a})) = = 00}}

Then, in the frequency domain, data is inserted at intervals of L _a subcarriers, N _a point inverse Fourier transform is performed, and N _ag point cyclic prefix is added.

3, a kind of synchronization method based on the OFDM synchronous training sequence that the method for claim 1 generates, it is characterized in that, successively by rough timing synchronization, fractional frequency offset estimation, integer frequency offset estimation, fine timing synchronization, to complete the synchronization The estimation of the accurate starting position of OFDM symbol comprises the following steps:

Step 1: Delay the non-regular symbol S _a as an autocorrelation of an equal-division signal length to obtain P _a (d); make a delay to the regular symbol S _n as an autocorrelation of an equal-division signal length to obtain P _n (d); Delaying the regular symbol S _n is the autocorrelation of half the effective symbol length to obtain P _f (d), and then calculate the energy for P _a (d), P _n (d) and P _f (d) The sum is divided by the total energy of the signal in the correlation window to obtain the average autocorrelation P(d), find the peak of P(d), and initially estimate the starting position of the OFDM symbol

Step 2: According to the P _f (d) obtained in Step 1 and

,calculate The phase angle of , thus estimating the fractional part of the frequency offset

and parity η of integer frequency offset;

Step 3: According to the obtained P _a (d), P _n (d) and ,calculate

and , combined with the phase angle obtained in step 2 and η, estimated integer frequency offset

Step 4: Obtained according to Step 1

, extract the second equally divided signal of the regular symbol S _n , then perform frequency offset compensation on it, and then perform cyclic shift correlation with the second equally divided signal sample of the local regular symbol S _n to find the correlation peak, thus Estimate the precise starting position of OFDM symbols

4. The synchronization method according to claim 3, characterized in that, in said step 1, the time delay to S _a is M _a point, and the window length is the autocorrelation of (N _sym -M _a ) point to obtain P _a (d); Delaying time to S _n is M points, and the window length is the autocorrelation of (N _sym -M) points, so as to get P _n (d); Delaying time to S _n is LM/2 points, and the window length is (N _sym -LM/2) point autocorrelation, get P _f (d).

5. The synchronization method according to claim 3, characterized in that, in said step 1, the energy sum of P _a (d), P _n (d) and P _f (d) is calculated, and then divided by The total energy of the signal, the average autocorrelation P(d),

P P ((d d)) = = \frac{{| | {P P}_{a a} ((d d)) | |}^{22} + + {| | {P P}_{n no} ((d d)) | |}^{22} + + {| | {P P}_{f f} ((d d)) | |}^{22}}{{(({Σ Σ}_{m m = = d d}^{{d d + + N N}_{sym sym} - - {M m}_{a a}} {| | {r r}_{11,, m m + + {M m}_{a a}} | |}^{22}))}^{22} + + {(({Σ Σ}_{m m = = d d}^{{d d + + N N}_{sym sym} - - M m} {| | {r r}_{22,, m m + + M m} | |}^{22}))}^{22} + + {(({Σ Σ}_{m m = = d d}^{{d d + + N N}_{sym sym} - - N N / / 22} {| | {r r}_{22,, m m + + N N / / 22} | |}^{22}))}^{22}},,

Among them, r _{i, m} represent the i-th symbol, the data of the m-th sampling point.

6. The synchronization method according to claim 3, characterized in that said step 3 is to estimate the integer frequency offset when, first by

make an estimate f _a of the integer frequency offset,

{f f}_{a a} = = \{\begin{matrix} \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | |}} & {L L}_{a a} ((mod mod 22)) = = 11 \\ \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{a a} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | | | | λ λ ((mod mod 22)) = = η η}} & {L L}_{a a} ((mod mod 22)) = = 00 \end{matrix}

Then by

Make an estimate f _n of the integer frequency offset,

{f f}_{n no} = = \underset{λ λ}{arg arg min min} {{| | λ λ - - ((\frac{{L L}_{a a}}{22 π π} angle the angle {{{P P}_{n no} ((\overset{^^}{d d}))}} - - {\overset{^^}{f f}}_{F f})) | | | | λ λ ((mod mod 22)) = = η η}}

Obtain a system of indeterminate equations for integer frequency offsets:

\{\begin{matrix} {\overset{^^}{f f}}_{11} ((mod mod {L L}_{a a})) = = {f f}_{a a} ((mod mod {L L}_{a a})) \\ {\overset{^^}{f f}}_{I I} ((mod mod L L)) = = {f f}_{n no} ((mod mod L L)) \end{matrix}

Finally, use the remainder theorem in number theory to solve this system of indefinite equations, thereby estimating the integer frequency offset