技术领域technical field
本发明涉及基于加权分数傅里叶变换的GFDM系统的信号发射和接收技术。The invention relates to the signal transmission and reception technology of the GFDM system based on weighted fractional Fourier transform.
背景技术Background technique
GFDM载波体制是一种针对未来的5G技术的一种新的载波体制，它是以OFDM技术为基础发展而来的，由滤波多载波技术进一步演变而来。在未来的5G通信体制中，越来越注重多场景的结合，如M2M和更加密集复杂的通信网络和异构网等，而且需要更高的传输速率，更短的响应时间，并且在有限的频谱资源下传输更多的数据，这对4G技术所依托的OFDM技术是一个挑战。根据5G的场景需求，OFDM技术主要的缺点就是较大的带外功率辐射和缺乏波形的灵活性。较大的带外功率辐射会对相邻的频带上的数据产生干扰，会使数据产生失真，这样就需要较大的频带保护间隔，然而空闲的频带正逐渐成为最为稀缺的资源；在面对多样化的信道条件以及异构网时，波形灵活性的缺失可能会成为一个主要的缺点。在一个不完美的信道同步条件下，根据时频特性灵活设计的波形，会对时频残留的同步错误会有更强的鲁棒性。The GFDM carrier system is a new carrier system for future 5G technology. It is developed on the basis of OFDM technology and further evolved from filter multi-carrier technology. In the future 5G communication system, more and more attention will be paid to the combination of multiple scenarios, such as M2M and more dense and complex communication networks and heterogeneous networks, etc., and require higher transmission rates, shorter response times, and in limited Transmission of more data under spectrum resources is a challenge to the OFDM technology on which 4G technology is based. According to the requirements of 5G scenarios, the main disadvantages of OFDM technology are large out-of-band power radiation and lack of waveform flexibility. Larger out-of-band power radiation will interfere with the data on adjacent frequency bands, which will cause data distortion, which requires a larger frequency band guard interval, but the idle frequency band is gradually becoming the most scarce resource; in the face of The lack of waveform flexibility can be a major disadvantage when dealing with diverse channel conditions and heterogeneous networks. Under an imperfect channel synchronization condition, the waveform flexibly designed according to the time-frequency characteristics will have stronger robustness to the time-frequency residual synchronization errors.
2009年，Gerhard Fettweis的团队第一次提出GFDM系统的框架结构(文献1：《GFDM-Generalized Frequency Division Multiplexing》)，主要说明了GFDM系统相比于OFDM系统在峰均功率比和带外功率抑制方面的优势，但是在讨论峰均比的问题时在传输比特数一致的条件下，二者的子载波数并不相同，由于GFDM系统灵活的参数选择方案，其峰均功率比可以在一定的范围内变化。In 2009, the team of Gerhard Fettweis proposed the frame structure of GFDM system for the first time (Document 1: "GFDM-Generalized Frequency Division Multiplexing"), which mainly explained the peak-to-average power ratio and out-of-band power suppression of GFDM system compared with OFDM system However, when discussing the problem of peak-to-average ratio, under the condition that the number of transmitted bits is the same, the number of subcarriers of the two is not the same. Due to the flexible parameter selection scheme of the GFDM system, the peak-to-average power ratio can be within a certain range. changes within the range.
2012年，一种低复杂度的发射端和接收端装置在文献2(N.Michailow等于2012年公开的《Analysis of an alternative multi-carrier technique for next generationcellular systems》)和文献3(I.Gaspar等于2013年公开的《Low Complexity GFDMReceiver Based on Sparse Frequency Domain Processing》)中提出，这种装置利用高效的FFT运算，使先前的矩阵运算的复杂度大大降低，并且每一步的物理意义更加明确；在接收端，这种新型的装置采样的方法是匹配接收方法，所以会导致子载波间的干扰出现，为提升系统的性能，需要一种子载波干扰消除的方法提升系统的性能。In 2012, a low-complexity transmitter and receiver device was published in Document 2 (N.Michailow equals "Analysis of an alternative multi-carrier technique for next generation cellular systems" published in 2012) and Document 3 (I.Gaspar equals In the "Low Complexity GFDM Receiver Based on Sparse Frequency Domain Processing" published in 2013, it is proposed that this device uses efficient FFT operations to greatly reduce the complexity of previous matrix operations, and the physical meaning of each step is more clear; At the end, the sampling method of this new type of device is a matching receiving method, so it will cause interference between sub-carriers. In order to improve the performance of the system, a method for eliminating sub-carrier interference is needed to improve the performance of the system.
文献4(R.Datta等于2012年公开的《GFDM Interference Cancellation forFlexible Cognitive Radio PHY Design》)针对GFDM系统提出了单边和双边的串行干扰消除算法，其思想就是把MF接收器引入的相邻的子载波的干扰消除，其中子载波的消除算法是从第1个子载波到第K个子载波依次进行的，这种方法可以认为是单一串行干扰消除和并行干扰消除算法的混合，文献最后对两种算法的复杂度进行了分析。Document 4 ("GFDM Interference Cancellation for Flexible Cognitive Radio PHY Design" published by R.Datta in 2012) proposes a unilateral and bilateral serial interference cancellation algorithm for GFDM systems. The idea is to introduce MF receivers into adjacent Subcarrier interference cancellation, where the subcarrier cancellation algorithm is carried out sequentially from the 1st subcarrier to the Kth subcarrier, this method can be considered as a mixture of single serial interference cancellation and parallel interference cancellation algorithms, the literature finally discusses the two The complexity of the algorithm is analyzed.
2013年，文献5(Michailow,N.等于2013年公开的《G.Low peak-to-average powerratio for next generation cellular systems with generalized frequencydivision multiplexing Intelligent Signal Processing and CommunicationsSystems》)分析对比了不同系统的结构以及PAPR，包括OFDM系统、单载波频域均衡系统、单载波频分复用系统以及GFDM系统，说明了GFDM系统可以看成以上三种系统的广义形式，而且通过合理的成型参数选择GFDM系统的PAPR性能优于OFDM系统，并且成型滤波器参数越大，系统的PAPR性能越优。In 2013, document 5 (Michailow, N. equal to "G.Low peak-to-average powerratio for next generation cellular systems with generalized frequency division multiplexing Intelligent Signal Processing and Communications Systems" published in 2013) analyzed and compared the structures of different systems and PAPR , including OFDM system, single-carrier frequency-domain equalization system, single-carrier frequency-division multiplexing system, and GFDM system. It shows that the GFDM system can be regarded as the generalized form of the above three systems, and the PAPR performance of the GFDM system can be selected through reasonable shaping parameters. It is better than the OFDM system, and the larger the shaping filter parameter is, the better the PAPR performance of the system is.
发明内容Contents of the invention
本发明是为了获得更优的误码率性能，以及降低峰均功率比，从而提供一种基于加权分数傅里叶变换的GFDM系统的信号发射和接收方法。The purpose of the present invention is to obtain better bit error rate performance and reduce the peak-to-average power ratio, thereby providing a method for transmitting and receiving signals of a GFDM system based on weighted fractional Fourier transform.
基于加权分数傅里叶变换的GFDM系统的信号发射和接收方法，Signal transmission and reception method of GFDM system based on weighted fractional Fourier transform,
所述GFDM系统包括的K个子载波，每一个子载波有M个子符号；K、M均为正整数；The K subcarriers included in the GFDM system, each subcarrier has M subsymbols; K and M are positive integers;
该方法包括以下步骤：The method includes the following steps:
步骤一、在发射端，进行子载波阶数的分配操作，对每一个子载波上的数据都进行-α阶的加权分数傅里叶变换；Step 1. At the transmitting end, perform subcarrier order allocation operations, and perform -α-order weighted fractional Fourier transform on the data on each subcarrier;
步骤二、将不同的子载波映射给用户；Step 2, mapping different subcarriers to users;
步骤三、对数据进行GFDM调制，即：把输入的数据与GFDM调制矩阵A相乘，并进行加CP操作后发送至信道；Step 3, perform GFDM modulation on the data, that is: multiply the input data with the GFDM modulation matrix A, and send it to the channel after adding CP operation;
步骤四、接收端在接收到步骤三发送的信号后，对信号进行去CP操作，然后进行GFDM解调操作，获得GFDM解调后的数据；Step 4. After receiving the signal sent in step 3, the receiving end performs a de-CP operation on the signal, and then performs a GFDM demodulation operation to obtain GFDM demodulated data;
步骤五、对步骤四获得的GFDM解调后的数据进行解映射操作，根据发射端的子载波阶数分配进行与阶数相对应的加权分数傅里叶变换后输出。Step 5: Perform a demapping operation on the GFDM demodulated data obtained in Step 4, perform weighted fractional Fourier transform corresponding to the order according to the subcarrier order allocation at the transmitting end, and output it.
基于加权分数傅里叶变换的GFDM系统的信号发射和接收方法，Signal transmission and reception method of GFDM system based on weighted fractional Fourier transform,
所述GFDM系统包括的K个子载波，每一个子载波有M个子符号；K、M均为正整数；The K subcarriers included in the GFDM system, each subcarrier has M subsymbols; K and M are positive integers;
该方法包括以下步骤：The method includes the following steps:
步骤一、在发射端，首先对每一个子载波上的数据均进行1-α阶的加权分数傅里叶变换，将数据变换到频域；Step 1. At the transmitting end, first perform a 1-α-order weighted fractional Fourier transform on the data on each subcarrier, and transform the data into the frequency domain;
步骤二、在频域对数据进行复制，并依次排列成长度为2M的序列，并利用RC成型函数对该序列进行成型；Step 2, copying the data in the frequency domain, and sequentially arranging them into a sequence with a length of 2M, and using the RC shaping function to shape the sequence;
步骤三、将每个子载波数据叠加在一起，并对应相加，生成长度为K×M的数据；Step 3, superimposing each subcarrier data together, and correspondingly adding, generating data with a length of K×M;
步骤四、对步骤三获得的长度为K×M的数据进行IFFT变换，后发送至信道；Step 4, perform IFFT transformation on the data of length K×M obtained in step 3, and send it to the channel;
步骤五、接收端接收发射端发射的信号，并对长度为K×M的数据进行FFT变换，获得变换后的信号；Step 5, the receiving end receives the signal transmitted by the transmitting end, and performs FFT transformation on the data with a length of K×M to obtain the transformed signal;
步骤六、提取每一个子载波上的M个数据，并进行移位操作；Step 6, extracting M pieces of data on each subcarrier, and performing a shift operation;
步骤七、利用RC成型函数对步骤六移位后的数据进行成型，获得成型后信号；Step 7. Use the RC shaping function to shape the shifted data in step 6 to obtain the shaped signal;
步骤八、对每一个子载波上的数据进行M点的α-1阶的加权分数傅里叶变换后输出。Step 8: Perform M-point α-1 order weighted fractional Fourier transform on the data on each subcarrier and output it.
步骤一中，在发射端进行1-α阶的加权分数傅里叶变换把信号变换到频域，以及步骤八中的相应阶数的逆变换。In step 1, a weighted fractional Fourier transform of order 1-α is performed at the transmitting end to transform the signal into the frequency domain, and inverse transform of the corresponding order in step 8 is performed.
步骤二中，在进行成型处理后，位于中间的数据保持不变，呈“梯形”分布，两侧的数据为0，所述“梯形”的长度与成型函数参数β有关。In step 2, after the shaping process, the data in the middle remains unchanged, showing a "trapezoidal" distribution, and the data on both sides are 0, and the length of the "trapezoidal shape" is related to the shaping function parameter β.
步骤三中，每个子载波数据叠加在一起，并对应相加的过程中，干扰来自于相邻两个子载波位于“梯形”中的“斜坡”段，当β＝0时相邻的子载波间不存在干扰。In step 3, the data of each subcarrier is superimposed together, and during the corresponding addition process, the interference comes from the "slope" segment where two adjacent subcarriers are located in the "trapezoid", and when β=0, the adjacent subcarriers There are no distractions.
在步骤五之后，如果接收信号经过的是衰落信道，则对信号进行频域块均衡操作，所述频域块均衡操作包括ZF均衡和MMSE均衡。After Step 5, if the received signal passes through a fading channel, a frequency-domain block equalization operation is performed on the signal, and the frequency-domain block equalization operation includes ZF equalization and MMSE equalization.
本发明能够根据信道状态信息、用户需求灵活的单位载波块内的子载波数和WFRFT阶数，并且每一个子载波内的阶数可保持不同以达到系统性能的需求。本发明通过WFRFT预编码并合理的根据信道状况信息选择合适的变换阶数，使编码后的系统获得更优的误码率性能，并且拥有较低的峰均功率比。The present invention can flexibly determine the number of subcarriers and WFRFT orders in a unit carrier block according to channel state information and user requirements, and the orders in each subcarrier can be kept different to meet the requirements of system performance. The present invention uses WFRFT precoding and rationally selects a suitable transformation order according to channel state information, so that the coded system can obtain better bit error rate performance and have a lower peak-to-average power ratio.
附图说明Description of drawings
图1是广义的WFRFT-GFDM系统示意图；Fig. 1 is a generalized WFRFT-GFDM system schematic diagram;
图2是低复杂度的WFRFT-GFDM系统示意图；Figure 2 is a schematic diagram of a low-complexity WFRFT-GFDM system;
图3是GFDM收发两端的滤波器以及接收端信号幅度与噪声幅度对比示意图；Figure 3 is a schematic diagram of the filters at both ends of the GFDM transceiver and the comparison between the signal amplitude and the noise amplitude at the receiving end;
图4是QPSK调制的WFRFT预编码的GFDM系统在AWGN信道下的性能对比示意图；Figure 4 is a schematic diagram of the performance comparison of the QPSK modulated WFRFT precoded GFDM system under the AWGN channel;
图5是带有ZF均衡的BPSK调制的WFRFT预编码的GFDM系统在双离散信道下的性能仿真示意图；Fig. 5 is the performance simulation schematic diagram of the WFRFT precoded GFDM system with ZF equalized BPSK modulation under dual discrete channels;
图6是带有ZF均衡的16QAM调制的WFRFT预编码的GFDM系统在双离散信道下的性能仿真示意图；Fig. 6 is the performance emulation schematic diagram of the WFRFT precoded GFDM system of 16QAM modulation with ZF equalization under two discrete channels;
图7是带有MMSE均衡的BPSK调制的WFRFT预编码的GFDM系统在双离散信道下的性能仿真示意图；Fig. 7 is the performance simulation schematic diagram of the WFRFT precoded GFDM system with MMSE equalized BPSK modulation under dual discrete channels;
图8是带有MMSE均衡的16QAM调制的WFRFT预编码的GFDM系统在双离散信道下的性能仿真示意图；Fig. 8 is the performance simulation schematic diagram of the WFRFT precoded GFDM system with the 16QAM modulation of MMSE equalization under the double discrete channel;
图9是不同阶数的WFRF预编码的GFDM系统的PAPR仿真示意图；Fig. 9 is a PAPR simulation schematic diagram of a GFDM system with WFRF precoding of different orders;
具体实施方式Detailed ways
具体实施方式一、结合图1说明本具体实施方式，基于加权分数傅里叶变换的GFDM系统的信号发射和接收方法，DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 1. This specific embodiment is described in conjunction with FIG. 1, based on the signal transmission and reception method of the GFDM system of weighted fractional Fourier transform,
所述GFDM系统包括的K个子载波，每一个子载波有M个子符号；K、M均为正整数；The K subcarriers included in the GFDM system, each subcarrier has M subsymbols; K and M are positive integers;
该方法包括以下步骤：The method includes the following steps:
步骤一、在发射端进行子载波阶数的分配操作，即针对原GFDM系统包括的K个子载波，和每一个子载波上的M个子符号实施不同的WFRFT阶数，这样可以根据需求灵活的选取参数，本发明中为便于分析和简化系统，对每一个子载波上的数据都进行-α阶的加权分数傅里叶变换；Step 1. Perform the subcarrier order allocation operation at the transmitting end, that is, implement different WFRFT orders for the K subcarriers included in the original GFDM system and the M subsymbols on each subcarrier, so that it can be flexibly selected according to requirements Parameters, in the present invention, for the convenience of analysis and simplification of the system, the data on each subcarrier is all carried out the weighted fractional Fourier transform of -α order;
步骤二、进行子载波映射，可以把不同段的子载波映射给不同的用户，亦可根据用户的需求灵活的选取WFRFT参数和子载波长度，本专利为了分析简便，设定用户数量为单用户；Step 2. Carry out subcarrier mapping, which can map subcarriers of different segments to different users, and can also flexibly select WFRFT parameters and subcarrier lengths according to user needs. In order to simplify the analysis, this patent sets the number of users as a single user;
步骤三、对数据进行GFDM调制，即把输入的数据与GFDM调制矩阵A进行相乘，再进行加CP操作；Step 3: Carry out GFDM modulation to the data, that is, multiply the input data with the GFDM modulation matrix A, and then add CP operation;
步骤四、在数据经过无线信道后，首先进行去CP操作，再进行GFDM解调操作，具体有三种形式，有匹配接收机、ZF接收机和MMSE接收机；Step 4. After the data passes through the wireless channel, the CP removal operation is first performed, and then the GFDM demodulation operation is performed. There are three specific forms, including matching receivers, ZF receivers and MMSE receivers;
步骤五、在解映射操作之后，考虑子载波阶数匹配，进行与接收端阶数相对应的加权分数傅里叶变换。Step 5: After the demapping operation, considering subcarrier order matching, perform a weighted fractional Fourier transform corresponding to the order of the receiving end.
由于上述过程中，矩阵A的求解非常复杂，维数大不利于求逆操作，若矩阵A不存在逆矩阵，有可能会存在文献6(Matthe,M等于2014年公开的《G.Generalized FrequencyDivision Multiplexing in a Gabor Transform Setting Communications Letters》)中所述的ZF和MMSE接收机不适用的情况，并且用矩阵A对数据进行GFDM调制物理意义和过程不明确，所以本发明提出了图2中的低复杂度的WFRFT-GFDM系统的信号发射和接收方法，接收机为匹配滤波(MF)接收机，具体实施方式二。Due to the above process, the solution of matrix A is very complicated, and the large dimension is not conducive to the inversion operation. If there is no inverse matrix in matrix A, there may be literature 6 (Matthe, M is equal to "G.Generalized Frequency Division Multiplexing published in 2014 In a Gabor Transform Setting Communications Letters), the ZF and MMSE receivers described in) are not applicable, and the physical meaning and process of GFDM modulation of data with matrix A are not clear, so the present invention proposes the low complexity in Fig. 2 A method for transmitting and receiving signals of a high-degree WFRFT-GFDM system, the receiver is a matched filter (MF) receiver, the second specific embodiment.
具体实施方式二、基于加权分数傅里叶变换的GFDM系统的信号发射和接收方法，Specific embodiment two, the signal transmitting and receiving method of the GFDM system based on weighted fractional Fourier transform,
步骤一：在发射端如图1中的操作步骤一样，假设每一个子载波上进行的是相同阶数的WFRFT变换且用户数量为单用户，对每一个子载波上的数据进行1-α阶的WFRFT，把数据变换到频域；Step 1: At the transmitting end, the operation steps in Figure 1 are the same, assuming that the WFRFT transformation of the same order is performed on each subcarrier and the number of users is a single user, and the data on each subcarrier is 1-α order The WFRFT transforms the data into the frequency domain;
步骤二：在频域对数据进行复制，并依次排列，现序列的长度为2M，并用RC成型函数对于长为2M的信号进行成型，成型后中间的数据保持不变，两侧数据为0，中间数据呈“斜坡”状，且“斜坡”长度与成型函数参数β有关；Step 2: Copy the data in the frequency domain and arrange them sequentially. The length of the current sequence is 2M, and use the RC shaping function to shape the signal with a length of 2M. After shaping, the middle data remains unchanged, and the data on both sides is 0. The intermediate data is in the shape of a "slope", and the length of the "slope" is related to the shaping function parameter β;
步骤三：此时每一个子载波对应的数据长度为2M，把每个子载波数据叠加在一起对应相加，其中绝大多数为不变的中间部分的数据，且干扰来自于相邻的两个子载波的“斜坡”段，当β＝0时相邻的子载波间不存在干扰；Step 3: At this time, the data length corresponding to each sub-carrier is 2M, and the data of each sub-carrier is superimposed and correspondingly added, most of which are the data in the middle part that does not change, and the interference comes from two adjacent sub-carriers In the "slope" section of the carrier, when β=0, there is no interference between adjacent subcarriers;
步骤四：当所有数据按要求叠加后，对生成的KM长度的数据进行IFFT操作就得到待传输的信号；Step 4: After all the data are superimposed as required, the IFFT operation is performed on the generated KM length data to obtain the signal to be transmitted;
步骤五：经过信道后，对长度为KM的数据进行FFT操作；Step 5: After passing through the channel, perform FFT operation on the data whose length is KM;
步骤六：如果经过衰落信道，在此对信号进行频域块均衡操作，包括ZF均衡和MMSE均衡Step 6: If passing through a fading channel, perform frequency-domain block equalization on the signal, including ZF equalization and MMSE equalization
步骤七：提取每一个子载波上的M个数据，对数据进行移位(fftshift)操作，由于之前发射端的2倍过采样操作，此时的干扰位于数据中间段，两侧为不变的数据；Step 7: Extract M data on each subcarrier, and perform a shift (fftshift) operation on the data. Due to the previous 2 times oversampling operation at the transmitter, the interference at this time is located in the middle of the data, and the two sides are unchanged data ;
步骤八：再用接收端RC成型函数进行成型，两次成型操作使相邻载波间的干扰得以明显减小，而处于“斜坡”处的数据减小幅度并不明显；Step 8: Then use the RC shaping function at the receiving end to shape. The two shaping operations can significantly reduce the interference between adjacent carriers, and the data reduction at the "slope" is not obvious;
步骤九：对每一个子载波上的数据进行M点的α-1阶的WFRFT操作。Step 9: Perform an M-point α-1 order WFRFT operation on the data on each subcarrier.
本发明应用于基于4-WFRFT的GFDM系统中。The invention is applied in the GFDM system based on 4-WFRFT.
本发明中缩略语和关键术语定义：Definitions of abbreviations and key terms in the present invention:
WFRFT：Weighted-type fractional Fourier transform，加权分数傅立叶变换；WFRFT: Weighted-type fractional Fourier transform, weighted fractional Fourier transform;
GFDM：Generalized Frequency Division Multiplexing，广义频分复用；GFDM: Generalized Frequency Division Multiplexing, generalized frequency division multiplexing;
HC：Hybrid Carrier，混合载波；HC: Hybrid Carrier, hybrid carrier;
BER：Bit Error Rate，误码率；BER: Bit Error Rate, bit error rate;
PAPR：Peak to Average Power Ratio，峰均功率比；PAPR: Peak to Average Power Ratio, peak-to-average power ratio;
ZF：Zero Forcing，迫零；ZF: Zero Forcing, zero forcing;
MMSE：Minimum Mean Square Error，最小均方误差。MMSE: Minimum Mean Square Error, minimum mean square error.
本发明用到的技术包络离散四项加权分数傅里叶变换(WFRFT)和经典的GFDM技术。The techniques used in the present invention include discrete four-item weighted fractional Fourier transform (WFRFT) and classic GFDM techniques.
WFRFT理论：WFRFT theory:
对于长度为N的离散信号d，则d的α阶离散四项加权分数傅里叶变换是：Fα[d]＝Wα[d]，其中Fα表示四项加权分数傅里叶变换，Wα是加权矩阵，在不会引起歧义的情况下，在本发明里，把Wα简记为W，表示为：For a discrete signal d whose length is N, the α-order discrete four-item weighted fractional Fourier transform of d is: Fα [d]=Wα [d], where Fα represents the four-item weighted fractional Fourier transform, Wα is a weighting matrix. In the case of not causing ambiguity, in the present invention, Wα is abbreviated as W, expressed as:
W＝A0αI+A1αF+A2αΓI+A3αΓF (1)W＝A0α I+A1α F+A2α ΓI+A3α ΓF (1)
这里A0α～A3α是加权系数定义如下：Here A0α ~ A3α are weighting coefficients defined as follows:
I是N×N单位矩阵，F是N×N离散傅里叶变换矩阵。Γ是置换矩阵，它每一行每一列只有一个元素非零，具体可以表如下：I is an N×N identity matrix, and F is an N×N discrete Fourier transform matrix. Γ is a permutation matrix. It has only one element in each row and column that is non-zero. The details can be expressed as follows:
另外加权分数傅里叶逆变换可以表示为：F-α[d]＝W-α[d]，其中W-α表示Wα的逆矩阵，可以证明W是一个酉矩阵，则根据酉矩阵的性质，W-1＝WH。并且可以证明矩阵Wα满足变换阶数的可加性，即Wα+β＝WαWβ。需要指出的是，本发明提及的混合载波系统是通过WFRFT变换实现的。In addition, the weighted fractional Fourier inverse transform can be expressed as: F-α [d]=W-α [d], where W-α represents the inverse matrix of Wα , it can be proved that W is a unitary matrix, then according to the unitary matrix Properties, W-1 = WH . And it can be proved that the matrix Wα satisfies the additivity of the transformation order, that is, Wα+β =Wα Wβ . It should be pointed out that the mixed carrier system mentioned in the present invention is realized through WFRFT transformation.
GFDM系统：GFDM system:
对于GFDM系统，N＝K*M个符号，分布在K个子载波上，每个子载波有M个子符号，dk,m表示第k个子载波上第m个子符号，每一个数据都进行相应的脉冲成型操作，成型滤波器可以表示为For the GFDM system, N=K*M symbols are distributed on K subcarriers, each subcarrier has M subsymbols, dk,m represents the mth subsymbol on the kth subcarrier, and each data has a corresponding pulse Shaping operation, the shaping filter can be expressed as
每一个gk,m[n]都是原型滤波器g(n)时间和频率的偏移。待传输的符号就可以表示为，Each gk,m [n] is a time and frequency offset of the prototype filter g(n). The symbol to be transmitted can be expressed as,
用矩阵的形式可以表示为：In matrix form it can be expressed as:
x＝A·d (6)x=A·d (6)
其中：A是KM*KM的传输矩阵，可以表示为A＝(g0,0…gK-1,0g0,1…gK-1,M-1)。在接收端，经过信道均衡后，接收信号可以表示为：Where: A is the transmission matrix of KM*KM, which can be expressed as A=(g0,0 ...gK-1,0 g0,1 ...gK-1,M-1 ). At the receiving end, after channel equalization, the received signal can be expressed as:
对于GFDM解调器，存在三种解调方法：For GFDM demodulators, there are three demodulation methods:
(1)、匹配接收器(MF)BMF＝AH，这种接收方式把每一个子载波的信噪比最大化，但是尤其当应用非正交的传输脉冲时，会引入载波间干扰，使系统的误码性能较差。(1), matching receiver (MF) BMF = AH , this receiving method maximizes the signal-to-noise ratio of each subcarrier, but especially when non-orthogonal transmission pulses are applied, inter-carrier interference will be introduced, The bit error performance of the system is poor.
(2)、ZF接收，BZF＝A-1。这种接收方式可以完全去除系统的自干扰(即载波间干扰)，但是会对信道噪声加强。而且这种方式必须保证矩阵A是可逆的，并且当矩阵A维数较大时，系统的复杂度较高。(2) ZF receives, BZF =A-1 . This receiving method can completely remove system self-interference (that is, inter-carrier interference), but it will strengthen channel noise. Moreover, this method must ensure that the matrix A is reversible, and when the dimension of the matrix A is large, the complexity of the system is high.
(3)、MMSE接收。这种均衡方式能够在自干扰和噪声加强之间进行折中。(3), MMSE reception. This equalization method can make a compromise between self-interference and noise enhancement.
在此之后，文献2～3提出了一种低复杂度的GFDM系统的收发两端的装置模型，这种实现方式相当于用高效的DFT运算实现矩阵A，并且矩阵A的物理意义并不明确，这种用这种FFT的方式可以更加明确各部分的物理意义。After that, Documents 2-3 proposed a low-complexity device model for the transceiver at both ends of the GFDM system. This implementation is equivalent to using efficient DFT operations to realize matrix A, and the physical meaning of matrix A is not clear. This way of using this FFT can clarify the physical meaning of each part more clearly.
在GFDM系统中，某以特定的子载波的干扰仅仅来自于其“左右”的两个相邻的子载波上数据的干扰。应用β＝0.3的RC成型滤波器的条件下，每一个子载波上的有用信号和干扰信号的大小示意图如图3所示。In a GFDM system, the interference of a specific subcarrier only comes from the interference of data on its "left and right" two adjacent subcarriers. Under the condition of applying an RC shaping filter of β=0.3, the schematic diagram of the size of the useful signal and the interference signal on each subcarrier is shown in FIG. 3 .
如图3所示，当有用信号的功率没有损失的时候，该符号点上也不存在子载波间的干扰，但是当有用信号的功率损失越大时，其干扰也就越大，这也就使该判决点上的信号干扰比(SINR)从“正反”两个方面变小，即有用信号功率变小干扰功率变大。进而我们知道系统的误码率和系统的信号干扰比紧密相关，所以GFDM系统的误码率特性才会由于这两方面的作用而下降。现行的提升GFDM系统的误码率的方法仅仅考虑降低子载波间的干扰，并且基于串行干扰消除的模式也存在复杂度高的缺点。As shown in Figure 3, when there is no power loss of the useful signal, there is no interference between subcarriers at this symbol point, but when the power loss of the useful signal is greater, the interference is greater, which means Make the signal-to-interference ratio (SINR) at the decision point smaller from the "positive and negative" aspects, that is, the useful signal power becomes smaller and the interference power becomes larger. Furthermore, we know that the bit error rate of the system is closely related to the signal-to-interference ratio of the system, so the bit error rate characteristics of the GFDM system will decline due to the effects of these two aspects. The current method of improving the bit error rate of the GFDM system only considers reducing the interference between subcarriers, and the mode based on serial interference cancellation also has the disadvantage of high complexity.
本发明应用WFRFT预编码的方式实现了GFDM系统的多目标联合优化问题。一方面GFDM系统的提出是基于OFDM系统的高带外功率问题，另一方面OFDM系统自身面临的高峰均功率比的缺点，且在双离散信道条件下系统的特性并没有得到很好的体现。本专利利用WFRFT阶数可调性，使WFRFT预编码的GFDM系统在保持其在双选信道条件下系统误码率提升或不变的条件下，有效的降低其PAPR，且不影响其带外功率抑制效果。The invention implements the multi-objective joint optimization problem of the GFDM system by using the WFRFT precoding manner. On the one hand, the GFDM system is proposed based on the high out-of-band power problem of the OFDM system. On the other hand, the OFDM system itself faces the shortcomings of the peak-to-average power ratio, and the characteristics of the system under the condition of dual discrete channels have not been well reflected. This patent utilizes the adjustable WFRFT order, so that the WFRFT precoded GFDM system can effectively reduce its PAPR without affecting its out-of-band under the condition that the system bit error rate is improved or remains unchanged under the condition of dual channel selection. power suppression effect.
如图4所示，GFDM系统由于脉冲成型操作，子载波之间不再正交，且随着成型参数的增大，产生的子载波间的自干扰也随之增大，对系统误码率的影响也就越大，图中分别给出了同一脉冲成型参数条件下，不同WFRFT阶数的误码率性能。传统的GFDM系统(α＝0)由于FFT变换能把产生的自干扰平均分配到每一个子载波上，故其性能最优，随着变换阶数的增加(由α＝0到α＝1)WFRFT系统性能在AWGN信道条件下越来越差。As shown in Figure 4, due to the pulse shaping operation of the GFDM system, the subcarriers are no longer orthogonal, and as the shaping parameters increase, the self-interference between the subcarriers also increases, which affects the system bit error rate. The greater the impact, the figure shows the bit error rate performance of different WFRFT orders under the same pulse shaping parameter conditions. The traditional GFDM system (α=0) has the best performance because the FFT transform can distribute the generated self-interference evenly to each subcarrier. As the transform order increases (from α=0 to α=1) WFRFT system performance is getting worse under AWGN channel conditions.
图5和图6分别给出了带有ZF均衡的BPSK/16QAM调制的WFRFT预编码的GFDM系统在双离散信道下的性能，信道模型为ITU PED-B信道，包含3个瑞利衰落径，最大多普勒频移为33Hz，2、3径的延迟为10ns和20ns，功率增益为-3.6dB和-7.2dB。如仿真图所示，随着调制阶数的增加，不同阶数WFRFT预编码的GFDM系统误码率之间的差异逐渐变小，直至差别不大。这是由两点原因造成的，一方面在AWGN信道模型下，GFDM系统在(α＝0)时性能最优；另一方面，在双离散信道模型下，由于WFRFT其特有的性质，在某个阶数αopt上与信道参数相契合，可以得到和α＝0和α＝1相似的性能。Figure 5 and Figure 6 show the performance of the WFRFT precoded GFDM system with BPSK/16QAM modulation with ZF equalization under dual discrete channels. The channel model is ITU PED-B channel, including 3 Rayleigh fading paths, The maximum Doppler frequency shift is 33Hz, the delays of the 2nd and 3rd paths are 10ns and 20ns, and the power gains are -3.6dB and -7.2dB. As shown in the simulation diagram, as the modulation order increases, the difference between the bit error rates of GFDM systems with different orders of WFRFT precoding gradually becomes smaller until the difference is not significant. This is caused by two reasons. On the one hand, under the AWGN channel model, the performance of the GFDM system is optimal when (α=0); The order αopt fits the channel parameters, and the performance similar to α=0 and α=1 can be obtained.
图7和图8给出了带有MMSE均衡的BPSK/16QAM调制的WFRFT预编码的GFDM系统的性能。图7中的信道参数和ZF均衡时保持一致，在BPSK调制模式下，分数阶α＝0.5性能较优，且由于传统的GFDM系统(α＝0)。图8中的信道模型ITU Veh-B信道模型：有6个瑞利衰落径，时延分别为0、310、710、1090、1730、2510ns，平均路径增益分别为0、-1.0、-9.0、-10.0、-15.0、-20.0dB，采样频率为10MHz，车辆速度为120km/h。在此信道模型下的16QAM调制的系统，α＝0.5性能较优，同样其性能优于传统的GFDM系统(α＝0)。Figure 7 and Figure 8 show the performance of the WFRFT precoded GFDM system with MMSE equalized BPSK/16QAM modulation. The channel parameters in Fig. 7 are consistent with ZF equalization. In the BPSK modulation mode, the performance of fractional order α=0.5 is better, and it is due to the traditional GFDM system (α=0). Channel model ITU Veh-B channel model in Figure 8: There are 6 Rayleigh fading paths, the delays are 0, 310, 710, 1090, 1730, 2510ns, and the average path gains are 0, -1.0, -9.0, -10.0, -15.0, -20.0dB, the sampling frequency is 10MHz, and the vehicle speed is 120km/h. In the 16QAM modulated system under this channel model, the performance of α=0.5 is better, and its performance is also better than that of the traditional GFDM system (α=0).
所以，在双选信道模型条件下，WFRFT预编码的GFDM系统可以在某个阶数上达到比传统的GFDM系统(α＝0)相似或者更优的误码率性能。Therefore, under the condition of the dual channel selection model, the WFRFT precoded GFDM system can achieve similar or better bit error rate performance than the traditional GFDM system (α = 0) in a certain order.
图9利用了WFRFT的另一优势，即可以灵活的调节系统的峰均功率比。在分数域(α＝0.3和α＝0.5)，GFDM系统的PAPR可以得到有效的降低。Figure 9 utilizes another advantage of WFRFT, that is, the peak-to-average power ratio of the system can be flexibly adjusted. In fractional domain (α=0.3 and α=0.5), the PAPR of GFDM system can be effectively reduced.
综合分析图5-9可得，WFRFT预编码的GFDM系统在提升或不影响系统误码率的同时可以有效的降低系统的PAPR，实现了关于GFDM系统的多目标的联合性能提升问题。进而在多目标的实现过程中根据具体的实现目标进行最优参数的选择问题。A comprehensive analysis of Figure 5-9 shows that the GFDM system with WFRFT precoding can effectively reduce the system PAPR while improving or not affecting the system bit error rate, and realize the multi-objective joint performance improvement problem of the GFDM system. Then in the multi-objective realization process, the optimal parameter selection problem is carried out according to the specific realization goal.
本发明的系统是传统的GFDM系统的广义的形式，该系统充分利用了加权分数傅里叶变换的阶数可调性来使GFDM系统具有更广义的性能，包括较低的PAPR和复杂信道模型下较好的误码率性能。The system of the present invention is a generalized form of the traditional GFDM system, which makes full use of the adjustable order of the weighted fractional Fourier transform to make the GFDM system have a more generalized performance, including lower PAPR and complex channel models better bit error rate performance.
本发明与文献4的不同点在于提出了一种WFRFT预编码的GFDM系统及其低复杂度的形式，对双选信道下误码率的性能进行了有效性的分析。The difference between the present invention and Document 4 is that a WFRFT precoded GFDM system and its low-complexity form are proposed, and the effectiveness of the bit error rate performance under dual channel selection is analyzed.
本发明提出的WFRFT-GFDM系统通过参数的灵活调整和选择可以等效为更加广义的三种系统的合并。The WFRFT-GFDM system proposed by the present invention can be equivalent to a combination of three systems in a more generalized sense through the flexible adjustment and selection of parameters.
本发明有助于5G体制下波形的混合设计与应用。The invention contributes to the hybrid design and application of waveforms under the 5G system.
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