CN108964731B - A fast convolution-free hybrid carrier continuous stream transmission method without cyclic prefix filtering - Google Patents

Abstract

A fast convolution-free mixed-carrier continuous stream transmission method without cyclic prefix filtering is used in the field of wireless communication. The invention can solve the problems of high out-of-band leakage in the existing method and low spectral efficiency caused by adding a cyclic prefix before each mixed carrier symbol in the existing method. In the present invention, multiple subbands are transmitted in parallel at the same time, and each subband is preprocessed by weighted Fourier transform, and then mapped to different frequency bands through filtering. The invention uses fast convolution to complete filtering, and can effectively suppress out-of-band leakage of sub-bands. Each sub-band can flexibly select the sub-band width and set different weighted Fourier transform modulation orders. The modulation orders of different subbands may be the same, or their optimal modulation orders may be set according to the equalization rule, so as to optimize the bit error rate performance. In addition, adjusting the modulation order can also suppress the peak-to-average ratio. The appropriate modulation order can be selected according to the requirements of the system on the peak-to-average ratio and the equalization rule adopted by the receiver.

Description

A fast convolution-free hybrid carrier continuous stream transmission method without cyclic prefix filtering

technical field

The present invention relates to the field of wireless communication, in particular to a method for continuous stream transmission of mixed carriers without cyclic prefix filtering based on fast convolution.

Background technique

In modern communication systems, Orthogonal Frequency Division Multiplexing (OFDM) technology is widely used due to its high spectral efficiency and strong anti-multipath fading capability. However, it has high side lobe power, so it has strict requirements on the synchronization of transmission. In order to suppress the out-of-band power and reduce the synchronization requirements of the system, scholars have proposed a variety of techniques, such as Filter bank multi-carrier (FBMC), Filtered-OFDM (Filtered-OFDM), Generalized Frequency Division Multiplexing (Generalized frequency division multiplexing, GFDM) and universal filtered multi-carrier (Universal filtered multi-carrier, UFMC) (Vakilian, V.; Wild, T.; Schaich, F.; ten Brink, S. & Frigon, J.F. Universal-filteredmulti-carrier technique for wireless systems beyond LTE 2013 IEEE Globecom Workshops (GC Wkshps), 2013, 223-228) et al. These techniques all use filtering to suppress out-of-band power leakage. Meanwhile, in recent years, a hybrid carrier design concept based on Weighted-type fractional Fourier transform (WFRFT) (Mei L, Sha X J, Ran Q W, et al. Research on the application of 4-weighted fractional Fourier transform in communication system [J]. Science China (Information Sciences), 2010, 53(6): 1251-1260.) has received extensive attention due to its ability to integrate traditional single-carrier and multi-carrier systems. In "Weighted Fractional Fourier Transform and Its Application in Communication Systems" (Merlin. Weighted Fractional Fourier Transform and Its Application in Communication Systems [D]. Harbin: Harbin Institute of Technology, 2010: 51- 60), the WFRFT-based hybrid carrier system successfully integrates the traditional single-carrier and multi-carrier systems, and fuses two different carrier components in a weighted combination. The energy of the hybrid carrier signal can be evenly distributed in the time-frequency plane, which can improve the anti-interference performance of the system (Wang K, Sha X, Mei L, et al. Performance Analysis of Hybrid Carrier System with MMSE Equalization over Doubly-Dispersive Channels [J]. IEEE Communications Letters, 2012, 16(7):1048-1051). The original WFRFT hybrid carrier transmission method is in the carrier frequency offset (Mei L, Zhang Q, Sha X, et al. WFRFT Precoding for Narrowband Interference Suppression in DFT-Based Block Transmission Systems [J]. IEEE Communications Letters, 2013, 17 (10 ): 1916-1919) and Inter-Symbol Interference and Inter-Carrier Interference Suppression (Li Y, Sha X, Zheng F C, et al. Low Complexity Equalization of HCMSystems with DPFFT Demodulation over Doubly-Selective Channels [J]. IEEE SignalProcessing Letters, 2014 , 21(7):862-865) and other directions have good performance and have been paid attention by the academic and industrial circles.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the shortcomings of high out-of-band leakage of the existing method, and the existing method is to transmit in "block", adding a cyclic prefix before each mixed carrier symbol, resulting in low spectral efficiency, and proposes a fast convolution based method. A method for continuous stream transmission of hybrid carriers without cyclic prefix filtering.

The fast convolution-free cyclic prefix filtering hybrid carrier continuous stream transmission method includes the following steps:

p＝1,2,…,P，再将P段预编码后的数据拼接成连续的数据流s_k(n)，n＝0,1,…,m-1，m为数据流的总点数；Step 1: After the continuous data stream Dk of each subband is independently generated, _k =1, 2,...,K, where _K is the number of subbands, divide Dk into P segments according to a given length Q, and divide the P segments into P segments. After the data stream is precoded by the precoding matrix, the coded data is obtained

p=1,2,...,P, and then splicing the precoded data of P segments into a continuous data stream _sk (n), n=0,1,...,m-1, m is the total number of points in the data stream ;

取出三个连续不重叠分块信号s_k,q-1,s_k,q,s_k,q+1的中间的N_k,b个符号，得到重叠分块信号

其中，N_k,b是L_k,b的2倍；当q＝1时，在两个连续不重叠分块信号s_k,1,s_k,2前补L_k,b个零后取出中间的N_k,b个符号，完成前述的重叠分块操作。Step 2: Perform non-overlapping blocks of length L _k,b on the precoded continuous data stream _sk (n), for the signal of the qth block, it is expressed as _sk,q ,

Take out N _k,b symbols in the middle of three consecutive non-overlapping block signals _sk,q-1 , _sk,q , _sk,q+1 to obtain overlapping block signals

Among them, N _k,b is 2 times of L _k,b ; when q=1, after two consecutive non-overlapping block signals _sk,1 , _sk,2 are filled with L _k,b zeros and the middle is taken out The N _k,b symbols of , complete the aforementioned overlapping block operation.

进行N_k,b点的傅里叶变换；Step 3: Block the overlapping signal

Carry out the Fourier transform of the N _k,b point;

Step 4: Copy the Fourier transform result directly M _k times and splicing it end to end to form the data of N points, perform dot multiplication with the coefficient _ek of the frequency domain filter of N points corresponding to the subband, complete the frequency domain filtering, and obtain The result P _k after each subband is filtered in the frequency domain;

Step 5: After adding the results of the frequency domain filtering of each subband obtained in Step 4, perform inverse Fourier transform at N points to obtain

的中间L个符号，完成重叠保留操作，得到输出信号y(n)的不重叠分块信号

将得到的

个分块信号y_q拼接得到y(n)，并经过上变频处理后发出；其中，2L＝N；Step 6: Take out

The middle L symbols of , complete the overlapping reservation operation, and obtain the non-overlapping block signal of the output signal y(n).

will get

A block signal y _q is spliced to obtain y(n), and sent out after up-conversion processing; wherein, 2L=N;

其中，L是2的幂，N是L的2倍；Step 7: Perform down-conversion processing on the received signal sent in step 6 and pass through the channel to obtain a mixed carrier baseband signal r(n), and perform non-overlapping blocks of length L on the mixed carrier baseband signal r(n); The signal of the qth block, denoted as r _q , take out the middle N symbols of three consecutive non-overlapping block signals r _q-1 , r _q , r _q+1 to obtain overlapping block signals

where L is a power of 2 and N is 2 times L;

进行N点的傅里叶变换；Step 8: Block the overlapping signal

Perform Fourier transform of N points;

Step 9: performing equalization and subband filtering on the block signal after the Fourier transform in step 8;

其中，N_k,b＝2L_k,b，L_k,b＝L/M_k，M_k为第k个子带对应的插值倍数；Step 10: Perform inverse Fourier transform on the data after equalization and sub-band filtering in step 9 _, and obtain

Wherein, N _k,b =2L _k,b , L _k,b =L/M _k , and M _k is the interpolation multiple corresponding to the kth subband;

的中间L_k,b个数据x_k,q，组成数据流x_k；再按长度Q分成P段，每段记为x_k,p，各段分别进行逆预编码

变换，得到

再将逆预编码后的P个结果组合得到各子带的接收信号

Step 11: Keep each block

The middle L _k,b pieces of data x _k,q form the data stream x _k ; then it is divided into P segments according to the length Q, and each segment is denoted as x _k,p , and each segment is reversely precoded

transform, get

Then combine the P results after inverse precoding to obtain the received signal of each subband

The beneficial effects of the present invention are:

The invention introduces subband filtering into the mixed carrier system to suppress out-of-band leakage, and expands the structure of the traditional mixed carrier system. At the same time, the original hybrid carrier transmission method is based on "block" transmission, that is, a cyclic prefix (Cyclic Prefix, CP) is added before each hybrid carrier symbol, while the present invention proposes a continuous stream transmission method, and the hybrid carrier symbol does not add CP, Increased spectral efficiency.

In the existing sub-band filtering communication system, the transmission waveform of each sub-band is a single carrier or a multi-carrier signal. The present invention proposes that each sub-band can flexibly select the transmitted waveform, and the transmitted signal is a mixed carrier signal, wherein the single Carrier and multi-carrier signals are two special cases. The invention provides a continuous stream transmission method of mixed carrier without cyclic prefix filtering. Multiple sub-bands are transmitted in parallel at the same time. After each sub-band is preprocessed by weighted Fourier transform, it is mapped to different frequency bands through filtering. The fast convolution can complete the linear convolution process of time domain filtering, and has the advantages of low complexity and high flexibility. The invention uses fast convolution to complete filtering, and can effectively suppress out-of-band leakage of sub-bands. Each sub-band can flexibly select the sub-band width and set different weighted Fourier transform modulation orders. The weighted Fourier transform modulation orders of different sub-bands can be the same, or the optimal modulation orders can be set according to the equalization rule, so as to optimize the bit error rate performance. In addition, adjusting the modulation order can also suppress the Peak to Average Power Ratio (PAPR). Under the parameters given in the embodiment, the out-of-band leakage suppression between subbands is reduced by about 20dB compared with the original hybrid carrier system. It can also be seen from the examples that the PAPR of a single subband of the present invention is effectively suppressed. At the same time, the system proposed in the present invention no longer relies on the use of CP, which improves the spectral efficiency of the system. The present invention names the proposed system as a cyclic prefix-free filtering hybrid carrier system, which is an extension of the traditional hybrid carrier system, further flexes the waveform design, suppresses the out-of-band leakage of the sub-band, does not use CP, and improves the system reliability. Spectral efficiency.

Description of drawings

Fig. 1 is a block diagram of the present invention;

2 is a schematic diagram of a system receiver module of the present invention;

Fig. 3 is the single subband power spectrum comparison diagram of the present invention and the traditional hybrid carrier system;

4 is a power spectrum comparison diagram of the present invention and a traditional hybrid carrier system;

5 is a comparison diagram of the peak-to-average power ratio of a single subband of the present invention and a traditional hybrid filter system;

Fig. 6 is under the ZF equalization criterion, the bit error rate performance diagram of the present invention under the fixed frequency selection channel;

7 is a bit error rate performance diagram of the present invention under a fixed frequency selection channel under the MMSE equalization criterion;

FIG. 8 is a bit error rate performance diagram under the random frequency selection channel of the present invention under the ZF equalization criterion;

FIG. 9 is a bit error rate performance diagram under the random frequency selection channel of the present invention under the MMSE equalization criterion;

FIG. 10 is a schematic diagram of overlapping blocks of data streams.

Detailed ways

Embodiment 1: The method for continuous stream transmission of mixed carriers without cyclic prefix filtering based on fast convolution includes the following steps:

The system structure proposed by the present invention is shown in FIG. 1 . The transmitter part consists of a set of interpolation filters, and the receiver part consists of a set of corresponding sampling filters. The core of the patent is to select different modulation orders for WFRFT precoding for each subband at the transmitting end. After each subband at the receiving end is subjected to matched filtering and equalization processing, the corresponding subband is subjected to inverse precoding processing, so as to determine the symbol. The position is transformed from the time domain to the fractional domain. The operation of precoding makes the selection of waveform flexible. For different detection algorithms, selecting the optimal modulation order α can make the bit error performance optimal. And can take into account the system's requirements for PAPR, adjust α. From the literature (Mei L, Sha X J, Ran Q W, et al. Research on the application of 4-weighted fractional Fourier transform in communication system [J]. Science China (Information Sciences), 2010, 53(6): 1251-1260), The multi-carrier modulation process via WFRFT precoding can be regarded as a mixed-carrier system. With the change of α, the proportion of the single-carrier component and the multi-carrier component is changing. In the system proposed by the present invention, each user occupies one subband, and different subbands can select the same modulation order or different modulation orders, so the transmission method proposed by the present invention belongs to flexible mixed carrier transmission . At the same time, another core of the present invention is to use fast convolution to complete the filtering operation of each subband of the non-CP hybrid carrier system, and for the fast convolution filtering structure of the transmitter, the equalization processing is completed at the receiving end based on the fast convolution algorithm with the corresponding matched filter. This structure can not only effectively suppress out-of-band leakage of sub-bands, but also, unlike the traditional hybrid carrier system, this structure no longer relies on the use of CP, that is, the transmitter transmits a continuous stream of hybrid carriers without CP.

As shown in Fig. 1, for the system of the present invention, the modulation process can be mapped to several multi-carrier baseband signals. After the mixed carrier signal is generated through WFRFT precoding processing, the demodulation process can be mapped to the baseband received signal through the synthesis filter bank. By analyzing the filter bank, it is processed by inverse precoding. Specifically, after each precoded signal is up-sampled and filtered by a corresponding interpolation filter, the signal is modulated to a certain carrier frequency and limited to a corresponding frequency band, and then superimposed to form a composite signal. The number of carriers is equal to the number of interpolation filters. At the receiving end, after the synthesized signal is filtered and down-sampled by a set of sampling filters, the original precoded signals of each channel are obtained respectively, and then the original signals are obtained through inverse precoding processing.

The system proposed in the present invention completes the realization of the interpolation filter by means of fast convolution. For each subband, it can be considered that the mapping of the baseband signal is completed by means of interpolation filtering. The data transmitted in each subband is processed by corresponding precoding. It can be assumed here that each subband continuous flow signal is a weighted fractional domain signal of order -α. After the WFRFT transformation of order α, the original signal is transformed from a weighted fractional domain signal of order -α to a time domain signal. The present invention uses the overlap-preserving method to complete the time-domain filtering process in the frequency domain, and similarly, the overlap-add method can be used to complete the time-domain filtering process in the frequency domain.

In the system proposed in the present invention, for each subband, it can be considered that the mapping of the baseband signal is completed by means of interpolation filtering based on fast convolution. The input of each subband is a continuous data stream, and different subbands are identified by k. Let L _k,b and L be the lengths of non-overlapping segments before and after interpolation, respectively, N _k,b and N are the corresponding overlapping segment lengths, and the subscript b indicates that L _k,b and N _k,b are Non-overlapping segment length and overlapping segment length before interpolation for the kth subband. Wherein, N _k,b =N/M _k is an integer, M _k is an interpolation multiple and a sampling multiple of the kth subband, and N is a power of 2.

进行预编码后，得到预编码后的数据

p＝1,2,…,P，再将P段预编码后的数据拼接成连续的数据流s_k(n)，n＝0,1,…,m-1；Step 1: After the continuous data stream Dk of each subband is independently generated, _k =1, 2,...,K, where _K is the number of subbands, divide Dk into P segments according to a given length Q, and divide the P segments into P segments. The data stream uses a precoding matrix

After precoding, the precoded data is obtained

p=1,2,...,P, and then splicing the precoded data of P segments into a continuous data stream _sk (n), n=0,1,...,m-1;

其中，N_k,b是L_k,b的2倍；当q＝1时，在两个连续不重叠分块信号s_k,1,s_k,2前补L_k,b个零后取出中间的N_k,b个符号，完成前述的重叠分块操作。Step 2: Perform non-overlapping blocks of length L _k,b on the precoded continuous data stream _sk (n), for the signal of the qth block, it is expressed as _sk,q , _sk,q = [s _k,q (0) s _k,q (1)…s _k,q (L _k,b -1)] ^T ; take out three consecutive non-overlapping block signals s _k,q-1 ,s _k, N _{k, b} symbols in the middle of _q , s _{k, q+1} to obtain overlapping block signals

Among them, N _k,b is 2 times of L _k,b ; when q=1, after two consecutive non-overlapping block signals _sk,1 , _sk,2 are filled with L _k,b zeros and the middle is taken out The N _k,b symbols of , complete the aforementioned overlapping block operation.

进行N_k,b点的傅里叶变换；Step 3: Block the overlapping signal

Carry out the Fourier transform of the N _k,b point;

Step 4: Copy the Fourier transform result directly M _k times and splicing it end to end to form the data of N points, perform dot multiplication with the coefficient _ek of the frequency domain filter of N points corresponding to the subband, complete the frequency domain filtering, and obtain The result P _k after each subband is filtered in the frequency domain;

Step 5: After adding the results of the frequency domain filtering of each subband obtained in Step 4, perform inverse Fourier transform at N points to obtain

的中间L个符号，完成重叠保留操作，得到输出信号y(n)的不重叠分块信号y_q，y_q＝[y_q(0) y_q(1)…y_q(L-1)]^T；将得到的

个分块信号y_q拼接得到y(n)，并经过上变频处理后发出；其中，2L＝N；Step 6: Take out

The middle L symbols of , complete the overlapping reservation operation, and obtain the non-overlapping block signal y _q of the output signal y(n), y _q =[y _q (0) y _q (1)...y _q (L-1)] ^T ; will get

A block signal y _q is spliced to obtain y(n), and sent out after up-conversion processing; wherein, 2L=N;

其中，L是2的幂，N是L的2倍；Step 7: Perform down-conversion processing on the received signal sent in step 6 and pass through the channel to obtain a mixed carrier baseband signal r(n), and perform non-overlapping blocks of length L on the mixed carrier baseband signal r(n); The signal of the qth block, expressed as r _q , r _q =[r _q (0) r _q (1)...r _q (L-1)] ^T ; take out three consecutive non-overlapping block signals r _{q- 1} , r _q , and the middle N symbols of r _q+1 to obtain overlapping block signals

where L is a power of 2 and N is 2 times L;

进行N点的傅里叶变换；Step 8: Block the overlapping signal

Perform Fourier transform of N points;

Step 9: performing equalization and subband filtering on the block signal after the Fourier transform in step 8;

其中，N_k,b＝2L_k,b，L_k,b＝L/M_k，M_k为第k个子带对应的插值倍数；Step 10: Perform inverse Fourier transform on the data after equalization and sub-band filtering in step 9 _, and obtain

Wherein, N _k,b =2L _k,b , L _k,b =L/M _k , and M _k is the interpolation multiple corresponding to the kth subband;

的中间L_k,b个数据x_k,q，组成数据流x_k；再按长度Q分成P段，每段记为

p＝1,2,…,P，各段分别进行逆预编码

变换，得到

再将逆预编码后的P个结果组合得到各子带的接收信号

Step 11: Keep each block

The middle L _k,b data x _k,q form the data stream x _k ; then it is divided into P segments according to the length Q, and each segment is denoted as

p=1,2,...,P, each segment is reversely precoded

transform, get

Then combine the P results after inverse precoding to obtain the received signal of each subband

Abbreviation Definitions:

Description of the main variables:

alpha Modulation order of the weighted Fourier transform k Subband ID L_k,b The length of the non-overlapping segment before the kth subband interpolation, b is the abbreviation of basic. L the length of the interpolated non-overlapping segments N_k,b The length of the overlapping segment before the kth subband interpolation, b is the abbreviation of basic. N the length of the interpolated overlapping segment M_k Interpolation multiples and sampling multiples of the kth subband Q segment length of continuous stream P The number of segments of a continuous stream B total system bandwidth beta Roll-off factor of root raised cosine filter

Filter description and complexity analysis:

The present invention takes the root raised cosine filter as an example, and uses the fast convolution method to complete the equivalent operation of time domain filtering in the frequency domain. In the simulation example of the present invention, a root raised cosine filter with roll-off coefficient β=0.125 is used for description. For the actual system, the roll-off coefficient can be adjusted according to the needs. However, the system proposed in the present invention is not limited to using a root raised cosine filter. There are relevant literatures on the optimization design method of subband filter. In the literature (Yli-Kaakinen J, Renfors M. Optimization of flexible filter banks based on fast-convolution [C]//IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2014: 1-11), it is proposed to minimize The optimal design method based on the filter passband and stopband fluctuations; in the literature (Yli-Kaakinen J, Renfors M. Optimized burst truncation in fast-convolution filter bank based waveform generation [C]//IEEE, International Workshop on Signal Processing In Advances in Wireless Communications. IEEE, 2015:71-75), a filter design method with time-frequency localization characteristics as the first goal is proposed. Technicians can refer to relevant materials for filter design.

A major feature of the present invention is that, for the hybrid carrier system, the filtering is completed by means of fast convolution, which greatly reduces the complexity of the algorithm compared with the traditional time domain filtering. At the same time, in terms of implementation, the operation of fast convolution can use parallel processing to speed up the processing speed.

Compared with the traditional hybrid carrier system, the system of the present invention increases the filtering operation and improves the algorithm complexity. However, the operation based on fast convolution significantly reduces the complexity compared with the traditional temporal filtering.

For comparison under a unified standard, the total number of carriers in the mixed-carrier system is set to N, L sub-carriers are actually used, and the measure of complexity is the number of multiplication operations required to transmit LU symbols. For comparison, traditional OFDM systems are also listed in Table 1. For the system of the present invention, for a subband k of an RRC filter with a normalized bandwidth of N _k,b /N and a roll-off coefficient of β, the calculation amount required to transmit UL _k,b symbols can be approximated as (UL _k,b logQ+4UL _k,b )+(UNlogN)+UN _k,b (β+logN _k,b ). Among them, Q is the segment length of the continuous stream composed of UL _k,b symbols.

Table 1 Transmitter computational complexity of several multi-carrier technologies

As shown in Table 1, the approximate transmitter complexity of the four systems is listed. For the system of the present invention, since the frequency domain filter coefficient is 0 in the stopband and 1 in most of the passband, the computational complexity can be saved. However, before and after the fast Fourier transform/inverse fast Fourier transform calculation of fast convolution, the operation of overlapping preservation reduces the computational efficiency to a certain extent. For time-domain filtering mixed-carrier systems, the filtering operation of time-domain linear convolution greatly increases the complexity of the algorithm. Filtering in the frequency domain based on fast convolution is essentially equivalent to filtering in the time domain, which can suppress out-of-band leakage, but greatly reduces the algorithm complexity. It is worth noting that the present invention does not simply use fast convolution to replace time domain filtering, but designs the structure of the traditional hybrid carrier receiver accordingly, so that matched filtering and equalization operations at the receiving end can be organically integrated. Therefore, the mixed carrier signal is no longer dependent on the use of the CP, and the spectral efficiency is improved. However, each subband adopts a root raised cosine filter and maps it to the corresponding frequency band. Since a transition band is introduced to suppress the out-of-band, the number of subcarriers occupied by each subband also increases, which will also bring about a decrease in spectral efficiency. Therefore, compared with the hybrid carrier system filtered in the time domain, the system proposed in the present invention can effectively improve the spectral efficiency. However, compared with the unfiltered hybrid carrier system, the spectral efficiency is not significantly improved.

p＝1,2,…,P，再将P段预编码后的数据拼接成连续的数据流s_k(n)的具体过程为：Embodiment 2: This embodiment differs from Embodiment 1 in that: in step 1, _Dk is divided into P segments according to a given length Q, and after the data stream of P segments is precoded by using a precoding matrix, the encoded data

p=1,2,...,P, and the specific process of splicing the precoded data of the P segments into a continuous data stream _sk (n) is as follows:

D _k =[D ^T _k,1 D ^T _k,2 ...D ^T _k,P ] ^T

D _k,p = [D _k,p (0) D _k,p (1)…D _k,p (Q-1)] ^T

表示第k个子带第1个分段的数据信号进行预编码后得到的数据的转置；

表示第k个子带第1个分段的数据信号进行预编码后得到的数据的转置；

表示第k个子带第P个分段的数据信号进行预编码后得到的数据的转置；where _sk is the vector representation of _sk (n); D ^T _k,1 represents the transposition of the data signal of the first segment of the kth subband; D ^T _k,2 represents the first segment of the kth subband The transposition of the data signal; D ^T _k,P represents the transposition of the data signal of the p-th segment of the k-th subband; D _k,p (0) represents the data signal of the p-th segment of the k-th subband. the first data _{signal point} of the Qth data signal point in the data signal with the pth segment;

represents the transposition of the data obtained after precoding the data signal of the first segment of the kth subband;

represents the transposition of the data obtained after precoding the data signal of the first segment of the kth subband;

represents the transposition of the data obtained after precoding the data signal of the p-th segment of the k-th subband;

α_k为子带k的加权分数傅里叶变换的调制阶数；The precoding matrix is a weighted fractional Fourier transform matrix of order Q

α _k is the modulation order of the weighted fractional Fourier transform of subband k;

的表达式具体为：the matrix

The expression is specifically:

是加权系数，定义如下：in

is the weighting coefficient, defined as follows:

where I _Q is a Q×Q unit matrix, F _Q is a Q×Q discrete Fourier transform matrix; T _Q is a permutation matrix, each row and each column has only one non-zero element, which is specifically expressed as follows:

即

为

对应的逆预编码矩阵。α_k的小标k用于区分不同子带的加权傅里叶变换调制阶数α。并且，根据文献(Mei L,ShaX J,Ran Q W,et al.Research on the application of 4-weighted fractionalFourier transform in communication system[J].Science China(InformationSciences),2010,53(6):1251-1260)，经由WFRFT预编码的多载波调制过程可视为混合载波系统。由上述的公式可知，WFTFR变换是由原函数和其傅里叶变换后的函数加权求和得到的。同时，随着α在[0,1]内变化，其单载波分量和多载波分量的比重在发生变化。当α＝0时，只有单载波分量，混合载波系统变成单载波系统；当α＝1时，只有多载波分量，混合载波系统变成OFDM系统。可将调制阶数α限定在[0,1]内，通过自由选择α，来调整单载波和多载波的比重，以发挥其对抗信道畸变的优势，这便是混合载波调制的机理。In addition, the weighted inverse fractional Fourier transform can be expressed as

which is

for

The corresponding inverse precoding matrix. The subscript k of α _k is used to distinguish the weighted Fourier transform modulation order α of different subbands. And, according to the literature (Mei L, ShaX J, Ran QW, et al. Research on the application of 4-weighted fractional Fourier transform in communication system [J]. Science China (Information Sciences), 2010, 53(6): 1251-1260 ), the multi-carrier modulation process via WFRFT precoding can be regarded as a mixed-carrier system. It can be seen from the above formula that the WFTFR transform is obtained by the weighted summation of the original function and its Fourier transformed function. At the same time, as α changes within [0,1], the proportions of its single-carrier components and multi-carrier components are changing. When α=0, there is only a single-carrier component, and the mixed-carrier system becomes a single-carrier system; when α=1, there is only a multi-carrier component, and the mixed-carrier system becomes an OFDM system. The modulation order α can be limited within [0,1], and the proportion of single carrier and multi-carrier can be adjusted by freely selecting α, so as to exert its advantages against channel distortion, which is the mechanism of hybrid carrier modulation.

Other steps and parameters are the same as in the first embodiment.

的表达式为：Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is: as shown in FIG. 10 , in the second step, three continuous non-overlapping block signals _sk,q-1 , _sk,q are taken out , s k, N _{k, b} symbols in the middle of _q+1 to obtain overlapping block signals

The expression is:

为N_k,b阶的单位矩阵，记2L_k,s为相邻重叠分块信号间的重叠样本数，则N_k,b＝L_k,b+2L_k,s；本发明取L_k,s＝L_k,b/2，即N_k,b＝2L_k,b；值得指出的是，2L_k,s的长度可结合滤波器的时域响应长度进行设计，非本发明重点，未予讨论。Among them, R _b is the overlapping block matrix of the transmitter,

is a unit matrix of order N _k,b , and 2L _k,s is the number of overlapping samples between adjacent overlapping block signals, then N _k,b =L _k,b +2L _k,s ; the present invention takes L _{k, s} =L _k,b /2, that is, N _k,b =2L _k,b ; it is worth noting that the length of 2L _k,s can be designed in combination with the time domain response length of the filter, which is not the focus of the present invention and is not given. discuss.

Other steps and parameters are the same as in the first or second embodiment.

Embodiment 4: This embodiment is different from one of Embodiments 1 to 3 in that: in the step 4, the Fourier transform result is directly copied M _k times and spliced end to end to form the data of N points, which corresponds to the subband Do point multiplication with the coefficients _ek of the frequency-domain filter of N points to complete the frequency-domain filtering, and the specific process of obtaining the result _Pk after frequency-domain filtering of each subband is as follows:

为N_k,b点傅里叶变换矩阵，

表示增益修正后的滤波器系数矩阵，B_k是第k个子带滤波器的3dB带宽；M_k表示插值倍数，对于所有子带，有L_k,bM_k＝N。Λ_k表示以第k个子带对应的插值滤波器频域响应为对角线元素的N×N矩阵，Λ_k＝diag(e_k)，diag(·)表示以括号内的数作为对角线元素生成对角矩阵；

表示M_k行1列的全1矩阵，

表示N_k,b阶的单位阵，

表示克罗内可(Kronecker)积。in,

is the Fourier transform matrix of N _k,b points,

represents the gain-modified filter coefficient matrix, B _k is the 3dB bandwidth of the kth subband filter; M _k represents the interpolation multiple, and for all subbands, L _k,b M _k =N. Λ _k represents an N×N matrix with the frequency domain response of the interpolation filter corresponding to the kth subband as the diagonal elements, Λ _k =diag(e _k ), diag( ) represents the number in the brackets as the diagonal Elements generate a diagonal matrix;

represents an all-one matrix with M _k rows and 1 column,

represents the identity matrix of order N _k,b ,

Represents the Kronecker product.

Each subband implements filtering in the frequency domain using fast convolution. Therefore, each subband filter only needs to design different weight coefficients on the corresponding taps in the frequency domain. The filter can be designed with the frequency domain coefficients of the root raised cosine filter, and the maximum weight in the passband is set to 1. To adjust the center frequency of the subband, move the non-zero value of (1+β)N _k,b on the FFT unit at point N, and the minimum moving distance corresponds to the frequency change (ie frequency resolution) Δf =B/N, where B is the total bandwidth of the system. Correspondingly, the matched filter corresponding to the receiving end can do the same movement.

The non-zero part of the coefficient _ek of the frequency domain filter is directly sampled and generated according to the normalized frequency domain formula H(f) of the root raised cosine filter:

得到滤波器系数的非零值。The 3dB bandwidth of the frequency domain filter is N _k,b point, the total number of e _k points is N point, and the number of non-zero points is (1+β)N _k,b point. where β is the roll-off coefficient, f ₀ =Δf·N _{k, b} /2 is the cutoff frequency, Δf is the frequency resolution, f is the frequency, and f is discretely sampled,

Get the non-zero values of the filter coefficients.

Other steps and parameters are the same as one of the first to third embodiments.

具体为：Embodiment 5: This embodiment differs from one of Embodiments 1 to 4 in that: in the step 5, the results of the frequency domain filtering of each subband obtained in the step 4 are added, and then an inverse Fourier transform of N points is performed. ,get

Specifically:

为F_N共轭转置矩阵，F_N为N点傅里叶变换矩阵，[F_N]_p,d＝N^-1/2e^{-j2π(p-1)(d-1)/N}。in,

is F _N conjugate transpose matrix, F _N is N-point Fourier transform matrix, [F _N ] _p,d =N ^-1/2 e ^{-j2π(p-1)(d-1)/N} .

Other steps and parameters are the same as one of the first to fourth embodiments.

Embodiment 6: This embodiment differs from one of Embodiments 1 to 5 in that: the expression of the block signal y _q in the step 6 is:

Wherein, O is the overlapping reservation matrix of the transmitter, O=[0 _L×L/2 I _L 0 _L×L/2 ], and I _L is the L-order identity matrix.

Other steps and parameters are the same as one of the specific embodiments one to five.

的表达式为：Embodiment 7: The difference between this embodiment and one of Embodiments 1 to 6 is that in the step 7, the block signal is overlapped

The expression is:

Wherein, R is the receiver overlapping block matrix, R=[0 _N×(LL/2) I _N 0 _N×(LL/2) ], and I _N is an N-order identity matrix.

Other steps and parameters are the same as one of Embodiments 1 to 6.

Embodiment 8: This embodiment differs from Embodiment 1 to Embodiment 7 in that: in the step 9, the specific process of performing equalization and sub-band filtering on the block signal after the Fourier transform in step 8 is as follows:

After obtaining the equalization coefficient matrix Φ according to different equalization rules, the equalization coefficient matrix Φ and the filter coefficient matrix Π _k of different subbands are multiplied and merged, and then point multiplied with the Fourier transform result of N points; The result is divided into _Mk sections by length _Nk,b , superimposes, completes downsampling filtering, obtains the data _Qk,q after the downsampling filtering of the kth subband qth subsection; Described different equalization criteria are Zero forcing criterion and minimum mean square error criterion;

Here, E ^T is the transposition of E, because the present invention adopts paired sampling filters and interpolation filters, the filter coefficient matrix Π _k after the gain correction of the receiving end is the same as that of the transmitter. Φ is the frequency domain equalization coefficient matrix, which can be obtained according to the ZF criterion or the MMSE criterion;

The equalization coefficient matrix Φ is specifically:

When the minimum mean square error criterion is adopted, the equalization coefficient matrix Φ is:

When the zero-forcing criterion is adopted, the equalization coefficient matrix Φ is:

Φ=diag(1/h _i ), i=1,2,...,N

的主对角线元素，H_N×N为多径信道矩阵，F_N为N维的傅里叶变换矩阵，

为F_N的共轭转置矩阵，σ²为噪声方差，

为h_i的共轭。Among them, _hi is

The main diagonal elements of , H _N×N is the multipath channel matrix, F _N is the N-dimensional Fourier transform matrix,

is the conjugate transpose matrix of F _N , σ ² is the noise variance,

is the conjugate of _hi .

At the receiving end, the present invention adopts the fast convolution method to complete the sampling filtering. The equalization process is added, and its implementation block diagram is shown in Figure 2. In Figure 2, the value of the stopband part of the filter is 0, and after multiplication and merging with the equalization coefficient, it is still 0, which is not marked in the figure.

It can be found that a simple one-point tap equalization is used here, and the equalizer coefficients can be multiplied and combined with the filter coefficients. The feasibility of this simplified single-tap equalizer design concept is presented in the literature (Zhao J, Wang W, GaoX. Transceiver design for fast-convolution multicarrier systems in multipathfading channels [C]//International Conference on Wireless Communications&Signal Processing. IEEE, 2015:1-5) were described. The present invention has been simulated and verified under different equalization criteria in combination with different weighted transformation modulation orders. To minimize inter-segment interference, the overlap between segments should be significantly larger than the channel length. At the same time, the multipath channel matrix H _N×N will be progressively diagonalized by the Fourier transform matrix, and the degree of diagonalization increases as the number of Fourier transform points N increases. That is, the larger N is, the better the compensation effect of channel distortion is by the _equalization coefficient generated by taking the main line element hi.

Other steps and parameters are the same as one of the first to seventh embodiments.

的表达式为：Embodiment 9: The difference between this embodiment and one of Embodiments 1 to 8 is that: in step 10, the data after equalization and sub-band filtering in step 9 is subjected to N _{k, b} point inverse Fourier transform to obtain

The expression is:

为N_k,b点傅里叶逆变换矩阵。in

is the inverse Fourier transform matrix of N _k,b points.

Other steps and parameters are the same as one of Embodiments 1 to 8.

的中间L_k,b个数据x_k,q，组成数据流x_k；再按长度Q分成P段，每段记为

各段分别进行逆预编码

变换，得到

再将逆预编码后的P个结果组合得到各子带的接收信号

具体为：Embodiment 10: The difference between this embodiment and one of Embodiments 1 to 9 is that each block is reserved in the step 11.

The middle L _k,b data x _k,q form the data stream x _k ; then it is divided into P segments according to the length Q, and each segment is denoted as

Inverse precoding for each segment

transform, get

Then combine the P results after inverse precoding to obtain the received signal of each subband

Specifically:

为L_k,b阶的单位矩阵。x^T _k,1表示第k个子带第1个不重叠分块数据信号的转置；x^T _k,2表示第k个子带第2个不重叠分块数据信号的转置；

表示第k个子带第

个不重叠分块数据信号的转置；数据流x_k由

个不重叠分块数据x_k,q拼接而成，再将其按长度Q分成成P段，每段数据信号记为

表示第k个子带第1个分段的数据信号的转置；

表示第k个子带第2个分段的数据信号的转置；

表示第k个子带第P个分段的数据信号的转置；

表示第k个子带第1个分段的数据逆预编码变换后得到的结果的转置；

表示第k个子带第2个分段的数据逆预编码变换后得到的结果的转置；

表示第k个子带第P个分段的数据逆预编码变换后得到的结果的转置；where O _b is the receiver overlap retention matrix,

is the identity matrix of order L _k,b . x ^T _k,1 represents the transposition of the first non-overlapping block data signal of the kth subband; x ^T _k,2 represents the transposition of the second non-overlapping block data signal of the kth subband;

represents the kth subband

The transpose of a non-overlapping block data signal; the data stream x _k is given by

The non-overlapping block data x _{k, q} are spliced together, and then divided into P segments according to the length Q, and each segment of data signal is recorded as

represents the transposition of the data signal of the first segment of the kth subband;

represents the transposition of the data signal of the second segment of the kth subband;

represents the transpose of the data signal of the p-th segment of the k-th subband;

represents the transposition of the result obtained after the inverse precoding transformation of the data of the first segment of the kth subband;

represents the transposition of the result obtained after the data inverse precoding transformation of the second segment of the kth subband;

represents the transposition of the result obtained after the inverse precoding transformation of the data of the p-th segment of the k-th subband;

Other steps and parameters are the same as one of Embodiments 1 to 9.

Example 1:

The most significant advantage of the system proposed by the present invention over the traditional hybrid carrier system is the steep out-of-band attenuation. Out-of-band leakage will bring about signal interference between sub-bands, so the system proposed in the present invention has fast out-of-band attenuation, and can better utilize the "gap" between fragmented spectrum resources.

The basic simulation parameters are set as: the modulation order of the weighted transform α=0.5, N=2048, L=1024, the root raised cosine filter roll-off coefficient β=0.125, the length of the weighted transform precoding Q= 64. The overlapping block length N _k,b =128. In the simulation, the initial data signals are all generated by 4QAM modulation, and channel coding is not used. In the simulation, each subband uses the same overlapping block length and the same weighted transform modulation order. FIG. 3 compares the power spectrum of a certain subband of the system proposed by the present invention using the root raised cosine filter and the traditional hybrid carrier system not using the root raised cosine filter for filtering. In the simulation, a root raised cosine filter was used with a roll-off factor β=0.125. It can be seen from FIG. 3 that the system proposed by the present invention can better suppress the side lobes. Meanwhile, under the same spectral efficiency, the power spectrum of the modulated signal of the system proposed by the present invention is compared with that of the traditional hybrid carrier system. The actual number of carriers used by the two systems is 1024. The results are shown in Figure 4, the interference between adjacent subbands is below -30dB, and the interference between subbands is small. It should be pointed out that, in the system of the present invention, the bandwidth and center frequency of each subband can be adjusted freely. Also, the roll-off factor of the filter can be changed to change the out-of-band rejection performance.

Peak-to-average power ratio (PAPR) is defined as the ratio of the maximum instantaneous power to the average power of a signal:

Among them, s(n) represents the transmitted time-domain signal, and E[·] represents the expected value. The power amplifier of the wireless communication system transmitter has a maximum power limit. In order to ensure that no nonlinear distortion occurs after the signal passes through the power amplifier, the power amplifier is required to work in the linear working region, that is, the maximum instantaneous power of the transmitter signal generally cannot exceed the maximum output power of the power amplifier. The high PAPR of the signal can impair the communication performance of the system. The complementary cumulative distribution function (CCDF) is used to evaluate the PAPR performance of the system, which is defined as the probability that the actual peak-to-average power ratio of the signal exceeds the threshold peak-to-average power ratio PAPR ₀ :

CCDF=Pr[PAPR>PAPR ₀ ]

Among them, Pr[·] represents the probability. We know that for mixed carrier system, its PAPR value is between OFDM system and DFT-S-OFDM (Sha Xuejun, Mei Lin, Zhang Qinyu. Weighted Fractional Fourier Transform and Its Application in Communication System [M]. People's Posts and Telecommunications Press, 2016: 81-83). The OFDM system and the DFT-S-OFDM system are hybrid carrier systems under a specific weighted transform modulation order. The fast convolution-based filtering hybrid carrier system proposed in the present invention not only retains the flexibility of the traditional hybrid carrier system to adjust the PAPR according to different modulation orders, but also the filtering operation can further reduce the PAPR to a certain extent.

FIG. 5 takes a single subband as an example to compare the PAPR characteristics of the system of the present invention with the traditional hybrid carrier system. In the simulation, the basic simulation parameters are the same as above, and the 4QAM modulation mode is adopted. The occupied number of subcarriers corresponding to the 3dB bandwidth of the subband of the system of the present invention is 128 (N _k,b =128), and the other single subbands of the system occupy 128 subcarriers. As can be seen from the figure, when a single subband is used for data transmission by one user, the PAPR of the signal at the transmitter of the system of the present invention is significantly smaller than that of the traditional hybrid carrier system. Among them, OFDM can be regarded as a mixed carrier system with α=1, and DFT-S-OFDM can be regarded as a mixed carrier system with α=0. Under the same modulation order, the PAPR performance of the system of the present invention is better than that of the traditional hybrid carrier system. Moreover, for the system of the present invention, when the transmitted original data is a time domain signal, that is, when α=0, it has the best PAPR performance.

Embodiment 2:

This embodiment simulates the bit error rate performance of the method of the present invention.

Based on the foregoing introduction to the system receiver of the present invention, combined with the characteristics of the system, an equalizer design based on fast convolution is adopted at the receiving end. This receiver design no longer requires the transmitted signal to carry the cyclic prefix CP. The system of the present invention does not depend on the CP structure, thereby improving the spectrum efficiency, and at the same time, under the frequency selection channel, the bit error rate performance close to that of the original mixed carrier system can be achieved. The present invention proposes that an appropriate modulation order can be selected at the transmitting end according to the ZF or MMSE-based equalization criterion adopted for equalization and the requirements of the system for PAPR. It should be noted that, each subband can select different modulation order α according to different requirements. In contrast, the simulation of the present invention is illustrated with a single subband. If it is a multi-subband system, the bit error rate of each subband can be averaged. Meanwhile, in the following simulation, the segment length Q for precoding of continuous stream segments is set to 64.

Under the fixed frequency selection channel, the system of the present invention is simulated. The simulation uses a three-path channel, the channel delay is [0, 5, 10] chips, the channel impulse response is [1, -0.5, 0.3] and the energy is normalized. The basic parameters are set as: the modulation order of the weighted transformation α=0, 0.5, 1, N=2048, L=1024, the RRC filter roll-off coefficient β=0.125, and the 3dB bandwidth occupied by a single subband is 128 subcarriers, namely N _k,b =128. The initial continuous stream signals are all generated using 4QAM modulation, and none of them use channel coding. The receivers are assumed to have ideal channel state information.

It can be seen from Fig. 6 and Fig. 7 that for the system proposed in the present invention, when the single-carrier component contained in the data transmitted by the sub-band is higher, the sub-band is more similar to the broadband single-carrier system, and the frequency diversity can be better utilized, and the bit error rate is reduced. better rate performance.

Under the random frequency selection channel, Monte Carlo simulation of the performance of the system of the present invention is carried out. The relative time delay of each path is [0, 10, 20, 30, 50, 70] chips, and the average power of each path is [0, -3.6, -7.2, -10.8, -18, -25.2] dB. The basic parameters are set as: the modulation order of the weighted transformation α=0, 0.5, 1, N=2048, L=1024, the RRC filter roll-off coefficient β=0.125, and the 3dB bandwidth occupied by a single subband is 128 subcarriers, namely N _k,b =128. The initial continuous stream signals are all generated using 4QAM modulation, and none of them use channel coding. In order to reflect the randomness of the fading channel, 1000 random channels are generated, each channel is simulated 1000 times, and the average is taken.

It can be seen from FIG. 8 and FIG. 9 that under the random frequency selection channel, the hybrid carrier system based on fast convolution filtering proposed by the present invention presents different bit errors under different equalization rules and different weighted modulation order α precoding. rate performance. Under the ZF criterion, when the subband transmits multi-carrier data (ie α=1), it has the best bit error rate performance. Under the MMSE criterion, when the subband transmits single-carrier data (ie, α=0), it has the best bit error rate performance. Therefore, for the system of the present invention, if only the bit error rate performance is considered, when the receiver adopts the ZF criterion for equalization, the modulation order α of the precoding matrix can be selected as α=1; if the receiver adopts the MMSE criterion for equalization, the precoding matrix is selected. The modulation order α=0 of the coding matrix. At the same time, the modulation order will also affect the size of the PAPR. When there are more single-carrier components in the system, that is, when α is close to 0, the PAPR is smaller. Therefore, the appropriate modulation order α can be selected according to the requirements of the system for PAPR and the equalization rule adopted by the receiver.

The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (10)

1. A continuous flow transmission method of mixed carrier wave without cyclic prefix filtering based on fast convolution is characterized in that: the continuous flow transmission method of the mixed carrier without the cyclic prefix filtering comprises the following steps:

the method comprises the following steps: continuous data stream D per sub-band_kIndependently generating K as 1,2, …, K as the number of sub-bands, and dividing D_kDividing the data into P sections according to a given length Q, and precoding P section data streams by using a precoding matrix to obtain precoded data

Then splicing the P sections of pre-coded data into a continuous data stream s_k(n), n is 0,1, …, m-1, m is the total number of points of the data stream;

step two: for the pre-coded continuous data stream s_k(n) a length L_k,bFor the signal of the q-th block, denoted s_k,q，

Take out three consecutive capsulesOverlapping block signals s_k,q-1,s_k,q,s_k,q+1Is N in the middle_k,bOne symbol to obtain an overlapped block signal

Wherein N is_k,bIs L_k,b2 times of the total weight of the composition; when q is 1, the blocking signal s is not overlapped in two consecutive blocks_k,1,s_k,2Anterior supplement L_k,bTaking out the middle N after zero_k,bSymbol, finishing the overlapping block operation;

step three: will overlap the block signal

Carry out N_k,bFourier transform of the points;

step four: directly copying the Fourier transform result to M_kThe data of N points are formed by splicing the sub-bands end to end, and the coefficient e of the frequency domain filter of the N points corresponding to the sub-band_kPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-band_k；

Step five: adding the results of the frequency domain filtering of each sub-band obtained in the step four, and then performing inverse Fourier transform of N points to obtain

Step six: taking out

The middle L symbols of the output signal y (n) are obtained by completing the overlap-preserving operation_q(ii) a Will obtain

A block signal y_qSplicing to obtain y (n), and sending out the y (n) after up-conversion treatment; wherein 2L ═ N;

step seven: carrying out down-conversion processing on the received signals which are sent out in the sixth step and pass through the channel to obtain a mixed carrier baseThe signal r (n) is used for carrying out non-overlapping partitioning with the length of L on the mixed carrier baseband signal r (n); for the q-th block signal, denoted r_qTaking out three continuous non-overlapping block signals r_q-1,r_q,r_q+1Obtaining an overlapped block signal by the middle N symbols

Wherein L is a power of 2 and N is 2 times L;

step eight: will overlap the block signal

Carrying out Fourier transform of N points;

step nine: equalizing and sub-band filtering the block signals subjected to Fourier transform in the step eight;

step ten: n is carried out on the data after the equalization and the sub-band filtering are carried out in the step nine_k,bInverse point Fourier transform to obtain

Wherein N is_k,b＝2L_k,b，L_k,b＝L/M_k，M_kThe interpolation multiple corresponding to the kth subband;

step eleven: reserving each partition

Middle L of_k,bData x_k,qForm a data stream x_k(ii) a Then divided into P sections according to the length Q, and each section is marked as

Each segment is respectively carried out inverse precoding

Is transformed to obtain

Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band

2. The method of claim 1, wherein the method for continuous stream transmission without cyclic prefix filtering is characterized in that: in the first step, D is_kDividing the data into P sections according to a given length Q, and precoding P section data streams by using a precoding matrix to obtain precoded data

Then splicing the P sections of pre-coded data into a continuous data stream s_kThe specific process of (n) is as follows:

D_k＝[D^T _k,1 D^T _k,2…D^T _k,P]^T

D_k,p＝[D_k,p(0) D_k,p(1)…D_k,p(Q-1)]^T

wherein s is_kIs s is_k(n) a vector representation; d^T _k,1A transpose of the data signal representing the 1 st segment of the k-th sub-band; d^T _k,2A transpose of the data signal representing the 2 nd segment of the kth subband; d^T _k,PA transpose of the data signal representing the P-th segment of the k-th sub-band; d_k,p(0) Representing the 1 st data signal point in the data signal of the p segment of the kth subband; d_k,p(1) Representing the 2 nd data signal point in the data signal of the p segment of the kth subband; d_k,p(Q-1) indicating a Q-th data signal point in the data signal of the p-th segment of the k-th subband;

the transposition of data obtained after precoding a data signal of a 1 st subsection of a kth sub-band is represented;

the data transposition obtained after precoding the data signal of the 2 nd subsection of the kth sub-band is shown;

the transposition of data obtained after precoding a P-th segmented data signal of a kth sub-band is represented;

weighted fractional Fourier transform matrix with precoding matrix of Q order

α_kA modulation order that is a weighted fractional fourier transform of subband k;

the matrix

The expression (c) is specifically:

wherein

Is a weighting coefficient defined as follows:

wherein I_QIs a QxQ identity matrix, F_QIs QxQ discreteA Fourier transform matrix; t is_QIs a permutation matrix, and each row and each column only has one non-zero element, which is specifically expressed as follows:

3. the method for continuous stream transmission without cyclic prefix filtering and mixed carrier wave based on fast convolution as claimed in claim 1 or 2, characterized in that: taking out three continuous non-overlapping block signals s in the second step_k,q-1,s_k,q,s_k,q+1Is N in the middle_k,bOne symbol to obtain an overlapped block signal

The expression of (a) is:

wherein R is_bThe block matrices are overlapped for the transmitter,

is N_k,bIdentity matrix of order, note 2L_k,sFor the number of overlapping samples between adjacent overlapping block signals, then N_k,b＝L_k,b+2L_k,s(ii) a Get L_k,s＝L_k,b2, i.e. N_k,b＝2L_k,b。

4. The method of claim 3, wherein the method comprises: in the fourth step, the Fourier transform result is directly copied into M_kSplicing the data of N points in parallel end to form N point data, and the frequency of the N points corresponding to the sub-bandCoefficient e of the domain filter_kPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-band_kThe specific process comprises the following steps:

wherein,

is N_k,bA matrix of point-fourier transforms is formed,

representing the gain-corrected filter coefficient matrix, B_kIs the 3dB bandwidth of the kth subband filter; m_kRepresenting the interpolation multiple, for all subbands, there is L_k,bM_k＝N；Λ_kRepresenting an NxN matrix, Lambda, with the frequency-domain response of the interpolation filter as diagonal elements_k＝diag(e_k)，

Representing the generation of a diagonal matrix with the numbers in brackets as diagonal elements;

represents M_kA full 1 matrix of rows and columns,

represents N_k,bA unit matrix of an order of a plurality of units,

represents the Kronecker product;

coefficient e of the frequency domain filter_kIs based on root balanceNormalized frequency domain equation h (f) for the chord filter direct sampling generation:

wherein beta is the roll-off coefficient, f₀＝△f·N_k,bIs the cut-off frequency, Δ f is the frequency resolution, f is the frequency;

the 3dB bandwidth of the frequency domain filter is N_k,bPoint, e_kThe total number of points of (1+ beta) N is N points, and the number of non-zero points is (1+ beta) N_k,bAnd (4) point.

5. The method of claim 4, wherein the method for continuous stream transmission without cyclic prefix filtering is characterized in that: in the fifth step, the results of the frequency domain filtering of each sub-band obtained in the fourth step are added and then subjected to N-point Fourier inverse transformation to obtain

The method specifically comprises the following steps:

wherein,

is an N-point inverse Fourier transform matrix.

6. The method of claim 5, wherein the method comprises: the block signal y in the sixth step_qThe expression of (a) is:

wherein O is reserved for transmitter overlapMatrix, O ═ 0_L×L/2 I_L 0_L×L/2]，I_LIs an identity matrix of order L.

7. The method of claim 6, wherein the method comprises: overlapping the block signals in the step seven

The expression of (a) is:

wherein, R is a receiver overlapped block matrix, and R is [0 ]_N×(L-L/2) I_N 0_N×(L-L/2)]，I_NIs an identity matrix of order N.

8. The method of claim 7, wherein the method for continuous stream transmission without cyclic prefix filtering is characterized in that: in the ninth step, the specific process of equalizing and sub-band filtering the block signals after fourier transform in the eighth step is as follows:

firstly, obtaining an equalization coefficient matrix phi according to different equalization rules, and then, enabling the equalization coefficient matrix phi and filter coefficient matrixes pi of different sub-bands_kAfter multiplication and combination, performing point multiplication with the Fourier transform result of the N points; the result is expressed in length N_k,bAre equally divided into M_kSegment, overlap, finish the down-sampling filtering, get the data Q after the Q subsection of the kth sub-band_k,q(ii) a The different equalization rules are zero forcing criterion and minimum mean square error criterion;

here, E^TIs the transpose of E; because the invention adopts paired sampling filters andinterpolation filter, so the gain corrected filter coefficient matrix pi of the receiving end_kSame as the transmitter;

the equalization coefficient matrix Φ is specifically:

when the minimum mean square error criterion is adopted, the equalization coefficient matrix Φ is:

when the zero forcing criterion is adopted, the equalization coefficient matrix Φ is:

Φ＝diag(1/h_i),i＝1,2,…,N

wherein h is_iIs composed of

Main diagonal element of (1), H_N×NFor a multipath channel matrix, F_NIs a Fourier transform matrix of N dimensions,

is F_NConjugate transpose matrix of σ²In order to be the variance of the noise,

is h_iConjugation of (1).

9. The method of claim 8, wherein the method for continuous stream transmission without cyclic prefix filtering is characterized in that: in the step ten, N is carried out on the data after the equalization and the sub-band filtering in the step nine_k,bInverse point Fourier transform to obtain

The expression of (a) is:

wherein

Is N_k,bAnd (4) a point Fourier inverse transformation matrix.

10. The method of claim 9, wherein the method for continuous stream transmission without cyclic prefix filtering is characterized in that: the first step is to reserve each block

Middle L of_k,bData x_k,qForm a data stream x_k(ii) a Then divided into P sections according to the length Q, and each section is marked as

Each segment is respectively carried out inverse precoding

Is transformed to obtain

Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band

The method specifically comprises the following steps:

wherein, O_bThe matrix is reserved for the receiver overlap-add,

is L_k,bAn identity matrix of order;

x^T _k,1a transpose representing the 1 st non-overlapping block data signal of the kth sub-band; x is the number of^T _k,2Representing a transpose of the kth subband 2 nd non-overlapping block data signal;

indicating the kth sub-band

Transposing of non-overlapping block data signals; data stream x_kBy

Individual non-overlapping block data x_k,qSplicing, dividing the signal into P sections according to the length Q, and recording each section of data signal as

A transpose of the data signal representing the 1 st segment of the k-th sub-band;

a transpose of the data signal representing the 2 nd segment of the kth subband;

a transpose of the data signal representing the P-th segment of the k-th sub-band;

the transposition of a result obtained after the data of the 1 st subsection of the kth sub-band is subjected to inverse pre-coding transformation is shown;

the transposition of a result obtained after the data of the 2 nd subsection of the kth subband are subjected to inverse pre-coding transformation is shown;

and the transposition of the result obtained after the data of the P-th subsection of the kth sub-band is subjected to inverse pre-coding transformation is shown.

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