CN108964731B - Mixed carrier continuous flow transmission method based on fast convolution and without cyclic prefix filtering - Google Patents

Mixed carrier continuous flow transmission method based on fast convolution and without cyclic prefix filtering Download PDF

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CN108964731B
CN108964731B CN201810966467.XA CN201810966467A CN108964731B CN 108964731 B CN108964731 B CN 108964731B CN 201810966467 A CN201810966467 A CN 201810966467A CN 108964731 B CN108964731 B CN 108964731B
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CN108964731A (en
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梅林�
林旭
沙学军
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Harbin Institute of Technology
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

A mixed carrier continuous flow transmission method based on fast convolution and without cyclic prefix filtering is used in the field of wireless communication. The invention can solve the problems of high out-of-band leakage of the existing method and low frequency spectrum efficiency caused by adding the cyclic prefix before each mixed carrier symbol in the existing method. According to the invention, a plurality of sub-bands are simultaneously transmitted in parallel, and each sub-band is mapped to different frequency bands through filtering after weighted Fourier transform preprocessing is carried out on each sub-band. The invention uses fast convolution to complete filtering, and can effectively inhibit out-of-band leakage of the sub-band. Each sub-band can flexibly select the width of the sub-band and set different weighted Fourier transform modulation orders. The modulation orders of different sub-bands can be the same, and the optimal modulation orders can be set according to the equilibrium rule, so that the bit error rate performance is optimal. Moreover, the peak-to-average ratio can be suppressed by adjusting the modulation order. The method can select a proper modulation order by combining the requirement of the system on the peak-to-average ratio and considering the equalization rule adopted by the receiver.

Description

Mixed carrier continuous flow transmission method based on fast convolution and without cyclic prefix filtering
Technical Field
The invention relates to the field of wireless communication, in particular to a continuous flow transmission method of a mixed carrier wave without cyclic prefix filtering based on fast convolution.
Background
In modern communication systems, Orthogonal Frequency Division Multiplexing (OFDM) technology is widely used due to its high spectral efficiency and strong resistance to multipath fading. But it has high side lobe power and thus has strict requirements on the synchronization of the transmission. In order to suppress out-of-band power to reduce the requirement of the system for synchronization, researchers have proposed various techniques, such as Filter bank multi-carrier (FBMC), Filtered OFDM (Filtered-OFDM), Generalized Frequency Division Multiplexing (GFDM), and general Filtered multi-carrier (UFMC) (Vakilian, v.; Wild, t.; Schaich, f.; ten Brink, S. & Frigon, j.f. Universal-Filtered multi-carrier for wireless systems bearings and LTE 2013 IEEE globec works (GC Wkshps),2013, 223-. Both of these techniques use filtering to suppress out-of-band power leakage. Meanwhile, in recent years, a mixed carrier design concept (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 Science 2010,53(6): 1251-. In the weighted fractional Fourier transform and its application in a communication system (Mellin. weighted fractional Fourier transform and its application in a communication system [ D ]. Harbin: Harbin university of industry, 2010: 51-60), a mixed carrier system based on WFRFT successfully integrates the traditional single carrier and multi-carrier systems, and fuses two different carrier components in a weighted combination manner. The energy of the mixed Carrier signal can be uniformly distributed in a time-frequency plane, and the anti-interference performance of the System can be improved (Wang K, Sha X, Mei L, et al. The conventional WFRFT hybrid carrier Transmission method has good performance in the directions of carrier frequency offset (Mei L, Zhang Q, Sha X, et al. WFRFT Precoding for narrow band Interference Suppression in DFT-Based Block Transmission Systems [ J ]. IEEE Communications Letters,2013,17(10): 1916-.
Disclosure of Invention
The invention aims to solve the defects that the prior method has high out-of-band leakage and low spectrum efficiency caused by the fact that the prior method transmits according to blocks and a cyclic prefix is added in front of each mixed carrier symbol, and provides a continuous flow transmission method of filtering mixed carriers without the cyclic prefix based on fast convolution.
The method for transmitting the continuous stream of the mixed carrier wave without the cyclic prefix filtering based on the fast convolution comprises the following steps:
the method comprises the following steps: continuous data stream D per sub-bandkIndependently generating K as 1,2, …, K as the number of sub-bands, and dividing DkDividing the data into P sections according to a given length Q, and precoding P section data streams by using a precoding matrix to obtain coded data
Figure BDA0001775085830000021
P is 1,2, …, P, and then the P segments of pre-coded data are spliced into a continuous data stream sk(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 sk(n) a length Lk,bFor the signal of the q-th block, denoted sk,q，
Figure BDA0001775085830000022
Taking out three consecutive non-overlapping block signals sk,q-1,sk,q,sk,q+1Is N in the middlek,bOne symbol to obtain an overlapped block signal
Figure BDA0001775085830000023
Wherein N isk,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 blocksk,1,sk,2Anterior supplement Lk,bTaking out the middle N after zerok,bAnd (4) completing the overlapping block operation.
Step three: will overlap the block signal
Figure BDA0001775085830000024
Carry out Nk,bFourier transform of the points;
step four: directly copying the Fourier transform result to MkThe 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-bandkPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-bandk；
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
Figure BDA0001775085830000025
Step six: taking out
Figure BDA0001775085830000026
The middle L symbols of the output signal y (n) are obtained by completing the overlap-preserving operation
Figure BDA0001775085830000027
Will obtain
Figure BDA0001775085830000028
A block signal yqSplicing to obtain y (n), and sending out the y (n) after up-conversion treatment; wherein 2L ═ N;
step seven: performing down-conversion processing on the received signals which are sent out in the sixth step and pass through the channel to obtain mixed carrier baseband signals r (n), and performing non-overlapping partitioning with the length of L on the mixed carrier baseband signals r (n); for the q-th block signal, denoted rqTaking out three continuous non-overlapping block signals rq-1,rq,rq+1Obtaining an overlapped block signal by the middle N symbols
Figure BDA0001775085830000031
Wherein L is a power of 2 and N is 2 times L;
step eight: will overlap the block signal
Figure BDA0001775085830000032
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 ninek,bInverse point Fourier transform to obtain
Figure BDA0001775085830000033
Wherein N isk,b＝2Lk,b，Lk,b＝L/Mk，MkThe interpolation multiple corresponding to the kth subband;
step eleven: reserving each partition
Figure BDA0001775085830000034
Middle L ofk,bData xk,qForm a data stream xk(ii) a Then divided into P sections according to the length Q, and each section is marked as xk,pEach segment is respectively inverse pre-coded
Figure BDA0001775085830000035
Is transformed to obtain
Figure BDA0001775085830000036
Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band
Figure BDA0001775085830000037
The invention has the beneficial effects that:
the invention introduces sub-band filtering into the mixed carrier system to inhibit out-of-band leakage, and expands the structure of the traditional mixed carrier system. Meanwhile, the original mixed carrier transmission method is based on 'block' transmission, namely, a Cyclic Prefix (CP) is added in front of each mixed carrier symbol, while the invention provides a continuous flow transmission method, and the CP is not added in the mixed carrier symbols, thereby improving the spectrum efficiency.
In the existing subband filtering communication system, each subband transmission waveform is a single carrier or a multi-carrier signal. The invention discloses a continuous flow transmission method of mixed carrier wave without cyclic prefix filtering, a plurality of sub-bands are simultaneously transmitted in parallel, and each sub-band is mapped to different frequency bands through filtering after weighted Fourier transform preprocessing is carried out on each sub-band. And 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 inhibit out-of-band leakage of the sub-band. Each sub-band can flexibly select the width of the sub-band and set different weighted Fourier transform modulation orders. The weighted Fourier transform modulation orders of different sub-bands can be the same, and the optimal modulation orders can be set according to the equilibrium rule, so that the bit error rate performance is optimal. Also, adjusting the modulation order can suppress the Peak to Average Power Ratio (PAPR). Under the parameters given by the embodiment, the out-of-band rejection leakage between the sub-bands is reduced by about 20dB compared with the original mixed carrier system. It can also be seen in the embodiment that the PAPR of the single sub-band of the present invention is effectively suppressed. Meanwhile, the system provided by the invention does not depend on the use of the CP any more, and the frequency spectrum efficiency of the system is improved. The invention names the system as a mixed carrier system without cyclic prefix filtering, which is an extension of the traditional mixed carrier system, further flexibly designs the waveform, inhibits the out-of-band leakage of a sub-band, does not use CP, and improves the spectrum efficiency of the system.
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FIG. 1 is a block diagram of the present invention;
FIG. 2 is a schematic diagram of a receiver module of the system of the present invention;
FIG. 3 is a graph comparing the single subband power spectrum of the present invention with a conventional hybrid carrier system;
FIG. 4 is a graph comparing the power spectrum of the present invention with a conventional hybrid carrier system;
FIG. 5 is a graph comparing the peak-to-average power ratio of a single subband of the present invention with a conventional hybrid filtering system;
FIG. 6 is a diagram of the bit error rate performance of the present invention under a fixed frequency-selective channel under the ZF equalization criterion;
FIG. 7 is a diagram of the bit error rate performance of the present invention under a fixed frequency-selective channel under the MMSE equalization criterion;
FIG. 8 is a diagram of bit error rate performance under the random frequency selection channel of the present invention under the ZF equalization criterion;
FIG. 9 is a diagram of bit error rate performance under a random frequency selective channel according to the present invention under MMSE equalization criterion;
fig. 10 is a schematic diagram of data stream overlap blocks.
Detailed Description
The first embodiment is as follows: the method for transmitting the continuous stream of the mixed carrier wave without the cyclic prefix filtering based on the fast convolution comprises the following steps:
the structure of the system proposed by the present invention is shown in fig. 1. The transmitter part is formed by a set of interpolation filters and the receiver part is formed by a corresponding set of sampling filters. The core of the patent lies in that each sub-band at the transmitting end can select different modulation orders to carry out WFRFT precoding, and after each sub-band at the receiving end is subjected to matched filtering and equalization processing, the corresponding sub-band is subjected to inverse precoding processing, so that the symbol decision position is converted from the time domain to the fractional domain. The pre-coding operation makes the selection of the waveform flexible, and the optimal modulation order alpha is selected according to different detection algorithms, so that the error bit performance is optimal. And the alpha can be adjusted according to the requirement of the system on the PAPR. The multi-carrier modulation process via WFRFT precoding is known as a mixed carrier system 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-. As alpha changes, the specific gravity of the single carrier component and the multi-carrier component changes. In the system provided by the invention, each user occupies one sub-band, and different sub-bands can select the same modulation order and also can select different modulation orders, so that the transmission method provided by the invention belongs to flexible mixed carrier transmission. Meanwhile, another core of the invention is that the filtering operation of each sub-band of the CP-free mixed carrier system is completed by utilizing the fast convolution, and the equalization processing and the corresponding matched filtering are completed at the receiving end based on the fast convolution algorithm aiming at the fast convolution filtering structure of the transmitter. The structure can effectively inhibit the out-of-band leakage of the sub-band, and is different from the traditional mixed carrier system, and the structure does not depend on the use of a CP (content provider), namely, the transmitting end transmits CP-free mixed carrier continuous flow.
As shown in fig. 1, for the system of the present invention, the modulation process may be mapped to a plurality of paths of multicarrier baseband signals, and the signals are first processed by WFRFT precoding to generate mixed carrier signals, and then processed by a synthesis filter bank, and the demodulation process may be mapped to baseband received signals, and then processed by an analysis filter bank and inverse precoding. Specifically, after each path of pre-coded signals are up-sampled and filtered by a corresponding interpolation filter, the signals are modulated to a certain carrier frequency and limited in a corresponding frequency band, and then are superposed to form a composite signal. The number of carriers is equal to the number of interpolation filters. At a receiving end, the synthesized signal is filtered and down-sampled by a group of sampling filters to respectively obtain original pre-coded signals of each path, and then the original signals are obtained through inverse pre-coding processing.
The system provided by the invention completes the realization of the interpolation filter in a fast convolution mode. For each subband, the mapping of the baseband signal can be considered to be done in an interpolation filtered manner. And the data transmitted for each sub-band is processed by a corresponding precoding. It can be assumed here that each sub-band continuous stream signal is a weighted fractional domain signal of the order- α, and after WFRFT transformation of the order- α, the original signal is transformed into a time domain signal by the weighted fractional domain signal of the order- α. The invention uses the overlap-and-hold method to complete the time-domain filtering process in the frequency domain, and similarly, the time-domain filtering process can be completed in the frequency domain by using the overlap-and-add method.
In the system provided by the invention, for each sub-band, the mapping of the baseband signal can be considered to be completed in a manner of interpolation filtering based on fast convolution. Each subband is fed as a continuous data stream, with k identifying the different subbands. Note Lk,bL is the length of the non-overlapping segment before and after interpolation, Nk,bWith N being the corresponding overlapping segment length, subscript b indicating Lk,bAnd Nk,bThe non-overlapping segment length and the overlapping segment length before interpolation for the k-th subband. Wherein N isk,b＝N/MkIs an integer, MkN is a power of 2 for the interpolation and sampling multiples of the kth subband.
The method comprises the following steps: continuous data stream D per sub-bandkIndependently generating K as 1,2, …, K as the number of sub-bands, and dividing DkDividing the data into P segments according to a given length Q, and adopting a precoding matrix to the P segment data stream
Figure BDA0001775085830000051
After precoding, obtaining precoded data
Figure BDA0001775085830000052
P is 1,2, …, P, and then the P segments of pre-coded data are spliced into a continuous data stream sk(n)，n＝0,1,…,m-1；
Step two: for the pre-coded continuous data stream sk(n) a length Lk,bFor the signal of the q-th block, denoted sk,q，sk,q＝[sk,q(0) sk,q(1)…sk,q(Lk,b-1)]T(ii) a Taking out three consecutive non-overlapping block signals sk,q-1,sk,q,sk,q+1Is N in the middlek,bOne symbol to obtain an overlapped block signal
Figure BDA0001775085830000053
Figure BDA0001775085830000054
Wherein N isk,b Is 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 blocksk,1,sk,2Anterior supplement Lk,bTaking out the middle N after zerok,bAnd (4) completing the overlapping block operation.
Step three: will overlap the block signal
Figure BDA0001775085830000061
Carry out Nk,bFourier transform of the points;
step four: directly copying the Fourier transform result to MkThe 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-bandkPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-bandk；
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
Figure BDA0001775085830000062
Step six: taking out
Figure BDA0001775085830000063
The middle L symbols of the output signal y (n) are obtained by completing the overlap-preserving operationq，yq＝[yq(0) yq(1)…yq(L-1)]T(ii) a Will obtain
Figure BDA0001775085830000064
A block signal yqSplicing to obtain y (n), and sending out the y (n) after up-conversion treatment; wherein 2L ═ N;
step seven: performing down-conversion processing on the received signals which are sent out in the sixth step and pass through the channel to obtain mixed carrier baseband signals r (n), and performing non-overlapping partitioning with the length of L on the mixed carrier baseband signals r (n); for the q-th block signal, denoted rq，rq＝[rq(0) rq(1)…rq(L-1)]T(ii) a Three consecutive non-overlapping block signals r are takenq-1,rq,rq+1Obtaining an overlapped block signal by the middle N symbols
Figure BDA0001775085830000065
Figure BDA0001775085830000066
Wherein L is a power of 2 and N is 2 times L;
step eight: will overlap the block signal
Figure BDA0001775085830000067
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 ninek,bInverse point Fourier transform to obtain
Figure BDA0001775085830000068
Figure BDA0001775085830000069
Wherein N isk,b＝2Lk,b，Lk,b＝L/Mk，MkThe interpolation multiple corresponding to the kth subband;
step eleven: reserving each partition
Figure BDA00017750858300000610
Middle L ofk,bData xk,qForm a data stream xk(ii) a Then divided into P sections according to the length Q, and each section is marked as
Figure BDA00017750858300000611
P is 1,2, …, P, each segment is inverse pre-coded
Figure BDA00017750858300000612
Is transformed to obtain
Figure BDA00017750858300000613
Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band
Figure BDA00017750858300000614
Abbreviation definition:
Figure BDA0001775085830000071
description of the main variables:
α modulation order of weighted Fourier transform
k Sub-band identification
Lk,b The length of the non-overlapping segment before the kth subband interpolation, b is an abbreviation for basic.
L Length of interpolated non-overlapping segments
Nk,b The length of the overlapping segment before the k-th subband interpolation, b is an abbreviation for basic.
N Length of interpolated overlapping segments
Mk Interpolation multiple and sampling multiple of kth sub-band
Q Segment length of continuous stream
P Number of segments of continuous stream
B Total bandwidth of system
β Roll-off coefficient of root-raised cosine filter
Filter specification and complexity analysis:
the invention takes a root raised cosine filter as an example and completes the equivalent operation of time domain filtering in a frequency domain by using a fast convolution mode. In the simulation example of the present invention, a root raised cosine filter with a roll-off coefficient β of 0.125 is used for illustration. The actual system can adjust the roll-off coefficient according to the requirement. The system of the present invention is not limited to the use of root raised cosine filters. There are related documents studying the optimal design method of the sub-band filter. In the literature (Yli-Kaakinen J, Renfors M. optimization of flexible filter base on fast-constraint [ C ]// IEEE International Conference on Acoustics, Speech and Signal processing. IEEE,2014:1-11), an optimization design method based on the criterion of minimizing the pass band and stop band fluctuations of the filter is proposed; in the literature (Yli-Kaakinen J, Renfors M. optimized burst centering in fast-dependent volume filter bank based generation [ C ]// IEEE, International Workshop on Signal Processing Advances in Wireless communications. IEEE,2015:71-75), a filter design method with time-frequency localization characteristics as the first objective is proposed. The skilled person can refer to the relevant information for filter design.
The invention has the advantages that aiming at the mixed carrier system, the filtering is completed by adopting a fast convolution mode, and compared with the traditional time domain filtering, the algorithm complexity is greatly reduced. Meanwhile, in the aspect of implementation, parallel processing can be used for fast convolution operation, and the processing speed is increased.
Compared with the traditional mixed carrier system, the system increases the operation of filtering and improves the algorithm complexity. But the operation based on fast convolution reduces the complexity significantly compared with the traditional time domain filtering.
In order to perform comparison under a unified standard, the total number of mixed carrier system carriers is set to be N, L subcarriers are actually used, and the complexity measure is the number of multiplication operations required for sending LU symbols. For comparison, a conventional OFDM system is also listed in table 1. For the system of the invention, for a certain normalized bandwidth is Nk,b(ii)/N and transmit UL using subband k of RRC filter with roll-off coefficient βk,bThe amount of computation required for a symbol can be approximated as (UL)k,blogQ+4ULk,b)+(UNlogN)+UNk,b(β+logNk,b). Wherein Q is ULk,bFormed by symbolsSegment length of the continuous stream.
TABLE 1 transmitter computation complexity for several multicarrier techniques
Figure BDA0001775085830000081
As shown in table 1, the approximate transmitter complexity for 4 systems is listed. For the system of the invention, the frequency domain filter coefficient is 0 on the stop band and is 1 on most pass bands, so the operation amount can be saved. However, the fast convolution operation reduces the computational efficiency to some extent by the overlap-and-hold operation before and after performing the fft/ifft calculation. For the time-domain filtering mixed carrier system, the filtering operation of time-domain linear convolution greatly improves the algorithm complexity. The filtering is finished in the frequency domain based on the fast convolution, and is essentially equivalent to the filtering finished in the time domain, so that the out-of-band leakage can be inhibited, and the algorithm complexity is greatly reduced. It is worth pointing out that the invention does not simply use fast convolution instead of time-domain filtering, but designs the structure of the traditional hybrid carrier receiver accordingly, so that the matching filtering and the equalization operation at the receiving end can be organically integrated. Thus, the mixed carrier signal is not dependent on the use of the CP, and the frequency spectrum efficiency is improved. However, each sub-band uses a root-raised cosine filter and then is mapped to a corresponding frequency band, and since a transition band is introduced for suppressing out-of-band, the number of sub-carriers occupied by each sub-band is increased, and the frequency spectrum efficiency is also reduced. Therefore, compared with a mixed carrier system of time domain filtering, the system provided by the invention can effectively improve the frequency spectrum efficiency. But with the unfiltered mixed carrier system, the spectral efficiency is not improved significantly.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, D iskDividing the data into P sections according to a given length Q, and precoding P section data streams by using a precoding matrix to obtain coded data
Figure BDA0001775085830000091
P is 1,2, …, P, and P segments are precodedAre spliced into a continuous data stream skThe specific process of (n) is as follows:
Dk＝[DT k,1 DT k,2…DT k,P]T
Dk,p＝[Dk,p(0) Dk,p(1)…Dk,p(Q-1)]T
Figure BDA0001775085830000092
Figure BDA0001775085830000093
wherein s iskIs s isk(n) a vector representation; dT k,1A transpose of the data signal representing the 1 st segment of the k-th sub-band; dT k,2A transpose of the data signal representing the 1 st segment of the k-th sub-band; dT k,PA transpose of the data signal representing the P-th segment of the k-th sub-band; dk,p(0) Representing the 1 st data signal point in the data signal of the p segment of the kth subband; dk,p(1) Representing the 2 nd data signal point in the data signal of the p segment of the kth subband; dk,p(Q-1) indicating a Q-th data signal point in the data signal of the p-th segment of the k-th subband;
Figure BDA0001775085830000094
the transposition of data obtained after precoding a data signal of a 1 st subsection of a kth sub-band is represented;
Figure BDA0001775085830000095
the transposition of data obtained after precoding a data signal of a 1 st subsection of a kth sub-band is represented;
Figure BDA0001775085830000096
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
Figure BDA0001775085830000097
αkA modulation order that is a weighted fractional fourier transform of subband k;
the matrix
Figure BDA0001775085830000101
The expression (c) is specifically:
Figure BDA0001775085830000102
wherein
Figure BDA0001775085830000103
Is a weighting coefficient defined as follows:
Figure BDA0001775085830000104
wherein IQIs a QxQ identity matrix, FQIs a qxq discrete fourier transform matrix; t isQIs a permutation matrix, and each row and each column only has one non-zero element, which is specifically expressed as follows:
Figure BDA0001775085830000105
additionally, the weighted fractional inverse Fourier transform can be expressed as
Figure BDA0001775085830000106
Namely, it is
Figure BDA0001775085830000107
Is composed of
Figure BDA0001775085830000108
A corresponding inverse precoding matrix. Alpha is alphakWith small scale k for distinguishing different sub-bandsThe weighted fourier transform modulation order α. Furthermore, according to the literature (Mei L, Sha X J, Ran Q W, et al]Science China (Information Sciences),2010,53(6): 1251-. From the above formula, the WFTFR transform is obtained by weighted summation of the original function and its fourier transformed function. At the same time, with alpha at [0,1 ]]And (4) internal change, wherein the specific gravity of the single carrier component and the multi-carrier component is changed. When alpha is 0, only a single carrier component exists, and the mixed carrier system becomes a single carrier system; when α is 1, only the multi-carrier component, the mixed carrier system becomes an OFDM system. The modulation order alpha can be limited to [0,1 ]]In the method, the proportion of single carrier and multi-carrier is adjusted by freely selecting alpha to play the advantage of resisting channel distortion, which is the mechanism of mixed carrier modulation.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: as shown in fig. 10, in the second step, three consecutive non-overlapping block signals s are extractedk,q-1,sk,q,sk,q+1Is N in the middlek,bOne symbol to obtain an overlapped block signal
Figure BDA0001775085830000111
The expression of (a) is:
Figure BDA0001775085830000112
wherein R isbThe block matrices are overlapped for the transmitter,
Figure BDA0001775085830000113
Figure BDA0001775085830000114
is Nk,bIdentity matrix of order, note 2Lk,sFor adjacent overlapping blocks between signalsThe number of overlapping samples of (1), thenk,b＝Lk,b+2Lk,s(ii) a The invention takes Lk,s＝L k,b2, i.e. Nk,b＝2Lk,b(ii) a It is worth pointing out that 2Lk,sThe length of (c) 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 discussed.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: in the fourth step, the Fourier transform result is directly copied into MkThe 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-bandkPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-bandkThe specific process comprises the following steps:
Figure BDA0001775085830000115
wherein,
Figure BDA0001775085830000116
is Nk,bA matrix of point-fourier transforms is formed,
Figure BDA0001775085830000117
Figure BDA0001775085830000118
representing the gain-corrected filter coefficient matrix, BkIs the 3dB bandwidth of the kth subband filter; mkRepresenting the interpolation multiple, for all subbands, there is Lk,bMk＝N。ΛkRepresenting an NxN matrix, Λ, with the frequency domain response of the interpolation filter corresponding to the kth subband as diagonal elementsk＝diag(ek) Diag (·) denotes generating a diagonal matrix with a number in parentheses as a diagonal element;
Figure BDA0001775085830000119
Figure BDA00017750858300001110
represents MkA full 1 matrix of rows and columns,
Figure BDA00017750858300001111
represents Nk,bA unit matrix of an order of a plurality of units,
Figure BDA00017750858300001112
representing the Kronecker product.
Each sub-band 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 by selecting the frequency domain coefficient of a root raised cosine filter, and the maximum weight in a passband is set to be 1. If the center frequency of the sub-band is to be adjusted, (1+ β) Nk,bThe non-zero value of (a) is shifted on the FFT unit at N points, and the frequency change (i.e., frequency resolution) Δ f corresponding to the minimum shift distance is equal to B/N, where B is the total bandwidth of the system. Correspondingly, the matched filter corresponding to the receiving end does the same movement.
Coefficient e of the frequency domain filterkIs generated according to the normalized frequency domain formula h (f) of the root-raised cosine filter by direct sampling:
Figure BDA0001775085830000121
the 3dB bandwidth of the frequency domain filter is Nk,bPoint, ekThe total number of points of (1+ beta) N is N points, and the number of non-zero points is (1+ beta) Nk,bAnd (4) point. Wherein beta is the roll-off coefficient, f0＝Δf·Nk,b(iii) a cutoff frequency, [ delta ] f a frequency resolution, [ delta ] f a frequency, discrete sampling of f,
Figure BDA0001775085830000122
resulting in non-zero values for the filter coefficients.
Other steps and parameters are the same as those in one of the first to third embodiments.
Detailed DescriptionFifthly: the difference between this embodiment and one of the first to fourth embodiments is: in the fifth step, the results of the frequency domain filtering of each sub-band obtained in the fourth step are added and then N-point Fourier inverse transformation is carried out to obtain
Figure BDA0001775085830000123
The method specifically comprises the following steps:
Figure BDA0001775085830000124
wherein,
Figure BDA0001775085830000125
is FNConjugate transpose matrix, FNIs an N-point Fourier transform matrix, [ F ]N]p,d＝N-1/2e-j2π(p-1)(d-1)/N。
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: the block signal y in the sixth stepqThe expression of (a) is:
Figure BDA0001775085830000126
where O is the transmitter overlap reservation matrix, and O ═ 0L×L/2 IL 0L×L/2]，ILIs an identity matrix of order L.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is: overlapping the block signals in the step seven
Figure BDA0001775085830000127
The expression of (a) is:
Figure BDA0001775085830000128
wherein, R is a receiver overlapped block matrix, and R is [0 ]N×(L-L/2) IN 0N×(L-L/2)]，INIs an identity matrix of order N.
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The specific implementation mode is eight: the present embodiment differs from one of the first to seventh embodiments 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-bandskAfter multiplication and combination, performing point multiplication with the Fourier transform result of the N points; the result is expressed in length Nk,bAre equally divided into MkSegment, overlap, finish the down-sampling filtering, get the data Q after the Q subsection of the kth sub-bandk,q(ii) a The different equalization criteria are a zero forcing criterion and a minimum mean square error criterion;
Figure BDA0001775085830000131
here, ETFor the transposition of E, the invention adopts a pair of sampling filter and interpolation filter, so the coefficient matrix pi of the filter after the gain correction of the receiving endkAs with the transmitter. Phi is a frequency domain equalization coefficient matrix which can be obtained according to a ZF criterion or an MMSE criterion;
the equalization coefficient matrix Φ is specifically:
when the minimum mean square error criterion is adopted, the equalization coefficient matrix Φ is:
Figure BDA0001775085830000132
when the zero forcing criterion is adopted, the equalization coefficient matrix Φ is:
Φ＝diag(1/hi),i＝1,2,…,N
wherein h isiIs composed of
Figure BDA0001775085830000133
Main diagonal element of (1), HN×NFor a multipath channel matrix, FNIs a Fourier transform matrix of N dimensions,
Figure BDA0001775085830000134
is FNConjugate transpose matrix of σ2In order to be the variance of the noise,
Figure BDA0001775085830000135
is hiConjugation of (1).
At a receiving end, the sampling filtering is completed by adopting a fast convolution mode. The equalization process is added and its implementation block diagram is shown in fig. 2. In fig. 2, the stopband portion of the filter is 0, and after being multiplied by the equalization coefficient and combined, the stopband portion remains 0, which is not shown in the figure.
It can be seen that a simple single point tap equalization is used and the equalizer coefficients can be combined by multiplication with the filter coefficients. The feasibility of this simplified single-tap equalizer design concept is described in the literature (Zhao J, Wang W, Gao x. driver design for fast-dependent multiplexing systems in multiplexing channels C]//International Conference on Wireless Communications&Signal processing. ieee,2015: 1-5). The invention combines different weighted transformation modulation orders and carries out simulation verification under different equilibrium criteria. In order to minimize the inter-segment interference, the overlap between segments should be significantly larger than the channel length. At the same time, a multipath channel matrix HN×NIt is progressively diagonalized by the fourier transform matrix, the degree of diagonalization increasing with the number N of fourier transform points. That is, the larger N is, the greater the element h of the principal diagonal is takeniThe generated equalization coefficient has better compensation effect on channel distortion.
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: the present embodiment differs from the first to eighth embodiments in that: in the step ten, N is carried out on the data after the equalization and the sub-band filtering in the step ninek,bInverse point Fourier transform to obtain
Figure BDA0001775085830000141
The expression of (a) is:
Figure BDA0001775085830000142
wherein
Figure BDA0001775085830000143
Is Nk,bAnd (4) a point Fourier inverse transformation matrix.
Other steps and parameters are the same as those in one to eight of the embodiments.
The detailed implementation mode is ten: the present embodiment differs from one of the first to ninth embodiments in that: the first step is to reserve each block
Figure BDA0001775085830000144
Middle L ofk,bData xk,qForm a data stream xk(ii) a Then divided into P sections according to the length Q, and each section is marked as
Figure BDA0001775085830000145
Each segment is respectively carried out inverse precoding
Figure BDA0001775085830000146
Is transformed to obtain
Figure BDA0001775085830000147
Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band
Figure BDA0001775085830000148
The method specifically comprises the following steps:
Figure BDA0001775085830000149
Figure BDA00017750858300001410
Figure BDA00017750858300001411
Figure BDA00017750858300001412
Figure BDA00017750858300001413
wherein, ObThe matrix is reserved for the receiver overlap-add,
Figure BDA00017750858300001414
Figure BDA00017750858300001415
is Lk,bAn identity matrix of order. x is the number ofT k,1A transpose representing the 1 st non-overlapping block data signal of the kth sub-band; x is the number ofT k,2Representing a transpose of the kth subband 2 nd non-overlapping block data signal;
Figure BDA0001775085830000151
indicating the kth sub-band
Figure BDA0001775085830000152
Transposing of non-overlapping block data signals; data stream xkBy
Figure BDA0001775085830000153
Individual non-overlapping block data xk,qSplicing, dividing into P sections according to length Q, and recording each section of data signal as
Figure BDA0001775085830000154
Figure BDA0001775085830000155
A transpose of the data signal representing the 1 st segment of the k-th sub-band;
Figure BDA0001775085830000156
a transpose of the data signal representing the 2 nd segment of the kth subband;
Figure BDA0001775085830000157
a transpose of the data signal representing the P-th segment of the k-th sub-band;
Figure BDA0001775085830000158
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;
Figure BDA0001775085830000159
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;
Figure BDA00017750858300001510
the transposition of a result obtained after the inverse pre-coding transformation of the data of the P-th subsection of the kth sub-band is shown;
other steps and parameters are the same as those in one of the first to ninth embodiments.
The first embodiment is as follows:
the most significant advantage of the proposed system over conventional mixed carrier systems is the steep out-of-band attenuation. Out-of-band leakage can bring signal interference among sub-bands, so that the system provided by the invention has fast out-of-band attenuation and can better utilize 'gaps' among fragmented frequency spectrum resources.
The basic simulation parameters are set as follows: modulation order α of weighted transform is 0.5, N is 2048, L is 1024, root-raised cosine filter roll-off coefficient β is 0.125, length Q of precoding by weighted transform for segment of continuous stream is 64, and length N of overlapped block is setk,b128, copiesThe real intermediate initial data signals are generated by adopting 4QAM modulation, and channel coding is not used. In the simulation, the same overlapped block length and the same weighted transform modulation order are used for each sub-band. Fig. 3 compares the power spectrum of a certain subband of the system proposed by the present invention using a root raised cosine filter with the power spectrum of a conventional hybrid carrier system without using a root raised cosine filter for filtering. In the simulation, the roll-off factor β of the root-raised cosine filter used is 0.125. As can be seen from fig. 3, the system proposed by the present invention can suppress side lobes well. Meanwhile, the power spectrum of the modulated signal of the system provided by the invention is compared with the power spectrum of the modulated signal of the traditional mixed carrier system under the same spectrum efficiency. The number of carriers actually used by both systems is 1024. As a result, as shown in FIG. 4, the interference between adjacent subbands is-30 dB or less, and the interference between subbands is small. It should be noted that, in the system of the present invention, the bandwidth and the center frequency of each sub-band can be freely adjusted. And, the out-of-band rejection performance can be changed by changing the roll-off coefficient of the filter.
The peak-to-average power ratio (PAPR) is defined as the ratio of the maximum instantaneous power of a signal to the average power:
Figure BDA0001775085830000161
where s (n) represents the transmitted time-domain signal, E [ ·]Indicating the expected value. There is a maximum power limit for the power amplifier of the transmitter of the wireless communication system. In order to ensure that the signal is not distorted non-linearly after passing through the power amplifier, it is required that the power amplifier operates in a linear operating region, i.e. 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 may compromise the communication performance of the system. A Complementary Cumulative Distribution Function (CCDF) is used to evaluate the PAPR performance of the system, which is defined as the actual PAPR of the signal exceeding the PAPR threshold0Probability of (c):
CCDF＝Pr[PAPR>PAPR0]
wherein Pr [. cndot. ] represents the probability. It is known that for mixed carrier systems, the PAPR value is between OFDM systems and DFT-S-OFDM (sars army, mellin, zungyu weighted fractional fourier transform and its application in communication systems [ M ]. people post press, 2016: 81-83). And the OFDM system and the DFT-S-OFDM system are mixed carrier systems under a specific weighted transformation modulation order. The filtering mixed carrier system based on the fast convolution provided by the invention not only reserves the flexibility of adjusting the PAPR of the traditional mixed carrier system according to different modulation orders, but also can further reduce the PAPR to a certain extent through the filtering operation.
Fig. 5 illustrates a single subband, comparing the PAPR characteristic of the inventive system with that of a conventional mixed carrier system. In simulation, basic simulation parameters are the same as above, a 4QAM modulation mode is adopted, and the number of occupied sub-carriers corresponding to 3dB bandwidth of a sub-band of the system is 128 (N)k,b128) for each subband, the remaining system single subbands each occupy 128 subcarriers. It can be seen from the figure that, when a single subband is used for transmitting data by one user, the PAPR of the signal at the transmitting end of the system of the present invention is significantly smaller than the PAPR of the conventional mixed carrier system. Here, OFDM may be regarded as a mixed carrier system where α is 1, and DFT-S-OFDM may be regarded as a mixed carrier system where α is 0. Under the same modulation order, the PAPR performance of the system of the invention is superior to that of the traditional mixed carrier system. And, for the system of the present invention, when the original data to be transmitted is a time domain signal, that is, α is 0, it has the best PAPR performance.
Example two:
this embodiment simulates the bit error rate performance of the method of the present invention.
Based on the introduction of the system receiver of the invention, the receiver adopts the equalizer design based on the fast convolution at the receiving end in combination with the characteristics of the system. The receiver design no longer requires the transmitted signal to carry the cyclic prefix CP. The system of the invention does not depend on a CP structure, improves the spectrum efficiency, and simultaneously can achieve the bit error rate performance which is close to that of the original mixed carrier system under the frequency selection channel. The invention provides that a proper modulation order can be selected at a transmitting end according to the balancing rule based on ZF or MMSE adopted by balancing and the requirement of a system on PAPR. It should be noted that each subband may select a different modulation order α according to different requirements. And the simulation of the present invention is illustrated with a single subband. In the case of a multi-subband system, the error rate of each subband can be averaged. Meanwhile, in the following simulation, the segment length Q for precoding of the continuous stream segments is set to 64.
The system of the invention is simulated under a fixed frequency-selective channel. Simulation Using three-Path channels, channel delay [0, 5, 10 ]]Chip, channel impulse response of [1, -0.5, 0.3%]And carrying out energy normalization processing. The basic parameters are set as follows: the modulation order α of the weighted transform is 0, 0.5, 1, N is 2048, L is 1024, the RRC filter roll-off coefficient β is 0.125, and the single subband occupies 128 subcarriers, i.e., Nk,b128. The initial continuous flow signals are generated by adopting 4QAM modulation, and channel coding is not used. The receiving end assumes ideal channel state information.
As can be seen from fig. 6 and fig. 7, for the system of the present invention, when the higher the single carrier component included in the data transmitted by the sub-band, the more similar the sub-band is to the wideband single carrier system, the better the frequency diversity can be utilized, and the better the bit error rate performance.
Under the random frequency selection channel, Monte Carlo simulation is carried out on the performance of the system. The relative time delay of each path is [0, 10, 20, 30, 50, 70 ]]Each chip, the average power of each path is [0, -3.6, -7.2, -10.8, -18, -25.2%]dB. The basic parameters are set as follows: the modulation order α of the weighted transform is 0, 0.5, 1, N is 2048, L is 1024, the RRC filter roll-off coefficient β is 0.125, and the single subband occupies 128 subcarriers, i.e., Nk,b128. The initial continuous flow signals are generated by adopting 4QAM modulation, and channel coding is not used. In order to reflect the randomness of the fading channel, 1000 random channels are generated, and each channel is simulated 1000 times and averaged.
As can be seen from fig. 8 and fig. 9, in the random frequency selective channel, the hybrid carrier system based on fast convolution filtering according to the present invention exhibits different bit error rate performances under different equalization laws and different weighting modulation order α precoding. Under the ZF criterion, when the sub-band transmits multi-carrier data (i.e., α ═ 1), the best bit error rate performance is achieved. Under the MMSE criterion, when a sub-band transmits single carrier data (i.e., 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 performs equalization by using the ZF criterion, the modulation order α of the precoding matrix may be selected to be 1; and if the receiver adopts the MMSE criterion for equalization, selecting the modulation order alpha of the precoding matrix to be 0. Meanwhile, the modulation order also affects the size of the PAPR. The PAPR is smaller when the system single carrier component is more, i.e., α is close to 0. Therefore, the system can select a proper modulation order alpha by combining the requirement of the system on the PAPR and considering the equalization rule adopted by the receiver.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope 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-bandkIndependently generating K as 1,2, …, K as the number of sub-bands, and dividing DkDividing 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
Figure FDA0002769770300000011
Then splicing the P sections of pre-coded data into a continuous data stream sk(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 sk(n) a length Lk,bFor the signal of the q-th block, denoted sk,q，
Figure FDA0002769770300000012
Take out three consecutive capsulesOverlapping block signals sk,q-1,sk,q,sk,q+1Is N in the middlek,bOne symbol to obtain an overlapped block signal
Figure FDA0002769770300000013
Wherein N isk,bIs Lk,b2 times of the total weight of the composition; when q is 1, the blocking signal s is not overlapped in two consecutive blocksk,1,sk,2Anterior supplement Lk,bTaking out the middle N after zerok,bSymbol, finishing the overlapping block operation;
step three: will overlap the block signal
Figure FDA0002769770300000014
Carry out Nk,bFourier transform of the points;
step four: directly copying the Fourier transform result to MkThe 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-bandkPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-bandk；
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
Figure FDA0002769770300000015
Step six: taking out
Figure FDA0002769770300000016
The middle L symbols of the output signal y (n) are obtained by completing the overlap-preserving operationq(ii) a Will obtain
Figure FDA0002769770300000017
A block signal yqSplicing 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 rqTaking out three continuous non-overlapping block signals rq-1,rq,rq+1Obtaining an overlapped block signal by the middle N symbols
Figure FDA0002769770300000018
Wherein L is a power of 2 and N is 2 times L;
step eight: will overlap the block signal
Figure FDA0002769770300000019
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 ninek,bInverse point Fourier transform to obtain
Figure FDA0002769770300000021
Wherein N isk,b＝2Lk,b，Lk,b＝L/Mk，MkThe interpolation multiple corresponding to the kth subband;
step eleven: reserving each partition
Figure FDA0002769770300000022
Middle L ofk,bData xk,qForm a data stream xk(ii) a Then divided into P sections according to the length Q, and each section is marked as
Figure FDA0002769770300000023
Each segment is respectively carried out inverse precoding
Figure FDA0002769770300000024
Is transformed to obtain
Figure FDA0002769770300000025
Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band
Figure FDA0002769770300000026
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 iskDividing 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
Figure FDA0002769770300000027
Then splicing the P sections of pre-coded data into a continuous data stream skThe specific process of (n) is as follows:
Dk＝[DT k,1 DT k,2…DT k,P]T
Dk,p＝[Dk,p(0) Dk,p(1)…Dk,p(Q-1)]T
Figure FDA0002769770300000028
Figure FDA0002769770300000029
wherein s iskIs s isk(n) a vector representation; dT k,1A transpose of the data signal representing the 1 st segment of the k-th sub-band; dT k,2A transpose of the data signal representing the 2 nd segment of the kth subband; dT k,PA transpose of the data signal representing the P-th segment of the k-th sub-band; dk,p(0) Representing the 1 st data signal point in the data signal of the p segment of the kth subband; dk,p(1) Representing the 2 nd data signal point in the data signal of the p segment of the kth subband; dk,p(Q-1) indicating a Q-th data signal point in the data signal of the p-th segment of the k-th subband;
Figure FDA00027697703000000210
the transposition of data obtained after precoding a data signal of a 1 st subsection of a kth sub-band is represented;
Figure FDA00027697703000000211
the data transposition obtained after precoding the data signal of the 2 nd subsection of the kth sub-band is shown;
Figure FDA00027697703000000212
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
Figure FDA0002769770300000031
αkA modulation order that is a weighted fractional fourier transform of subband k;
the matrix
Figure FDA0002769770300000032
The expression (c) is specifically:
Figure FDA0002769770300000033
wherein
Figure FDA0002769770300000034
Is a weighting coefficient defined as follows:
Figure FDA0002769770300000035
wherein IQIs a QxQ identity matrix, FQIs QxQ discreteA Fourier transform matrix; t isQIs a permutation matrix, and each row and each column only has one non-zero element, which is specifically expressed as follows:
Figure FDA0002769770300000036
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 stepk,q-1,sk,q,sk,q+1Is N in the middlek,bOne symbol to obtain an overlapped block signal
Figure FDA0002769770300000037
The expression of (a) is:
Figure FDA0002769770300000038
wherein R isbThe block matrices are overlapped for the transmitter,
Figure FDA0002769770300000039
Figure FDA00027697703000000310
is Nk,bIdentity matrix of order, note 2Lk,sFor the number of overlapping samples between adjacent overlapping block signals, then Nk,b＝Lk,b+2Lk,s(ii) a Get Lk,s＝Lk,b2, i.e. Nk,b＝2Lk,b。
4. The method of claim 3, wherein the method comprises: in the fourth step, the Fourier transform result is directly copied into MkSplicing 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 filterkPerforming point multiplication to complete frequency domain filtering to obtain frequency domain filtered result P of each sub-bandkThe specific process comprises the following steps:
Figure FDA0002769770300000041
wherein,
Figure FDA0002769770300000042
is Nk,bA matrix of point-fourier transforms is formed,
Figure FDA0002769770300000043
representing the gain-corrected filter coefficient matrix, BkIs the 3dB bandwidth of the kth subband filter; mkRepresenting the interpolation multiple, for all subbands, there is Lk,bMk＝N；ΛkRepresenting an NxN matrix, Lambda, with the frequency-domain response of the interpolation filter as diagonal elementsk＝diag(ek)，
Figure FDA0002769770300000044
Representing the generation of a diagonal matrix with the numbers in brackets as diagonal elements;
Figure FDA0002769770300000045
Figure FDA0002769770300000046
represents MkA full 1 matrix of rows and columns,
Figure FDA0002769770300000047
represents Nk,bA unit matrix of an order of a plurality of units,
Figure FDA0002769770300000048
represents the Kronecker product;
coefficient e of the frequency domain filterkIs based on root balanceNormalized frequency domain equation h (f) for the chord filter direct sampling generation:
Figure FDA0002769770300000049
wherein beta is the roll-off coefficient, f0＝△f·Nk,bIs the cut-off frequency, Δ f is the frequency resolution, f is the frequency;
the 3dB bandwidth of the frequency domain filter is Nk,bPoint, ekThe total number of points of (1+ beta) N is N points, and the number of non-zero points is (1+ beta) Nk,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
Figure FDA00027697703000000410
The method specifically comprises the following steps:
Figure FDA00027697703000000411
wherein,
Figure FDA00027697703000000412
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 stepqThe expression of (a) is:
Figure FDA00027697703000000413
wherein O is reserved for transmitter overlapMatrix, O ═ 0L×L/2 IL 0L×L/2]，ILIs an identity matrix of order L.
7. The method of claim 6, wherein the method comprises: overlapping the block signals in the step seven
Figure FDA0002769770300000051
The expression of (a) is:
Figure FDA0002769770300000052
wherein, R is a receiver overlapped block matrix, and R is [0 ]N×(L-L/2) IN 0N×(L-L/2)]，INIs 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-bandskAfter multiplication and combination, performing point multiplication with the Fourier transform result of the N points; the result is expressed in length Nk,bAre equally divided into MkSegment, overlap, finish the down-sampling filtering, get the data Q after the Q subsection of the kth sub-bandk,q(ii) a The different equalization rules are zero forcing criterion and minimum mean square error criterion;
Figure FDA0002769770300000053
here, ETIs the transpose of E; because the invention adopts paired sampling filters andinterpolation filter, so the gain corrected filter coefficient matrix pi of the receiving endkSame 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:
Figure FDA0002769770300000054
when the zero forcing criterion is adopted, the equalization coefficient matrix Φ is:
Φ＝diag(1/hi),i＝1,2,…,N
wherein h isiIs composed of
Figure FDA0002769770300000055
Main diagonal element of (1), HN×NFor a multipath channel matrix, FNIs a Fourier transform matrix of N dimensions,
Figure FDA0002769770300000061
is FNConjugate transpose matrix of σ2In order to be the variance of the noise,
Figure FDA0002769770300000062
is hiConjugation 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 ninek,bInverse point Fourier transform to obtain
Figure FDA0002769770300000063
The expression of (a) is:
Figure FDA0002769770300000064
wherein
Figure FDA0002769770300000065
Is Nk,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
Figure FDA0002769770300000066
Middle L ofk,bData xk,qForm a data stream xk(ii) a Then divided into P sections according to the length Q, and each section is marked as
Figure FDA0002769770300000067
Each segment is respectively carried out inverse precoding
Figure FDA0002769770300000068
Is transformed to obtain
Figure FDA0002769770300000069
Then combining the P results after inverse pre-coding to obtain the receiving signal of each sub-band
Figure FDA00027697703000000610
The method specifically comprises the following steps:
Figure FDA00027697703000000611
Figure FDA00027697703000000612
Figure FDA00027697703000000613
Figure FDA00027697703000000614
Figure FDA00027697703000000615
wherein, ObThe matrix is reserved for the receiver overlap-add,
Figure FDA00027697703000000616
Figure FDA00027697703000000617
is Lk,bAn identity matrix of order;
xT k,1a transpose representing the 1 st non-overlapping block data signal of the kth sub-band; x is the number ofT k,2Representing a transpose of the kth subband 2 nd non-overlapping block data signal;
Figure FDA00027697703000000618
indicating the kth sub-band
Figure FDA00027697703000000619
Transposing of non-overlapping block data signals; data stream xkBy
Figure FDA00027697703000000620
Individual non-overlapping block data xk,qSplicing, dividing the signal into P sections according to the length Q, and recording each section of data signal as
Figure FDA0002769770300000071
Figure FDA0002769770300000072
A transpose of the data signal representing the 1 st segment of the k-th sub-band;
Figure FDA0002769770300000073
a transpose of the data signal representing the 2 nd segment of the kth subband;
Figure FDA0002769770300000074
a transpose of the data signal representing the P-th segment of the k-th sub-band;
Figure FDA0002769770300000075
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;
Figure FDA0002769770300000076
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;
Figure FDA0002769770300000077
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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