CN109547181B - Short filter, single carrier system and multi-carrier system - Google Patents

Short filter, single carrier system and multi-carrier system Download PDF

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CN109547181B
CN109547181B CN201811169369.XA CN201811169369A CN109547181B CN 109547181 B CN109547181 B CN 109547181B CN 201811169369 A CN201811169369 A CN 201811169369A CN 109547181 B CN109547181 B CN 109547181B
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屈代明
田苑
刘泽
江涛
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Huazhong University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0048—Allocation of pilot signals, i.e. of signals known to the receiver
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H04L27/3444—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power by applying a certain rotation to regular constellations
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits
    • H04L27/3845—Demodulator circuits; Receiver circuits using non - coherent demodulation, i.e. not using a phase synchronous carrier
    • H04L27/3854—Demodulator circuits; Receiver circuits using non - coherent demodulation, i.e. not using a phase synchronous carrier using a non - coherent carrier, including systems with baseband correction for phase or frequency offset
    • H04L27/3872—Compensation for phase rotation in the demodulated signal

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Abstract

The invention discloses a short filter, a single carrier system and a multi-carrier system, comprising: the length of the short wave filter is set as M +1, and the impulse response sequence is as follows: g (k), k ═ M/2., M/2, where k denotes the sample point number; the impulse response sequence needs to satisfy the following conditions: the impulse response sequence is symmetrical about an original point, and the value of the impulse response sequence at the original point is A; the sum of squares of any two points of the impulse response sequence which is symmetrical about k-M/4 is A2(ii) a The frequency response sequence corresponding to the impulse response sequence is M-order discrete Fourier transform of the impulse response sequence, the frequency response sequence is symmetrical about an original point, the value of the frequency response sequence at the original point is 0, and the number of effective frequency points of the frequency response sequence is 2L-1. A multicarrier system includes the short wave filter. The invention reduces the computational complexity in a filter bank communication system.

Description

Short filter, single carrier system and multi-carrier system
Technical Field
The present invention relates to the field of wireless communication technologies, and in particular, to a short filter, a single carrier system, and a multi-carrier system.
Background
However, in the case of implementing the FBMC system by Fast Fourier Transform (FFT), the longer the Filter length is, the more the number of FFT points is, the higher the processing complexity is, and meanwhile, the transmission delay of the signal is determined by the signal length, the longer the Filter length is, the longer the signal length is, and the longer the tail is, the larger the transmission delay is, and the larger the transmission delay is.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to solve the technical problems of high processing complexity and high processing delay caused by overlong length of a filter in the prior communication system.
In order to achieve the above object, in a first aspect, the present invention provides a short filter, in a general case, the number of nonzero coefficients of the filter used in the FBMC system is KM +1, and K is a natural number greater than 1, and the number of nonzero coefficients of the short filter designed in the present invention is equal to or less than M, where M is the total carrier number of the FBMC system and is also the number of sampling points in complex symbol intervals of the FBMC. The specific design method comprises the following steps: the length of the short wave filter is M +1, and the impulse response sequence is as follows: g (k), wherein k is-M/2.., M/2, where k denotes a sample point number and M is an even number;
the impulse response sequence is symmetrical about an original point, and the value of the impulse response sequence at the original point is A, wherein A is a natural number;
the sum of squares of any two points of the impulse response sequence which is symmetrical about k-M/4 is A2；
The frequency response sequence corresponding to the impulse response sequence is M-order discrete Fourier transform of the impulse response sequence, the frequency response sequence is symmetrical about an original point, the value of the frequency response sequence at the original point is 0, the number of effective frequency points of the frequency response sequence is 2L-1, and L is an integer greater than or equal to 1.
Optionally, the impulse response sequence is symmetric about an origin, and a value at the origin is a, specifically:
Figure GDA0002305589520000021
optionally, the sum of squares of any two points of the impulse response sequence symmetric about k-M/4 is a2The method specifically comprises the following steps:
g(M/4-k)2+g(M/4+k)2＝A2,0≤k≤M/4。
optionally, the frequency response sequence corresponding to the impulse response sequence is M-order discrete fourier transform of the impulse response sequence, the frequency response sequence is symmetric with respect to an origin, and a value at the origin is 0, the number of effective frequency points of the frequency response sequence is 2L to 1, specifically:
Figure GDA0002305589520000022
wherein g (f) represents a frequency response sequence.
Alternatively, when L is 3, the number of effective frequency points of the short filter is 5, and the corresponding short filter is expressed as:
from the three samples 0, M/4, M/2, the following system of equations is obtained according to the conditions given above:
Figure GDA0002305589520000031
solving to obtain: g (0) ═ 0.6036a, G (± 1) ═ 0.25A, G (± 2) ═ 0.0518A.
Alternatively, when L is 4, the number of effective frequency points of the short filter is 7, and the corresponding short filter is expressed as:
Figure GDA0002305589520000032
taking four sampling points of 0, M/8, M/4 and M/2, the following equation system is obtained:
Figure GDA0002305589520000033
solving to obtain: g (0) ═ 0.6036A, G (± 1) ═ 0.2553A, G (± 2) ═ 0.0518A, G (± 3) ═ 0.0053A.
Alternatively, the short filter may be applied to a filter bank-based multi-carrier system and a filter bank-based single-carrier system.
In a second aspect, the present invention provides a single carrier system, where the single carrier system operates based on a filter bank, each filter operates on a different subcarrier, and the filter in the filter bank is the short filter provided in the first aspect;
the single carrier system divides the data symbols to be sent into data symbol segments and sequences the data symbol segments, processes the data symbol segments to be sent according to the sequence numbers of the data symbol segments, comprises windowing and FFT, and adopts the short filter to map the processed data symbols to a plurality of subcarriers.
Optionally, the single carrier system multiplies the short filter filtered symbols by
Figure GDA0002305589520000041
And then modulated onto different subcarriers.
In a third aspect, the present invention provides a multi-carrier system, where the multi-carrier system works based on a filter bank, each filter works on a different subcarrier, and a filter in the filter bank is the short filter provided in the first aspect;
and the multi-carrier system multiplies a real number symbol sequence to be sent by a phase twiddle factor to obtain a real and imaginary staggered symbol sequence, and maps the processed data symbols to a plurality of subcarriers by adopting the short filter.
Alternatively, let am,nIs a real number symbol to be sent, m represents a subcarrier sequence number, and n represents a time sequence number; the multi-carrier system will am,nMultiplied by a phase rotation factor
Figure GDA0002305589520000042
After a, am,nChanging original real number into real-imaginary interleaving, and multiplying the short-filter-filtered symbol by
Figure GDA0002305589520000043
And then modulated onto different subcarriers.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
the length of the filter provided by the invention is set to be the same as the total number of the subcarriers of the filter bank, and the frequency response sequence of the filter takes a non-zero value only at a finite point, so that the computational complexity of the filter bank-based communication system is reduced.
The method obtains the unit impulse response function of the filter through inverse Fourier transform based on the finite frequency points, establishes an equation set with the frequency domain response function as an unknown number according to set conditions, and solves the equation set, so that the calculation complexity is reduced.
Drawings
Fig. 1 is a block diagram of a transmitting end of an FBMC system based on a filter bank according to the present invention;
fig. 2 is a block diagram of a receiving end of an FBMC system based on a filter bank according to the present invention;
fig. 3 is a schematic diagram of a specific implementation framework of a transmitting end of an FBMC system based on a filter bank according to the present invention;
fig. 4 is a schematic diagram of a unit impulse response function of a prototype filter provided by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a short filter, comprising: the length of the short filter is set to be the same as the total number of sub-carriers of the filter bank, and the frequency response sequence of the short filter takes a non-zero value only at a finite point so as to reduce the computational complexity in the filter bank communication system. Based on the finite frequency point number, a unit impulse response function of the prototype filter is obtained through inverse Fourier transform, an equation set with the frequency domain response function as an unknown number is established according to specific conditions, and solution is carried out.
Optionally, the present invention provides a short filter, the length of the prototype filter is set to be LgM +1, its impulse response sequence is:
g(k),k＝-M/2,...,M/2
wherein k represents the serial number of the sampling point, and the impulse response of the designed filter needs to satisfy the following conditions:
(1) symmetrical about the origin, and the value at the origin is A;
g(0)＝A；
g(k)＝g(-k),k＝-M/2,...,M/2
(2) the sum of squares between any two points symmetric about k-M/4 is A2；
g(M/4-k)2+g(M/4+k)2＝A2,0≤k≤M/4
(3) The sequence of frequency responses corresponding to g (k) is noted as:
Figure GDA0002305589520000051
g (f) is M-order discrete Fourier transform of g (k), wherein f is an integer and represents the f-th frequency point, and the f-th frequency point satisfies the following conditions: g (f) ≧ G (-f), and for | f ≧ L, G (f) ≧ 0, i.e., the number of effective frequency points is 2L-1.
Therefore, combining the above conditions, the prototype filter should be designed to satisfy the following equation set:
Figure GDA0002305589520000061
and solving the above equation set to obtain the impulse corresponding sequence of the filter.
In a specific embodiment, let the number of effective frequency points of the filter be 5, i.e. L equals 3, and the corresponding short filter is expressed as:
Figure GDA0002305589520000062
from the three samples 0, M/4, M/2, the following system of equations is obtained according to the conditions given above:
Figure GDA0002305589520000063
solving to obtain: g (0) ═ 0.6036a, G (± 1) ═ 0.25A, G (± 2) ═ 0.0518A.
In a specific embodiment, assuming that the number of effective frequency points of the filter is 7, i.e., L is 4, the short filter can be expressed as:
Figure GDA0002305589520000064
taking four samples of 0, M/8, M/4, and M/2 according to the conditions given above, the following equation is obtained:
Figure GDA0002305589520000071
solving to obtain: g (0) ═ 0.6036A, G (± 1) ═ 0.2553A, G (± 2) ═ 0.0518A, G (± 3) ═ 0.0053A.
Alternatively, the filter designed according to the above method can be applied to a filter bank based multi-carrier system (FBMC), and the specific steps of the transmitting end are shown in fig. 1, where am,nIs a real number symbol, m represents a subcarrier number, n represents a time number, am,nMultiplied by a phase rotation factor
Figure GDA0002305589520000072
Then, the original full real number is changed into real-imaginary interleaving, and the obtained real-imaginary interleaving symbol sequence is processed by
Figure GDA0002305589520000073
Multiple upsampling, filtering with the filter described above, and multiplying
Figure GDA0002305589520000074
Modulating the signals to different carriers, adding the signals of all subcarriers to obtain a final sending signal, wherein the step of a receiving end is the reverse process of the sending end.
Fig. 2 shows a block diagram of a receiving end, which is a reverse process of the transmitting end in fig. 1.
Alternatively, the filter designed in accordance with the above-described method may be applied to a filter bank single carrier communication system employing such a filter. Dividing a data symbol to be transmitted into data symbol sections and coding serial numbers, processing the data symbol sections to be transmitted according to the serial numbers of the data symbol sections, wherein the data symbol sections to be transmitted comprise windowing and FFT, and mapping the processed data symbols onto a plurality of subcarriers by adopting a filter bank technology, wherein the filter is designed by using the filter designed by the method, after the data symbol sections to be transmitted are processed according to the serial numbers of the data symbol sections so that the data symbol sections are mapped onto the plurality of subcarriers, for even-numbered data symbol sections, even-numbered subcarriers transmit real numbers and odd-numbered subcarriers transmit imaginary numbers, for odd-numbered data symbol sections, even-numbered subcarriers transmit imaginary numbers and odd-numbered subcarriers transmit real numbers, and cooperation transmission of data between adjacent data symbol sections is realized.
The specific steps of the transmitting end are shown in fig. 3: the signal is segmented and intercepted by a sliding window and then is windowed, then is converted into a frequency domain by FFT (fast Fourier transform), is mapped onto a carrier after being subjected to real and virtual interleaving extraction, and then is subjected to a series of modulation steps (including IFFT (inverse fast Fourier transform), filter bank filtering, dislocation addition and the like) of a filter bank-based modulation system transmitting end.
Alternatively, in the single-carrier communication system, the added window may also adopt the impulse response sequence of the filter designed by the method.
The technical scheme provided by the invention is described by specific embodiments.
Example 1
In this embodiment, the total number M of subcarriers is 64, and under this specific condition, the impulse response function of the prototype filter is set as:
g(k),k＝-32,...,32
where k represents the time, the designed filter impulse response function needs to satisfy the following condition:
(1) symmetrical about the origin, and the value at the origin is 1;
g(0)＝1；
g(k)＝g(-k),k＝-32,...,32
(2) the sum of squares between any two points symmetric about k 16 is 1;
g(16-k)2+g(16+k)2＝1,0≤k≤16
(3) the sequence of frequency responses corresponding to g (k) is noted as:
Figure GDA0002305589520000081
g (f) is M-order discrete Fourier transform of g (k), wherein f is an integer and represents the f-th frequency point, and the f-th frequency point satisfies the following conditions: g (f) ≧ G (-f), and for | f ≧ L, G (f) ≧ 0, i.e., the number of effective frequency points is 2L-1.
Assuming that the number of filter effective frequency points is 5, i.e., L is 3, the prototype filter can be expressed as:
Figure GDA0002305589520000082
from the conditions given above, the following system of equations is obtained with three samples 0,16, 32:
Figure GDA0002305589520000091
solving to obtain: g (0) ═ 0.6036a, G (± 1) ═ 0.25A, G (± 2) ═ 0.0518A.
Assuming that the number of effective frequency points of the filter is 7, the prototype filter can be expressed as:
Figure GDA0002305589520000092
taking four samples of 0,8,16,32, the following system of equations is obtained:
Figure GDA0002305589520000093
solving to obtain: g (0) ═ 0.6036A, G (± 1) ═ 0.2553A, G (± 2) ═ 0.0518A, G (± 3) ═ 0.0053A.
In one example, a is 1, where the unit impulse response function of the prototype filter is as shown in fig. 4, and fig. 4 is the impulse response of the prototype filter in this case, i.e., g [0],. g [64 ].
Example 2
The preset conditions of this embodiment are that the impulse response sequence satisfying the conditions is applied to a single-carrier communication system based on a filter bank as a window, the total number N of subcarriers is 1024, the number M of data symbols transmitted within the time T is 64, and the symbol sequence to be transmitted { a }0,a1,a2,. is complex sign, and the overlap factor K of the filter used is 4. Under this specific condition, the implementation steps can be expressed as:
(1) the data symbol sequence to be sent is subject to a sliding window with the length of 64, and data symbols are intercepted in a sliding way at intervals of 32 points to obtain the segment x of the nth data symbolnThe symbols above are:
Figure GDA0002305589520000101
xn[i]＝a32(n-1)+i,0≤i≤63,(n≠0)
wherein x is0[i]Indicates the value of the data symbol segment with the sequence number 0, xn[i]The symbol segment whose index is not 0 is represented.
(2) Denote by g a window vector of length 64, for the nth data symbol segment xnR is obtained after windowingn：
rn＝Diag(g)·xn
The function of the Diag function is to convert the vector into a diagonal matrix form, and an impulse response sequence g [ i ] corresponding to the window vector g satisfies the following conditions:
Figure GDA0002305589520000102
g (f) is the 64 th order discrete Fourier transform of g (k), wherein k is an integer and represents the k frequency point, and the following conditions are met: g (f) ≧ G (-f), and for | f ≧ L, G (f) ≧ 0, i.e., the number of effective frequency points is 2L-1.
(3) R is transformed by 64-point discrete Fourier transformnConversion to frequency domain form Rn：
Rn＝FFT(rn)
The FFT function represents Fourier transform, and the value of the m-th element is recorded as Rn[m]。
(4) For the nth data symbol segment, E obtained after further modulationnM th element of (1) is marked as En[m]When n is an even number, it can be expressed as:
Figure GDA0002305589520000103
when n is an odd number, En[m]Can be expressed as:
Figure GDA0002305589520000111
wherein the content of the first and second substances,
Figure GDA0002305589520000112
the function functions as a real part of the computation,
Figure GDA0002305589520000113
the function is to take the imaginary part.
(5) 64 elements En[m]Mapping to 1024 sub-carriers, mthInformation on subcarriers In[m]Expressed as:
Figure GDA0002305589520000114
(6)In[m]the signal s is converted to the time domain by IFFT and multiplied by a filter of length 1025n[k]Can be expressed as:
wherein g' k represents the impulse response of the filter, satisfying:
Figure GDA0002305589520000116
equivalent to pair In[m]Carrying out 1024-point IFFT;
(8) all the s obtained by the steps aren[k]Performing sequential displacement 512 accumulation to obtain the final transmission signal s [ k ]]。
Figure GDA0002305589520000118
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A short filter, comprising: the length of the short filter is M +1, and the impulse response sequence is as follows: g (k), wherein k is-M/2,.., M/2, wherein k represents the serial number of the sampling point, M is an even number, the number of the nonzero coefficients of the short filter is less than or equal to M, and M is the total carrier number of the FBMC system and the number of the sampling points in the complex symbol interval of the FBMC;
the impulse response sequence is symmetrical about an original point, and the value of the impulse response sequence at the original point is A, wherein A is a natural number;
the sum of squares of any two points of the impulse response sequence which is symmetrical about k-M/4 is A2；
The frequency response sequence corresponding to the impulse response sequence is M-order discrete Fourier transform of the impulse response sequence, the frequency response sequence is symmetrical about an original point, the value of the frequency response sequence at the original point is 0, the number of effective frequency points of the frequency response sequence is 2L-1, and L is an integer greater than or equal to 1.
2. The short filter of claim 1, wherein the impulse response sequence is symmetric about an origin, and takes a value a at the origin, specifically:
Figure FDA0002305589510000011
3. the short filter of claim 1, wherein the sum of squares of any two points of the impulse response sequence symmetric about k-M/4 is a2The method specifically comprises the following steps:
g(M/4-k)2+g(M/4+k)2＝A2,0≤k≤M/4。
4. the short filter according to claim 1, wherein the frequency response sequence corresponding to the impulse response sequence is M-order discrete fourier transform of the impulse response sequence, the frequency response sequence is symmetric with respect to an origin, and takes a value of 0 at the origin, and the number of effective frequency points of the frequency response sequence is 2L to 1, specifically:
Figure FDA0002305589510000012
wherein g (f) represents a frequency response sequence.
5. A short filter as claimed in any one of claims 1 to 4, wherein when L is 3, the number of effective frequency points of the short filter is 5, and the corresponding short filter is expressed as:
Figure FDA0002305589510000021
from the three samples 0, M/4, M/2, the following system of equations is obtained according to the conditions given above:
Figure FDA0002305589510000022
solving to obtain: g (0) ═ 0.6036a, G (± 1) ═ 0.25A, G (± 2) ═ 0.0518A.
6. A short filter as claimed in any one of claims 1 to 4, wherein when L is 4, the number of effective frequency points of the short filter is 7, and the corresponding short filter is expressed as:
Figure FDA0002305589510000023
taking four sampling points of 0, M/8, M/4 and M/2, the following equation system is obtained:
Figure FDA0002305589510000024
solving to obtain: g (0) ═ 0.6036A, G (± 1) ═ 0.2553A, G (± 2) ═ 0.0518A, G (± 3) ═ 0.0053A.
7. A single carrier system operating on the basis of a filter bank, each filter operating on a different subcarrier, characterized in that the filters in the filter bank are short filters according to any one of claims 1 to 6;
the single carrier system divides the data symbols to be sent into data symbol segments and sequences the data symbol segments, carries out windowing and FFT processing on the data symbol segments to be sent according to the sequence numbers of the data symbol segments, adopts the short filter to map the processed data symbols onto a plurality of subcarriers, transmits a real number part and an odd number subcarrier transmission imaginary number part for even number data symbol segments, and transmits a real number part and an odd number subcarrier transmission imaginary number part for odd number data symbol segments and odd number subcarriers to realize cooperative data sending between adjacent data symbol segments.
8. The single-carrier system of claim 7, wherein the single-carrier system multiplies the short-filter-filtered symbols by the short-filter-filtered symbols
Figure FDA0002305589510000031
And then modulated onto different subcarriers.
9. A multi-carrier system operating on the basis of a filter bank, each filter operating on a different sub-carrier, characterized in that the filters in the filter bank are short filters according to any of claims 1 to 6;
and the multi-carrier system multiplies a real number symbol sequence to be sent by a phase twiddle factor to obtain a real and imaginary staggered symbol sequence, and maps the processed data symbols to a plurality of subcarriers by adopting the short filter.
10. The multi-carrier system of claim 9 wherein a ism,nIs a real number symbol to be sent, m represents a subcarrier sequence number, and n represents a time sequence number; the multi-carrier system will am,nMultiplied by a phase rotation factorAfter a, am,nChanging original real number into real-imaginary interleaving, and multiplying the short-filter-filtered symbol by
Figure FDA0002305589510000033
And then modulated onto different subcarriers.
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