Signal equalization method, equalizer and storage medium for orthogonal time-frequency space system
阅读说明：本技术 正交时频空系统的信号均衡方法、均衡器及存储介质 (Signal equalization method, equalizer and storage medium for orthogonal time-frequency space system ) 是由 高晖 程俊强 许文俊 别志松 陆月明 于 2019-08-28 设计创作，主要内容包括：本发明公开了正交时频空系统的信号均衡方法,包括：获取时延-多普勒域接收向量；对所述接收向量矩阵化,得到时延-多普勒域接收信号矩阵；对所述接收信号矩阵进行二维快速傅里叶变换；对变换结果向量化,得到处理后接收向量；通过信道估计获取信道信息特征矩阵；根据所述信道信息特征矩阵计算时延-多普勒域信道矩阵的特征值分解,得到对角阵；求所述对角阵的逆矩阵,得到处理后信道信息逆矩阵；将所述处理后接收向量和处理后信道信息逆矩阵相乘,得到乘积向量；将所述乘积向量矩阵化,得到乘积矩阵；以及对所述乘积矩阵进行二维快速傅里叶逆变换,将变换结果向量化,并输出所述均衡后接收向量。本发明还公开了均衡器以及计算机可读存储介质。(The invention discloses a signal equalization method of an orthogonal time-frequency space system, which comprises the following steps: acquiring a delay-Doppler domain receiving vector; performing matrixing on the receiving vector to obtain a time delay-Doppler domain receiving signal matrix; performing two-dimensional fast Fourier transform on the received signal matrix; vectorizing the transformation result to obtain a processed receiving vector; acquiring a channel information characteristic matrix through channel estimation; calculating eigenvalue decomposition of a time delay-Doppler domain channel matrix according to the channel information eigenvalue matrix to obtain a diagonal matrix; solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix; multiplying the processed receiving vector and the processed channel information inverse matrix to obtain a product vector; performing matrixing on the product vector to obtain a product matrix; and performing two-dimensional inverse fast Fourier transform on the product matrix, vectorizing a transform result, and outputting the equalized received vector. The invention also discloses an equalizer and a computer readable storage medium.)
1. A signal equalization method for an orthogonal time-frequency space system, the method comprising:
acquiring a delay-Doppler domain receiving vector;
performing matrixing on the delay-Doppler domain receiving vector to obtain a delay-Doppler domain receiving signal matrix;
performing two-dimensional fast Fourier transform (2D-FFT) on the time delay-Doppler domain received signal matrix, and vectorizing a transform result to obtain a processed received vector;
acquiring a channel information characteristic matrix through channel estimation, wherein the channel information characteristic matrix is determined by any row or any column of a channel matrix of a delay-Doppler domain;
calculating the eigenvalue decomposition of the channel matrix according to the channel information eigenvalue matrix to obtain a diagonal matrix of the channel matrix;
solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix;
multiplying the processed receiving vector and the processed channel information inverse matrix to obtain a product vector;
performing matrixing on the product vector to obtain a product matrix; and
and performing two-dimensional inverse fast Fourier transform (2D-IFFT) on the product matrix, vectorizing a transformation result to obtain a balanced receiving vector, and outputting the balanced receiving vector as a receiving signal.
2. The method of claim 1, wherein the obtaining the channel information characterization matrix comprises:
acquiring any row or any column of the channel matrix through pilot-assisted channel estimation or blind channel estimation;
obtaining a first column of the channel matrix through a column/row position relation of a dual cyclic channel matrix;
and performing matrixing on the first column of the channel matrix to generate the channel information characteristic matrix.
3. The method of claim 1, wherein the calculating the eigenvalue decomposition of the delay-doppler domain channel matrix from the channel information eigenvalue matrix to obtain the diagonal matrix of the channel matrix comprises:
performing 2D-FFT on the channel information characteristic matrix to obtain a 2D-FFT conversion result; and
vectorizing the 2D-FFT conversion result to obtain a 2D-FFT conversion result vector; and
and diagonalizing the result vector to obtain the diagonal matrix.
4. The method according to claim 1 or 3, wherein the 2D-FFT comprises:
performing FFT on all columns of the channel information characteristic matrix to obtain a new matrix; and
the FFT is performed for all rows of the new matrix.
5. The method of claim 1, wherein said inverting the diagonal matrix comprises: directly solving the inverse matrix delta of the diagonal matrix delta-1。
6. The method of claim 1, wherein said inverting the diagonal matrix comprises: inverse matrix of noise-containing diagonal matrix delta is solved
7. The method of claim 1, wherein performing a 2D-IFFT on the product matrix comprises:
performing IFFT operation on all columns of the product matrix to obtain a new matrix; and
performing an IFFT operation on all rows of the new matrix.
8. An equalizer, comprising:
the receiving vector processing module is used for acquiring a delay-Doppler domain receiving vector; performing matrixing on the delay-Doppler domain receiving vector to obtain a delay-Doppler domain receiving signal matrix; performing two-dimensional fast Fourier transform (2D-FFT) on the time delay-Doppler domain received signal matrix; vectorizing a conversion result to obtain a processed receiving vector;
the channel matrix processing module is used for acquiring a channel information characteristic matrix through channel estimation, wherein the channel information characteristic matrix is determined by any row or any column of a channel matrix of a delay-Doppler domain; calculating eigenvalue decomposition of the channel matrix according to the channel information eigenvalue matrix to obtain a diagonal matrix of the channel matrix; solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix; and
the equalization module is used for multiplying the processed receiving vector and the processed channel information inverse matrix to obtain a product vector; performing matrixing on the product vector to obtain a product matrix; and performing two-dimensional inverse fast Fourier transform (2D-IFFT) on the product matrix, vectorizing a transformation result to obtain a balanced receiving vector, and outputting the balanced receiving vector.
9. A computing device, comprising:
at least one processor;
a memory; and
a bus connecting the at least one processor and the memory; wherein the content of the first and second substances,
the at least one processor is configured to execute the memory-stored module of machine-readable instructions to perform the method of any of claims 1 to 7.
10. A computer-readable medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1 to 7.
Technical Field
The present invention relates to mobile communication technologies, and in particular, to a signal equalization method, an equalizer, and a computer-readable storage medium for an orthogonal time-frequency-space system.
Background
Orthogonal Frequency Division Multiplexing (OFDM) is one of the most widely used communication technologies, and is mainly used for resisting multipath effects causing inter-symbol interference and simultaneously realizing high-rate data transmission.
However, future wireless communication networks, such as 5G/B5G, will face highly dynamic communication channel environments, such as in high mobility scenarios (e.g., high-speed rail) and millimeter wave (mmWave) communications. The highly dynamic channel exhibits double dispersion properties including time dispersion due to multipath and frequency dispersion due to doppler broadening. OFDM modulation used by current communication systems can be used to combat Inter Symbol Interference (ISI) due to time dispersion. However, Inter-Carrier Interference (ICI) caused by frequency dispersion can significantly impair the performance of the OFDM system.
In this case, an Orthogonal Time Frequency Space (OTFS) modulation technique is developed. Specifically, an OTFS system applying an OTFS modulation technique first carries transmission information in a delay-doppler domain, and expands each delay-doppler domain information symbol to a whole time-frequency domain within a certain range at a transmitting end through Inverse Symplectic Finite Fourier Transform (ISFFT), thereby ensuring that each symbol in an OTFS frame experiences a relatively stable channel, i.e., a double-dispersion channel is converted into a channel almost free of frequency/time dispersion. At the receiving end, the OTFS system converts the received information of the time-frequency domain into a delay-doppler domain through a Symplectic Finite Fourier Transform (SFFT) to perform operations such as equalization and the like, so as to combat ICI caused by a high-speed moving scene. Therefore, the OTFS, as a novel multi-carrier modulation technique, can effectively combat a highly dynamic communication channel environment, and exhibits strong robustness to high doppler spread.
For the OTFS system, the complexity of the equalizer at the receiving end is very important for its practical application. The existing OTFS system equalization techniques are mainly classified into two types: the first is a nonlinear equalization method, which has good bit error rate performance but high complexity, so the practicability is low; the second type is linear equalization, but conventional linear equalization techniques generally involve inverting the channel matrix, and the complexity of matrix inversion and matrix multiplication is O ((NM)3) Wherein, N is the number of OTFS symbols, and M is the number of subcarriers. Clearly, for the larger data dimensions in real-world communications, the complexity of matrix inversion is unacceptable.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a signal equalization method for an orthogonal time-frequency space system.
The method may specifically include: acquiring a delay-Doppler domain receiving vector; performing matrixing on the delay-Doppler domain receiving vector to obtain a delay-Doppler domain receiving signal matrix; performing two-dimensional fast Fourier transform (2D-FFT) on the time delay-Doppler domain received signal matrix, and vectorizing a transform result to obtain a processed received vector; acquiring a channel information characteristic matrix through channel estimation, wherein the channel information characteristic matrix is determined by any row or any column of a channel matrix of a delay-Doppler domain; calculating the eigenvalue decomposition of the channel matrix according to the channel information eigenvalue matrix to obtain a diagonal matrix of the channel matrix; solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix; multiplying the processed receiving vector and the processed channel information inverse matrix to obtain a product vector; performing matrixing on the product vector to obtain a product matrix; and performing two-dimensional inverse fast Fourier transform (2D-IFFT) on the product matrix, vectorizing a transformation result to obtain a balanced receiving vector, and outputting the balanced receiving vector as a receiving signal.
The obtaining of the channel information feature matrix may include: acquiring any row or any column of the channel matrix through pilot-assisted channel estimation or blind channel estimation; obtaining a first column of the channel matrix through a column/row position relation of a dual cyclic channel matrix; and matrixing the first column of the channel matrix to generate the channel information characteristic matrix.
Wherein, the calculating the eigenvalue decomposition of the delay-doppler domain channel matrix according to the channel information eigenvalue matrix to obtain the diagonal matrix of the channel matrix comprises: performing 2D-FFT on the channel information characteristic matrix to obtain a 2D-FFT conversion result; vectorizing the 2D-FFT conversion result to obtain a 2D-FFT conversion result vector; and diagonalizing the result vector to obtain the diagonal matrix.
The above 2D-FFT includes: performing FFT on all columns of the channel information characteristic matrix to obtain a new matrix; and performing FFT on all rows of the new matrix.
The above-mentioned inverse matrix of the diagonal matrix is obtained by: directly solving the inverse matrix delta of the diagonal matrix delta-1。
Or, the above-mentioned obtaining the inverse matrix of the diagonal matrix includes: inverse matrix of noise-containing diagonal matrix delta is solved
The performing 2D-IFFT on the product matrix comprises: performing IFFT operation on all columns of the product matrix to obtain a new matrix; and performing an IFFT operation on all rows of the new matrix.
The embodiment of the invention provides an equalizer of an orthogonal time-frequency space system, which comprises the following components:
the receiving vector processing module is used for acquiring a delay-Doppler domain receiving vector; performing matrixing on the delay-Doppler domain receiving vector to obtain a delay-Doppler domain receiving signal matrix; performing two-dimensional fast Fourier transform (2D-FFT) on the time delay-Doppler domain received signal matrix; vectorizing a conversion result to obtain a processed receiving vector;
the channel matrix processing module is used for acquiring a channel information characteristic matrix through channel estimation, wherein the channel information characteristic matrix is determined by any row or any column of a channel matrix of a delay-Doppler domain; calculating eigenvalue decomposition of the channel matrix according to the channel information eigenvalue matrix to obtain a diagonal matrix of the channel matrix; solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix; and
the equalization module is used for multiplying the processed receiving vector and the processed channel information inverse matrix to obtain a product vector; performing matrixing on the product vector to obtain a product matrix; and performing two-dimensional inverse fast Fourier transform (2D-IFFT) on the product matrix, vectorizing a transformation result to obtain a balanced receiving vector, and outputting the balanced receiving vector as a receiving signal.
Still further, an embodiment of the present invention provides a computing device, including:
at least one processor;
a memory; and
a bus connecting the at least one processor and the memory; wherein the content of the first and second substances,
the at least one processor is configured to execute the machine-readable instruction module stored in the memory to perform the signal equalization method of the orthogonal time-frequency space system.
Still further, an embodiment of the present invention provides a computer-readable medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the signal equalization method for an orthogonal time-frequency space system.
The equalization method provided by the embodiment of the invention fully utilizes the dual cycle property of the OTFS system delay-Doppler domain channel, performs high-efficiency characteristic value decomposition on the channel matrix through two-dimensional fast Fourier transform, and further realizes low-complexity linear equalization based on the two-dimensional fast Fourier transform, so that the calculation complexity is greatly reduced compared with the existing OTFS linear equalizer. In addition, the low complexity linear equalizer only utilizes the channel information characteristic matrix H', i.e. one row or one column of the channel matrix H, during the equalization process, while the conventional linear equalizer needs to utilize the complete channel matrix H, so the low complexity linear equalizer also greatly reduces the spatial complexity of the equalization, i.e. reduces the storage space requirement of the equalizer.
Drawings
FIG. 1 is a schematic diagram of the overall structure of an
FIG. 2 is a schematic diagram of an ISFFT/SFFT transform according to some embodiments of the invention;
figure 3a is a schematic diagram of a delay-doppler domain channel impulse response according to some embodiments of the present invention;
figure 3b is a schematic diagram of a channel matrix in the delay-doppler domain in accordance with some embodiments of the present invention;
fig. 4 is a schematic flow chart illustrating a signal equalization method of an orthogonal time-frequency space system according to some embodiments of the present invention;
FIG. 5 is a schematic diagram illustrating a comparison of the complexity of an equalization method according to some embodiments of the present invention and a prior art equalization method;
fig. 6 is a schematic diagram comparing bit error rates of an equalization method according to some embodiments of the present invention with a conventional equalization method;
FIG. 7 is a diagram illustrating an equalizer according to some embodiments of the present invention; and
fig. 8 is a diagram illustrating a hardware structure of an equalizer according to some embodiments of 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 specific embodiments and the accompanying drawings.
As described above, OTFS modulation, as a novel multi-carrier modulation technique, can effectively combat a highly dynamic communication channel environment, and exhibits strong robustness against doppler spread.
Fig. 1 is a schematic diagram of the overall structure of an
In addition, as shown in fig. 1, the OTFS transmitter 101 may include an ISFFT transmission window 1011 and an OFDM modulator 1012 therein. The OTFS receiving end 102 may include an OFDM demodulator 1021, an SFFT receiving window 1022, and an equalizer 1033 inside.
The OTFS transmitting end 101 may divide the delay-doppler domain in advance, divide the delay-doppler domain into M × N delay-doppler grids Γ, and transmit a two-dimensional transmit sequence x [ k, l ] of the delay-doppler domain at the grid Γ, where k is 0, …, N-1, l is 0, …, M-1. Then, the ISFFT transmission window 1011 of the OTFS transmitting end 101 may convert the two-dimensional transmission sequence in the delay-doppler domain from the delay-doppler domain to the time-frequency domain through ISFFT transformation, so as to obtain a two-dimensional transmission sequence X [ N, M ] in the time-frequency domain, and perform windowing, where N is 0, …, N-1, M is 0, …, and M-1. Next, the OFDM modulator 1012 of the OTFS sending end 101 performs OFDM modulation on the preprocessing result to obtain a time domain transmission signal s (t). Then, the OTFS sender 101 may send the time-domain transmission signal s (t) to the LTV channel 103.
After receiving the time domain receiving signal r (t) from the LTV channel 103, the OFDM demodulator 1021 of the OTFS receiving end 102 first obtains a two-dimensional receiving sequence Y [ n, m ] of the time-frequency domain through OFDM demodulation, and then performs SFFT transform processing on the two-dimensional receiving sequence Y [ n, m ] of the time-frequency domain through the SFFT receiving window 1022, so as to obtain a two-dimensional receiving sequence Y [ k, l ] of the delay-doppler domain. At this time, since Inter Doppler Interference (IDI) caused by a high-speed moving scene still reduces the signal-to-noise ratio of the received signal, the receiving end needs to add an equalizer 1033 to equalize the two-dimensional received sequence y [ k, l ] of the delay-Doppler domain.
FIG. 2 shows an ISFFT/SFFT transform according to an embodiment of the invention. As can be seen from fig. 2, the ISFFT/SFFT transform is actually a two-dimensional inverse fourier transform/two-dimensional fourier transform, and for a transmission symbol occupying each lattice point in the delay-doppler domain, the entire time-frequency domain within a certain range is expanded through the transform, so that a proper equalization detection scheme can be designed at the receiving end to obtain full diversity gain.
In addition, as can be seen from fig. 1, the model of the
As mentioned above, the existing OTFS system employs nonlinear and linear equalization techniques with high complexity and low practicability. In order to effectively reduce the complexity of the OTFS equalization processing, the embodiment of the present invention may implement linear equalization by using two-dimensional fast fourier transform based on the dual cycle property of the OTFS channel in the delay-doppler domain, thereby reducing the complexity of the equalization processing. It should be noted that, in the embodiment of the present invention, the OTFS system employs ideal transmit/receive pulses, and both the transceiver and the transceiver can be configured as a single antenna.
The dual cycle nature of the delay-doppler domain channel of the OTFS system will first be described in detail below with reference to specific figures and examples.
As mentioned above, the OTFS system performs an ISFFT transform and an SFFT transform at the transmitting end and the receiving end, respectively, and both transforms are essentially two-dimensional fourier (inverse) transforms. Thus, in the case that the OTFS system employs an ideal transmit/receive pulse, the input-output relationship of the OTFS system in the delay-doppler domain may be represented as a two-dimensional cyclic convolution, and when the two-dimensional cyclic convolution is represented as a matrix/vector relationship, the channel matrix corresponding to the delay-doppler domain channel will exhibit a double-cycle property. For convenience of description, a matrix having a dual cyclic property will be referred to as a dual cyclic matrix hereinafter.
Specifically, suppose that the two-dimensional transmission sequence of the delay-doppler domain at the transmitting end of the OTFS system is x [ k, l ], where k is 0, …, N-1, l is 0, …, M-1; the method comprises the following steps of receiving a two-dimensional receiving sequence y [ k, l ] of a delay-Doppler domain at a receiving end of the OTFS system, wherein k is 0, …, M-1, l is 0, … and M-1. The input-output relationship of the OTFS system in the delay-doppler domain can be represented by the following formula (1):
wherein, the number of P multi-paths,<·>Nwhich represents the operation of the modulo N operation,
As can be seen from the above formula (1), the input-output relationship between the delay and the doppler domain of the OTFS system is a two-dimensional cyclic convolution. When the above relationship is expressed in a matrix/vector form, the following formula (2) can be obtained:
y＝Hx+z (2)
where H is the NM by NM channel matrix. Furthermore, in the embodiment of the present invention, the channel matrix H is a dual cyclic matrix, i.e. the sub-matrices of the channel matrix H exhibit block cyclic property, wherein each sub-matrix is a cyclic matrix.
The specific structure of the channel matrix H can be shown in the following formula (3):
wherein H0、H1、…、HM-2And HM-1Are all sub-matrices of the channel matrix H and are circulant matrices.
Figure 3a shows a delay-doppler domain channel impulse response according to an embodiment of the present invention. As shown in fig. 3a, the impulse response of the delay-doppler domain channel depends on the characteristics of the channel itself, i.e. on the delay spread and doppler spread of the channel.
Fig. 3b shows the channel matrix in the delay-doppler domain according to an embodiment of the present invention. As shown in fig. 3b, the channel matrix H corresponding to the OTFS system based on ideal pulses has a dual cycle property.
It is known that a dual circulant matrix can be diagonalized by a Two-Dimensional discrete fourier Transform (2D-DFT) matrix. Considering that FFT is a fast algorithm for implementing DFT, the embodiment of the present invention performs eigenvalue decomposition on the channel matrix H with dual cycle property by using two-dimensional fast fourier transform (2D-FFT), so as to implement diagonalization on the channel matrix H, and the diagonalization process may only use any row or any column of the channel matrix H.
The method for diagonalizing the channel matrix H according to the embodiment of the present invention will be described in detail below.
First, a two-dimensional DFT matrix and a two-dimensional IDFT matrix are defined, wherein the two-dimensional DFT matrix can be represented by the following formula (4), and the two-dimensional IDFT matrix can be represented by the following formula (5).
Wherein, FMRepresenting M-point DFT matrix, FNRepresenting an N-point DFT matrix.
It is known that the column vector of the IDFT matrix of two-dimensional NM × NM is the eigenvector of the corresponding NM × NM double-circulant matrix, and therefore, the channel matrix H having the double-circulant property may have an eigenvalue decomposition as shown in the following formula (6):
H＝Ξ-1ΔΞ (6)
where Δ is a diagonal matrix whose diagonal elements are eigenvalues of the channel matrix H.
For simplicity, in the embodiment of the present invention, in the eigenvalue decomposition process of the channel matrix H, i.e., in the above equation (6), the diagonal matrix Δ may be obtained by only any one row or any one column of the channel matrix H. Specifically, the diagonal matrix Δ may be represented by the following formula (7):
Δ＝diag(vec(FNH′FM)) (7)
wherein, diag (a) operation means forming a diagonal matrix by using elements of the vector a, and vec (a) operation means vectorizing the matrix a by columns.
H' is referred to as a channel information characteristic matrix in the embodiment of the present invention. In addition, it should be noted that the channel information characteristic matrix H' may be a matrix formed by any row or any column of the channel matrix H. Since the channel matrix H has a dual cycle property, any row or any column of the channel matrix H is known, and all other rows or all other columns can be obtained according to the positional relationship between each row and each column. For example, in an embodiment of the present invention, the channel information characteristic matrix H' may be generated using the first column of the channel matrix H. Specifically, if h1In the first column of the channel matrix H, H' is undivec (H)1) Wherein operation unwec (a) is the inverse operation of vec (a), which means that vector a is matrixed. It can be seen that, in the embodiment of the present invention, the eigenvalue decomposition of the channel matrix H can be obtained only by using the channel information eigenvalue matrix, that is, any row or any column of the channel matrix H.
Note that the Fast Fourier Transform (FFT) is a fast algorithm of the Discrete Fourier Transform (DFT), and thus, in an embodiment of the present invention, the two-dimensional discrete fourier transform (2D-DFT) is implemented using the two-dimensional fast fourier transform (2D-FFT).
In an embodiment of the present invention, a new operator may be defined as shown in the following formula (8), and the eigenvalue decomposition of the channel matrix H may be obtained by the new operator:
the operation operator shown in the above formula (8) mainly includes the following two steps:
first, a 2D-FFT operation is performed on the matrix A.
Specifically, the FFT operation is performed on all columns of the matrix a; then, performing FFT operation on all rows of the obtained new matrix;
secondly, vectorizing the result obtained in the first step.
Similarly, an operator similar to equation (8) is definedAn operation of performing two-dimensional inverse fast fourier transform (2D-IFFT) on the matrix a and vectorizing the 2D-IFFT transform result is shown. The 2D-IFFT transformation includes: performing an Inverse Fast Fourier Transform (IFFT) operation on all columns of the matrix; and performing an IFFT operation on all rows from which the new matrix is obtained.
Based on the above equation (7) and equation (8), the following equation (9) can be derived, and as can be seen from the following equation (9), the diagonal matrix Δ obtained by decomposing the eigenvalues of the dual circulant matrix H can be obtained by 2D-FFT transformation from only the first column of H:
Δ＝diag(vFFT2(H′)) (9)
in the embodiment of the present invention, after the eigenvalue decomposition of the channel matrix H is obtained, a low-complexity linear equalizer implemented by two-dimensional fast fourier transform (2D-FFT) may be used to equalize the received signal, thereby avoiding the high-complexity matrix inversion operation in the conventional linear equalizer.
Specifically, the eigenvalue decomposition of the channel matrix H, i.e. the above equation (6) is substituted into the vectorized system output-output relationship model (i.e. the above equation (2)), so as to obtain another expression of the OTFS system input-output relationship as shown in the following equation (10):
y＝Ξ-1ΔΞx+z (10)
in this case, when a Zero Forcing (ZF) linear equalization scheme is employed, the output of the equalizer can be represented by the following equation (11):
xZF＝Ξ-1Δ-1Ξy＝vIFFT2(unvec(Δ-1×vFFT2(unvec(y)))) (11)
wherein x isZFRepresents the equalizer output sequence, and y is the receiving sequence of the receiving end in the delay-doppler domain.
Further considering the influence of noise, when a Minimum Mean Square Error (MMSE) linear equalization method is adopted, the output of the equalizer can be represented by the following formula (12):
wherein the content of the first and second substances,
In the embodiment of the present invention, the vector obtained according to the above equation (11) and equation (12) is output as the final received signal.
As can be seen from the above equations (11) and (12), the computation complexity of the low complexity linear equalizer is only O (nmolog)2(NM)), compared to the existing OTFS linear equalizer O ((NM)3) The computational complexity of (2) is greatly reduced. In addition, the low complexity linear equalizer only utilizes the channel information characteristic matrix H', i.e. one row or one column of the channel matrix H, during the equalization process, while the conventional linear equalizer needs to utilize the complete channel matrix H, so the low complexity linear equalizer also greatly reduces the spatial complexity of the equalization, i.e. reduces the storage space requirement of the equalizer.
In view of the above research results, an embodiment of the present invention provides a signal equalization method for an orthogonal time-frequency space system. Fig. 4 shows a flow chart of a signal equalization method according to an embodiment of the present invention. As shown in fig. 4, the method includes the steps of:
and step 410, obtaining a delay-Doppler domain receiving vector y, and matrixing the delay-Doppler domain receiving vector y to obtain a delay-Doppler domain receiving signal matrix.
In an embodiment of the present invention, the delay-doppler domain receiving vector y may be an output of the SFFT receiving window 1022 in the OTFS receiving end 102 in the
In this
Specifically, in an embodiment of the present invention, the 2D-FFT transformation may include: performing FFT operation on all columns of the time delay-Doppler domain received signal matrix; and performing FFT operation on all rows of the obtained new matrix.
In embodiments of the present invention, the channel information characterization matrix H' may be obtained by pilot-based channel estimation or blind channel estimation without pilot assistance.
In the embodiment of the present invention, the channel information H' may be obtained by performing vector matrixing on any row or any column of the NM × NM channel matrix H.
In general, the first column of the channel matrix H may be used to determine the channel information characterization matrix H'. Specifically, since a certain column/row of the channel matrix in the delay-doppler domain can be usually obtained directly by the channel estimation method, a first column of the channel matrix can be further obtained by the column/row position relationship of the dual cyclic matrix H, and then, the obtained first column of the channel matrix in the delay-doppler domain can be further matrixed, thereby obtaining the channel information feature matrix H'.
In the embodiment of the present inventionThe calculating eigenvalue decomposition of the channel matrix H may include performing 2D-FFT on the channel information eigenvalue matrix H', and vectorizing the 2D-FFT result, that is, performing the new operator vFFT described in the above formula (8)2And (h) calculating to obtain a 2D-FFT transformation result vector. And then diagonalizing the vector of the 2D-FFT transformation result to generate a diagonal matrix, namely delta.
It should be noted that, the execution of the steps 410-411 and 420-422 may be performed in parallel without being separated, and the execution order is not limited in the embodiment of the present invention. In the embodiment of the present invention, after obtaining the processed receiving vector and the processed channel information inverse matrix, the following steps may be performed.
And 431, performing matrixing on the product vectors to obtain a product matrix.
In this
In an embodiment of the present invention, the 2D-IFFT transformation may include: performing IFFT operation on all columns of the product matrix; and performing an IFFT operation on all rows from which the new matrix is obtained.
And 433, outputting the equalized receiving vector as a receiving signal.
In the embodiment of the present invention, the process shown in fig. 4 may be referred to as 2D-FFT zero-forcing equalization, also referred to as FFT for short2-ZF equalization.
The embodiment of the invention fully utilizes the characteristic of double circulation of the OTFS channel in the time delay-Doppler domain, and carries out two-dimensional fast Fourier transform on the channel matrixEfficient eigenvalue decomposition is carried out, and low-complexity ZF linear equalization is further realized based on two-dimensional fast Fourier transform. The linear equalization process does not have matrix inversion operation, the operation with the highest complexity in the whole process is two-dimensional fast Fourier transform, and the complexity is only O (NMlog)2(NM)), thereby greatly reducing the computational complexity of linear equalization of OTFS systems. In addition, the equalization method does not use a complete channel matrix, but only adopts the first column of the channel matrix to complete the whole equalization process, thereby greatly reducing the space complexity and also reducing the occupation rate of the storage space of the related equipment.
In other embodiments of the present invention, in the
The embodiment of the invention fully utilizes the characteristic of double circulation of the OTFS channel in the time delay-Doppler domain, carries out high-efficiency characteristic value decomposition on the channel matrix through two-dimensional fast Fourier transform, and further realizes MMSE linear equalization with low complexity based on the two-dimensional fast Fourier transform. The linear equalization process does not have matrix inversion operation, the operation with the highest complexity in the whole process is two-dimensional fast Fourier transform, and the complexity is only O (NMlog)2(NM)), thereby greatly reducing the computational complexity of linear equalization of OTFS systems. In addition, the equalization method does not use a complete channel matrix, and only adopts any row or any column of the channel matrix to complete the whole equalization process, so that the space complexity is greatly reduced, and the occupation rate of the storage space of the related equipment is also reduced.
To demonstrate the practical performance of various embodiments of the present invention, the inventors performed multiple monte carlo simulation experiments. Fig. 5 and 6 show the results of the simulation test. Fig. 5 is a schematic diagram illustrating a comparison between the complexity of the equalization method according to some embodiments of the present invention and the complexity of the existing equalization method; fig. 6 is a schematic diagram illustrating bit error rate comparison between the equalization method according to some embodiments of the present invention and the existing equalization method.
The simulation experiment shown in fig. 5 uses the number of complex multiplications involved in the equalization process as a measure, and gives the FFT proposed by the embodiment of the present invention2-ZF equalization method and FFT2The complexity of the MMSE equalization method is contrasted with the other two linear equalizers. The first comparison scheme is traditional MMSE equalization based on matrix inversion, and the second comparison scheme is frequency domain ZF equalization based on a kronecker product. As can be seen from fig. 5, the complexity of the two linear equalization methods provided by the embodiment of the present invention is much lower than that of the linear equalizer of the existing OTFS system.
The simulation experiment shown in FIG. 6 shows the FFT proposed by the embodiment of the present invention2-ZF equalization method and FFT2The MMSE equalization method compares the bit error rate with the other two linear equalizers. The first comparison scheme is traditional MMSE equalization based on matrix inversion, and the second comparison scheme is frequency domain ZF equalization based on a kronecker product. As can be seen from fig. 6, compared to the conventional linear equalizer of the OTFS system, the two linear equalization methods provided by the present invention do not have any loss in bit error rate performance.
Based on the foregoing signal equalization method for an orthogonal time-frequency space system, an embodiment of the present invention provides an
a received vector processing module 701, configured to obtain a delay-doppler domain received vector; performing matrixing on the delay-Doppler domain receiving vector to obtain a delay-Doppler domain receiving signal matrix; performing two-dimensional fast Fourier transform (2D-FFT) on the time delay-Doppler domain received signal matrix; vectorizing a conversion result to obtain a processed receiving vector;
a channel matrix processing module 702, configured to obtain a channel information feature matrix through channel estimation, where the channel information feature matrix is determined by any row or any column of a channel matrix in a delay-doppler domain; calculating eigenvalue decomposition of a delay-Doppler domain channel matrix according to the channel information characteristic matrix to obtain a diagonal matrix of the delay-Doppler domain channel matrix; solving an inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix; and
an equalizing module 703, configured to multiply the processed received vector by the processed channel information inverse matrix to obtain a product vector; performing matrixing on the product vector to obtain a product matrix; and performing two-dimensional inverse fast Fourier transform (2D-IFFT) on the product matrix, vectorizing a transformation result to obtain a balanced receiving vector, and outputting the balanced receiving vector.
In an embodiment of the present invention, the received vector processing module 701 may include:
a receive vector obtaining unit 7011, configured to obtain a delay-doppler domain receive vector;
a matrixing unit 7012, configured to matrixing the delay-doppler domain received vector to obtain a delay-doppler domain received signal matrix;
a transforming unit 7013, configured to perform two-dimensional fast fourier transform 2D-FFT on the delay-doppler domain received signal matrix; and
a vectorization unit 7014, configured to vectorize the transform result to obtain a processed received vector.
In an embodiment of the present invention, the channel matrix processing module 702 may include:
a channel information feature matrix obtaining unit 7021, configured to obtain a channel information feature matrix through channel estimation;
an eigenvalue decomposition unit 7022, configured to calculate eigenvalue decomposition of a delay-doppler domain channel matrix according to the channel information eigenvalue matrix, so as to obtain a diagonal matrix of the delay-doppler domain channel matrix; and
an inverse unit 7023, configured to solve the inverse matrix of the diagonal matrix to obtain a processed channel information inverse matrix.
It should be noted that, eigenvalue decomposition unit 7022 performs 2D-FFT on the channel information eigen matrix to obtain a 2D-FFT transformation result; vectorizing the 2D-FFT result, and diagonalizing the vectorized result.
The inverse unit 7023 may further consider the influence of noise to calculate an inverse matrix including the noise diagonal matrix Δ
In an embodiment of the present invention, the equalizing module 703 may include:
a product unit 7031, configured to multiply the processed received vector by the processed channel information inverse matrix to obtain a product vector;
a second matrixing unit 7032, configured to matrixing the product vector to obtain a product matrix;
an inverse transformation unit 7033, configured to perform two-dimensional inverse fast fourier transform 2D-IFFT on the product matrix, and vectorize a transformation result to obtain a balanced received vector; and
an output unit 7034 is configured to output the equalized reception vector.
An embodiment of the present invention further provides a computing device, an internal structure of which mainly includes, as shown in fig. 8: at least one
Embodiments of the present invention also provide a computer readable medium, on which a computer program is stored, which when executed by a processor implements the equalization method shown in fig. 4 described above.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
In addition, well known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown within the provided figures for simplicity of illustration and discussion, and so as not to obscure the invention. Furthermore, devices may be shown in block diagram form in order to avoid obscuring the invention, and also in view of the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform within which the present invention is to be implemented (i.e., specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the invention, it should be apparent to one skilled in the art that the invention can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative instead of restrictive.
While the present invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic ram (dram)) may use the discussed embodiments.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
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