A symbol-level precoding method based on minimizing weighted mean square error criterion

Abstract

The present invention is a symbol-level precoding method based on the criterion of minimizing the weighted mean square error. The cell base station uses the channel state information collected in the uplink channel and the user's transmission symbol information to perform symbol-level precoding on the transmission symbol and transmit the signal to provide high-throughput transmission for the downlink. The method is based on the concept of favorable interference area in symbol-level precoding and the criterion of minimizing the weighted mean square error in traditional precoding. The precoding scheme for the symbol is designed to minimize the weighted mean square error between the received signal to be demodulated and the constellation point located in the constructed interference area. By designing the expression of the favorable interference area of ​​the symbol and preprocessing the optimization problem according to the internal symbol points that cannot be optimized, the process of solving the precoding scheme is converted into a low-complexity non-negative least squares problem. On the basis of increasing the lower complexity compared to the traditional linear precoding, the symbol error rate of the wireless communication system is reduced.

Description

Technical Field

[0001] The invention belongs to the field of communication, and in particular relates to a low-complexity and high-performance symbol-level precoding method applicable to a MISO communication system and based on a criterion of minimizing a weighted mean square error. Background Art

[0002] With the development of the information age, the demand for wireless communication data transmission has greatly increased, and the increase in the number of base station antennas has significantly improved the utilization of the spectrum. At the same time, the large-scale antenna array on the base station side can provide a high degree of freedom for communication. In addition, since the computing power of the base station is much higher than that of the terminal, usually complex calculations will be transferred to the base station, thereby reducing the reception complexity of the mobile terminal.

[0003] In order to give full play to the spatial freedom and further reduce the interference within and between cells, precoding technology has become the focus of downlink research. "Precoding" refers to the design of the transmitted signal that uses channel state information and possible data symbol information to direct the expected data symbols to the intended user while limiting the interference between users.

[0004] Traditional precoding regards user data as Gaussian distribution. It is not necessary to know the user data during precoding, and only the channel state information is needed. This is called block-level precoding. If the base station uses two types of information, modulation mode and user data, in addition to channel state information during precoding, the performance of precoding will be further improved, which is called symbol-level precoding. Different from block-level precoding, symbol-level precoding simultaneously exploits channel state information and transmission symbol characteristics and information, so symbol-level precoding has achieved good gains in some indicators. Summary of the invention

[0005] Technical problem: The purpose of the present invention is to provide a low-complexity and high-performance symbol-level precoding method based on the minimum weighted mean square error criterion. Provide a high-throughput and low-complexity symbol-level precoding solution to improve the performance of wireless communication systems.

[0006] Technical solution: To achieve the above-mentioned purpose, a symbol-level precoding method based on minimizing the weighted mean square error criterion of the present invention comprises the following steps:

[0007] Step 1: In a wireless communication transmission system, a base station collects channel state information through an uplink channel and obtains transmission symbol information of a user;

[0008] Step 2: Based on the known user transmitted symbols, constrain the target signal to be within the favorable interference region of the user symbol, and minimize the weighted mean square error between the user's demodulated received signal and the target signal as the objective function to obtain the precoding design optimization problem;

[0009] Step 3, a universal design is performed on the favorable interference region of the user symbol, thereby converting the precoding design optimization problem into an optimization problem in the form of non-negative least squares;

[0010] Step 4, performing low-complexity preprocessing on the precoding design optimization problem according to the internal symbol points in the user symbols that cannot be optimized, thereby reducing the computational complexity required to solve the optimization problem;

[0011] Step 5, solving the non-negative least squares optimization problem after low-complexity preprocessing to obtain a symbol-level precoding scheme.

[0012] in:

[0013] In step 1, the wireless communication transmission system is a MISO system, the base station is equipped with multiple antennas, and there are multiple single-antenna terminals in the cell; the channel state information collected in the uplink channel is perfect channel state information, and the user transmission symbols known to the base station use orthogonal amplitude modulation and phase shift keying modulation.

[0014] The favorable interference area in step 2 is defined as an area with a lower symbol error rate than that on the original symbol point constellation diagram, usually an outward extension area of ​​the boundary constellation point; the favorable interference area of ​​the frequency shift keying modulation symbol is a conical area extending outward from the constellation point, and the favorable interference area of ​​the orthogonal amplitude modulation symbol is divided into three types: the first is that the favorable interference area of ​​the side external symbol is the straight line range extending outward from it, the second is that the favorable interference area of ​​the diagonal symbol is the square area extending outward from it, and the third is that the favorable interference area of ​​the internal symbol point is itself; the favorable interference area has less than or equal to two boundaries, and the base station determines the standardized favorable interference area boundary according to the user's transmitted symbol.

[0015] The user received signal to be demodulated in step (2) is expressed as:

[0016]

[0017] Among them, h k is the frequency domain channel matrix from the base station to user k, with a dimension of N×1, u is the base station's transmitted signal, with a dimension of N×1, n k It has zero mean and variance σ 2 Additive Gaussian white noise, Meaning that element k belongs to the set In the above equation, K is the number of users in the cell and N is the number of base station transmitting antennas. When high-order modulation is used, the receiving end needs to rescale the received signal for correct demodulation, so a is introduced. k and γ, where represents the predetermined receiving-end processing coefficient (non-zero complex number), is the gain factor in the precoding scheme used to scale the signal to meet the symbol-level transmit power constraint is the symbol-level transmit power constraint at the base station side; the target signal of user k is defined as The target signal is constrained to be the transmitted symbol s of user k k The favorable interference area The internal representation is: Based on the known user symbol information, the weighted mean square error between the received signal of user k and the target signal can be expressed as:

[0018]

[0019] where ω k is the weight of user k, For n k Take the expectation, |·| is the modulus value of the complex number; express the transmitted signal u as u=γx, where is the symbol-level power scaling factor, and x is the transmitted signal without power constraints; then construct a new diagonal matrix A, Ω and vector n, as follows

[0020] A = diag{a 1 ,a 2 ,...,a K}

[0021] Ω=diag{ω 1 ,ω 2 ,...,ω K}

[0022] n=[n 1 ,n 2 ,...,n K ] T

[0023]

[0024] Where diag{...} means that the elements in the brackets are used as diagonal elements to form a diagonal matrix, A is the diagonal matrix composed of the receiving end processing coefficients, Ω is the diagonal matrix composed of user weights, and n is the vector composed of the receiving end noise. is a vector composed of the target signal at the receiving end; therefore, the precoding design optimization problem of minimizing the weighted mean square error between the demodulated received signal and the target signal can be expressed as:

[0025]

[0026] where ||·|| 2 is the two-norm of the vector, It means taking the square root of the elements in the matrix Ω. It means taking the expectation of noise, It means x and As the variable minimization objective function; st means the constraint on the variable.

[0027] The favorable interference region of the user symbol in step (3) is expressed as

[0028]

[0029] where μ k and ν k are the two normalized boundaries of the favorable interference region of user k symbol, and for The projection length on the two boundaries, the target signal The real and imaginary parts of can be expressed as

[0030]

[0031]

[0032] in and Indicates taking the real part and taking the imaginary part, constructing a diagonal matrix M R 、M I 、N R 、N I And the vector δ is as follows

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where diag{·} means constructing a diagonal matrix with the elements in the brackets, and further constructing a block diagonal matrix So under the constraint The target signal vector The real number expression is

[0039]

[0040] Where δ≥0 means that all elements of the vector δ are greater than 0, is the target signal vector, s=[s 1 ,s 2 ,...,sK ] T is the user symbol vector.

[0041] The precoding design optimization problem in step (3) is expressed as

[0042]

[0043] Taking the expectation of the noise vector n, the optimization problem can be transformed into

[0044]

[0045] in For the defined block diagonal matrix, the remaining matrices and vectors are defined as follows

[0046]

[0047]

[0048] From Cholesky decomposition Get the upper triangular matrix C and construct the matrix B = C -1 and vector Then the above optimization problem can be transformed into

[0049]

[0050] This is the non-negative least squares problem transformed from the original optimization problem.

[0051] The favorable interference area of ​​the internal symbol points in the user symbols that cannot be optimized in step 4 is themselves, so there is no boundary; when the transmitted symbols are all orthogonal amplitude modulation symbols, Λ is a diagonal matrix with non-zero diagonal elements; when the real part or imaginary part of the user transmitted symbol is inside, the diagonal element of the corresponding position of Λ is 0, and the 0 in the diagonal element makes the corresponding column in BΛ all 0, and also keeps the corresponding element of δ in the optimization process 0, that is, some elements in δ do not need to be optimized; so it can be defined

[0052]

[0053]

[0054]

[0055] in is the set of numbers of non-zero diagonal elements in Λ, for The cardinality of The corresponding sequence number for B belongs to the set The matrix consists of columns, The corresponding sequence number for Λ belongs to the set The diagonal matrix composed of the diagonal elements of The corresponding sequence number for δ belongs to the set The vector of elements, so the original non-negative least squares problem can be transformed into

[0056]

[0057] Compared with the original non-negative least squares problem, the above optimization problem reduces the optimization variable dimension from 2K to

[0058] Beneficial effect: The present invention provides a low-complexity, high-performance symbol-level precoding method based on the criterion of minimizing the weighted mean square error. By establishing an optimization problem with the optimization goal of minimizing the difference between the received signal to be demodulated and the target signal and the constraint that the target signal is located in the favorable interference area of ​​the user symbol, a low-complexity, high-performance symbol-level precoding algorithm with performance significantly better than the classical linear precoding method is studied. The favorable interference area of ​​the symbol is generally designed, and the optimization problem is preprocessed according to the internal symbol points that cannot be optimized to reduce the complexity. The original problem is converted into a non-negative least squares problem of extremely low complexity for solution. In this way, in today's information age where there is a large demand for wireless communication data transmission, a high-throughput, low-complexity symbol-level precoding scheme is provided, thereby improving the performance of the wireless communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Schematic diagram of favorable interference areas for phase shift keying modulation symbols and orthogonal amplitude modulation symbols.

[0060] Figure 2 Schematic diagram of a low-complexity, high-performance symbol-level precoding transmission system based on the minimization of the weighted mean square error criterion.

[0061] Figure 3 The figure is a flow chart of a low-complexity and high-performance symbol-level precoding method based on minimizing the weighted mean square error criterion. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0063] The embodiment of the present invention discloses a low-complexity, high-performance symbol-level precoding method based on minimizing the weighted mean square error criterion, which mainly includes the following steps:

[0064] (1) The base station collects channel state information through the uplink channel and obtains the user's transmission symbol information;

[0065] (2) constraining the target signal to be within the favorable interference region of the user symbol, with the objective function being to minimize the weighted mean square error between the demodulated received signal and the target signal;

[0066] (3) A universal design of the favorable interference region of the symbol is performed to transform the original problem into a non-negative least squares problem;

[0067] (4) Preprocessing the optimization problem based on the internal symbol points that cannot be optimized to reduce the complexity;

[0068] (5) Solve the non-negative least squares problem after preprocessing to obtain the symbol-level precoding scheme.

[0069] Below Figure 2 As shown in the figure, a low-complexity, high-performance symbol-level precoding transmission system based on the minimum weighted mean square error criterion is used as an example. The cell is equipped with a base station, and the base station side is equipped with an antenna array with N transmitting antennas. There are K legal users in the cell, and each user is equipped with a single receiving antenna. The channel from the base station to user k is Assume that the base station collects channel state information through the uplink channel and knows that the channel matrix H = [h 1 ,h 2 ...,h K ] T In each symbol duration, the K frequency shift keying modulation symbols or orthogonal amplitude modulation symbols to be sent to K users can be expressed as where s k is the symbol sent to user k. The symbol vector s will be mapped to the transmitted signal vector by the symbol level precoder SLP(·) Right now

[0070] u=SLP(s,H,σ 2 )

[0071] where n k is the zero-mean additive Gaussian noise of terminal k, and its variance is σ 2 The received signal at terminal k is

[0072]

[0073] in When high-order modulation is used, the receiving end needs to rescale the received signal for correct demodulation. The received signal to be demodulated can be expressed as:

[0074]

[0075] in is a non-zero complex number representing a predetermined processing coefficient, is the gain factor in the precoding scheme used to scale the signal to meet the symbol-level transmit power constraint

[0076] The favorable interference area is defined as the area on the constellation diagram where the symbol error rate is lower than the original symbol point, usually the outward extension area of ​​the boundary constellation point. Figure 1 As shown in the middle gray area, the favorable interference area of ​​the frequency shift keying modulation symbol is the cone area extending outward from the constellation point, and the favorable interference area of ​​the orthogonal amplitude modulation symbol is divided into three types: the favorable interference area of ​​the side external symbol is the straight line range extending outward, the favorable interference area of ​​the diagonal symbol is the square area extending outward, and the favorable interference area of ​​the internal symbol point is itself. The target signal of user k is The target signal is constrained to be the transmitted symbol s of user k k The favorable interference area It can be expressed as:

[0077]

[0078] Based on the known user symbol information, the weighted mean square error between the received signal of user k and the target signal can be expressed as:

[0079]

[0080] where ω k is the weight of user k, For n k Take the expectation, |·| is the modulus value of the complex number. The transmitted signal u can be expressed as u=γx, where is the symbol-level power scaling factor, and x is the transmitted signal without power constraints. Then define

[0081] A = diag{a 1 ,a 2 ,...,a K}

[0082] Ω=diag{ω 1 ,ω 2 ,...,ω K}

[0083] n=[n 1 ,n 2 ,...,n K ] T

[0084]

[0085] Therefore, the optimization problem of minimizing the weighted mean square error between the received signal to be demodulated and the target signal can be expressed as:

[0086]

[0087] where ||·|| 2 is the two-norm of the vector. Considering the statistical distribution of noise, the above optimization problem can be transformed into

[0088]

[0089] This problem is called the primal optimization problem.

[0090] The boundary of the favorable interference region is Figure 1 In The base station can determine the standard favorable interference region boundary based on the user's transmission symbol. Based on the user symbol and the boundary of the favorable interference region, the favorable interference region of user k can be expressed as

[0091]

[0092] Target signal The real and imaginary parts of can be expressed as

[0093]

[0094]

[0095] Define the diagonal matrix and vector as follows

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Further construct the block diagonal matrix So under the constraint The target signal vector The real number expression is

[0102]

[0103] Based on this, the original optimization problem can be expressed in the real number domain as

[0104]

[0105] in

[0106]

[0107]

[0108] By further defining as well as The optimization goal is The gradient of

[0109]

[0110] Where f is the optimization target of the optimization problem. Since f is a variable Convex function on an open set, then the optimal We can set the above gradient to 0 to get

[0111]

[0112] Substituting into the original optimization problem, the optimization problem can be written as

[0113]

[0114] From Cholesky decomposition Get the upper triangular matrix C and define B = C -1 and Then the above optimization problem can be transformed into

[0115]

[0116] This is the non-negative least squares problem transformed from the original optimization problem.

[0117] Internal symbol points are similar Figure 1 middle The internal constellation points of these points have favorable interference areas of themselves, so there is no boundary. Therefore, when all transmitted symbols are orthogonal amplitude modulation symbols, Λ is a diagonal matrix with non-zero diagonal elements. When the real or imaginary part of the user's transmitted symbol is inside, the diagonal element of the corresponding position of Λ is 0. The 0 in the diagonal element makes the corresponding column in BΛ all 0, and also keeps the corresponding element of δ in the optimization process 0, that is, some elements in δ do not need to be optimized. So it can be defined

[0118]

[0119]

[0120]

[0121] in is the set of numbers of non-zero diagonal elements in Λ, for The cardinality of The corresponding sequence number for B belongs to the set The matrix consists of columns, The corresponding sequence number for Λ belongs to the set The diagonal matrix composed of the diagonal elements of The corresponding sequence number for δ belongs to the set Therefore, the original non-negative least squares problem can be transformed into

[0122]

[0123] Compared with the original non-negative least squares problem, the above optimization problem reduces the optimization variable dimension from 2K to The above optimization problem can be solved with extremely low complexity by the effective set method, which is only several times more complex than traditional linear precoding. The expression obtained and x, and then the transmitted signal u after symbol-level precoding can be obtained. The symbol-level precoder at the base station side can obtain the corresponding optimization problem according to each group of user symbols, thereby updating the transmitted signal at the symbol level.

[0124] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A symbol-level precoding method based on minimizing the weighted mean square error criterion, characterized in that The method comprises the following steps: Step 1: In a wireless communication transmission system, a base station collects channel state information through an uplink channel and obtains transmission symbol information of a user; Step 2: Based on the known user transmitted symbols, constrain the target signal to be within the favorable interference region of the user symbol, and minimize the weighted mean square error between the user's demodulated received signal and the target signal as the objective function to obtain the precoding design optimization problem; Step 3, a universal design is performed on the favorable interference region of the user symbol, thereby converting the precoding design optimization problem into an optimization problem in the form of non-negative least squares; Step 4, performing low-complexity preprocessing on the precoding design optimization problem according to the internal symbol points in the user symbols that cannot be optimized, thereby reducing the computational complexity required to solve the optimization problem; Step 5, solving the optimization problem in the form of non-negative least squares after low-complexity preprocessing to obtain a symbol-level precoding scheme; in, In step 1, the wireless communication transmission system is a MISO system, the base station is equipped with multiple antennas, and there are multiple single-antenna terminals in the cell; the channel state information collected in the uplink channel is perfect channel state information, and the user transmission symbols known to the base station use orthogonal amplitude modulation and phase shift keying modulation; The favorable interference area in step 2 is defined as an area with a lower symbol error rate than that on the original symbol point constellation diagram, usually an outward extension area of ​​the boundary constellation point; the favorable interference area of ​​the frequency shift keying modulation symbol is a conical area extending outward from the constellation point, and the favorable interference area of ​​the orthogonal amplitude modulation symbol is divided into three types: the first is that the favorable interference area of ​​the side external symbol is a straight line range extending outward from it, the second is that the favorable interference area of ​​the diagonal symbol is a square area extending outward from it, and the third is that the favorable interference area of ​​the internal symbol point is itself; the favorable interference area has less than or equal to two boundaries, and the base station determines the standardized favorable interference area boundary according to the user's transmitted symbol; The user received signal to be demodulated in step 2 is expressed as: Among them, h k is the frequency domain channel matrix from the base station to user k, with a dimension of N×1, u is the base station's transmitted signal, with a dimension of N×1, n k It has zero mean and variance σ 2 Additive Gaussian white noise, K = {1, 2, ..., K}, k∈K means that element k belongs to the set K, K is the number of users in the cell, and N is the number of base station transmitting antennas; when high-order modulation is used, the receiving end needs to rescale the received signal for correct demodulation, so a is introduced k and γ, where represents the predetermined receiving-end processing coefficient (non-zero complex number), is the gain factor in the precoding scheme used to scale the signal to meet the symbol-level transmit power constraint P T is the symbol-level transmit power constraint at the base station side; the target signal of user k is defined as The target signal is constrained to be the transmitted symbol s of user k k The favorable interference area D k The internal representation is: Based on the known user symbol information, the weighted mean square error between the received signal of user k and the target signal is expressed as: where ω k is the weight of user k, For n k Take the expectation, |·| is the modulus value of the complex number; express the transmitted signal u as u=γx, where is the symbol-level power scaling factor, and x is the transmitted signal without power constraints; then construct a new diagonal matrix A, Ω and vector n, as follows <h2 style=";text-align:left;direction:ltr">A = diag{a1,a2,...,a<h2 style=";text-align:left;direction:ltr"> K <h2 style=";text-align:left;direction:ltr">} Ω=diag{ω1,ω2,...,ω K } n=[n1,n2,...,n K ] T Where diag{...} means that the elements in the brackets are used as diagonal elements to form a diagonal matrix, A is the diagonal matrix composed of the receiving end processing coefficients, Ω is the diagonal matrix composed of user weights, and n is the vector composed of the receiving end noise. is a vector composed of the target signal at the receiving end; therefore, the precoding design optimization problem of minimizing the weighted mean square error between the demodulated received signal and the target signal is expressed as: Among them, ||·||2 is the two-norm of the vector, It means taking the square root of the elements in the matrix Ω, E n It means taking the expectation of noise, It means x and As the variable minimization objective function; st means the constraint on the variable; The favorable interference region of the user symbol in step 3 is expressed as where μ k and ν k are the two normalized boundaries of the favorable interference region of user k symbol, and for The projection length on the two boundaries, the target signal The real and imaginary parts of in and Indicates taking the real part and taking the imaginary part, constructing a diagonal matrix M R 、M I 、N R 、N I And the vector δ is as follows Where diag{·} means constructing a diagonal matrix with the elements in the brackets, and further constructing a block diagonal matrix So under the constraint The target signal vector The real number expression is Where δ±0 means that all elements of the vector δ are greater than 0, is the target signal vector, s=[s1,s2,...,s K ] T is the user symbol vector; The precoding design optimization problem in step 3 is expressed as Taking the expectation of the noise vector n, the optimization problem is transformed into in For the defined block diagonal matrix, the remaining matrices and vectors are defined as follows From Cholesky decomposition Get the upper triangular matrix C and construct the matrix B = C -1 and vector The above optimization problem is transformed into This is the non-negative least squares problem transformed from the original optimization problem; The favorable interference area of ​​the internal symbol points in the user symbols that cannot be optimized in step 4 is themselves, so there is no boundary; when the transmitted symbols are all orthogonal amplitude modulation symbols, Λ is a diagonal matrix with non-zero diagonal elements; when the real part or imaginary part of the user transmitted symbol is inside, the diagonal element of the corresponding position of Λ is 0, and the 0 in the diagonal element makes the corresponding column in BΛ all 0, and also keeps the corresponding element of δ in the optimization process 0, that is, some elements in δ do not need to be optimized; so it is defined Where T is the set of numbers of non-zero diagonal elements in Λ, K T is the cardinality of T and has K T ≤2K, B [:,j∈T] is the matrix composed of the columns of B whose serial numbers belong to the set T, Λ [jj∈T] is the diagonal matrix composed of the diagonal elements whose numbers belong to the set T, [j∈T] is the vector of elements whose serial numbers belong to the set T, so the original non-negative least squares problem is transformed into Compared with the original non-negative least squares problem, the above optimization problem reduces the optimization variable dimension from 2K to K T .

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