A robust symbol-level precoding method against channel aging effect

Abstract

The application provides a robust symbol-level precoding method against channel aging effect, wherein a cell base station uses channel state information affected by channel aging effect collected in uplink channel and user's sending symbol information to perform symbol-level precoding on sending symbols and transmit signals. The method proposes corresponding precoding schemes for two criteria of maximizing worst user's signal-to-interference-and-noise ratio and minimizing weighted mean square error between demodulation receiving signal and target constellation point. The precoding scheme design for maximizing worst user's signal-to-interference-and-noise ratio is converted into a fractional programming problem and solved, and the problem in the precoding scheme design for minimizing weighted mean square error is solved through an alternating optimization algorithm. The two schemes respectively improve user's signal-to-interference-and-noise ratio and reduce weighted mean square error between demodulation receiving signal and target constellation point while significantly reducing transmission symbol error rate.

Description

Technical Field

[0001] This invention belongs to the field of communications, and specifically relates to a robust symbol-level precoding method to combat channel aging effects. Background Technology

[0002] With the development of the information age, the demand for wireless communication data transmission has increased significantly. The increase in the number of base station antennas has significantly improved spectrum utilization, while the large-scale antenna arrays on the base station side can provide high degrees of freedom for communication. In addition, since the computing power of the base station is much higher than that of the terminal, complex calculations are usually transferred to the base station, thereby reducing the receiving complexity of the mobile terminal.

[0003] To fully utilize spatial freedom and further reduce intra- and inter-cell interference, precoding technology has become a key focus of current downlink research. "Precoding" refers to the design of transmitted signals that directs desired data symbols to the intended user by utilizing channel state information and information about possible data symbols, while limiting inter-user interference.

[0004] Traditional precoding treats user data as a Gaussian distribution, requiring only channel state information (CSO) during precoding, without needing to know the user data itself; this is called block-level precoding. If the base station uses both modulation scheme and user data information in addition to CSO during precoding, the performance of precoding will be further improved; this is called symbol-level precoding. Unlike block-level precoding, symbol-level precoding simultaneously develops both CSO and transmitted symbol characteristics, thus achieving significant gains in some metrics. Obtaining accurate CSO is a prerequisite for high-performance precoding. In static channel environments, accurate CSO can be obtained using conventional channel estimation methods. However, actual wireless channels are constantly changing, especially in mobile scenarios, where the rate of channel change is affected by the relative speed of the mobile device and the base station. The process of channel change from estimation to downlink transmission is called channel aging, and it is one of the important reasons for imperfect channel information in mobile environments. Summary of the Invention

[0005] Technical Problem: The purpose of this invention is to provide a robust symbol-level precoding method to combat channel aging effects. Two symbol-level precoding schemes for achieving high-quality transmission are provided based on two different criteria, thereby improving the performance of wireless communication systems.

[0006] Technical solution: To achieve the above-mentioned objective, the present invention provides a robust symbol-level precoding method against channel aging effects, comprising the following steps:

[0007] A robust symbol-level precoding method to combat channel aging effects includes the following steps:

[0008] Step 1: In a wireless communication transmission system, the base station collects aging channel state information through the uplink channel;

[0009] Step 2: Model the downlink channel based on the posterior channel model of the joint correlation channel model, thereby obtaining the received signal model affected by the channel aging effect;

[0010] Step 3: Based on the received signal model and the favorable interference area, and with the transmit power as a constraint, establish an optimization problem for maximizing the signal-to-interference-plus-noise ratio of the worst user.

[0011] Step 4: Transform the precoding design optimization problem into a fractional programming problem;

[0012] Step 5: Solve the fractional programming problem to obtain the symbol-level precoding scheme that maximizes the worst user signal-to-interference-plus-noise ratio;

[0013] Step 6: Based on the transmission signal model and the favorable interference area, and with the transmission power as a constraint, establish an optimization problem for minimizing the weighted mean square error between the received signal to be demodulated and the target constellation points.

[0014] Step 7: By fixing some variables and optimizing the remaining variables, two sub-problems are obtained, and the optimal solution form for each sub-problem is obtained.

[0015] Step 8: Construct an alternating optimization algorithm based on the optimal solution form of the subproblem, and solve the optimization problem to obtain a symbol-level precoding scheme that minimizes the weighted mean square error.

[0016] Preferably, in step 1, the wireless communication transmission system is a MISO system, wherein the base station is equipped with multiple antennas and transmits signals to multiple single-antenna terminals in the cell; the channel state information collected in the uplink channel is aged channel state information, that is, there is an interval between the time of collecting the channel state information in the uplink channel and the time of downlink transmission; the base station uses phase shift keying modulation to modulate the user transmit symbols.

[0017] Preferably, the posterior channel model in step 2 is represented as follows:

[0018]

[0019] Among them, h k It is the frequency domain channel matrix from the base station to user k, with dimensions N×1. It is the frequency domain channel matrix estimated by the base station from the uplink training sequence, with dimensions N×1, V D It is a matrix composed of discrete Fourier transform matrices, with dimensions N×F. vh N, V represents D The conjugate matrix, m kIt is a sparse vector with non-negative elements and dimension F. vh N×1, g k It is an element-independent random vector that follows a complex Gaussian distribution with variance of 1 and has dimension F. vh N×1, α k and The correlation coefficient related to moving speed and aging time introduced to model the time-varying channel using a first-order Markov model is the Hadamard product, where N is the number of base station transmit antennas, and F is the Hadamard product. vh It is an oversampling factor used to improve channel accuracy.

[0020] Preferably, the transmitted signal on the base station side in step 2 is represented as follows:

[0021]

[0022] Where, x c For transmitting signals, the dimension is N×1, s c =[s1,s2,...,s K ] T Send symbols to the user, with a dimension of K×1, where s k The symbol sent to user k, where K is the total number of users, σ 2 Let SLP(·) be the variance of the user-side complex Gaussian noise, and SLP(·) be the symbol-level precoder; the received signal of user k can be expressed as... Where n k The user-side noise follows a complex Gaussian distribution with variance σ. 2 Substituting into the posterior channel model, the received signal of user k is further expressed as:

[0023]

[0024] Where the matrix Define matrix Where matrix v i for If the i-th row is given, then the received signal of user k is further expressed as:

[0025]

[0026] Define variables The user's received signal model in step 2 is represented as follows:

[0027]

[0028] Where n k Follows the variance The complex Gaussian distribution.

[0029] Preferably, the advantageous interference area in step 3 Represented as

[0030]

[0031] in Representative located at The signal in μ k and ν k For the symbol s k Two standardized boundaries of the favorable interference region, This indicates the extent to which the signal extends along the two boundaries; further...

[0032]

[0033] in, and These represent taking the imaginary part and the real part, respectively. The target signal vector, δ≥0 means that all elements of δ are greater than 0, and the matrix M R M I N R and N I It is a diagonal matrix, constructed as follows:

[0034]

[0035]

[0036]

[0037]

[0038] Where diag{·} means constructing a diagonal matrix using the elements within the parentheses.

[0039] Preferably, the transmit power constraint in step 3 is expressed as follows:

[0040]

[0041] Where P T The maximum transmit power of the base station; the constraints introduced by the favorable interference area are expressed as follows:

[0042]

[0043] Where γ k Let be the rescaling factor at user k's receiver; the constraints introduced in the favorable interference region transform all interference into favorable interference, therefore the signal-to-interference-plus-noise ratio (SNR) at user k's receiver is expressed as:

[0044]

[0045] because The lower limit of the signal-to-interference-plus-noise ratio is expressed as:

[0046]

[0047] Therefore, the optimization problem established in step 3 for maximizing the signal-to-interference-plus-noise ratio (SIR) of the worst user is expressed as follows:

[0048]

[0049] in

[0050] Beneficial Effects: The robust symbol-level precoding method against channel aging effects provided by this invention utilizes a posterior channel model based on a joint correlation channel model and the concept of favorable interference regions in symbol-level precoding. It proposes corresponding precoding schemes for two criteria: maximizing the signal-to-interference-plus-noise ratio (SNR) for the worst-case user and minimizing the weighted mean square error (MSE) between the received signal to be demodulated and the target constellation point. The design of the precoding scheme maximizing the SNR for the worst-case user is transformed into a fractional programming problem, while the design of the precoding scheme minimizing the MSE is solved through an alternating optimization algorithm. Thus, in today's information age where mobile wireless communication systems have high data transmission demands, this invention provides two high-quality symbol-level precoding schemes for each criterion, thereby improving the performance of wireless communication systems. Attached Figure Description

[0051] Figure 1 A schematic diagram of the favorable interference region for phase shift keying modulation symbols;

[0052] Figure 2 A schematic diagram of a transmission system using a robust symbol-level precoding method to combat channel aging effects;

[0053] Figure 3 Flowchart of a robust symbol-level precoding method to combat channel aging effects. Detailed Implementation

[0054] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0055] The present invention discloses a robust symbol-level precoding method to combat channel aging effects, which mainly includes the following steps:

[0056] (1) In a wireless communication transmission system, the base station collects aging channel state information through the uplink channel;

[0057] (2) Model the downlink channel based on the posterior channel model based on the joint correlation channel model, and thus obtain the received signal model affected by the channel aging effect;

[0058] (3) Based on the received signal model and the favorable interference area, and with the transmit power as a constraint, an optimization problem is established for the criterion of maximizing the signal-to-interference-plus-noise ratio of the worst user.

[0059] (4) Transform the precoding design optimization problem into a fractional programming problem;

[0060] (5) Solve the fractional programming problem to obtain the symbol-level precoding scheme that maximizes the worst user signal-to-interference-plus-noise ratio;

[0061] (6) Based on the transmission signal model and favorable interference area, with the transmission power as a constraint, an optimization problem is established for the criterion of minimizing the weighted mean square error between the demodulated received signal and the target constellation point;

[0062] (7) By fixing some variables and optimizing the remaining variables, two sub-problems are obtained, and the optimal solution form of the corresponding sub-problems is obtained;

[0063] (8) Construct an alternating optimization algorithm based on the optimal solution form of the subproblem, and solve the optimization problem to obtain a symbol-level precoding scheme that minimizes the weighted mean square error.

[0064] The following is based on Figure 2 Taking a robust symbol-level precoding method against channel aging effects as an example, a cell is configured with one base station, and the base station is equipped with a uniform linear or area array antenna with N transmit antennas. There are K legitimate users in the cell, each equipped with a single receive antenna. The downlink transmission system operates in full-duplex mode, where time resources are divided into time slots, each time slot containing some uplink training symbols and N... ds There are h downlink transmission symbols. During the duration of a certain downlink transmission symbol, the downlink channel from the base station to user k is h. k ∈ N×1 Given the aged channel state information estimated by the base station from the uplink training symbols. Using a posterior channel model based on the joint correlation channel model, h k It can be modeled as

[0065]

[0066] in, It is a matrix composed of discrete Fourier transform matrices. V represents D The conjugate matrix, It is a sparse vector with non-negative elements. α is an element-independent random vector that follows a complex Gaussian distribution with variance of 1.k and The correlation coefficient related to moving speed and aging time is introduced for using a first-order Markov model to model the time-varying channel, denoted as the Hadamard product, where N is the number of base station transmit antennas, and F is the number of base station transmit antennas. vh The oversampling factor is used to improve channel accuracy; the user-transmitted symbol can be represented as s. c =[s1,s2,...,s K ] T ∈ K×1 , where s k Let K be the symbol sent to user k, where K is the total number of users. The received signal for user k can be represented as:

[0067]

[0068] in, n k Let user k terminals follow a mean of 0 and a variance of σ. 2 Additive noise with a complex Gaussian distribution. c ∈ N×1 The transmitted signal calculated by the symbol-level precoder SLP(·) is...

[0069]

[0070] in σ 2 This is information known to the base station. (From h) k The posterior channel model, the received signal can be further represented as

[0071]

[0072] in, The second term is the interference introduced by the aging channel state information, which can be simplified as follows:

[0073]

[0074] in, v i yes The i-th row. By defining... The received signal can be further represented as

[0075]

[0076] in Follows the pattern with mean 0 and variance of The signal to be demodulated follows a complex Gaussian distribution.

[0077]

[0078] Where γk The rescaling factor optimized for the symbol-level precoder.

[0079] Favorable interference regions are defined as areas on the constellation diagram with lower false sign rates compared to the original sign points, typically extending outwards from boundary constellation points, such as... Figure 1 As shown. The target signal for user k is The target signal is constrained to the transmitted symbol s of user k. k Favorable interference area The interior can be represented as:

[0080]

[0081] in

[0082]

[0083] in Representative located at The signal in μ k and ν k For the symbol s k The two standardized boundaries of the favorable interference region can be determined according to s k Easily obtained It indicates the extent to which the signal extends along the two boundaries.

[0084] First, consider a robust precoding design based on the criterion of maximizing the worst-case user signal-to-interference-plus-noise ratio (SIR). This involves constraining the rescaled, noise-free received signal within a favorable interference region. This expression can be further written as This constraint transforms all user interference into beneficial interference; therefore, the signal-to-interference-plus-noise ratio (SNR) for user k can be expressed as:

[0085]

[0086] in because Therefore, the lower bound of SINR can be expressed as

[0087]

[0088] Based on this, the robust symbol-level precoding design problem that maximizes the worst user signal-to-interference-plus-noise ratio can be expressed as:

[0089]

[0090] Where P T Let be the maximum power of the transmitter. and Representing taking the imaginary and real parts respectively, by defining the following matrix

[0091]

[0092]

[0093] This optimization problem can be further transformed into

[0094]

[0095] in, I2 represents an identity matrix with dimension 2×2. M R M I N R and N I It is a diagonal matrix, constructed as follows:

[0096]

[0097]

[0098]

[0099]

[0100] Where diag{·} denotes constructing a diagonal matrix using the elements within the parentheses. Since ΓΛ=ΛΓ, the first constraint in the above problem can be transformed into Λ -1 (Hx-Γs)=Γδ, which can be further combined with the third constraint to form

[0101] stΛ -1 (Hx-Γs)≥0

[0102] Therefore, the optimization problem can be further transformed into

[0103]

[0104] For simplicity, E is used here. k express This is a typical max-min fractional programming problem, which can be solved using the generalized Tinkelbach algorithm to obtain the optimal x and γ1,...,γ. K The transmitted signal x is further obtained. c Thus, a robust precoding design based on the criterion of maximizing the worst user signal-to-interference-plus-noise ratio is completed.

[0105] Secondly, robust precoding design based on the minimum weighted mean square error criterion is considered. The optimization problem established by the criterion of minimizing the weighted mean square error between the received signal to be demodulated and the target constellation points can be expressed as follows:

[0106]

[0107] in, To simplify the solution to the above problem, new variables η and ψ1,...,ψ are introduced. K and define The above problem can be further written as

[0108]

[0109] in Furthermore, the real number expression of the above problem can be represented as:

[0110]

[0111] in Fixed variables ψ1,...,ψ K The first subproblem of the above problem can be represented as:

[0112]

[0113] The optimal solution to this problem can be expressed as follows:

[0114]

[0115]

[0116]

[0117] Where δ,x,η represent the optimal δ,x,η, and B comes from the Choliski decomposition B. T B = N(I) 2K -ΨHP),

[0118]

[0119]

[0120]

[0121] With variables x, δ, and η > 0, the second subproblem of minimizing the weighted mean square error in step 7 can be expressed as follows:

[0122]

[0123] By relating the objective function to ψ k Setting the gradient to zero, we can obtain the following expression:

[0124]

[0125] in If the above expression is non-negative, then it is optimal for the second subproblem. Therefore, the following alternating optimization algorithm can be proposed:

[0126] a. Initialize ψ1=ψ2=...=ψ K =1.

[0127] b. Fix ψ1,...,ψ K Calculate the optimal δ, x, and η for the first subproblem.

[0128] c. Fixing δ, x, and η, calculate the optimal ψ for the second subproblem. k .

[0129] d. Iterate through steps b and c until the stopping iteration condition is met.

[0130] This algorithm can obtain better x,δ,ψ1,...,,ψ K ,η, and further obtain a better x c and γ1,...,γ K Thus, a robust precoding design based on the minimum weighted mean square error criterion is completed.

[0131] Based on the two criteria of maximizing the worst user signal-to-interference-plus-noise ratio and minimizing the weighted mean square error, the symbol-level precoder on the base station side can obtain and solve the corresponding optimization problem for each set of user symbols according to the above method, thereby providing a robust precoding scheme and updating the transmitted signal at the symbol level.

[0132] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A robust symbol-level precoding method to combat channel aging effects, characterized in that, Includes the following steps: Step 1: In a wireless communication transmission system, the base station collects aging channel state information through the uplink channel; Step 2: Model the downlink channel based on the posterior channel model of the joint correlation channel model, thereby obtaining the received signal model affected by the channel aging effect; Step 3: Based on the received signal model and the favorable interference area, and with the transmit power as a constraint, establish an optimization problem for maximizing the signal-to-interference-plus-noise ratio of the worst user. Step 4: Transform the precoding design optimization problem into a fractional programming problem; Step 5: Solve the fractional programming problem to obtain the symbol-level precoding scheme that maximizes the signal-to-interference-plus-noise ratio (SIR) for the worst user; the optimization problem established based on the criterion of maximizing the SIR for the worst user is expressed as: in, As the lower bound of the signal-to-interference-plus-noise ratio, the matrix , This is the frequency domain channel matrix estimated by the base station from the uplink training sequence. The correlation coefficients related to mobile speed and aging time are introduced to model the time-varying channel using a first-order Markov model. In order to transmit signals, Total number of users , For users The rescaling factor at the receiving end, For the area of ​​favorable interference, This is the maximum transmit power of the base station; Step 6: Based on the transmission signal model and favorable interference region, and using the transmit power as a constraint, an optimization problem is established to minimize the weighted mean square error between the demodulated received signal and the target constellation points. The problem is expressed as follows: Among them, variables ,matrix , To conform to the variance is The complex Gaussian distribution, To model the correlation coefficients related to mobile speed and aging time introduced by the first-order Markov model for time-varying channels, the matrix... , Let be a sparse vector with non-negative elements, and a matrix. for The first row, matrix for The Nth line, It is a matrix composed of discrete Fourier transform matrices. The variance of the complex Gaussian noise on the user side is represented by the matrix. , Located in a favorable interference area Signals, matrices ; Step 7: By fixing some variables and optimizing the remaining variables, two sub-problems are obtained, and the optimal solution form for each sub-problem is obtained. Step 8: Construct an alternating optimization algorithm based on the optimal solution form of the subproblem, and solve the optimization problem to obtain a symbol-level precoding scheme that minimizes the weighted mean square error.

2. The robust symbol-level precoding method against channel aging effects according to claim 1, characterized in that: In step 1, the wireless communication transmission system is a MISO system, in which the base station is equipped with multiple antennas and transmits signals to multiple single-antenna terminals in the cell; the channel state information collected in the uplink channel is aged channel state information, that is, there is an interval between the time when the channel state information is collected in the uplink channel and the time when the downlink transmission occurs. The base station uses phase shift keying to modulate the user transmit symbols.

3. A robust symbol-level precoding method against channel aging effects according to claim 2, characterized in that: The posterior channel model in step 2 is represented as follows: in, It is from base station to user The frequency domain channel matrix, with dimension , It is the frequency domain channel matrix estimated by the base station from the uplink training sequence, with dimensions of , It is a matrix composed of discrete Fourier transform matrices, with dimension 1. , express The conjugate matrix, It is a sparse vector with non-negative elements and dimension . , It is an element-independent random vector that follows a complex Gaussian distribution with variance of 1 and has dimension . , and The correlation coefficients related to mobile speed and aging time are introduced to model the time-varying channel using a first-order Markov model. For Hadama accumulation, The number of base station transmit antennas. It is an oversampling factor used to improve channel accuracy.

4. A robust symbol-level precoding method against channel aging effects according to claim 3, characterized in that: The transmitted signal from the base station side in step 2 is represented as follows: in, To transmit a signal, the dimension is , Send symbols to users, with dimensions of ,in To send to users symbols, Total number of users The variance of complex Gaussian noise on the user side. For symbol-level precoders; users The received signal can be represented as ,in The user-side noise follows a complex Gaussian distribution with variance . Substituting into the posterior channel model, the user The received signal is further represented as: Where the matrix Define matrix , where the matrix for The Okay, then the user The received signal is further represented as: Define variables The user's received signal model in step 2 is represented as follows: in Follows the variance The complex Gaussian distribution.

5. A robust symbol-level precoding method against channel aging effects according to claim 4, characterized in that: The advantageous interference area in step 3 Represented as: in Representative located at The signal in and For symbols Two standardized boundaries of the favorable interference region, This indicates the extent to which the signal extends along the two boundaries; further, we have: in, and These represent taking the imaginary part and the real part, respectively. The target signal vector, , express All elements of the matrix are greater than 0. , , , and It is a diagonal matrix, constructed as follows: in This indicates that a diagonal matrix is ​​constructed using the elements within the parentheses.

6. A robust symbol-level precoding method against channel aging effects according to claim 5, characterized in that: The transmit power constraint in step 3 is expressed as follows: in The maximum transmit power of the base station; the constraints introduced by the favorable interference area are expressed as: in For users The rescaling factor at the receiving end; The constraints introduced in the favorable interference region transform all interference into favorable interference, thus the user The signal-to-interference-plus-noise ratio (SIR) at the receiver is expressed as: because The lower limit of the signal-to-interference-plus-noise ratio is expressed as: 。 7. A robust symbol-level precoding method against channel aging effects according to claim 6, characterized in that: The precoding optimization problem in step 4 is transformed without loss of optimality into: in , The dimension is The identity matrix, and the definitions of the remaining variables are as follows: in for The real number representation; Then we have: For simplicity, parameters are used here. express .

8. A robust symbol-level precoding method against channel aging effects according to claim 7, characterized in that: The demodulated received signal in step 6 is represented as follows: The target constellation point is a point located within a favorable interference area; To simplify the solution of the optimization problem based on the criterion of minimizing the weighted mean square error between the received signal to be demodulated and the target constellation points, a new variable is introduced. and and define If k = (1, 2, ..., K), then we have: Where the matrix Furthermore: Where the matrix ,matrix .

9. A robust symbol-level precoding method against channel aging effects according to claim 8, characterized in that: The first sub - problem of minimizing the weighted mean - square error problem in step 7 is obtained by fixing the variables in the original problem and is expressed as: The optimal solution is expressed as: in Indicates the optimal , From Jolisky's decomposition , Fixed variables and The second subproblem of minimizing the weighted mean square error in step 7 is expressed as: By relative to the objective function Setting the gradient to zero, we get the expression: Where the matrix If the expression is non-negative, then it is the optimal expression for the second subproblem. .

10. A robust symbol-level precoding method against channel aging effects according to claim 9, characterized in that: The alternating optimization algorithm in step 8 includes: a. Initialization ; b. Fixed Calculate the optimal solution for the first subproblem. , and ; c. Fixed , and Calculate the optimal solution for the second subproblem. ; d. Iterate through steps b and c until the stopping iteration condition is met.

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