Digital demodulation method based on GAMP algorithm

Abstract

The invention belongs to the technical field of wireless communication, and relates to a digital demodulation method based on a GAMP algorithm. For a scene that the number of radio frequency links of a base station is less than that of users, the digital demodulation method comprises the following steps: the base station receives superposed signals input by multiple users; estimating a user input signal to obtain an initial solution of optimal estimation; determining a prior distribution of the user input signal; calculating conditional posteriori distribution of the user input signal and the noise-free user input signal modulated by the analog matrix, wherein the conditional posteriori distribution comprises expectation and variance; and obtaining a column of estimation results and corresponding variances based on a GAMP algorithm, wherein the estimation results are modulation data. The analog matrix adopted by the digital demodulation method demodulates the multi-user modulation signals under the condition that the number of radio frequency links of a base station is smaller than the number of users, and the modulation information of the multiple users is recovered by using fewer observation signals, namely, the users with the number larger than that of the radio frequency links can be served by using a limited number of radio frequency links.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a digital demodulation method based on the GAMP algorithm. Background Technology

[0002] For large-scale arrays, the dramatic increase in the number of array elements allows for the formation of very sharp, high-gain beams that can be aimed directly at target users, improving the signal-to-noise ratio (SNR) of the received signal. However, sharp, high-gain beams have extremely high directivity, causing a sharp drop in the signal power of users outside the beam. While this can suppress inter-user interference in traditional multi-user systems, with a large number of users, a few sharp beams will not be able to cover all users, leading to loss of user information.

[0003] The existing uplink multi-user beamforming concept is to design the receive beam so as not to sacrifice the signal-to-noise ratio of any user. Existing technologies include: multicast beamforming for a single network, where all users request common information from the transmitter and extend it to multiple network scenarios, with different user groups requesting different information from the transmitter.

[0004] Traditional multi-user beamforming designs face two main challenges: one is minimizing transmit power while meeting the minimum signal-to-noise ratio (SNR) requirement to improve Quality of Service (QoS); the other is maximizing the minimum SNR that satisfies the total transmit power limit. Both problems have been proven to be NP-hard, and therefore various approximation techniques have been demonstrated to be applicable to different scenarios.

[0005] The core problem in multi-user beamforming design is maximizing the minimum received signal-to-noise ratio (SNR) while satisfying the constant mode constraint of the phase shifter. Both problems are relaxed to semi-definite programming (SDP) problems, solvable using modern interior-point methods. Existing techniques include a Successive Linear Approximation (SLA) algorithm for QoS problems, based on Second-Order Cone Programming (SOCP). Another proposed technique is a Multiplicative Update (MU) algorithm based on a proportional fair agent, which is essentially a geometric mean smoothing of the minimum SNR objective. Experiments show that MU-SLA achieves a minimum SNR comparable to SLA but higher than all other algorithms. Furthermore, MU-SLA has a lower average computation time than SLA but higher than all other gradient-based methods.

[0006] In summary, for scenarios where the number of base station RF links is less than the number of users, a multi-user beam is designed to maximize the minimum received signal-to-noise ratio while satisfying the constant mode constraint of the phase shifter. This requires designing an analog matrix and performing digital demodulation to avoid losing signals from some users due to beam pointing issues. Summary of the Invention

[0007] The purpose of this invention is to propose a digital demodulation method based on the GAMP algorithm for scenarios where the number of base station radio frequency links is less than the number of users. By relying on the designed analog matrix, the underdetermined observation under modulation constraints is optimized, avoiding the loss of some user signals due to beam pointing problems, and ensuring the demodulation of multi-user modulated signals when the number of users is greater than the number of radio frequency links.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a digital demodulation method based on the GAMP algorithm, specifically for scenarios where the number of base station radio frequency links is less than the number of users. The digital demodulation method includes the following steps: S10. The base station receives multi-user input signals, which are the superposition of several user input signals; S11. Estimate the user input signal to obtain the initial solution of the optimal estimate; S12. Determine the prior distribution of the user input signal; S13. Calculate the conditional posterior distribution of the user input signal and the noise-free user input signal after analog matrix modulation; the conditional posterior distribution includes expectation and variance; S14. Based on the GAMP algorithm, a series of estimation results and their corresponding variances are obtained. The estimation results are the modulation data.

[0009] As one possible implementation, the multi-user input signal received by the base station in S10 is denoted as... Its expression is: ; in, The analog matrix used for large-scale array base stations; For the first Channel vectors corresponding to each user; For the first One user input signal; For noise; The channel matrix; , For the first The angle of incidence of the user input signal. Total number of users; for A user input signal, ; ; ,in It follows a cyclic Gaussian distribution with a mean of 0.

[0010] As one possible implementation method, simulation matrix Obtained through the following method: S100. The design problem of beam synthesizer is determined and simplified based on the principle of maximizing the lowest signal-to-noise ratio; The simplification is predicated on the following conditions: the number of antennas is much greater than the number of RF links and the noise follows an independent cyclic Gaussian distribution; S101. Vectorize the simplified beam synthesizer design problem and transform it into a convex optimization problem; S102. Solve and iterate the convex optimization problem, and construct the simulation matrix based on the obtained final normalized vector. .

[0011] As one possible implementation, the convex optimization problem is solved through iterative gradient descent and normalization processes to obtain the final normalized vector; The convergence condition for the normalization iteration is: , Not greater than 0.0001; where, For the first Normalized vector; For the first Normalized vector.

[0012] As one possible implementation, the initial solution of the optimal estimate in S11 is denoted as... Its expression is: ; in, To estimate the matrix, ; The channel matrix; for The conjugate transpose of; The analog matrix used for large-scale array base stations; for The conjugate transpose of; This refers to the multi-user input signals received by the base station.

[0013] As one possible implementation, the prior distribution of the user input signal in S12 is denoted as... Its expression is: ; in, It is 0.5; The Dirac function / impact function; for User input signal.

[0014] As one possible implementation, in S13 Each user input signal is denoted as The noise-free user input signal after analog matrix modulation is denoted as... ,make ,but The conditional posterior distribution is: ; in, The expected value of the input signal; The observation variance of the input signal; The prior distribution of the user input signal; This represents the total number of radio frequency links. It is 0.5; The Dirac function / impact function; Calculated using Gaussian approximation Expectation under conditional posterior distribution and variance Specifically: ; ; but The conditional posterior distribution is: in, The expected value of the received signal; The observation variance of the received signal; These are normalization parameters; Observational noise for received signals; Solving by Gaussian approximation Expectations and variance Specifically: ; .

[0015] As one possible implementation, the estimation result in S14 is denoted as Its expression is: ; The variance corresponding to the estimation result is denoted as Its expression is: .

[0016] As one possible implementation, starting from the initial solution of the optimal estimate in S11, the GAMP algorithm is applied iteratively, and after the iteration terminates, a series of estimation results and their corresponding variances are obtained.

[0017] As one possible implementation, the initial solution of the optimal estimate is expressed as: ; Its corresponding variance is expressed as: ; ; in, This indicates that, in the initial state, the expected initial value is 0. The iterative expression for the estimation result is: ; in, ; ; ; ; ; ; in, For the t-th iteration; Let m be the m rows and n columns of matrix B; for Conjugate matrix; ; ; ; ; in, The expected value of the input signal; The observation variance of the input signal; This refers to the number of radio frequency links; The expected value of the received signal; This represents the observation variance of the received signal.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The present invention proposes a digital demodulation method based on the GAMP algorithm, which can demodulate multi-user modulated signals in scenarios where the number of base station radio frequency links is less than the number of users, thereby optimizing underdetermined observations under modulation constraints and avoiding the loss of some user signals.

[0019] 2. The digital demodulation method based on the GAMP algorithm proposed in this invention can recover the modulation information of multiple users with fewer observed signals, allowing one radio frequency link to serve multiple users at the same time, that is, it can use a limited number of radio frequency links to serve more users than the number of radio frequency links.

[0020] 3. In the process of designing the digital demodulation method, this invention constructs an analog matrix that successfully achieves coherent combining of signals from multiple users and has a performance gain of approximately 10 dB compared to a random phase matrix. Attached Figure Description

[0021] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 Here is a flowchart of a digital demodulation method based on the GAMP algorithm; Figure 2 The graph shows the change of bit error rate of a signal with a random phase matrix as a function of signal-to-noise ratio. Figure 3 The graph shows the change in bit error rate of the signal with signal-to-noise ratio using the analog matrix of the present invention. Detailed Implementation

[0022] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0023] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0024] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one" or similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, "at least one of a, b, or c" can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0025] This invention aims to provide a digital demodulation method based on the GAMP algorithm to solve the problem of the number of users being limited by the number of radio frequency links, that is, to serve more users than the number of radio frequency links can be utilized with a limited number of radio frequency links. Specific implementation methods are as follows: This invention provides a digital demodulation method based on the GAMP algorithm, specifically for scenarios where the number of base station radio frequency links is less than the number of users. (See also...) Figure 1 The digital demodulation method includes the following steps: S10. The base station receives multi-user input signals, which are the superposition of several user input signals; As one possible implementation, the multi-user input signal received by the base station is denoted as... Its expression is: ; in, The analog matrix used for large-scale array base stations; For the first Channel vectors corresponding to each user; For the first One user input signal; For noise; The channel matrix; ; For the first The angle of incidence of the user input signal; Total number of users; for A user input signal, ; ; ,in It follows a cyclic Gaussian distribution with a mean of 0.

[0026] As one possible implementation method, simulation matrix Obtained through the following method: S100. The design problem of beam synthesizer is determined and simplified based on the principle of maximizing the lowest signal-to-noise ratio; The simplification is predicated on the following conditions: the number of antennas is much greater than the number of RF links and the noise follows an independent cyclic Gaussian distribution; For example, "far greater than" specifically means: the number of antennas is no less than ten times the number of radio frequency links, for example, eleven times, twelve times, or fifteen times.

[0027] For example, the design problem of a beam synthesizer is expressed as: ; in, For simulation matrix; For the first There are [number] users, and the total number of users is [number]. ; For the first The channel vector corresponding to each user and , For users The angle of incidence; For noise; These are constraints; For the first There are [number] radio frequency links, and the total number of radio frequency links is [number]. ; Indicates the first in the base station There are [number] antennas, and the total number of antennas is [number]. ; and As an example, design a radio frequency link number of N The total number of users served at the same time is K The number of antennas is M Large-scale array base stations, and Preferred, take M Greater than or equal to 32.

[0028] The signal received by the base station is a superposition of several user signals, expressed as: ; in, This refers to the multi-user input signals received by the base station; The analog matrix used for large-scale array base stations; The channel matrix; for K One user input signal; For the first k One user input signal; For noise; Among them, for users In other words, its angle of incidence is The corresponding channel vector is , The expression is: ; Summation Transformed into matrix form, that is: ; in, ; ; Among them, matrix Unsatisfactory rank; … Corresponding to antenna number 0 respectively... M -1 is the center frequency of antenna number 1; j represents the imaginary part; Indicates the distance between the two antennas; It represents the speed of light.

[0029] For example, the simplified beam synthesizer design problem is expressed as: ; ; in, These are constraints; For the first One radio frequency link; Indicates the first in the base station One antenna.

[0030] S101. Vectorize the simplified beam synthesizer design problem and transform it into a convex optimization problem; For example, the vectorization design problem of a beam synthesizer is expressed as: ; ; in, , representing the simulation matrix The vectorized form; for The conjugate transpose of; These are constraints; This represents the total number of radio frequency links. This represents the total number of antennas.

[0031] For example, Obtained through the following process: ; in, The channel covariance matrix, ; Channel vector transpose; Represents the identity matrix.

[0032] For example, the convex optimization problem is denoted as The expression is: ; in, A constant greater than 0; Let be the approximate objective function constructed; As constraints, it represents middle All vectors are 1; This represents the total number of radio frequency links. This represents the total number of antennas.

[0033] S102. Solve and iterate the convex optimization problem, and construct the simulation matrix based on the obtained final normalized vector. .

[0034] For example, this convex optimization problem is solved using the gradient descent method, and the resulting iterative vector representing the analog phase shifter is denoted as... The expression is: ; in, ; For the first Normalized vector; express right After finding the derivative and in The value at; = , A constant greater than 0 This represents the total number of antennas.

[0035] For example, iteration This process terminates and yields the final normalized vector. The expression is: .

[0036] The convergence condition for the normalization iteration is: , Not greater than 0.0001; where, For the first Normalized vector; For the first Normalized vector.

[0037] S11. Estimate the user input signal to obtain the initial solution of the optimal estimate; As one possible implementation, the initial solution for the optimal estimate is denoted as... Its expression is: ; in, To estimate the matrix, ; The channel matrix; for The conjugate transpose of; The analog matrix used for large-scale array base stations; for The conjugate transpose of; This refers to the multi-user input signals received by the base station.

[0038] S12. Determine the prior distribution of the user input signal; As one possible implementation, the prior distribution of the user input signal is denoted as... Its expression is: ; in, It is 0.5; The Dirac function / impact function; for User input signal.

[0039] S13. Calculate the conditional posterior distribution of the user input signal and the noise-free user input signal after analog matrix modulation; the conditional posterior distribution includes expectation and variance; As one possible implementation method, Each user input signal is denoted as The noise-free user input signal after analog matrix modulation is denoted as... ,make ,but The conditional posterior distribution is: ; in, The expected value of the input signal; The observation variance of the input signal; The prior distribution of the user input signal; This represents the total number of radio frequency links. It is 0.5; The Dirac function / impact function; Calculated using Gaussian approximation Expectation under conditional posterior distribution and variance Specifically: ; ; but The conditional posterior distribution is: in, The expected value of the received signal; The observation variance of the received signal; These are normalization parameters; Observational noise for received signals; Solving by Gaussian approximation Expectations and variance Specifically: ; .

[0040] S14. Based on the GAMP algorithm, a series of estimation results and their corresponding variances are obtained. The estimation results are the modulation data. As one possible implementation, the estimation result is denoted as Its expression is: ; The variance corresponding to the estimation result is denoted as Its expression is: .

[0041] As one possible implementation, starting from the initial solution of the optimal estimate in S11, the GAMP algorithm is applied iteratively, and after the iteration terminates, a series of estimation results and their corresponding variances are obtained.

[0042] As one possible implementation, the initial solution of the optimal estimate is expressed as: ; Its corresponding variance is expressed as: ; ; in, This indicates that, in the initial state, the expected initial value is 0. The iterative expression for the estimation result is: ; in, ; ; ; ; ; ; in, For the t-th iteration; Let m be the m rows and n columns of matrix B; for Conjugate matrix; ; ; ; ; in, The expected value of the input signal; The observation variance of the input signal; This refers to the number of radio frequency links; The expected value of the received signal; This represents the observation variance of the received signal.

[0043] This design allows for demodulation of multi-user modulated signals in scenarios where the number of base station radio frequency links exceeds the number of users, enabling optimization of underdetermined observations under modulation constraints and avoiding the loss of some user signals.

[0044] See Figures 2 to 3 The figure shows the experimental results comparing the bit error rate of signals using the GAMP algorithm, random phase matrix, and simulated matrix of this invention as a function of signal-to-noise ratio. Figure 2 The graph shows the change of bit error rate of a signal with a random phase matrix as a function of signal-to-noise ratio. Figure 3 The graph shows the change in bit error rate of a signal using an analog matrix as a function of signal-to-noise ratio.

[0045] As shown in the figure, under the conditions of 16, 32, and 64 antennas, 4 RF links, and 6, 8, and 10 users respectively, for the same number of users, the bit error rate performance of the random phase matrix remains basically unchanged as the number of antennas increases, while the bit error rate performance of the analog matrix of this invention improves. It can be deduced that the random phase matrix cannot achieve coherent combining of user signals, while the analog matrix of this invention combines noise signals along with signals from multiple antennas without changing the signal-to-noise ratio.

[0046] The analog matrix invented in this paper successfully achieves coherent combining of different signals from multiple users. Compared to a random phase matrix, the analog matrix of this invention has a performance gain advantage of approximately 10 dB.

[0047] The digital demodulation method based on the GAMP algorithm proposed in this invention enables the simulation matrix of this invention to demodulate multi-user modulated signals when the number of base station radio frequency links is less than the number of users, thereby optimizing underdetermined observations under modulation constraints and avoiding the loss of some user signals. By using fewer observed signals, the modulation information of multiple users can be recovered, allowing one radio frequency link to serve multiple users simultaneously, that is, it is possible to use a limited number of radio frequency links to serve more users than the number of radio frequency links.

[0048] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the description of the drawings, in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components. A single processor or other unit can implement several of the functions listed in the specification. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0049] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications fall within the scope of the invention and its equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A digital demodulation method based on the GAMP algorithm, for scenarios where the number of base station radio frequency links is less than the number of users, characterized in that, The digital demodulation method includes the following steps: S10. The base station receives a multi-user input signal, wherein the multi-user input signal is the superposition of several user input signals; S11. Estimate the user input signal to obtain the initial solution of the optimal estimate; S12. Determine the prior distribution of the user input signal; S13. Calculate the conditional posterior distribution of the user input signal and the noise-free user input signal after analog matrix modulation; the conditional posterior distribution includes expectation and variance; S14. Based on the GAMP algorithm, a series of estimation results and their corresponding variances are obtained, and the estimation results are the modulation data.

2. The digital demodulation method based on the GAMP algorithm according to claim 1, characterized in that, The multi-user input signal received by the base station in S10 is denoted as Its expression is: ； in, The analog matrix used for large-scale array base stations; For the first Channel vectors corresponding to each user; For the first One user input signal; For noise; The channel matrix; ; For the first The angle of incidence of the user input signal; Total number of users; for A user input signal, ; ; ,in It follows a cyclic Gaussian distribution with a mean of 0.

3. The digital demodulation method based on the GAMP algorithm according to claim 2, characterized in that, Simulation matrix Obtained through the following method: S100. The design problem of beam synthesizer is determined and simplified based on the principle of maximizing the lowest signal-to-noise ratio; The simplification is predicated on the following conditions: the number of antennas is much greater than the number of radio frequency links and the noise follows an independent cyclic Gaussian distribution. S101. Vectorize the simplified beam synthesizer design problem and transform it into a convex optimization problem; S102. Solve and iterate the convex optimization problem, and construct the simulation matrix based on the obtained final normalized vector. .

4. The digital demodulation method based on the GAMP algorithm according to claim 3, characterized in that, The convex optimization problem is solved by iterative gradient descent and normalization processes to obtain the final normalized vector; The convergence condition for the normalization iteration is: , Not greater than 0.0001; where, For the first Normalized vector; For the first Normalized vector.

5. The digital demodulation method based on the GAMP algorithm according to claim 2, characterized in that, The initial solution of the optimal estimate in S11 is denoted as... Its expression is: ； in, To estimate the matrix, ; The channel matrix; for The conjugate transpose of; The analog matrix used for large-scale array base stations; for The conjugate transpose of; This refers to the multi-user input signals received by the base station.

6. The digital demodulation method based on the GAMP algorithm according to claim 2, characterized in that, The prior distribution of the user input signal in S12 is denoted as follows: Its expression is: ； in, It is 0.5; The Dirac function / impact function; for User input signal.

7. The digital demodulation method based on the GAMP algorithm according to claim 2, characterized in that, In S13 Each user input signal is denoted as The noise-free user input signal after analog matrix modulation is denoted as... ,make ,but The conditional posterior distribution is: ； in, The expected value of the input signal; The observation variance of the input signal; The prior distribution of the user input signal; This represents the total number of radio frequency links. It is 0.5; The Dirac function / impact function; Calculated using Gaussian approximation Expectation under conditional posterior distribution and variance Specifically: ； ； but The conditional posterior distribution is: in, The expected value of the received signal; The observation variance of the received signal; These are normalization parameters; Observational noise for received signals; Solving by Gaussian approximation Expectations and variance Specifically: ； 。 8. The digital demodulation method based on the GAMP algorithm according to claim 2, characterized in that, The estimation result in S14 is denoted as Its expression is: ； The variance corresponding to the estimation result is denoted as Its expression is: 。 9. The digital demodulation method based on the GAMP algorithm according to claim 8, characterized in that, Starting with the initial solution of the optimal estimate in S11, the GAMP algorithm is applied iteratively. After the iteration terminates, a series of estimation results and their corresponding variances are obtained.

10. The digital demodulation method based on the GAMP algorithm according to claim 9, characterized in that, The initial solution of the optimal estimate is expressed as: ； Its corresponding variance is expressed as: ； ； in, This indicates that, in the initial state, the expected initial value is 0. The iterative expression for the estimation result is: ； in, ; ； ； ； ； ； in, For the t-th iteration; Let m be the m rows and n columns of matrix B; for Conjugate matrix; ； ； ； ； in, The expected value of the input signal; The observation variance of the input signal; This refers to the number of radio frequency links; The expected value of the received signal; This represents the observation variance of the received signal.

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