Hybrid precoding method and system of multi-user millimeter wave system

Abstract

The invention discloses a hybrid precoding method and system for a multi-user millimeter wave system, and the method comprises the steps: constructing an RIS-assisted multi-user millimeter wave joint beam forming optimization problem model with the minimization of a mean square error between a received signal and a transmitted signal as a target through a channel from a base station to a reconfigurable intelligent surface and a channel from the intelligent surface to a user; based on the optimization problem model, constructing a closed-form solution of an optimal digital beam forming matrix based on a KKT condition; obtaining norm constraints of the analog precoder and the phase shifter based on a popular optimization method according to constraint conditions of the analog precoder and the phase shifter; and substituting a closed-form solution for implementing the optimal digital beam forming matrix into a target function MSE, and realizing an approximate optimal solution of an analog pre-coding matrix and an RIS reflection beam forming matrix by using an alternating minimization method. The reconfigurable intelligent reflecting surface is adopted, so that the probability of communication interruption caused by communication blockage can be obviously reduced, and the reliability of a communication system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a hybrid precoding method and system for a multi-user millimeter wave system. Background Art

[0002] In current communication systems, millimeter waves, due to their abundant spectrum resources, are considered a potential technology for meeting the high data rate requirements of current and future wireless networks. However, millimeter waves have a short wavelength, resulting in severe path loss. Despite this, their short wavelength allows for the deployment of large-scale antenna arrays to provide high array gain and improve link quality. Although severe path loss can be compensated for by high array gain, the highly directional beam and high penetration loss from obstructions degrade the link quality of millimeter wave transmissions. Therefore, relay-assisted millimeter wave communication systems have been proposed as a solution.

[0003] With recent advances in electromagnetic metasurface technology, reconfigurable smart surfaces (RIS) are being considered as a cost-effective and energy-efficient alternative to relay systems. RIS can control the reflection behavior of incident electromagnetic signals through reflective elements implemented with low-cost programmable passive components. RIS constructively combines the signals from the reflective elements to create a spectrally efficient wireless propagation environment, eliminating the need for additional RF chains and thermal noise. Furthermore, RIS are easy to manufacture, compact, lightweight, and can be applied to building facades, walls, and other surfaces, offering numerous advantages. Given the numerous benefits offered by RIS, there has been work on the design of RIS-assisted multiple-input, single-output (MISO) communication systems. Therefore, multi-user systems are of great significance. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a hybrid precoding method and system for a multi-user millimeter wave system. The hybrid precoding method for a multi-user millimeter wave system includes:

[0005] Through the channels from the base station to the reconfigurable smart surface and from the smart surface to the user, a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is constructed with the goal of minimizing the mean square error between the received and transmitted signals.

[0006] Based on the multi-user millimeter wave joint beamforming optimization problem model, a closed-form solution of the optimal digital beamforming matrix based on the KKT condition is constructed;

[0007] According to the constraints of the analog precoder and phase shifter, the normal mode constraints of the analog precoder and phase shifter are obtained based on the popular optimization method;

[0008] The closed-form solution of the optimal digital beamforming matrix is ​​substituted into the objective function MSE, and the approximate optimal solutions of the analog precoding matrix and the RIS reflective beamforming matrix are achieved using the alternating minimization method.

[0009] Preferably, the process of constructing a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received signal and the transmitted signal includes:

[0010] Representing the received signals of the end users, and obtaining a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model based on the received signals using an improved mean square error as a performance metric and optimization target;

[0011] Calculating according to the received signal and the RIS-assisted multi-user millimeter wave joint beamforming optimization problem model, obtaining a hybrid precoding and phase shift problem model for a RIS-assisted MU millimeter wave communication system jointly designed based on the MMES criterion;

[0012] Based on the hybrid precoding and phase shift problem model, as well as the transmit power constraint and constant modulus constraint of the phase shifter, an optimization problem is obtained, and then a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received signal and the transmitted signal is obtained.

[0013] Preferably, the signal expression of the received signal is:

[0014]

[0015] The expression of the RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is:

[0016]

[0017] in, is satisfied The transmitted signal vector, P is the total transmission power, K is the number of users, n~CN(0,σ 2 I K ) is the additive Gaussian noise vector, is the phase shift matrix of the reconfigurable smart surface, where each Ψ r All satisfied is the millimeter wave channel between RIS and BS, is the millimeter wave channel vector between the kth UE and RIS, where “digital precoder” Analog Precoder at the same time

[0018] Preferably, the process of obtaining a hybrid precoding and phase shift problem model for a RIS-assisted MU millimeter wave communication system jointly designed based on the MMES criterion includes:

[0019] Substituting formula (1) into formula (2), where ζ is the scaling factor, the hybrid precoding and phase shift problem model is calculated as:

[0020]

[0021] Based on the hybrid precoding and phase shift problem model, as well as the transmit power constraint and constant modulus constraint of the phase shifter, the optimization problem is obtained, and then the final multi-user millimeter wave joint beamforming optimization problem model is obtained as follows:

[0022]

[0023] Among them, N t The number of transmitting antennas, R is the number of RIS reflector array elements.

[0024] Preferably, based on the multi-user millimeter wave joint beamforming optimization problem model, the process of constructing a closed-form solution of the optimal digital beamforming matrix based on the KKT condition includes:

[0025] By fixing F RF and Ψ to derive the optimal digital precoding matrix F BB and scaling factor ζ, then according to the KKT condition, formula (4) is used as The function of Take the derivative and set it to zero to find the optimal solution The closed-form solution of .

[0026] Preferably, by fixing F RF and Ψ to derive the optimal digital precoding matrix F BB The process of finding the scaling factor ζ includes:

[0027] Ignore F RF ,Ψ constraint, definition The multi-user millimeter wave joint beamforming optimization problem model is rewritten as:

[0028]

[0029] The formula expression of the scaling factor ζ is:

[0030]

[0031] The optimal The closed-form solution is

[0032]

[0033] The best Substituting the closed-form solution of and ζ into equation (5), the new mean square error is derived as follows:

[0034]

[0035] Preferably, according to the constraints of the analog precoder and the phase shifter, the process of obtaining the normal mode constraints of the analog precoder and the phase shifter based on the popular optimization method includes:

[0036] The optimization problem in formula (5) is reduced to the following:

[0037]

[0038]

[0039] Among them, for complex-valued variables (F RF ,Ψ), the corresponding scalar function J(F RF ,Ψ), the conjugate gradient is defined as

[0040] Then, the manifold optimization algorithm is used to find the derivative function J(F RF ,Ψ) respectively about F RF , the conjugate gradient of Ψ is defined by Then according to d(J(A))=tr(P -1 d(P)P -1 ), apply the matrix gradient formula to solve J(F RF ,Ψ) respectively about F RF The conjugate gradient of and Ψ is:

[0041]

[0042] The present invention also provides a hybrid precoding system for a multi-user millimeter wave system, comprising:

[0043] A model building module is used to construct a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received and transmitted signals through the channels from the base station to the reconfigurable smart surface and from the smart surface to the user;

[0044] An initial solution module is used to construct a closed-form solution of an optimal digital beamforming matrix based on KKT conditions based on the multi-user millimeter wave joint beamforming optimization problem model;

[0045] A constraint acquisition module, configured to obtain normal mode constraints of the analog precoder and the phase shifter based on the constraints of the analog precoder and the phase shifter and based on a popular optimization method;

[0046] The target solving module is used to substitute the closed-form solution of the optimal digital beamforming matrix into the objective function MSE, and use the alternating minimization method to achieve the approximate optimal solution of the analog precoding matrix and the RIS reflection beamforming matrix.

[0047] An electronic device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 7 when executing the computer program.

[0048] A computer-readable storage medium storing a computer program, wherein the computer program implements the method according to any one of claims 1 to 7 when executed by a processor.

[0049] Compared with the prior art, the present invention has the following advantages and technical effects:

[0050] The method of the present invention models the beamforming problem of a RIS-assisted millimeter-wave communication system when there is congestion on the communication path. Using the proposed MMSE-based popular alternating optimization algorithm, it achieves near-optimal solutions for the RIS phase shift, digital precoder, and analog precoder, achieving superior performance compared to similar algorithms. Compared to the comparison algorithm, the proposed algorithm does not require initialization of the phase shift between the analog precoder and the RIS; instead, it can be randomly generated without compromising performance. Regarding the design of the RIS-assisted communication system, the present invention considers a multi-user MISO millimeter-wave communication system, rather than a single-user MISO millimeter-wave communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0052] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0053] Figure 2 A diagram of a RIS-assisted multi-user millimeter wave communication system according to an embodiment of the present invention;

[0054] Figure 3 1 is a diagram showing simulation results of the signal-to-noise ratio and spectrum efficiency of an embodiment of the present invention;

[0055] Figure 4 This is a simulation result diagram of the number of user terminals and spectrum efficiency according to an embodiment of the present invention;

[0056] Figure 51 is a diagram showing the simulation results of the number of transmitting antennas and spectrum efficiency according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0058] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0059] The embodiment of the present invention adopts a multi-user millimeter wave communication system considering RIS assistance in the downlink, which is equipped with N t antennas and N RF The BS of the uniform linear array (ULA) of the radio frequency chain communicates with K single-antenna user equipments (UEs) through a RIS with R reflective array elements arranged in the form of a uniform planar array (UPA), where N s ≤N RF <<N t In practical applications, a RIS is usually attached with a RIS controller to control the phase shift (PS) of its reflection unit and communicate with the BS through a dedicated wireless link to coordinate transmission and exchange channel state information (CSI).

[0060] like Figure 1-5 As shown, this embodiment provides a hybrid precoding method for a multi-user millimeter wave system, including the following steps:

[0061] S1. Using the channels from the base station to the reconfigurable smart surface and from the smart surface to the user, a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is constructed with the goal of minimizing the mean square error (MSE) between the received and transmitted signals.

[0062] S2. Based on the problem model, construct a closed-form solution of the optimal digital beamforming matrix based on the KKT condition;

[0063] S3. According to the constraints of the analog precoder and phase shifter, a method based on popular optimization is proposed to solve the normal mode constraints of the analog precoder and phase shifter.

[0064] S4. Substitute the closed-form solution of the optimal digital beamforming matrix into the objective function MSE, and use the alternating minimization method to achieve the approximate optimal solution of the analog precoding matrix and the RIS reflection beamforming matrix.

[0065] Furthermore, a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is constructed with the goal of minimizing the mean square error (MSE) between the received and transmitted signals. The specific process includes:

[0066] The signal received by the end user is expressed as:

[0067]

[0068] The improved MSE is used as the performance metric and optimization target, and the RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is:

[0069]

[0070] Substituting formula (1) into formula (2), where ζ is the scaling factor, after mathematical operations, the hybrid precoding and phase shift problem of the RIS-assisted MU millimeter wave communication system jointly designed based on the MMES criterion is modeled as:

[0071]

[0072] The MSE expression derived from equation (3), as well as the transmit power constraint and constant modulus constraint of the phase shifter, gives the optimization problem. The above objective function can then be rewritten as follows:

[0073]

[0074] in, is satisfied The transmitted signal vector, P is the total transmit power, K is the number of users, N t The number of transmitting antennas, R is the number of RIS reflector elements, n~CN(0,σ 2 I K ) is the additive Gaussian noise vector. is the phase shift matrix of the reconfigurable smart surface. r All satisfied Millimeter wave channel between RIS and BS mmWave channel vector between the kth UE and RIS Among them, "digital precoder" "Analog Precoder" at the same time

[0075] Furthermore, a closed-form solution of the optimal digital beamforming matrix based on the KKT condition is constructed through the problem model. The specific process includes:

[0076] First, by fixing F RFand Ψ to derive the optimal digital precoding matrix F BB and scaling factor ζ.

[0077] Specifically, first ignore F RF ,Ψ constraint, definition The objective function is rewritten as:

[0078]

[0079] It is worth noting that due to the limitation of transmission power, it can be proved by contradiction that the optimal solution must be to maximize the total transmission power, that is, the optimal ζ is given by the following formula:

[0080]

[0081] Then, according to the Karush-Kuhn-Tucker (KKT) condition, formula (4) is used only as its Next, for Taking the derivative and setting it to zero, we solve The solution.

[0082] Therefore, the optimal The closed-form solution is:

[0083]

[0084] The best Substituting the closed-form solution and ζ into formula (5), after some mathematical derivation, the new MSE is obtained:

[0085]

[0086] Furthermore, based on the constraints of the analog precoder and phase shifter, a method based on popular optimization is proposed to solve the normal mode constraint. The specific process includes:

[0087] The optimization problem in formula (5) can be reduced to the following optimization problem:

[0088]

[0089] Among them F RF ,Ψ need to satisfy the normal mode constraint. In order to deal with the normal mode constraint, the MO method can be applied to obtain the local optimal F RF ,Ψ. The basic idea of ​​MO algorithm is to consider the normal mode constraint for F RF,Ψ defines a Riemannian manifold and iteratively updates the optimization variable function in the Riemannian gradient direction (i.e., the projection of the Euclidean conjugate gradient to the tangent space of a point on the Riemannian manifold) in a manner similar to the traditional Euclidean gradient descent algorithm. The most difficult part of directly using the MO method here is to derive the conjugate gradient in Euclidean space to obtain the associated Riemannian gradient. It should be noted that for complex-valued variables (F RF ,Ψ), the corresponding scalar function J(F RF ,Ψ), the conjugate gradient is defined as

[0090] Using the manifold optimization (MO) algorithm, it is necessary to find the derivative function J(F RF ,ψ) respectively about F RF , the conjugate gradient of ψ. By defining Then according to d(J(A))=tr(P -1 d(P)P -1 ), apply the matrix gradient formula to solve J(F RF ,Ψ) respectively about F RF The conjugate gradient of and ψ is:

[0091]

[0092] Finally, according to the conjugate gradient obtained above, combined with the MO algorithm, we can get F RF ,Ψ, the MO method can be applied to solve problems with constant modulus constraints.

[0093] Furthermore, through the closed-form solution of the optimal digital beamforming matrix, the optimal solutions for the analog precoding matrix and the RIS reflective beamforming matrix are achieved using the alternating minimization structure method. The specific process includes:

[0094] Using the derived Euclidean conjugate gradient, the MO method only obtains the solution of one variable each time, and the other variable related to it is not optimized. Therefore, this embodiment repeats the above process, that is, adopts an alternating strategy to finally obtain F RF and the approximate optimal solution of Ψ, and finally the obtained F RF Combined with formula (4) and formula (5), we can get F BB .

[0095] Table 1

[0096]

[0097]

[0098] like Figure 3-5As shown, this embodiment evaluates the performance of the design proposed by the present invention through simulation. Unless otherwise specified, for the millimeter wave channel, we assume that N t =48, N RF =N s =K=6, R=100, LB=LI=5, SNR is defined as The total transmission power is set to P = 1. The antenna spacing is

[0099] This embodiment further provides a hybrid precoding system for a multi-user millimeter wave system, including:

[0100] A model building module is used to construct a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received and transmitted signals through the channels from the base station to the reconfigurable smart surface and from the smart surface to the user;

[0101] An initial solution module is used to construct a closed-form solution of an optimal digital beamforming matrix based on KKT conditions based on the multi-user millimeter wave joint beamforming optimization problem model;

[0102] A constraint acquisition module, configured to obtain normal mode constraints of the analog precoder and the phase shifter based on the constraints of the analog precoder and the phase shifter and based on a popular optimization method;

[0103] The target solving module is used to substitute the closed-form solution of the optimal digital beamforming matrix into the objective function MSE, and use the alternating minimization method to achieve the approximate optimal solution of the analog precoding matrix and the RIS reflection beamforming matrix.

[0104] An electronic device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 7 when executing the computer program.

[0105] A computer-readable storage medium storing a computer program, wherein the computer program implements the method according to any one of claims 1 to 7 when executed by a processor.

[0106] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A hybrid precoding method for a multi-user millimeter wave system, characterized in that: include: Through the channels from the base station to the reconfigurable smart surface and from the smart surface to the user, a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is constructed with the goal of minimizing the mean square error between the received signal and the transmitted signal. Based on the multi-user millimeter wave joint beamforming optimization problem model, a closed-form solution of the optimal digital beamforming matrix based on the KKT condition is constructed; According to the constraints of the analog precoder and the phase shifter, the normal mode constraints of the analog precoder and the phase shifter are obtained based on the popular optimization method; The closed-form solution of the optimal digital beamforming matrix is ​​substituted into the objective function MSE, and the approximate optimal solution of the analog precoding matrix and the RIS reflective beamforming matrix is ​​achieved using the alternating minimization method.

2. The method according to claim 1, characterized in that The process of constructing the RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received signal and the transmitted signal includes: Representing the received signal of the terminal user, and obtaining a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model based on the received signal and taking the improved mean square error as the performance metric and optimization target; Calculate according to the received signal and the RIS-assisted multi-user millimeter wave joint beamforming optimization problem model to obtain a hybrid precoding and phase shift problem model of a RIS-assisted MU millimeter wave communication system jointly designed based on the MMES criterion; According to the hybrid precoding and phase shift problem model, as well as the transmit power constraint and constant modulus constraint of the phase shifter, an optimization problem is obtained, and then a RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received signal and the transmitted signal is obtained.

3. The method according to claim 2, characterized in that The signal expression of the received signal is: The expression of the RIS-assisted multi-user millimeter-wave joint beamforming optimization problem model is: in, is satisfied The transmitted signal vector, P is the total transmission power, K is the number of users, n~CN(0,σ 2 I K ) is the additive Gaussian noise vector, is the phase shift matrix of the reconfigurable smart surface, where each Ψ r All satisfied is the millimeter wave channel between RIS and BS, is the millimeter wave channel vector between the kth UE and RIS, where "digital precoder" "Analog Precoder" at the same time 4. The method according to claim 3, characterized in that The process of obtaining the hybrid precoding and phase shift problem model of the RIS-assisted MU millimeter wave communication system jointly designed based on the MMES criterion includes: Substituting formula (1) into formula (2), where ζ is a scaling factor, the hybrid precoding and phase shift problem model is calculated as: According to the hybrid precoding and phase shift problem model, as well as the transmit power constraint and constant modulus constraint of the phase shifter, the optimization problem is obtained, and then the final multi-user millimeter wave joint beamforming optimization problem model is obtained as follows: Among them, N t The number of transmitting antennas, R is the number of RIS reflector array elements.

5. The method according to claim 1, characterized in that: Based on the multi-user millimeter wave joint beamforming optimization problem model, the process of constructing a closed-form solution of the optimal digital beamforming matrix based on the KKT condition includes: By fixing F RF and Ψ to derive the optimal digital precoding matrix F BB and scaling factor ζ, then according to the KKT condition, formula (4) is used as The function of Take the derivative and set it to zero to find the optimal solution The closed form solution of .

6. The method according to claim 5, characterized in that By fixing F RF and Ψ to derive the optimal digital precoding matrix F BB The process of finding the scaling factor ζ includes: Ignore F RF ,Ψconstraint,definition The multi-user millimeter wave joint beamforming optimization problem model is rewritten as: The formula expression of the scaling factor ζ is: The optimal The closed-form solution is The best Substituting the closed-form solution and ζ into equation (5), the new mean square error is derived as:

7. The method according to claim 1, characterized in that According to the constraints of the analog precoder and the phase shifter, the process of obtaining the normal mode constraints of the analog precoder and the phase shifter based on the popular optimization method includes: The optimization problem in formula (5) is reduced to the following: Among them, for complex-valued variables (F RF ,Ψ), the corresponding scalar function J(F RF ,Ψ), the conjugate gradient is defined as Then, the manifold optimization algorithm is used to derive the function J(F RF ,Ψ) respectively about F RF , the conjugate gradient of Ψ is defined by Then according to d(J(A))=tr(P -1 d(P)P -1 ), and use the matrix gradient formula to solve J(F RF ,Ψ) respectively about F RF The conjugate gradient of and Ψ is:

8. A hybrid precoding system for a multi-user millimeter wave system, characterized in that: include: A model building module is used to build a RIS-assisted multi-user millimeter wave joint beamforming optimization problem model with the goal of minimizing the mean square error between the received signal and the transmitted signal through channels from the base station to the reconfigurable smart surface and from the smart surface to the user; An initial solution module, used for constructing a closed-form solution of an optimal digital beamforming matrix based on KKT conditions based on the multi-user millimeter wave joint beamforming optimization problem model; A constraint acquisition module, used for obtaining the normal mode constraints of the analog precoder and the phase shifter based on the constraint conditions of the analog precoder and the phase shifter and based on the popular optimization method; The target solving module is used to substitute the closed-form solution of the optimal digital beamforming matrix into the target function MSE, and use the alternating minimization method to achieve the approximate optimal solution of the analog precoding matrix and the RIS reflection beamforming matrix.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method described in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method described in any one of claims 1 to 7 is implemented.

Images