1-bit DAC precoding optimization design method suitable for large-scale MU-MIMO system

Abstract

The invention discloses a 1-bit DAC precoding optimization design method suitable for a large-scale MU-MIMO system, and the method comprises the steps: setting base station data configuration, and modulating an input symbol vector; quantizing the modulated input signal by using a 1-bit DAC (Digital-to-Analog Converter); generating a complex cyclic symmetric Gaussian random channel matrix H by adopting Rayleigh distribution; designing a signal of a receiver end; establishing a 1-bit DAC precoding optimization problem based on a minimum mean square error according to the average transmitting power of the base station and a 1-bit DAC character set constraint; a mean square error between a recovery signal and an input signal is minimized by utilizing a designed ADMM-HB method under the constraint of the average transmitting power of a base station and a 1-bit DAC character set. According to the method, the ADMM-HB method is used in the optimization process, the signal mean square error of the receiving end and the transmitting end can be minimized with low calculation complexity, the system efficiency is improved, the system hardware cost and power consumption are reduced, and the method better conforms to engineering practical application.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication, and particularly relates to a 1-bit DAC precoding optimization design method applicable to large-scale MU-MIMO systems. Background Art

[0002] As one of the key technologies of 5G, large-scale MIMO technology has attracted extensive attention from the academic and scientific research communities and has been deeply studied since it was proposed because of its excellent performance. Large-scale MU-MIMO means that the number of antennas at the base station is increased by one or two orders of magnitude, reaching hundreds or even thousands, and the number of base station antennas is much larger than the user equipment it serves. In this way, a base station can serve more users at the same time, increasing the network throughput. By using the spatial degrees of freedom provided by the large-scale antenna array at the base station, the utilization efficiency of spectrum resources is significantly improved, effectively solving the problem of increasingly tight spectrum resources. Precoding technology is a signal processing technology used in communication systems. By performing matrix transformation on the transmitted signal at the transmitter, the signal quality at the receiver is maximized, path interference is reduced, and the transmission efficiency and reliability of the signal are improved.

[0003] Precoding technology is a signal processing technology used in communication systems. By performing matrix transformation on the transmitted signal at the transmitter, the signal quality at the receiver is maximized, path interference is reduced, and the transmission efficiency and reliability of the signal are improved. The basic idea of precoding is that the transmitter obtains all or part of the channel state information and then designs the transmitted signal accordingly to achieve the purpose of eliminating interference. Using an excellent precoding algorithm can enable the user side in the cell to only perform simple processing on the received signal during downlink communication. This can not only solve the user interference problem in large-scale MU-MIMO systems, but also greatly reduce the pressure on the user side, further exploring and utilizing the spatial multiplexing advantage of MIMO technology. Therefore, designing a precoding algorithm with low complexity and capable of meeting high-quality communication is a key link in large-scale MU-MIMO systems.

[0004] Constant envelope precoding can ignore the amplitude distortion of the power amplifier and the problem of too high PAPR because it generates signals with a constant amplitude. As a special case of constant envelope precoding, 1-bit DAC precoding can effectively reduce energy consumption, hardware cost and complexity, and thus has become a research hotspot.

[0005] The constraints of the 1-bit DAC precoding problem are taken from a discrete non-convex set, which is an NP-hard optimization problem. In existing 1-bit DAC precoding algorithms, such as C2PO which is based on the Neumann series expansion and approximates the inversion by truncating the series to the first two terms, it has good performance in MIMO systems with large-scale antenna arrays (the number of transmit antennas > 128). However, C2PO has many hyperparameters and is inconvenient to use. The iterative discrete estimation algorithm proposes a general precoding algorithm framework applicable to discrete character sets based on the alternating direction method of multipliers (ADMM). The LADMM algorithm, on the basis of ADMM, also adopts the way of constraint relaxation and proposes a linearization scheme to further reduce the algorithm complexity. Most of these previous studies relax the constraints to a convex set for solution. Since these precoding algorithms use the way of constraint relaxation, the solutions obtained can only be regarded as an approximate solution of the original problem, and may not even be a local optimal solution. Summary of the Invention

[0006] Objective of the Invention: In order to overcome the deficiencies in the prior art, a low-complexity 1-bit DAC precoding optimization design method applicable to large-scale MU-MIMO systems based on the alternating direction method of multipliers (ADMM) and the heavy ball method (HB) is provided. This method equivalently transforms the constraints of the 1-bit DAC precoding problem into the intersection of two convex sets. After injecting it into the ADMM framework, the heavy ball (HB) method is used to solve the precoding factor during the optimization process. The ADMM-HB method can converge with only a few iterations, greatly reducing the complexity, and can obtain a better bit error rate, and can better meet the application in engineering practice.

[0007] Technical Solution: To achieve the above objective, the present invention provides a 1-bit DAC precoding optimization design method applicable to large-scale MU-MIMO systems, including the following steps:

[0008] S1: Configure the base station information and modulate the original binary data to generate the input signal s;

[0009] S2: Quantize the input signal s using a 1-bit DAC to obtain the transmitted signal x, and transmit the signal using the transmitter radio frequency link;

[0010] S3: Generate a complex circularly symmetric Gaussian random channel matrix H using the Rayleigh distribution;

[0011] S4: Design the signal at the receiver end:

[0012] Calculate the received signal y at the user end according to the channel state information, and then multiply the received signal by the precoding factor β to obtain the restored signal

[0013] S5: Based on the average transmit power of the base station and the 1-bit DAC character set constraint, establish a 1-bit DAC precoding optimization problem based on minimizing the mean square error;

[0014] S6: Use the designed ADMM-HB method to solve the 1-bit DAC precoding optimization problem established in step S5 under the constraints of the average transmit power of the base station and the 1-bit DAC character set, so that the mean square error between the recovered signal and the input signal s is minimized.

[0015] Furthermore, in step S1, set the average transmit power of the base station as P, equipped with B antennas to simulate the downlink transmission of the system, and at the same time provide services for U users. For the system, B >> U.

[0016] Furthermore, in step S3, assume that the base station can perfectly obtain the channel state information, and the channel matrix follows a Rayleigh distribution, that is Specifically, it is represented by MATLAB code as H = sqrt(1 / 2)*(randn(1,U)+1j*randn(1,U).

[0017] Furthermore, in step S4, the transmission process of the transmitted signal is interfered by additive noise, and the finally obtained recovered signal at the receiving end is additive white Gaussian noise, and each of its elements conforms to a complex Gaussian distribution with a mean of 0 and a variance of 1

[0018] Furthermore, in step S5, the transmitted signal x is jointly constrained by the average transmit power of the base station and 1-bit DAC, The set χ is the character set generated by 1-bit DAC, χ = l×{±1±j1}, where is determined by the average transmit power and the number of antennas of the base station; the minimum mean square error between the recovered signal and the input signal s is:

[0019] The 1-bit DAC precoding optimization problem is described as:

[0020]

[0021] Furthermore, in step S6, use the ADMM-HB precoding method to solve the closed-form solutions of variables x and β respectively, that is, solve problem (1), specifically including:

[0022] A1: First fix x to solve β, and problem (1) becomes the following optimization problem:

[0023]

[0024] By taking the derivative of the objective function with respect to β and setting it equal to 0, the update formula for β is obtained as follows:

[0025]

[0026] Then, for a fixed β, solve for x, and problem (1) becomes the following optimization problem:

[0027]

[0028] This is a combinatorial optimization problem where the variables take complex values. For convenience, it is transformed to the real domain, that is, let:

[0029]

[0030] Then problem (4) is equivalent to the following optimization problem:

[0031]

[0032] where, χ 1 = {-l, l};

[0033] Let to obtain the following 0-1 programming:

[0034]

[0035] where, B 01 ∈ {0, 1} 2B ;

[0036] To obtain the exact solution of the above optimization problem, the set B 01 is equivalently represented as the intersection of two convex sets. One of these two convex sets is the box function S b and a (2B - 1)-dimensional sphere S centered at with radius 2 ; that is, the following equivalent effect is obtained:

[0037]

[0038] Introduce auxiliary variables z 1 , z 2 , and it can be obtained that problem (7) is equivalent to:

[0039]

[0040] To transform the above formula into a form that can use the ADMM algorithm framework, define the indicator function δ C (x) of the set C as:

[0041]

[0042] Let Then the augmented Lagrangian function of equation (9) is:

[0043]

[0044] Then the variable z 1 , z 2 , w 1 , w 2 The corresponding iteration process is as follows:

[0045]

[0046] A2: Solve sub - problem (14) to obtain the update formula of ;

[0047] A3: Combine the update formula of β and iteratively update β according to the ADMM - HB method process, z 1 , z 2 , w 1 , w 2 ;

[0048] A4: Restore the of the last iteration to x, and apply the β of the last iteration and the restored x to the 1 - bit DAC precoding communication system.

[0049] Furthermore, the specific steps of step A2 include:

[0050] Sub - problem (14) is equivalent to the following optimization problem:

[0051]

[0052] Directly taking the derivative of equation (16) gives that the closed - form solution of requires matrix inversion. The update formula of obtained using the heavy - ball method is:

[0053]

[0054] where α 1 is the step - size coefficient, α 2 is equivalent to the friction coefficient, and v is the inertial distance.

[0055] Furthermore, in step A4, restoring requires mapping into the set of x, that is:

[0056]

[0057] The present invention proposes the ADMM-HB method to solve the 1-bit DAC precoding problem. In a large-scale MU-MIMO downlink system, by utilizing the rich degrees of freedom brought by the large-scale antenna array configured on the base station, a non-convex optimization problem including QPSK and 16QAM modulations, multi-user precoding, base station average transmit power constraint, and 1-bit DAC constraint is constructed to minimize the mean square error of the signals at the receiving and transmitting ends. Different from the existing methods, in a large-scale MU-MIMO downlink system, this method obtains an exact solution by performing equivalent constraint transformation on the 1-bit DAC precoding problem, thereby improving the system bit error rate performance, and further reducing the computational complexity in the variable update process through the HB algorithm, thus reducing the system hardware cost and energy consumption.

[0058] For the next-generation communication technologies, large-scale MU-MIMO systems will surely become an essential core technology. With its lower complexity and better bit error rate performance, ADMM-HB has become a better choice among the current precoding algorithms.

[0059] Advantageous effects: Compared with the prior art, for the 1-bit DAC precoding problem, the present invention proposes an ADMM-HB method using equivalent constraint transformation. The core is to equivalently transform the original non-convex combinatorial optimization problem into a convex optimization problem, and then solve the simple closed-form solutions of each sub-problem. And in the optimization process, using the ADMM-HB method only requires a relatively low computational complexity to minimize the mean square error of the signals at the receiving and transmitting ends, improving the system efficiency, reducing the system hardware cost and power consumption, and making it more in line with the actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the block diagram of the downlink of a large-scale MU-MIMO system;

[0061] Figure 2 is the convergence graph of the ADMM-HB method;

[0062] Figure 3 is the comparison graph of the BER performance of different methods under the 16QAM modulation mode. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] The following further clarifies the present invention in conjunction with the drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art to the present invention all fall within the scope defined by the appended claims of this application.

[0064] Example 1:

[0065] This example provides a 1-bit DAC precoding optimization design method applicable to large-scale MU-MIMO systems. Referring to Figure 1 , it includes the following steps:

[0066] S1: Configure the base station information, modulate the original binary data to generate the input signal s. The modulation method can be QPSK or 16QAM. Set the average transmit power of the base station as P, equip B antennas to simulate the downlink transmission of the system, and serve U users at the same time. For the system, B >> U.

[0067] S2: Use a 1-bit DAC to quantize the modulated input signal s to obtain the transmit signal x, and use the transmit-side radio frequency link to transmit the signal.

[0068] S3: Generate a complex circularly symmetric Gaussian random channel matrix H using the Rayleigh distribution. Assume that the base station can perfectly obtain the channel state information (CSI). The channel matrix follows the Rayleigh distribution, that is Specifically, it is represented by the MATLAB code as H = sqrt(1 / 2)*(randn(1,U)+1j*randn(1,U)).

[0069] S4: Design the signal at the receiver end: Calculate the received signal y at the user end according to the channel state information, and then multiply the received signal by the precoding factor β to obtain the recovered signal Due to the interference of additive noise during the transmission of the transmit signal, the finally obtained recovered signal at the receiving end where, is the additive white Gaussian noise, and each of its elements conforms to the complex Gaussian distribution with a mean of 0 and a variance of 1

[0070] S5: According to the average transmit power of the base station and the 1-bit DAC character set constraint, establish a 1-bit DAC precoding optimization problem based on minimizing the mean square error:

[0071] The transmit signal x is jointly constrained by the average transmit power of the base station and the 1-bit DAC, The set χ is the character set generated by the 1-bit DAC, χ = l×{±1±j1}, where is determined by the average transmit power and the number of antennas of the base station. The minimum mean square error between the recovered signal and the input signal s is: Therefore, the 1-bit DAC precoding problem can be described as:

[0072]

[0073] S6: Solve the 1-bit DAC precoding optimization problem established in step S5 under the constraints of the average transmit power of the base station and the 1-bit DAC symbol set by using the designed ADMM-HB method, so that the recovered signal and the mean square error between the input signal s is minimized.

[0074] In step S6, the ADMM-HB precoding method is used to solve the closed-form solutions of variables x and β respectively, that is, to solve problem (1), which specifically includes:

[0075] A1: First, fix x to solve for β, and problem (1) becomes the following optimization problem:

[0076]

[0077] By taking the derivative of the objective function with respect to β and setting it equal to 0, the following update formula for β is obtained:

[0078]

[0079] Then, for the fixed β, solve for x, and problem (1) becomes the following optimization problem:

[0080]

[0081] This is a combinatorial optimization problem with complex-valued variables. For convenience, it is transformed to the real domain for consideration, that is, let:

[0082]

[0083] Then problem (4) is equivalent to the following optimization problem:

[0084]

[0085] where χ 1 ={-l, l};

[0086] Let Then the following 0-1 programming is obtained:

[0087]

[0088] where, B 01 ∈{0, 1} 2B ;

[0089] To obtain the exact solution of the above optimization problem, the set B 01 is equivalently represented as the intersection of two convex sets, one of which is the box function S band a 2B - 1 dimensional sphere S centered at with a radius of . That is, the following equivalent effect is obtained: 2 .

[0090]

[0091] Introduce the auxiliary variable z 1 , z 2 . It is easy to obtain that equation (7) is equivalent to:

[0092]

[0093] To transform the above equation into a form that can use the ADMM algorithm framework, define the indicator function δ of set C C (x) as:

[0094]

[0095] Let Then the augmented Lagrangian function of equation (9) is:

[0096]

[0097] Then the variables z 1 , z 2 , w 1 , w 2 The corresponding iteration process is:

[0098]

[0099] A2: Solve the sub - problem (14) to obtain the update formula of :

[0100] Problem (14) is equivalent to the following optimization problem:

[0101]

[0102] Directly taking the derivative of equation (16) gives . The closed - form solution of requires matrix inversion, and the complexity of matrix inversion is very high. Therefore, refer to the idea of the heavy - ball method (HB) to avoid the complex calculations brought by matrix inversion. The update formula of

[0103]

[0104] obtained using the heavy - ball method is: α 1 is the step - size coefficient, α 2 is similar to the friction - coefficient, and v is the inertial distance.

[0105] A3: According to the update formula of β, update β iteratively according to the ADMM-HB method process. z 1 ,z 2 ,w 1 ,w 2 ;

[0106] A4: Restore the of the last iteration to x. Take the β of the last iteration and the restored x, which can be applied to the 1-bit DAC precoding communication system. Restoration needs to map to the set of x, that is:

[0107]

[0108] Embodiment 2:

[0109] Based on the solution provided in Embodiment 1, in order to verify the effect of the method of the present invention, a simulation experiment of the algorithm is carried out in this embodiment. The software MATLAB is used for simulation to verify the theoretical analysis. The specific simulation results and analysis are as follows:

[0110] As Figure 2 shown is the convergence graph of the ADMM-HB method. In this embodiment, the termination condition of the ADMM-HB method is set that the OFV no longer fluctuates significantly. After about 40 iterations, the OFV has basically completely stopped fluctuating or the fluctuation range is very small, which indicates that the algorithm is convergent.

[0111] As Figure 3 shown is the BER performance comparison graph of different methods under the 16QAM modulation mode. It can be clearly seen that the algorithm proposed by the present invention has extremely excellent performance under the 16QAM modulation mode. When the target bit error rate is 10 -4 , the algorithm proposed by the present invention is about 0.95 dB and 0.60 dB less than IDE2-100 and LADMM respectively.

[0112] It can be seen from the above simulation experiments that the ADMM-HB method has lower complexity and better performance. Therefore, the ADMM-HB method provided by the present invention is more efficient than other methods and is more conducive to engineering applications.

Claims

1. A 1-bit DAC precoding optimization design method suitable for large-scale MU-MIMO systems, characterized in that: The steps include: S1: configure base station information and modulate the original binary data to generate input signal s; S2: Use a 1-bit DAC to quantize the input signal s to obtain the transmit signal x, and use the transmitter RF link to transmit the signal; S3: Generate a complex cyclic symmetric Gaussian random channel matrix H using Rayleigh distribution; S4: Design the signal at the receiver end: The received signal y at the user end is calculated based on the channel state information, and then the received signal is multiplied by the precoding factor β to obtain the recovered signal S5: According to the average transmission power of the base station and the 1-bit DAC character set constraint, a 1-bit DAC precoding optimization problem based on minimizing the mean square error is established; S6: Using the designed ADMM-HB method, under the constraints of the base station average transmission power and the 1-bit DAC character set, solve the 1-bit DAC precoding optimization problem established in step S5 to make the recovered signal The mean square error between s and the input signal is minimized.

2. The 1-bit DAC precoding optimization design method applicable to a large-scale MU-MIMO system according to claim 1, characterized in that: In step S1, the average transmission power of the base station is set to P, and B antennas are equipped to simulate the downlink transmission of the system and provide services for U users at the same time. For the system, B>>U.

3. The 1-bit DAC precoding optimization design method applicable to a large-scale MU-MIMO system according to claim 2, characterized in that: In step S3, it is assumed that the base station can perfectly obtain the channel state information, and the channel matrix Using Rayleigh distribution, that is Specifically expressed in MATLAB code is H=sqrt(1 / 2)*(randn(1,U)+1j*randn(1,U).

4. The 1-bit DAC precoding optimization design method applicable to a large-scale MU-MIMO system according to claim 3, characterized in that: In step S4, the transmission process of the transmitted signal is interfered by additive noise, and the recovered signal finally obtained by the receiving end It is additive Gaussian white noise, each element of which conforms to a complex Gaussian distribution with a mean of 0 and a variance of 1.

5. The 1-bit DAC precoding optimization design method applicable to a large-scale MU-MIMO system according to claim 4, characterized in that: In step S5, the transmitted signal x is subject to the common constraints of the base station average transmission power and the 1-bit DAC. The set χ is the character set generated by the 1-bit DAC, χ = l×{±1±j1}, where Determined by the average transmission power of the base station and the number of antennas; recover the signal The minimum mean square error between the input signal s is: The 1-bit DAC precoding optimization problem is described as:

6. The 1-bit DAC precoding optimization design method applicable to a massive MU-MIMO system according to claim 5, characterized in that: In step S6, the ADMM-HB precoding method is used to solve the closed-form solutions of the variables x and β respectively, that is, to solve problem (1), which specifically includes: A1: First fix x to solve β, and problem (1) becomes the following optimization problem: By taking the derivative of the objective function with respect to β and setting it equal to 0, the update formula of β is obtained as follows: Then, solving for x for a fixed β, problem (1) becomes the following optimization problem: This is a combinatorial optimization problem with complex variables. For convenience, we transform it into the real number domain, that is, Then problem (4) is equivalent to the following optimization problem: Where, χ1={-l,l}; make The following 0-1 plan is obtained: Among them, B 01 ∈{0,1} 2B ; In order to obtain the exact solution to the above optimization problem, the set B 01 is equivalent to the intersection of two convex sets, one of which is the box function S b and one with The center of the ball The radius of the 2B-1 dimensional ball S2 is obtained, that is, the following equivalent effect is obtained: By introducing auxiliary variables z1 and z2, we can conclude that problem (7) is equivalent to: In order to transform the above formula into a form that can use the ADMM algorithm framework, define the indicative function δ of the set C C (x) is: make Then the augmented Lagrangian function of equation (9) is: Then the variable The corresponding iterative process of z1,z2,w1,w2 is: A2: Solve subproblem (14) and obtain The update formula of ; A3: Combine the update formula of β and iteratively update β according to the ADMM-HB method process. z1,z2,w1,w2; A4: The last iteration Recover to x, and apply the last iteration β and the recovered x to the 1-bit DAC precoding communication system.

7. The 1-bit DAC precoding optimization design method applicable to a massive MU-MIMO system according to claim 6, characterized in that: The step A2 specifically includes: Subproblem (14) is equivalent to the following optimization problem: Directly derive equation (16) to obtain The closed-form solution of requires matrix inversion, and the one obtained using the heavy sphere method is The update formula is: in, α1 is the step length coefficient, α2 is equivalent to the friction coefficient, and v is the inertia distance.

8. The 1-bit DAC precoding optimization design method applicable to a massive MU-MIMO system according to claim 7, characterized in that: Step A4 is used to restore Need to Mapped to the set of x, that is:

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