Optimization method and system for sensing OFDM-IM signal by PAPR based on ADMM

Abstract

The invention discloses an optimization method and system for sensing OFDM-IM signals by PAPR based on ADMM, and the method comprises the following steps: in order to reduce the peak-to-average power ratio of an OFDM-IM system, adding a small jitter signal in an idle subcarrier, keeping the signals in all active subcarriers unchanged, replacing the PAPR with an infinite norm as a target function, and carrying out the optimization of the PAPR in order to reduce the peak-to-average power ratio of the OFDM-IM system; constructing an optimization model by taking the maximum amplitude value of the small jitter signal as a constraint condition; based on an ADMM method, an optimization problem of the optimization model is decomposed into a plurality of sub-problems, and each sub-problem has a simple closed-form solution; and solving each sub-problem by adopting an ADMM method to obtain a signal optimization result. According to the method, the provided optimization model is solved by using the ADMM, so that the calculation complexity can be remarkably reduced while the peak-to-average power ratio performance and the bit error rate performance are ensured.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication, and particularly relates to an ADMM-based PAPR-aware OFDM-IM signal optimization method and system. Background Art

[0002] Index Modulation Orthogonal Frequency Division Multiplexing (OFDM-IM) is a technology developed on the basis of Orthogonal Frequency Division Multiplexing (OFDM). Different from OFDM technology, OFDM-IM divides subcarriers into two parts. One part carries information and is called active subcarriers; the other part does not carry information and is called idle subcarriers. Compared with OFDM, OFDM-IM has stronger anti-Inter-Carrier Interference (ICI) ability and higher energy efficiency performance. In the case of medium and low rate transmission, it has better Bit Error Ratio (BER). However, similar to OFDM, OFDM-IM also has a high Peak-to-average Power Ratio (PAPR). The high peak-to-average ratio will exceed the linear region of the power amplifier, ultimately resulting in signal distortion, thereby causing the BER at the receiving end to deteriorate. Although many optimization algorithms for suppressing the peak-to-average ratio have been proposed in the prior art, these methods either do not consider the unique structure of the OFDM-IM system or the computational complexity of the proposed algorithms is too high, which is not conducive to the design and implementation of practical systems. Summary of the Invention

[0003] Object of the Invention: To solve the problems of high peak-to-average ratio and high computational complexity of the OFDM-IM system, an ADMM (Alternating Direction Method of Multipliers)-based PAPR-aware OFDM-IM signal optimization method and system are provided. By using ADMM to solve the proposed optimization model, the computational complexity can be significantly reduced while ensuring the peak-to-average power ratio performance and bit error rate performance.

[0004] Technical Solution: To achieve the above object, the present invention provides an ADMM-based PAPR-aware OFDM-IM signal optimization method, including the following steps:

[0005] S1: To reduce the peak-to-average power ratio (PAPR) of the OFDM-IM system, a small jitter signal is added to the idle subcarriers, the signals in all active subcarriers remain unchanged, the PAPR is replaced with the infinity norm as the objective function, and the maximum amplitude value of the small jitter signal is used as the constraint condition to construct an optimization model;

[0006] S2: Based on the ADMM method, the optimization problem of the optimization model is decomposed into multiple sub-problems, and each sub-problem has a simple closed-form solution;

[0007] S3: The ADMM method is used to solve each sub-problem to obtain the signal optimization result.

[0008] Further, the step S1 specifically includes:

[0009] A1: The union of all active subcarrier index sets is represented as:

[0010]

[0011] Since the size of this union is K, the size of the union of idle subcarriers in all blocks And it is represented as The frequency domain representation of the added jitter signal is When the α-th subcarrier is an active subcarrier,

[0012] A2: The PAPR optimization problem is represented as

[0013]

[0014] Where R is the upper limit of the amplitude threshold of the added jitter signal, the purpose is to limit the influence of the jitter signal on the error, and X is the initial frequency domain transmitted signal;

[0015] A3: After removing the K zero elements of the active subcarriers in , it is represented as W, then formula (2) is represented as:

[0016]

[0017] Where x is the initial time domain transmitted signal, is obtained after deleting the active subcarrier index L.

[0018] Further, the step S2 specifically includes:

[0019] Introduce an auxiliary variable y, and let At this time, formula (3) will be converted into the following form:

[0020]

[0021] The augmented Lagrangian function of the optimization problem (4) is as follows:

[0022]

[0023] where \(z\in\) N×1 is the Lagrange multiplier corresponding to the constraint, and \(\rho>0\) is a penalty parameter; according to the ADMM method, the update steps for each variable are shown as follows:

[0024] \(y\) k+1 =\(\arg\min L\) ρ \((y, W\) k , z\) k ) (6)

[0025]

[0026] Formulas (6)-(8) are the decomposed sub-problems (6)-(8) respectively.

[0027] Furthermore, the solution of the sub-problem (6) in step S3 includes:

[0028] B1: Through formula (5), the sub-problem (6) is equivalent to solving the following problem (9):

[0029]

[0030] B2: To obtain the closed-form solution of problem (9), an approximation operator of the function is introduced; the approximation operator of function \(f\) is defined as follows:

[0031]

[0032] Let then problem (9) is equivalent to

[0033]

[0034] B3: To accurately obtain the solution of the approximation operator (10), calculate the approximation operator (10) and solve the optimization problem.

[0035] Furthermore, the calculation process of the approximation operator (10) in step B3 includes:

[0036] C1: Input \(v\), and let \(d = |w|\);

[0037] C2: Sort the vector \(d\) in descending order, i.e., \(d\) π(1) \(\geq d\) π(2) \(\geq d\) π(3) \(\geq d\) π(r) \(\geq d\) π(N) ;

[0038] C3: for j = 1, 2, ..., N

[0039] Let where d π(r) represents the r-th largest element in the vector d;

[0040]

[0041] C4: The approximation operator is

[0042]

[0043] Finally, y can be solved through formulas (11) and (12) k+1 .

[0044] Furthermore, the solution of sub-problem (7) in step S3 includes:

[0045] D1: Through formula (5), sub-problem (8) is equivalent to the following formula (13):

[0046]

[0047] That is:

[0048]

[0049] D2: For the problem in formula (14), its optimal solution satisfies the following conditions

[0050]

[0051] Since Therefore, we get

[0052]

[0053] D3: Project the result onto the feasible set of the constraint to finally obtain the expression of W k+1 :

[0054]

[0055] where θ is the phase angle of W.

[0056] The present invention also provides an ADMM-based PAPR-aware OFDM-IM signal optimization system, and the system includes a network interface, a memory, and a processor; wherein,

[0057] The network interface is used to realize the reception and transmission of signals during the process of receiving and sending information with other external network elements;

[0058] The memory is used to store computer program instructions that can run on the processor;

[0059] The processor is configured to execute the steps of the method for optimizing OFDM-IM signals with PAPR awareness based on ADMM when running the computer program instructions.

[0060] The present invention also provides a computer storage medium storing a program of a method for optimizing OFDM-IM signals with PAPR awareness based on ADMM. When the program of the method for optimizing OFDM-IM signals with PAPR awareness based on ADMM is executed by at least one processor, the steps of the method for optimizing OFDM-IM signals with PAPR awareness based on ADMM are implemented.

[0061] Beneficial effects: Compared with the prior art, for the problems of reducing the PAPR of the OFDM-IM system and reducing the computational complexity in the operation process, by utilizing the unique structure of the OFDM-IM system, a small jitter signal is added to the idle subcarriers. The addition of the small jitter signal can make the phases of the OFDM-IM signals randomly distributed, preventing the same phase situation from occurring, so as to achieve the purpose of suppressing PAPR. Then, the PAPR is replaced with the infinity norm as the objective function, and the maximum amplitude value of the small jitter signal is used as the constraint condition to construct an optimization model. The proposed optimization model is solved by the alternating direction method of multipliers. The simulation results show that the computational complexity can be significantly reduced while ensuring the PAPR performance and the BER performance. Description of the Drawings

[0062] Figure 1 is the convergence performance graph of the ADMM algorithm;

[0063] Figure 2 is the PAPR comparison graph of different algorithms under 16-QAM modulation;

[0064] Figure 3 is the BER performance of different algorithms under 16-QAM modulation. Detailed Embodiments

[0065] The present invention will be further clarified below with reference to 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 fall within the scope defined by the appended claims of this application.

[0066] Embodiment 1:

[0067] This embodiment provides a method for optimizing OFDM-IM signals with PAPR awareness based on ADMM, including the following steps:

[0068] S1: To reduce the peak-to-average power ratio (PAPR) of the OFDM-IM system, a small jitter signal is added to the idle subcarriers (see ) in the optimization problem (2). The signals in all active subcarriers remain unchanged. The PAPR is replaced by the infinity norm as the objective function, and the maximum amplitude value of the small jitter signal is used as the constraint condition to construct an optimization model.

[0069] Step S1 specifically includes:

[0070] A1: The union of all active subcarrier index sets is represented as:

[0071]

[0072] Since the size of this union is K, the size of the union of idle subcarriers in all blocks and it is represented as

[0073] The frequency domain representation of the added jitter signal is When the α-th subcarrier is an active subcarrier,

[0074]

[0075] A2: The PAPR optimization problem is expressed as

[0076]

[0077] where R is the upper limit of the amplitude threshold of the added jitter signal, aiming to limit the influence of the jitter signal on the error, and X is the initial frequency domain transmitted signal.

[0078] A3: After removing the K zero elements of the active subcarriers in , it is represented as W. Then, formula (2) is expressed as:

[0079]

[0080] where x is the initial time domain transmitted signal, is obtained after deleting the active subcarrier index L.

[0081] S2: Based on the ADMM method, the optimization problem of the optimization model is decomposed into multiple sub-problems, and each sub-problem has a simple closed-form solution.

[0082] Step S2 specifically includes:

[0083] Introduce an auxiliary variable y and let At this time, formula (3) is converted into the following form:

[0084]

[0085] The augmented Lagrangian function of the optimization problem (4) is as follows:

[0086]

[0087] where \(z\in\) N×1 is the Lagrange multiplier corresponding to the constraint, and \(\rho>0\) is a penalty parameter; according to the ADMM method, the update steps for each variable are as follows:

[0088] y k+1 =\(\arg\min L\) ρ (y, W k , z k ) (6)

[0089]

[0090] S3: Using the ADMM method, solve each sub-problem to obtain the signal optimization result.

[0091] The solution of sub-problem (6) includes:

[0092] B1: Through formula (5), sub-problem (6) is equivalent to solving the following problem (9):

[0093]

[0094] B2: To obtain the closed-form solution of problem (9), introduce the approximation operator of the function; the approximation operator of function \(f\) is defined as follows:

[0095]

[0096] Let then problem (9) is equivalent to

[0097]

[0098] B3: To accurately obtain the solution of the approximation operator (10), calculate the approximation operator (10) and solve the optimization problem.

[0099] The calculation process of the approximation operator (10) includes:

[0100] C1: Input \(v\), let \(d = |w|\);

[0101] C2: Sort the vector \(d\) in descending order, i.e., \(d\) π(1) \(\geq d\) π(2) \(\geq d\) π(3) \(\geq d\) π(r) \(\geq d\) π(N) ;

[0102] C3: for j = 1, 2, ..., N

[0103] Let where d π(r) represents the r-th largest element in the vector d;

[0104]

[0105] C4: The approximation operator is

[0106]

[0107] Finally, y can be solved through formulas (11) and (12) k+1 .

[0108] The solution of sub-problem (7) includes:

[0109] D1: Through formula (5), sub-problem (8) is equivalent to the following formula (13):

[0110]

[0111] That is:

[0112]

[0113] D2: For the problem in formula (14), its optimal solution satisfies the following conditions

[0114]

[0115] Since Therefore, we get

[0116]

[0117] D3: Project the result onto the feasible set of the constraint, and finally obtain the expression of W k+1 :

[0118]

[0119] where θ is the phase angle of W.

[0120] According to the calculation steps of the ADMM algorithm, the computational complexity of the entire algorithm can be obtained; the computational complexity of the ADMM algorithm mainly lies in the calculation of the approximation operator and the operation of the Fourier transform. The computational complexity of the approximation operator is The computational complexity of the Fourier transform is Therefore, the total computational complexity of the ADMM algorithm is Effectively reducing the computational complexity.

[0121] Example 2:

[0122] This embodiment provides an ADMM-based PAPR-aware OFDM-IM signal optimization system, which includes a network interface, a memory, and a processor. Among them, the network interface is used to receive and send signals during the process of receiving and sending information with other external network elements. The memory is used to store computer program instructions that can run on the processor. The processor is used to execute the steps of the above consensus method when running the computer program instructions.

[0123] This embodiment also provides a computer storage medium, which stores a computer program that can implement the methods described above when executed by a processor. The computer-readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital magnetic tapes or hard disk drives), and optical storage media (such as CDs, DVDs, or Blu-ray discs), etc. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a dedicated computer, device drivers that interact with specific devices of a dedicated computer, one or more operating systems, user applications, background services, background applications, etc.

[0124] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0125] This application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, so that the instructions executed by the processors of the computer or other programmable data processing devices generate for implementing in the process Figure 1One or more processes and / or blocks Figure 1 An apparatus for the functions specified in one or more blocks

[0126] Embodiment 3:

[0127] 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:

[0128] As Figure 1 shown is the convergence performance graph of the ADMM method. The residual error of the ADMM method is defined as:

[0129]

[0130] Figure 1 The ordinate in represents the value of the residual error, and the abscissa represents the number of iterations of the ADMM method. From Figure 1 the convergence performance, it can be seen that for the ADMM method provided by the present invention, the value of the residual error reaches 10-4 around the 8th iteration, and reaches 10-6 at the 20th iteration. The value of the residual error of the ADMM method drops rapidly in the early stage of iteration. When the number of iterations is around the 50th time, the value of the residual error starts to become flat, indicating that the ADMM method shows a convergence trend. Therefore, in the subsequent simulation experiments, the residual error value less than or equal to 10-6 is selected as the termination condition of ADMM, which is sufficient for practical applications. At this time, the corresponding number of iterations is 20 times.

[0131] In Figure 2 the peak-to-average power ratio performance of the signals optimized by the ADMM method, the CVX method, the ACE method, and the original unprocessed signal under 16-QAM modulation is compared. Among them, three different maximum amplitude values of small jitter signals are selected for the ADMM method and the CVX method respectively.

[0132] As Figure 2The figure shows the PAPR comparison diagram of different algorithms under 16-QAM modulation. When solving using the ADMM method and the CVX method under 16-QAM modulation, the maximum amplitudes of the small jitter signals are respectively selected as R = 0.15, 0.2, and 0.25. When the value of CCDF is 10-3, the peak-to-average power ratio value of the original unprocessed OFDM-IM signal is 10.3 dB, the peak-to-average power ratio value of the signal optimized by the ACE method is 10.3 dB, the peak-to-average power ratio of the signal optimized by the CVX method with multi-level jitter signals added is 6.6 dB. The peak-to-average power ratio values of the signals optimized by the ADMM method and the CVX method are similar. When R = 0.15, the peak-to-average power ratio value is 6.9 dB. When R = 0.2, the peak-to-average power ratio value is 6 dB. When R = 0.25, the peak-to-average power ratio value is 5.2 dB. From the above analysis, it can be concluded that under 16-QAM modulation, it has the same rule as under QPSK modulation, that is, the ADMM method has the same peak-to-average power ratio performance as the CVX method and is better than other cases. And as the maximum amplitude value of the small jitter signal increases, the suppression effect of the peak-to-average power ratio is getting better and better.

[0133] As Figure 3 The figure shows the BER performance diagram under 16-QAM modulation. At this time, the input back-off of the solid-state power amplifier used is 5 dB, and the smoothing factor is 2. When the maximum amplitude values of the small jitter signals are 0.15 and 0.2, the bit error rate performances of the ADMM method and the CVX method are both better than those of the ACE method and the original signal. However, when the maximum amplitude value of the small jitter signal is 0.25, the bit error rate performances of the ADMM method and the CVX method are both worse than those of the ACE method and the original signal. This is because as the maximum amplitude value of the small jitter signal increases, the bit error rate performance will become worse and worse.

[0134] From the above analysis, it can be seen that the peak-to-average power ratio performance and the bit error rate performance of the signal optimized by the ADMM method are similar to those of the CVX method and are better than other methods. However, the computational complexity of the ADMM method is significantly lower than that of the CVX method. In summary, the comprehensive performance of the ADMM method provided by the present invention is the best among all the comparison methods.

Claims

1. An optimization method for PAPR-aware OFDM-IM signals based on ADMM, characterized in that, It includes the following steps: S1: Add a small jitter signal to the idle subcarriers, keep the signals in all active subcarriers unchanged, replace the PAPR with the infinity norm as the objective function, and use the maximum amplitude value of the small jitter signal as the constraint condition to construct an optimization model; S2: Based on the ADMM method, decompose the optimization problem of the optimization model into multiple sub-problems, and each sub-problem has a closed-form solution; S3: Use the ADMM method to solve each sub-problem to obtain the signal optimization result.

2. The optimized method for PAPR-aware OFDM-IM signals based on ADMM according to claim 1, wherein The specific steps of step S1 include: A1: Represent the union of all active subcarrier index sets as: Since the size of the union is K, the size of the union of idle subcarriers in all blocks and denote it as Denote the frequency domain of the added jitter signal as When the α-th subcarrier is an active subcarrier, A2: Represent the PAPR optimization problem as where R is the upper limit of the amplitude threshold of the added jitter signal, the purpose is to limit the influence of the jitter signal on the error, and X is the initial frequency-domain transmitted signal; A3: After removing the K zero elements of the active subcarriers in and denoting it as W, the formula (2) is expressed as: where x is the initial time-domain transmitted signal, is obtained after deleting the active subcarrier index L.

3. An optimization method for PAPR-aware OFDM-IM signals based on ADMM according to claim 2, characterized in that, The specific steps of step S2 include: Introduce an auxiliary variable y and let At this time, formula (3) will be converted into the following form: Then the augmented Lagrangian function of the optimization problem (4) is: where \(z\in N×1 is the Lagrange multiplier corresponding to the constraint, \(\rho>0\) is a penalty parameter; according to the ADMM method, the update steps for each variable are shown as follows: y k+1 = argmin L ρ (y, W k , z k ) (6) Formulas (6)-(8) are the decomposed sub-problems (6)-(8) respectively.

4. A PAPR-aware OFDM-IM signal optimization method based on ADMM according to claim 3, characterized in that The solution of sub-problem (6) in step S3 includes: B1: Through formula (5), sub-problem (6) is equivalent to solving the following problem (9): B2: To obtain the closed-form solution of problem (9), introduce the approximation operator of the function; the approximation operator of function f is defined as follows: Let Then problem (9) is equivalent to B3: Calculate the approximation operator (10) and solve the optimization problem.

5. A PAPR-aware OFDM-IM signal optimization method based on ADMM according to claim 4, characterized in that, The calculation process of the approximation operator (10) in step B3 includes: C1: Input v, let d = |w|; C2: Sort the vector d in descending order, i.e., d π(1) ≥ d π(2) ≥ d π(3) ≥≥ d π(r) ≥≥ d π(N) ; C3： C4: The approximation operator is Finally, y can be solved through formulas (11) and (12). k+1 .

6. A method for optimizing OFDM-IM signals with PAPR perception based on ADMM according to claim 3, characterized in that, The solution of sub-problem (7) in step S3 includes: D1: Through formula (5), sub-problem (8) is equivalent to the following formula (13): That is: D2: For the problem in formula (14), its optimal solution satisfies the following conditions Since Therefore, it is obtained that D3: Project the result onto the feasible set of the constraints, and finally obtain the expression of W k+1 as follows: where θ is the phase angle of W.

7. An ADMM-based PAPR-aware OFDM-IM signal optimization system, characterized in that, The system includes a network interface, a memory, and a processor; among them, The network interface is used to realize the reception and transmission of signals during the process of receiving and sending information with other external network elements; The memory is used to store computer program instructions that can run on the processor; The processor is used to execute the steps of a PAPR-aware OFDM-IM signal optimization method according to any one of claims 1-6 when running the computer program instructions.

8. A computer storage medium, characterized in that: The computer storage medium stores a program of a PAPR-aware OFDM-IM signal optimization method based on ADMM. When the program of the PAPR-aware OFDM-IM signal optimization method based on ADMM is executed by at least one processor, the steps of a PAPR-aware OFDM-IM signal optimization method according to any one of claims 1-6 are realized.

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