A design method of a communication signal with low peak-to-average ratio and pre-distortion compensation

Abstract

The application discloses a design method of a low peak-to-average ratio and pre-distortion compensation communication signal, which comprises the following steps: step 1, constructing an optimization problem model with the target function of minimizing the error vector magnitude between an actual sending signal after a power amplifier and an ideal sending signal, and the constraint conditions of a sending signal peak-to-average power ratio and out-of-band radiation at a sending side of a wireless communication system; step 2, introducing auxiliary variables and increasing constraint conditions related to the introduced auxiliary variables, transforming the signal design problem obtained in step 1 to obtain a new optimization problem; step 3, linearizing the nonlinear function representing the power amplifier characteristics in the target function of the optimization problem obtained in step 2 by using a linearization method to obtain an approximate problem after linearization; and step 4, designing an alternating direction multiplier method based on Newton method updating to solve the approximate problem in step 3 to obtain an optimized sending signal. The application can effectively solve the problem that the high peak-to-average power ratio of a sending signal in an OFDM system leads to distortion through a power amplifier, improve the power amplifier efficiency and improve the power amplifier nonlinearity.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a design method of a low peak-to-average ratio and predistortion compensation communication signal. BACKGROUND

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology is the cornerstone of modern wireless communication systems, which can effectively combat channel frequency selective fading, overcome intersymbol interference, and be efficiently combined with multiple-input multiple-output technology to achieve high-speed data transmission. It is one of the most important technologies in modern mobile communication systems. However, OFDM systems are plagued by two key problems: the high peak-to-average power ratio of the transmitted signal and the nonlinear effects of the power amplifier, which limit its performance and efficiency. Therefore, in order to improve system performance, improve power amplifier efficiency, and improve power amplifier nonlinearity, it is urgent to develop effective peak-to-average power ratio suppression methods and power amplifier nonlinear digital predistortion compensation techniques.

[0003] Most existing methods treat peak-to-average power ratio suppression and digital predistortion compensation technology design as two independent problems, without fully considering the potential synergy between the two, and cannot effectively improve power amplifier nonlinearity and power amplifier efficiency at the same time. Therefore, proposing a joint peak-to-average ratio suppression and predistortion compensation communication signal design method is crucial to improving system performance and power amplifier efficiency.

[0004] Existing research has proposed a method that simultaneously reduces the peak-to-average power ratio of the transmitted signal and improves the nonlinearity of the power amplifier by adding a correction signal. However, this type of method is a heuristic algorithm, and the effectiveness of suppressing the signal peak-to-average power ratio and resisting power amplifier nonlinearity depends on the value of the preset scaling factor, and the performance is limited in reducing the signal peak-to-average power ratio. The present application proposes a low peak-to-average power ratio and predistortion compensation communication signal design method, which uses convex optimization theory to design a low-complexity iterative algorithm that can effectively suppress the peak-to-average power ratio of the transmitted signal while improving the nonlinearity of the power amplifier. SUMMARY

[0005] The present application provides a design method of a low peak-to-average ratio and predistortion compensation communication signal, which can effectively solve the problem of high peak-to-average power ratio of the transmitted signal in OFDM systems, improve the efficiency of the power amplifier, and improve the nonlinearity of the power amplifier.

[0006] Technical scheme: The design method of a low peak-to-average ratio and predistortion compensation communication signal according to the present application comprises the following steps:

[0007] Step 1, constructing an optimization problem model at a transmitting side of a wireless communication system, taking an error vector magnitude between an actual transmitting signal after passing through a power amplifier and an ideal transmitting signal as an objective function, and taking a peak-to-average power ratio of the transmitting signal and out-of-band radiation as constraint conditions;

[0008] Step 2, introducing auxiliary variables and adding constraint conditions related to the auxiliary variables, transforming the signal design problem obtained in Step 1 to obtain a new optimization problem;

[0009] Step 3, linearizing a nonlinear function representing a characteristic of the power amplifier in the objective function of the optimization problem obtained in Step 2 by using a linearization method to obtain an approximate problem after linearization;

[0010] Step 4, designing an alternating direction multiplier method based on Newton method updating to solve the approximate problem in Step 3 to obtain an optimized transmitting signal.

[0011] Further, in Step 1, the actual transmitting signal refers to a frequency domain signal obtained by performing discrete Fourier transform on a time domain signal after passing through the power amplifier, and the ideal transmitting signal refers to a modulated frequency domain signal expected to be transmitted.

[0012] Further, in Step 1, the peak-to-average power ratio of the transmitting signal is calculated by statistically sampling the time domain signal after L times upsampling, and the upsampling factor L is a positive integer greater than 1, and is 4.

[0013] Further, in Step 2, auxiliary variables are introduced, and linear equation constraints between the auxiliary variables and original optimization variables are added in the constraint conditions, so that the signal design problem in Step 1 is converted into a new optimization problem.

[0014] Further, in Step 2, the parameter μ>0 is a penalty factor, the parameter is set as a constant, the solution of the optimization problem obtained in Step 2 is regarded as an approximate solution of the signal design problem in Step 1, and when the value of the parameter μ is large enough, the error between the two is infinitely close to 0.

[0015] Further, in Step 3, the transformation characteristic between the input and output signals of the power amplifier is described by a nonlinear function, and the nonlinear function of the power amplifier is approximated as a linear transformation by using a nonlinear method, so that the nonlinear function representing the characteristic of the power amplifier in the objective function of the optimization problem in Step 2 is linearized to obtain an approximate problem.

[0016] Further, in Step 4, the alternating direction multiplier method based on Newton method updating is designed to solve the approximate problem in Step 3, which specifically includes the following steps:

[0017] Step 41, introduce the dual variable, i.e. Lagrange multiplier, write the augmented Lagrange function corresponding to the approximate problem, and divide the problem into several sub-problems according to the optimization variables;

[0018] Step 42, solve the sub-problem composed of the original variables by using the alternating iteration method;

[0019] Step 43, calculate the Hessian matrix of the dual function with respect to the dual variables, and update the dual variables by using the Newton gradient method;

[0020] Step 44, judge whether the update error of the sending signal is less than the pre-set error tolerance value, if yes, terminate the iteration, and take the sending signal obtained in step 42 as the final output solution; otherwise, jump back to step 42 and repeat the above steps.

[0021] Further, in step 4, through the solution of the above steps, until the iteration of the algorithm is terminated, the x solved in step 42 is taken as the optimized design sending signal, which has a low peak-to-average power ratio and can effectively resist the influence of the power amplifier nonlinearity.

[0022] Beneficial effects: compared with the prior art, the present application has the following remarkable advantages: the present application models the peak-to-average power ratio suppression and digital pre-distortion compensation technology in the OFDM system as a unified optimization problem model, can solve the problem that the high peak-to-average power ratio of the sending signal leads to serious distortion after the power amplifier, effectively improves the power amplifier nonlinearity, and improves the power amplifier efficiency; in addition, the alternating direction multiplier method based on the Newton method update has fast convergence speed, low calculation complexity, and is easy to realize. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 It is a method flowchart of the present application.

[0024] Figure 2 It is an error vector magnitude (EVM) performance schematic diagram of the signal design method of the present application.

[0025] Figure 3 It is a peak-to-average power ratio complementary cumulative distribution function (CCDF) curve schematic diagram of the signal design method of the present application.

[0026] Figure 4 It is a power spectral density (PSD) performance schematic diagram of the signal design method of the present application. DETAILED DESCRIPTION

[0027] AsFigure 1 As shown in the figure, a design method of a low peak-to-average ratio and pre-distortion compensation communication signal includes the following steps:

[0028] Step 1, constructing, at a transmitting side of a wireless communication system, an optimization problem model with a target function of minimizing an error vector magnitude between an actual transmitting signal after a power amplifier and an ideal transmitting signal, and constraint conditions of a peak-to-average power ratio and out-of-band radiation of the transmitting signal;

[0029] Step 2, introducing auxiliary variables and adding constraint conditions related to the introduced auxiliary variables, transforming the signal design problem obtained in Step 1 to obtain a new optimization problem;

[0030] Step 3, linearizing a nonlinear function representing a power amplifier characteristic in the target function of the optimization problem obtained in Step 2 by using a linearization method to obtain an approximate problem after linearization;

[0031] Step 4, designing an alternating direction multiplier method based on Newton method updating to solve the approximate problem in Step 3 to obtain an optimized transmitting signal.

[0032] The specific symbol and parameters of a given OFDM system are as follows: the total number of system subcarriers is N, which includes data subcarriers and idle subcarriers; let matrix S D represent a data subcarrier index matrix, which is a diagonal matrix with diagonal elements taking values of 0 or 1; S F represent an idle subcarrier index matrix, which satisfies the relationship S D +S F = I, where I is a unit matrix; let an expected frequency domain transmitting signal be The transmitting signal can adopt modulation modes such as BPSK, QPSK, QAM, etc.; let vector represent an actual frequency domain transmitting signal, and vector represent an L times up-sampled time domain transmitting signal, where the parameter L is an up-sampling factor and can take a value of 4; matrix is composed of N columns taken from an LN-point IFFT matrix; let a nonlinear function g(·) represent a transformation characteristic between input and output signals of a power amplifier; and parameters α and β represent a peak-to-average power ratio and an out-of-band radiation limit of the transmitting signal, respectively.

[0033] Step 1, constructing, at a transmitting side of an OFDM wireless communication system, an optimization problem model with a target function of minimizing an error vector magnitude between an actual transmitting signal after a power amplifier and an ideal transmitting signal, and constraint conditions of a peak-to-average power ratio and out-of-band radiation of the transmitting signal, which can be specifically described as:

[0034]

[0035]

[0036]

[0037] Fz = g(x)

[0038] Step 2, introducing auxiliary variables and and adding linear equality constraints of auxiliary variables and original optimization variables, so that the signal design problem obtained in step 1 is converted into a new optimization problem, which can be specifically described as:

[0039]

[0040]

[0041]

[0042] Fz = r

[0043] x = t

[0044] wherein the parameter μ>0 is a penalty factor, the present application sets the parameter as a constant, the solution of the optimization problem obtained in step 2 can be regarded as an approximate solution of the signal design problem in step 1, and when the value of the parameter μ is large enough, the error between the two is infinitely close to 0.

[0045] Step 3, linearizing the power amplifier nonlinear function in the objective function by using linearization method to obtain the linearized approximate problem, specifically, the nonlinear transformation between the input and output signals of the power amplifier can be expressed as:

[0046]

[0047] wherein g a (·) and g p (·) represent the signal amplitude and phase transformation functions through the power amplifier respectively. The nonlinear function can represent the input and output characteristics of various memoryless power amplifiers, and the present application gives a common solid-state power amplifier (SSPA) model as

[0048]

[0049] wherein p represents a parameter for controlling the smoothness of the linear region and the saturation region of the power amplifier, and A sat represents the input saturation voltage of the power amplifier.

[0050] Further, the above power amplifier nonlinear function can be linearized as:

[0051]

[0052] where represents the average linear gain of the power amplifier, vector represents the nonlinear distortion term. Generally, it is assumed that the OFDM time-domain transmit signal x is complex Gaussian distributed, and the distortion term d is uncorrelated with x. Therefore, the amplitude of the signal x satisfies Rayleigh distribution, denoted as |x i | = q i , i = 1, 2, …, LN, the average linear gain g0 can be calculated by the following formula:

[0053]

[0054] where represents the average power of the transmit signal x. Denote the input back-off (IBO) of the power amplifier as θ = q i / σ, the above formula can be further simplified as:

[0055]

[0056] This variable can be obtained by numerical calculation.

[0057] Then the approximate problem after linearization can be described as:

[0058]

[0059]

[0060]

[0061] Fz = r

[0062] x = t

[0063] Step 4, design an alternating direction multiplier method based on Newton method update to solve the approximate problem described in step 3, to obtain the optimized transmit signal. Specifically, it contains the following sub-steps:

[0064] Step 41, introduce the dual variable (i.e. Lagrange multiplier) Write the augmented Lagrangian function corresponding to the approximate problem as

[0065]

[0066] where the variable and is the Lagrange multiplier, and the parameter ρ > 0 is the penalty factor. Then, write the iteration process of the alternating direction multiplier method based on Newton method update to solve the above approximate problem as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] where k denotes the iteration number, the set and denote the Hessian matrix of the dual function with respect to the variables u and v, respectively. Then the alternating direction multiplier method based on the Newton method update includes solving the above sub-problems for the primal variables x, z, r, t, and the dual variables u and v.

[0073] Step 42, solve the sub-problem of the primal variables by using the alternating iteration method. Specifically, the sub-problem with respect to the variable z can be expressed as:

[0074]

[0075] This problem is a quadratic programming problem with a single quadratic constraint, and its optimal solution can be obtained by setting the derivative of the objective function to 0 and then projecting it to the feasible set of the constraint. Denote the solution of the above problem as Then it can be calculated by the following formula:

[0076]

[0077]

[0078]

[0079] The sub-problem with respect to the variable x can be written as:

[0080]

[0081]

[0082] In order to solve this problem, define x = c · a, where c > 0, Substitute the above problem to obtain

[0083]

[0084]

[0085]

[0086] where bk =t k -v k / ρ. The above problem is separable with respect to variables c and a, and its optimal solution satisfies the following relationship:

[0087]

[0088] Next, removing the variable c from the above problem, we get the following problem:

[0089]

[0090]

[0091]

[0092] Solving for the given information yields the following results:

[0093]

[0094] in Indicates taking The phase, variable λ k It can be a constraint. The corresponding Lagrange multipliers can be obtained using a binary search method. Thus, we can solve for... And x k +1 =c k+1 ·a k+1 .

[0095] The subproblem concerning variables r and t can be written as:

[0096]

[0097] This problem is an unconstrained quadratic programming problem, and its optimal solution can be calculated using the following formula:

[0098]

[0099]

[0100] in At this point, we have solved all the subproblems.

[0101] Step 43: Calculate the Hessian matrix of the dual function with respect to the dual variables, and update the dual variables using the Newton gradient method. Specifically, the dual function can be expressed as:

[0102]

[0103] The Hessian matrix of the dual function with respect to variables u and v can be calculated as follows:

[0104]

[0105]

[0106] Step 44, judging whether the sending signal update error is less than a pre-set error tolerance value, if yes, then terminating iteration, taking the sending signal obtained in step 42 as the final output solution; otherwise, jumping back to step 42 and repeating the above steps.

[0107] Through the above steps 41, 42, 43 and 44, until the algorithm iteration is terminated, the x obtained in step 42 is taken as the sending signal optimized by the present application, which has a low peak-to-average power ratio and can effectively counteract the nonlinear effect of the power amplifier.

[0108] In the simulation example provided by the present application, the sending signal adopts a 16-QAM modulation mode, and the maximum allowed error vector magnitude value according to the mobile communication standard is 12.5%. The baseline scheme 1, the baseline scheme 2 and the baseline scheme 3 are three schemes based on increasing the correction signal to realize peak-to-average power ratio suppression and digital pre-distortion compensation technology proposed in the prior art, and the baseline scheme 4 is a scheme only considering reducing the peak-to-average power ratio of the sending signal.

[0109] Figure 2 The error vector magnitude performance and the iteration number relationship curve of the signal design method of the joint peak-to-average power ratio suppression and digital pre-distortion compensation technology proposed by the present application is given. It can be seen that the convergence speed of the present application scheme is very fast, and the convergence performance is better, and the error vector magnitude value is 5.37% when converging. In addition, from the perspective of practical system application, the error vector magnitude can be reduced to below 12.5% only by 3 iterations of the present application scheme.

[0110] Figure 3 The complementary cumulative distribution function curve of the peak-to-average power ratio of the sending signal is given. It can be seen that when the complementary cumulative distribution function value is 10 -3 -6, the present application scheme can suppress the peak-to-average power ratio of the sending signal to about 4dB, which has a gain of more than 4.5dB compared with the baseline scheme 1, the baseline scheme 2 and the baseline scheme 3.

[0111] Figure 4The power spectral density performance curves of the transmitted signals after passing through the power amplifier represented by the SSPA model are given. The ideal signal represents the power spectral density curve obtained when the power amplifier is linear, and the nonlinear distortion signal represents the power spectral density curve obtained after the original expected transmitted signal passes through the power amplifier. It can be seen that the transmitted signal designed by the scheme has a power spectral density performance close to the ideal signal, indicating that the transmitted signal designed by the scheme can effectively counteract the nonlinearity of the power amplifier. In comparison, the performance of baseline scheme 1, baseline scheme 2, and baseline scheme 3 is slightly worse, and baseline scheme 4 has the worst power spectral density performance because it only considers suppressing the peak-to-average power ratio of the transmitted signal and does not have a digital predistortion compensation technology design, resulting in severe distortion of the signal after passing through the power amplifier.

[0112] In summary, the low peak-to-average ratio and predistortion compensation communication signal design method proposed in the present application can not only effectively suppress the peak-to-average power ratio of the transmitted signal, but also effectively improve the nonlinearity of the power amplifier.

Claims

1. A method for designing a communication signal with low peak-to-average ratio and predistortion compensation, characterized by, Comprising the following steps: Step 1, constructing, at a transmitting side of a wireless communication system, an optimization problem model with an objective function of minimizing an error vector magnitude between an actual transmitting signal after passing through a power amplifier and an ideal transmitting signal, and constraint conditions of a peak-to-average power ratio of the transmitting signal and out-of-band radiation; specifically described as: Fz=g(x); Step 2, introducing an auxiliary variable and increasing a constraint condition related to the introduced auxiliary variable, transforming the signal design problem obtained in Step 1 to obtain a new optimization problem; specifically described as: Fz=r x=t Wherein, the parameter μ>0 is a penalty factor, the parameter is set as a constant, the solution of the optimization problem obtained in Step 2 is regarded as an approximate solution of the signal design problem in Step 1, and when the value of the parameter μ is large enough, the error between the two is infinitely close to 0; Step 3, linearizing the nonlinear function representing the characteristics of the power amplifier in the objective function of the optimization problem obtained in Step 2 by using a linearization method to obtain an approximate problem after linearization; the nonlinear transformation between the input and output signals of the power amplifier is represented as: where g a (·) and g p (·) represent the signal amplitude and phase transformation function through the power amplifier, respectively, the non-linear function characterizes the input-output characteristics of various memoryless power amplifiers, and a common solid-state power amplifier (SSPA) model is given as where p represents a parameter that controls the smoothness of the linear region and the saturation region of the power amplifier, A sat represents the input saturation voltage of the power amplifier; The linearization of the above power amplifier nonlinear function is represented as: wherein represents the average linear gain of the power amplifier, the vector represents the nonlinear distortion term, assuming that the OFDM time-domain transmit signal x is complex Gaussian distributed, and the distortion term d is uncorrelated with x, thus, the amplitude of the signal x satisfies the Rayleigh distribution, denoted as |x i | = q i , i = 1, 2, …, LN, then the average linear gain is calculated by the following formula: where denotes the average power of the transmitted signal x, and let the input back-off of the power amplifier be θ = q i / σ, then the above equation further simplifies to: The variable is obtained through numerical calculation; Then the approximate problem after linearization is described as: Fz=r x=t Step 4, designing an alternating direction multiplier method based on Newton method update to solve the approximate problem in Step 3 to obtain an optimized transmitting signal; specifically, the following sub-steps are included: Step 41, introducing a dual variable to write an augmented Lagrangian function corresponding to the approximate problem as where the variables and are Lagrange multipliers, and the parameter p > 0 is a penalty factor; then, the iteration procedure for solving the above approximation problem based on the Newton method update of the alternating direction multipliers method is written as follows: where k denotes the iteration number, the set and denote the Hessian matrix of the dual function with respect to the variables u and v, respectively; then the alternating direction multiplier method based on Newton's method update comprises solving the above subproblems for the primal variables x, z, r, t, and the dual variables u and v. Step 42, solving a sub-problem composed of the original variable in an alternating iterative manner, the sub-problem about the variable z is represented as: The problem is a quadratic programming problem with a single quadratic constraint, whose optimal solution is obtained by setting the derivative of the objective function to zero and then projecting to the feasible set of the constraint, denoted as Then it is calculated by the following formula: The sub-problem about the variable x is written as: To solve this problem, define x = c a, where c > 0, Substituting the above equation into the problem gives where b k = t k -v k / p, the problem above is separable with respect to variables c and a, and its optimal solution satisfies the following relationship: Next, the variable c is removed from the above problem to obtain the following problem: Solving it obtains wherein denotes the phase of the variable k is the constraint the corresponding Lagrange multiplier, which is found by a bisection search, yields and x k+1 = c k+1 · a k+1 ; The sub-problem about the variables r and t is written as The problem is an unconstrained quadratic programming problem, and the optimal solution is calculated by the following formula: wherein The solution of all sub-problems has been completed; Step 43, calculating the Hessian matrix of the dual function about the dual variable, updating the dual variable by using the Newton gradient method, specifically, the dual function is represented as: The Hessian matrix of the dual function about the variables u and v is calculated as Step 44, judging whether the updating error of the transmitting signal is less than a pre-set error tolerance value, if yes, then terminating the iteration and taking the transmitting signal obtained in Step 42 as the final output solution; Otherwise, jump back to Step 42 and repeat the above steps.

2. The method of designing a low peak-to-average ratio and predistortion compensated communication signal of claim 1, wherein, In Step 1, the actual transmitting signal refers to a frequency domain signal obtained by performing discrete Fourier transform on a time domain signal after passing through a power amplifier, and the ideal transmitting signal refers to a modulated frequency domain signal expected to be transmitted.

3. The method of designing a low peak-to-average ratio and predistortion compensated communication signal of claim 1, wherein, In Step 1, the peak-to-average power ratio of the transmitting signal is calculated by counting the time domain signal after L times of upsampling, and the upsampling factor L is a positive integer greater than 1, taking 4 as an example.

4. The method of designing a low peak-to-average ratio and predistortion compensated communication signal of claim 1, wherein, In Step 2, an auxiliary variable is introduced, and a linear equation constraint of the auxiliary variable and the original optimization variable is added in the constraint condition, so that the signal design problem in Step 1 is converted into a new optimization problem.

5. The method of designing a low peak-to-average ratio and predistortion compensated communication signal of claim 1, wherein, In step 2, the parameter μ > 0 is a penalty factor, the solution of the optimization problem obtained in step 2 is regarded as an approximate solution of the signal design problem described in step 1, and when the parameter μ is large enough, the error between the two is infinitely close to 0.

6. The method of designing a low peak-to-average ratio and predistortion compensated communication signal of claim 1, wherein, In step 3, the transformation characteristics between the input and output signals of the power amplifier are described by a nonlinear function, and the nonlinear function of the power amplifier is approximated as a linear transformation by using a nonlinear method, so as to linearize the nonlinear function describing the characteristics of the power amplifier in the objective function of the optimization problem described in step 2, and an approximate problem is obtained.

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