Design method for communication signal with low peak-to-average ratio and predistortion compensation

Abstract

The invention discloses a design method of a low-peak-to-average-ratio and predistortion compensation communication signal, which comprises the following steps of: 1, constructing a low-peak-to-average-ratio predistortion compensation signal on a transmitting side of a wireless communication system by taking an error vector amplitude between an actual transmitting signal and an ideal transmitting signal which are minimized after passing through a power amplifier as a target function, an optimization problem model taking a sending signal peak-to-average power ratio and out-of-band radiation as constraint conditions; 2, introducing an auxiliary variable, adding a constraint condition related to the introduced auxiliary variable, and transforming the signal design problem obtained in the step 1 to obtain a new optimization problem; 3, linearizing a nonlinear function representing the characteristics of the power amplifier in the optimization problem objective function obtained in the step 2 by using a linearization method to obtain a linearized approximation problem; and step 4, designing an alternating direction multiplier method updated based on a Newton method to solve the approximation problem in the step 3, and obtaining an optimized sending signal. The invention can effectively solve the problem that the peak-to-average power ratio of the transmitted signal in the OFDM system is too high to cause distortion of the power amplifier, improve the efficiency of the power amplifier and improve the nonlinearity of the power amplifier.

Description

Technical Field

[0001] The invention relates to the technical field of wireless communication, and in particular to a design method for a low peak-to-average ratio and pre-distortion compensation communication signal. Background Art

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology is the cornerstone of modern wireless communication systems. It can effectively combat channel frequency selective fading, overcome inter-symbol interference, and can be efficiently combined with multiple-input multiple-output technology to achieve high-speed data transmission. It is one of the extremely 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 effect of the power amplifier, which limit its performance and efficiency. Therefore, in order to improve system performance, increase the efficiency of the power amplifier, and improve the nonlinearity of the power amplifier, it is urgent to develop effective peak-to-average power ratio suppression methods and power amplifier nonlinear digital pre-distortion compensation technology.

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

[0004] Existing research has proposed a method of simultaneously reducing the peak-to-average power ratio of the transmitted signal and improving the nonlinearity of the power amplifier by adding a correction signal. However, this type of method is a heuristic algorithm, and the effect of suppressing the peak-to-average power ratio of the signal and resisting the nonlinearity of the power amplifier depends on the value of the preset proportional factor, and the performance is limited in reducing the peak-to-average power ratio of the signal. The present invention proposes a design method for a low peak-to-average power ratio and pre-distortion compensation communication signal, which uses convex optimization theory to design a low-complexity iterative algorithm, which can effectively suppress the peak-to-average power ratio of the transmitted signal and improve the nonlinear distortion of the power amplifier. Summary of the invention

[0005] Purpose of the invention: The present invention provides a design method for low peak-to-average ratio and pre-distortion compensation communication signals, which can effectively solve the problem of distortion caused by excessive peak-to-average power ratio of the transmitted signal in the OFDM system, thereby improving the efficiency of the power amplifier and improving the nonlinearity of the power amplifier.

[0006] Technical solution: A design method for a low peak-to-average ratio and predistortion compensated communication signal according to the present invention comprises the following steps:

[0007] Step 1: construct an optimization problem model on the transmitting side of the wireless communication system with minimization of the error vector amplitude between the actual transmitted signal after passing through the power amplifier and the ideal transmitted signal as the objective function and with the peak-to-average power ratio of the transmitted signal and the out-of-band radiation as the constraints;

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

[0009] Step 3: linearize 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;

[0010] Step 4: Design an alternating direction multiplier method based on Newton's method to solve the approximate problem described in step 3 and obtain an optimized transmission signal.

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

[0012] Furthermore, in step 1, the peak-to-average power ratio of the transmitted signal is calculated by statistically calculating the time domain signal after L-fold upsampling, and the upsampling factor L is a positive integer greater than 1, and the value is 4.

[0013] Furthermore, in step 2, auxiliary variables are introduced, and linear equality constraints between the auxiliary variables and the original optimization variables are added to the constraint conditions, thereby converting the signal design problem described in step 1 into a new optimization problem.

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

[0015] Furthermore, 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 using a nonlinear method, thereby linearizing the nonlinear function describing the characteristics of the power amplifier in the objective function of the optimization problem described in step 2 to obtain an approximate problem.

[0016] Furthermore, in step 4, an alternating direction multiplier method based on Newton's method 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, to write the augmented Lagrangian function corresponding to the approximate problem, and divide it into several sub-problems according to the optimization variable;

[0018] Step 42, solving the sub-problems consisting of the original variables by using an alternating iteration method;

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

[0020] Step 44, determine whether the update error of the transmission signal is less than the preset error tolerance value. If so, terminate the iteration and use the transmission 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, by solving the above steps until the algorithm iteration is terminated, the x solved in step 42 is used as the optimized transmission signal, which has a low peak-to-average power ratio and can effectively counteract the nonlinear influence of the power amplifier.

[0022] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention models the peak-to-average power ratio suppression and digital pre-distortion compensation technology in the OFDM system as a unified optimization problem model, which can solve the problem of severe distortion of the power amplifier caused by the excessively high peak-to-average power ratio of the transmitted signal, effectively improve the nonlinearity of the power amplifier, and improve the efficiency of the power amplifier; in addition, the proposed alternating direction multiplier method based on Newton's method has a fast convergence speed, low computational complexity, and is easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0024] Figure 2 It is a schematic diagram of the Error Vector Magnitude (EVM) performance of the signal design method of the present invention.

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

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

[0027] like Figure 1 As shown, a design method for a low peak-to-average ratio and predistortion compensated communication signal comprises the following steps:

[0028] Step 1: construct an optimization problem model on the transmitting side of the wireless communication system with minimization of the error vector amplitude between the actual transmitted signal after passing through the power amplifier and the ideal transmitted signal as the objective function and with the peak-to-average power ratio of the transmitted signal and the out-of-band radiation as the constraints;

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

[0030] Step 3: linearize 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;

[0031] Step 4: Design an alternating direction multiplier method based on Newton's method to solve the approximate problem described in step 3 and obtain an optimized transmission signal.

[0032] Given the specific symbols and parameters of the OFDM system as follows: the total number of system subcarriers is N, which includes data subcarriers and idle subcarriers; the matrix S is D represents the data subcarrier index matrix, which is a diagonal matrix with diagonal elements taking values ​​of 0 or 1; S F represents the idle subcarrier index matrix, satisfying the relationship S D +S F =I, where I is the unit matrix; the desired frequency domain transmitted signal is The transmission signal can be modulated by BPSK, QPSK, QAM, etc. Represents the actual frequency domain transmitted signal, vector It represents the time domain transmission signal after L times upsampling. The parameter L is the upsampling factor, which can be 4. It is composed of N columns of the LN-point IFFT matrix; the nonlinear function g(·) represents the conversion characteristics between the input and output signals of the power amplifier; the parameters α and β represent the peak-to-average power ratio and out-of-band radiation limit of the transmitted signal respectively.

[0033] Step 1: On the transmitting side of the OFDM wireless communication system, an optimization problem model is constructed with the objective function of minimizing the error vector amplitude between the actual transmitted signal after the power amplifier and the ideal transmitted signal, and with the peak-to-average power ratio of the transmitted signal and the out-of-band radiation as the constraints. The specific model can be described as follows:

[0034]

[0035]

[0036]

[0037] Fz=g(x)

[0038] Step 2: Introduce auxiliary variables and And add linear equality constraints between auxiliary variables and original optimization variables, so as to transform the signal design problem obtained in step 1 into a new optimization problem, which can be specifically described as follows:

[0039]

[0040]

[0041]

[0042] Fz=r

[0043] x=t

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

[0045] Step 3: linearize the nonlinear function of the power amplifier in the objective function using a linearization method to obtain an approximate problem after linearization. Specifically, the nonlinear transformation between the input and output signals of the power amplifier can be expressed as:

[0046]

[0047] where g a (·) and g p (·) represent the signal amplitude and phase transformation functions after the power amplifier. This nonlinear function can characterize the input and output characteristics of various memoryless power amplifiers. The present invention provides a common solid-state power amplifier (SSPA) model as follows:

[0048]

[0049] Where p is the parameter that controls the smoothness of the linear and saturation regions of the power amplifier, A sat Represents the input saturation voltage of the power amplifier.

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

[0051]

[0052] in represents the average linear gain of the power amplifier, the vector represents the nonlinear distortion term. In general, it is assumed that the OFDM time domain transmitted signal x satisfies the complex Gaussian distribution, and the distortion term d is unrelated to x. Therefore, the amplitude of the signal x satisfies the Rayleigh distribution, and |x i |=q i ,i=1,2,…,LN, then the average linear gain g0 can be calculated by the following formula:

[0053]

[0054] in represents the average power of the transmitted signal x. The input back-off (IBO) of the power amplifier is θ=q i / σ, then 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 stated as:

[0058]

[0059]

[0060]

[0061] Fz=r

[0062] x=t

[0063] Step 4: Design an alternating direction multiplier method based on Newton's method to solve the approximation problem described in step 3 to obtain an optimized transmission signal. Specifically, it includes the following sub-steps:

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

[0065]

[0066] The variables and is the Lagrange multiplier, and the parameter ρ>0 is the penalty factor. Next, the iterative process of solving the above approximate problem by the alternating direction multiplier method based on Newton's method is written as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Where k represents the number of iterations, the set and Respectively represent the Hessian matrices of the dual function with respect to variables u and v. Then the alternating direction multiplier method based on Newton's method update includes solving the above sub-problems for the original variables x, z, r, t, and the dual variables u and v.

[0073] Step 42: Solve the subproblems of the original variables by alternating iteration. Specifically, the subproblem of the variable z can be expressed as:

[0074]

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

[0076]

[0077]

[0078]

[0079] The subproblem about variable x can be written as:

[0080]

[0081]

[0082] To solve this problem, define x = c·a, where c>0, Substituting into the above equation, we can get

[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, remove the variable c from the above problem and get the following problem:

[0089]

[0090]

[0091]

[0092] The solution is

[0093]

[0094] in Indicates taking The phase of the variable λ k Can be a constraint The corresponding Lagrange multiplier can be obtained by binary search. So far, we can solve And x k +1 =c k+1 ·a k+1 .

[0095] The subproblem about 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 by the following formula:

[0098]

[0099]

[0100] in So far, we have solved all sub-problems.

[0101] Step 43: Calculate the Hessian matrix of the dual function with respect to the dual variable, and use the Newton gradient method to update the dual variable. 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:

[0104]

[0105]

[0106] Step 44, determine whether the update error of the transmission signal is less than the preset error tolerance value. If so, terminate the iteration and use the transmission signal obtained in step 42 as the final output solution; otherwise, jump back to step 42 and repeat the above steps.

[0107] By solving the above steps 41, 42, 43, and 44 until the algorithm iteration is terminated, the x solved in step 42 is used as the transmission signal of the optimized design of the present invention, which has a low peak-to-average power ratio and can effectively resist the nonlinear influence of the power amplifier.

[0108] In the simulation example provided by the present invention, the transmitted signal adopts 16-QAM modulation mode, and the maximum allowable error vector amplitude value is 12.5% ​​according to the mobile communication standard. Baseline solution 1, baseline solution 2, and baseline solution 3 are three solutions proposed in existing literature based on adding correction signals to achieve peak-to-average power ratio suppression and digital pre-distortion compensation technology, and baseline solution 4 is a solution that only considers reducing the peak-to-average power ratio of the transmitted signal.

[0109] Figure 2 The relationship curve between the error vector amplitude performance and the number of iterations of the signal design method for the joint peak-to-average power ratio suppression and digital pre-distortion compensation technology proposed in the present invention is given. It can be seen that the scheme of the present invention converges very quickly and has better convergence performance. The error vector amplitude is 5.37% when it converges. In addition, from the perspective of actual system application, the scheme of the present invention only needs 3 iterations to reduce the error vector amplitude to less than 12.5%.

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

[0111] Figure 4The power spectral density performance curve of the transmitted signal after passing through the power amplifier characterized by the SSPA model is given. The ideal signal represents the power spectral density curve obtained when the power amplifier is assumed to be linear, and the nonlinear distortion signal represents the power spectral density curve obtained after the original desired transmitted signal passes through the power amplifier. It can be seen that the transmitted signal designed by the scheme of the present invention has a power spectral density performance close to that of the ideal signal, indicating that the transmitted signal designed by this scheme can effectively combat 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 only considers suppressing the peak-to-average power ratio of the transmitted signal, and there is no digital pre-distortion compensation technology design, resulting in severe distortion of the signal after passing through the power amplifier, and the power spectral density performance is the worst.

[0112] In summary, the low peak-to-average power ratio and pre-distortion compensation communication signal design method proposed in the present invention 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 low peak-to-average ratio and predistortion compensated communication signal, characterized in that: The steps include: Step 1: construct an optimization problem model on the transmitting side of the wireless communication system with the objective function of minimizing the error vector amplitude between the actual transmitted signal after passing through the power amplifier and the ideal transmitted signal, and with the peak-to-average power ratio of the transmitted signal and the out-of-band radiation as the constraints; Step 2: introducing auxiliary variables and adding constraints related to the introduced auxiliary variables, transforming the signal design problem obtained in step 1 to obtain a new optimization problem; Step 3: linearize 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; Step 4: Design an alternating direction multiplier method based on Newton's method to solve the approximate problem described in step 3 and obtain an optimized transmission signal.

2. The method for designing a low peak-to-average ratio and predistortion compensated communication signal as claimed in claim 1, characterized in that: In step 1, the actual transmission signal refers to the frequency domain signal obtained by performing discrete Fourier transform on the time domain signal after passing through the power amplifier, and the ideal transmission signal refers to the modulated frequency domain signal expected to be transmitted.

3. The method for designing a low peak-to-average ratio and predistortion compensated communication signal as claimed in claim 1, characterized in that: In step 1, the peak-to-average power ratio of the transmitted signal is calculated by statistically analyzing the time domain signal after L-fold upsampling. The upsampling factor L is a positive integer greater than 1 and has a value of 4.

4. The method for designing a low peak-to-average ratio and predistortion compensated communication signal according to claim 1, characterized in that: In step 2, auxiliary variables are introduced, and linear equality constraints between the auxiliary variables and the original optimization variables are added to the constraints, thereby converting the signal design problem described in step 1 into a new optimization problem.

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

6. The method for designing a low peak-to-average ratio and predistortion compensated communication signal as claimed in claim 1, characterized in that: 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 using a nonlinear method, thereby linearizing the nonlinear function describing the characteristics of the power amplifier in the objective function of the optimization problem described in step 2 to obtain an approximate problem.

7. The method for designing a low peak-to-average ratio and predistortion compensated communication signal as claimed in claim 1, characterized in that: In step 4, an alternating direction multiplier method based on Newton's method is designed to solve the approximate problem in step 3, which specifically includes the following steps: Step 41, introduce the dual variable, i.e., Lagrange multiplier, to write the augmented Lagrangian function corresponding to the approximate problem, and divide it into several sub-problems according to the optimization variable; Step 42, solving the sub-problems consisting of the original variables by using an alternating iteration method; Step 43, calculate the Hessian matrix of the dual function with respect to the dual variable, and use the Newton gradient method to update the dual variable; Step 44: determine whether the update error of the transmission signal is less than a preset error tolerance value. If so, terminate the iteration and use the transmission signal obtained in step 42 as the final output solution. Otherwise, jump back to step 42 and repeat the above steps.

8. The method for designing a low peak-to-average ratio and predistortion compensated communication signal as claimed in claim 7, characterized in that: In step 4, by solving the above steps until the algorithm iteration is terminated, the x solved in step 42 is used as the optimized transmission signal, which has a low peak-to-average power ratio and can effectively resist the nonlinear influence of the power amplifier.

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