A method for reconstructing a received signal for amplitude and phase grouping modulation

Abstract

The application discloses a kind of amplitude-phase grouping modulation-oriented received signal reconstruction methods, it is applicable to communication system receiving end, the amplitude-phase grouping modulation signal of distortion caused by power amplifier nonlinear amplification is reconstructed.The method is first to the frequency domain equalization of received signal, and eliminate the influence of power amplifier linear amplification;Then, the phase of received signal is adjusted, and demodulates additional phase;Subsequently, the amplitude of received signal is revised;Then, based on least square criterion, signal reconstruction optimization problem model is constructed, and least square optimization reconstruction is executed.Afterwards, additional phase demodulation, amplitude adjustment and least square optimization reconstruction are iteratively executed until the preset iteration number is reached, so as to obtain high-quality reconstructed signal.The application can effectively deal with nonlinear distortion at the receiving end of the communication system, realize high-quality signal reconstruction, thereby significantly improving the overall performance and power efficiency of the communication system.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a method for reconstructing received signals oriented towards amplitude-phase group modulation. Background Technology

[0002] In modern communication systems, power efficiency is one of the core metrics for measuring system performance, and improving the efficiency of the transmitting power amplifier is particularly crucial. To achieve this, the power amplifier is typically driven into the nonlinear operating region to maximize its energy conversion efficiency. However, this inevitably introduces a critical contradiction: when the power amplifier enters the nonlinear region, its input-output characteristics exhibit significant nonlinear effects, leading to non-negligible distortions in signal amplitude and phase. This nonlinear distortion causes the signal constellation diagram to warp during transmission, making it difficult for the receiver to accurately recover the original modulation information, ultimately resulting in increased bit error rate and decreased system throughput.

[0003] Amplitude-phase block modulation (APM) groups two adjacent signals in the time domain into a block, ensuring that the modulated signals satisfy certain properties in terms of power and phase. Specifically, the sum of the powers of two adjacent signals remains constant, while their phases are symmetrical about an additional phase. Utilizing these properties, the receiver can reconstruct signals distorted by nonlinear amplification, effectively suppressing nonlinear distortion and improving power efficiency. However, existing APM signal reconstruction methods still have several shortcomings, limiting their effectiveness in practical applications. First, existing reconstruction methods require receiving relatively long signal sequences to complete reconstruction, making it difficult to meet the real-time requirements of high-speed communication systems. Second, existing reconstruction methods are sensitive to phase ambiguity, leading to decreased reconstruction accuracy. Finally, under conditions of strong nonlinear distortion, existing reconstruction methods struggle to effectively recover the original signal, resulting in poor communication performance. These problems collectively restrict the practical application of APM. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method for reconstructing received signals based on amplitude and phase group modulation, so as to solve the technical problems of insufficient real-time performance and accuracy of existing methods, thereby further improving the communication performance and power efficiency of wireless communication systems.

[0005] Technical Solution: To achieve the above-mentioned objectives, this invention provides a method for reconstructing received signals based on amplitude and phase group modulation, comprising the following steps:

[0006] The received signal is frequency domain equalized, the effects of linear amplification by the power amplifier are eliminated, and the phase is adjusted, and the additional phase is demodulated;

[0007] The amplitude of the received signal is adjusted. Based on the adjusted received signal and the demodulated additional phase, a model for the optimization problem of receiving signal reconstruction is constructed, and least squares optimization reconstruction is performed. The optimization variables are two adjacent reconstructed signals, and the constraints include power constraints and phase constraints, which correspond to the power and phase properties of the amplitude-phase grouped modulation signal, respectively.

[0008] Iteratively perform additional phase demodulation, amplitude adjustment, and least squares optimized reconstruction until the termination condition is met to obtain the reconstructed signal.

[0009] Furthermore, after frequency domain equalization, the effect of linear amplification by the power amplifier is eliminated, and the original baseband signal is expressed as:

[0010]

[0011] Where 'a' represents the linear amplification factor of the power amplifier.

[0012] Furthermore, based on the average input power of the power amplifier Adjust the received raw baseband signal The phase of the signal, after adjustment, is represented as:

[0013]

[0014] Where exp(·) denotes an exponential function with base e, where e represents the natural base and j represents the complex unit. This represents the average input power of the power amplifier. The corresponding average phase shift.

[0015] Furthermore, based on the amplitude-phase group modulation received signal obtained by baseband demodulation after phase adjustment, for all two adjacent received signals y = [y1, y2]... T The additional phase in the amplitude-phase group modulation is demodulated according to the following formula:

[0016]

[0017] Where Ξ(·) represents mapping to the nearest phase modulation state space, angle(·) represents the angle operator, and |·| represents the modulus operator.

[0018] Furthermore, a weighted average method is used to adjust all adjacent pairs of received signals y = [y1, y2]. T The amplitude, after adjustment, is represented as:

[0019]

[0020] in,(·) TThe .* operator represents the transpose operator, and .* represents element-wise dot product. ε represents the square root operator, P represents the weighting coefficient, and P represents the sum of the normalized power of two adjacent signals in amplitude-phase group modulation.

[0021] Further, adjusting the amplitude of the received signal includes: adjusting the amplitude of the received signal using a weighted average method, performing baseband modulation to obtain an adjusted baseband signal; selecting the average power of the original baseband signal as a threshold power; if the power of the original baseband signal exceeds the threshold power, then using the amplitude of the adjusted baseband signal to replace the amplitude of the original baseband signal, but retaining the phase of the original baseband signal to obtain a further adjusted baseband signal, performing baseband demodulation on it to obtain a further adjusted received signal.

[0022] Furthermore, the power constraint is that the sum of the powers of two adjacent signals is a constant value, and the phase constraint is that the phases of two adjacent signals are symmetric about an additional phase. The property of phase symmetry is mathematically expressed on the unit circle. For all two adjacent further adjusted received signals... Construct the following signal reconstruction optimization problem:

[0023] The optimization objective is:

[0024] The constraint is: x H x = P,

[0025] Re(x H c) = 0,

[0026] in, x = [x1, x2] a This represents the reconstructed signal that needs to be optimized. Re(·) represents the real part operator, and min(·) represents the minimization operator. 2 The square operator is represented by , and the 2-norm operator is represented by . H This indicates the conjugate transpose.

[0027] Furthermore, by employing variable substitution, some unknown variables are replaced with known signals, simplifying the original optimization problem into the following new optimization problem:

[0028] The optimization objective is:

[0029] The constraint is: x H x = P,

[0030]

[0031] in, Compared to the original optimization problem, the phase constraint of the new optimization problem involves some variables x derived from the reconstructed signal. Replacement.

[0032] Furthermore, the closed-form optimal solution to the new optimization problem:

[0033]

[0034] in,

[0035]

[0036] The obtained x is the preliminary reconstruction signal.

[0037] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the received signal reconstruction method for amplitude-phase group modulation.

[0038] Beneficial effects: Compared with the prior art, the received signal reconstruction method for amplitude and phase group modulation proposed in this invention has the following advantages:

[0039] 1. In this invention, even if the power amplifier is in the nonlinear or even saturated amplification range, high-quality signal reconstruction can still be achieved at the receiving end.

[0040] 2. In this invention, the communication system can reconstruct the signal after receiving two signals, without accumulating a long signal sequence at the receiving end, thus achieving high real-time performance of the communication.

[0041] 3. In this invention, the phase of the received original baseband signal is adjusted directly by using the average phase offset corresponding to the average input power of the power amplifier. There is no need to sum the phases of the received signals to calculate the average phase offset, so there is no phase ambiguity problem. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the overall process of the received signal reconstruction method for amplitude and phase group modulation according to the present invention;

[0043] Figure 2 This is a detailed flowchart illustrating the received signal reconstruction method for amplitude and phase group modulation according to the present invention.

[0044] Figure 3 This is a schematic diagram illustrating the phase symmetry of the amplitude-phase group modulation signal represented in a unit circle, which is the method for reconstructing received signals for amplitude-phase group modulation according to the present invention.

[0045] Figure 4The diagram shows the constellation diagram simulation results of the received signal reconstruction method for amplitude and phase group modulation according to the present invention. (a) is the original signal constellation diagram, (b) is the signal constellation diagram after nonlinear amplification by a power amplifier, (c) is the signal constellation diagram after reconstruction by an existing method, and (d) is the signal constellation diagram after reconstruction by the method of the embodiment of the present invention.

[0046] Figure 5 The figure shows the simulation results of the symbol error rate of the received signal reconstruction method for amplitude-phase group modulation according to the present invention. Detailed Implementation

[0047] To better understand the purpose, solution, and effects of the present invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a received signal reconstruction method for amplitude-phase group modulation according to the present invention.

[0048] This invention provides a method for reconstructing amplitude-phase block modulated signals suitable for the receiver of a communication system. This method reconstructs amplitude-phase block modulated signals distorted by nonlinear amplification in a power amplifier at the receiver, effectively compensating for the nonlinear amplification effect of the power amplifier, achieving high-quality signal recovery, and thus improving the system's communication performance and power efficiency. Figure 1 As shown, this method first performs frequency domain equalization on the received signal to eliminate the influence of linear amplification by the power amplifier; then, it adjusts the phase of the received signal and demodulates the additional phase; subsequently, it corrects the amplitude of the received signal; next, it constructs a receiving signal reconstruction optimization problem model based on the adjusted received signal and the demodulated additional phase, and performs least-squares optimization reconstruction, where the optimization variables are two adjacent reconstructed signals, and the constraints include power constraints and phase constraints, corresponding to the power and phase properties of the amplitude-phase grouped modulation signal, respectively. Then, iteratively performing additional phase demodulation, amplitude adjustment, and least-squares optimization reconstruction continues until a preset termination condition is met, resulting in a high-quality reconstructed signal.

[0049] Specifically, the flow of the received signal reconstruction method for amplitude and phase group modulation in this embodiment of the invention is as follows: Figure 2 As shown, the specific steps include:

[0050] Step 1: Based on the estimated channel, perform frequency domain equalization on the received baseband signal to eliminate the influence of the channel.

[0051] Step 2: Eliminate the influence of linear amplification by the power amplifier in the received baseband signal s after frequency domain equalization. The resulting original baseband signal can be expressed as:

[0052]

[0053] Where 'a' represents the linear amplification factor of a known power amplifier.

[0054] Step 3: Based on the average input power of the power amplifier Adjust the received raw baseband signal The phase of the signal, after adjustment, can be expressed as:

[0055]

[0056] Where exp(·) denotes an exponential function with base e, where e represents the natural base and j represents the complex unit. This represents the average input power of the power amplifier. The corresponding average phase shift, This represents the baseband signal after phase adjustment.

[0057] Step 4: Demodulate the baseband signal after phase adjustment to obtain the amplitude-phase group modulation received signal.

[0058] Step 5: For all two adjacent received signals y = [y1, y2] T The additional phase in the amplitude-phase group modulation is demodulated according to the following formula:

[0059]

[0060] Where Ξ(·) represents mapping to the nearest phase modulation state space, angle(·) represents the angle operator, and |·| represents the modulus operator. This represents the additional phase obtained from demodulation.

[0061] Step 6: Use a weighted average method to adjust all adjacent pairs of received signals y = [y1, y2]. T The amplitude, after adjustment, the amplitude-phase group modulation received signal can be expressed as:

[0062]

[0063] in,(·) T The .* operator represents the transpose operator, and .* represents element-wise dot product. This represents the square root operator, ε represents the weighting coefficient, and P represents the normalized sum of the powers of two adjacent amplitude-phase group modulated signals. This indicates the amplitude-phase group modulation received signal after the amplitude has been adjusted.

[0064] Step 7: Perform baseband modulation on the adjusted amplitude and phase group modulated received signal to obtain the adjusted baseband signal.

[0065] Step 8: Select the average power of the original baseband signal as the threshold power. If the power of the original baseband signal exceeds the threshold power, use the amplitude of the adjusted baseband signal to replace the amplitude of the original baseband signal, but retain the phase of the original baseband signal to obtain the baseband signal after further adjustment.

[0066] Step 9: Perform baseband demodulation on the further adjusted baseband signal to obtain the further adjusted amplitude-phase group modulation received signal.

[0067] Step 10: For all two adjacent further adjusted received signals Construct the following signal reconstruction optimization problem:

[0068] The optimization objective is:

[0069] The constraint is: x H x = P,

[0070] Re(x H c) = 0,

[0071] in, x = [x1, x2] T This represents the reconstructed signal that needs to be optimized. Re(·) represents the real part operator, and min(·) represents the minimization operator. 2 The square operator is represented by , and the 2-norm operator is represented by . H This represents the conjugate transpose. The first constraint in the optimization problem corresponds to the power property of the amplitude-phase block modulated signal, namely, the sum of the powers of two adjacent signals is a constant value P. The second constraint corresponds to the phase property of the amplitude-phase block modulated signal, namely, the phases of two adjacent signals differ with respect to the additional phase. Symmetry. In this embodiment of the invention, this phase symmetry is represented in a unit circle, such as... Figure 3 As shown in the figure, the circular structure represents the unit circle, Im(·) represents the imaginary part operator, θ represents the angle of symmetry, and sin(·) and cos(·) represent the sine and cosine operators, respectively. According to... Figure 3 The equation can be written as follows:

[0072]

[0073] By rearranging the equation as necessary, the phase constraint conditions in the signal reconstruction optimization problem can be obtained.

[0074] Step 11: Using the variable substitution method, replace some unknown variables with known signals, simplifying the original optimization problem into the following new optimization problem:

[0075] The optimization objective is:

[0076] The constraint is: x H x = P,

[0077]

[0078] in, Compared to the original optimization problem, the phase constraint of the new optimization problem involves some variables x derived from the reconstructed signal. Replacement.

[0079] Step 12: Calculate the closed-form optimal solution to the new optimization problem:

[0080]

[0081] in,

[0082]

[0083] The obtained x is the preliminary reconstruction signal.

[0084] Step 13: Determine whether the number of iterations has reached the preset threshold (e.g., 10 times). If it has, output the final reconstructed signal; otherwise, jump to step 5.

[0085] To verify the effectiveness of the received signal reconstruction method for amplitude-phase group modulation provided in this embodiment of the invention, a simulation experiment was conducted. The simulation was performed with the power amplifier operating in the nonlinear amplification range. The nonlinear distortion amplitude-to-amplitude modulation (AM-AM) effect of the power amplifier used in the simulation was modeled using the Rapp model.

[0086]

[0087] Where A represents the amplitude of the input signal to the power amplifier, and G(A) represents the amplitude of the output signal to the power amplifier. g, A sat and s are the model parameters for the AM-AM effect of the power amplifier. The nonlinear distortion amplitude-to-phase modulation (AM-PM) effect of the power amplifier used in the simulation adopts a modified Rapp model:

[0088]

[0089] Where A represents the input signal amplitude of the power amplifier, Ψ(A) represents the phase shift of the power amplifier output signal relative to the input signal, and α, β, q1, and q2 are model parameters of the AM-PM effect of the power amplifier. The average phase shift corresponding to the average input power of the power amplifier is calculated using a modified Rapp model. The parameter settings involved in the simulation experiment are shown in Table 1.

[0090] Table 1 Simulation Experiment Parameter Settings

[0091]

[0092] Figure 4 The simulation results show that the signal reconstruction method proposed in this invention can effectively reconstruct distorted signals compared to existing nonlinear amplification methods that do not rely on mathematical optimization (see reference: Fan M, Yi C, Xu W, et al. Amplitude-phase-time block modulation for resisting nonlinear amplification and its application for energy-efficient wireless communications[J / OL]. IEEE Transactions on Communications, Early Access, 2024. DOI:10.1109 / TCOMM.2024.3478110).

[0093] Figure 5 The simulation results show that, compared with no signal reconstruction and existing signal reconstruction methods not based on mathematical optimization, this method can achieve better symbol error rate performance.

[0094] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the received signal reconstruction method for amplitude-phase group modulation described in the foregoing embodiments. The program code for implementing the method of this invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of this invention to be implemented. The program code can be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0095] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0096] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method of reconstructing a received signal for amplitude and phase packet modulation, characterized by, The method comprises the following steps: The received signal is subjected to frequency domain equalization, elimination of the influence of power amplifier linear amplification, phase adjustment, and demodulation of the additional phase; adjusting the amplitude of the received signal, constructing a received signal reconstruction optimization problem model based on the adjusted received signal and the demodulated additional phase, and performing least square optimization reconstruction, wherein the optimization variables are two adjacent reconstructed signals, and the constraint conditions include power constraints and phase constraints, which correspond to the properties of the amplitude-phase group modulation signal in power and phase, respectively; the power constraint condition is that the power sum of the two adjacent signals is a constant value, and the phase constraint condition is that the phase of the two adjacent signals is symmetric about the additional phase, and the property of phase symmetry is mathematically expressed on the unit circle; for all adjacent two further adjusted received signals , construct the following signal reconstruction optimization problem: The optimization objective is: ; The constraints are: ; ； wherein, denotes the reconstructed signal to be optimized, denotes the demodulated additional phase, denotes the power sum of the amplitude and phase grouped modulation of the two adjacent signals after normalization, denotes the real part operator, denotes the minimization operator, denotes the square operator, denotes the two-norm operator, denotes the conjugate transpose; The additional phase demodulation, amplitude adjustment, and least square optimization reconstruction are iteratively performed until a termination condition is reached, and a reconstructed signal is obtained.

2. The method of claim 1, wherein the method further comprises: a received baseband signal after frequency domain equalization , eliminating the effect of power amplifier linear amplification, the original baseband signal is represented as: ； wherein, represents the linear amplification factor of the power amplifier.

3. The method of claim 2, wherein the method further comprises: According to the average input power of the power amplifier , the phase of the received original baseband signal is adjusted, and the adjusted signal is represented as: ； wherein denotes an exponential function with base denotes the natural base, denotes the complex unit, denotes the average input power corresponding average phase offset.​ 4. The method of claim 1, wherein the method further comprises: Based on the amplitude-phase grouping modulation received signal obtained after the phase adjustment and baseband demodulation, for all adjacent two received signals , the additional phase in the amplitude-phase grouping modulation is demodulated according to the following formula: ； wherein, denotes a mapping to the nearest phase modulation state space, denotes the angle operator, denotes the modulo operator.

5. The method of claim 1, wherein the method further comprises: Using a weighted average method, the amplitudes of all adjacent two received signals are adjusted The adjusted amplitude-phase group modulation received signal is represented as: ； wherein denotes the transpose operator, denotes an element-wise multiplication, denotes the square root operator, denotes a weighting factor.

6. The amplitude and phase grouping modulation oriented received signal reconstruction method according to claim 1, characterized in that, The amplitude of the received signal is adjusted by using a weighted average method to adjust the amplitude of the received signal, baseband modulation is performed to obtain an adjusted baseband signal, the average power of the original baseband signal is selected as a threshold power, if the power of the original baseband signal exceeds the threshold power, the amplitude of the adjusted baseband signal is used to replace the amplitude of the original baseband signal, but the phase of the original baseband signal is retained to obtain a further adjusted baseband signal, and baseband demodulation is performed to obtain a further adjusted received signal.

7. The method of claim 1, wherein the method further comprises: determining a phase of the received signal; and determining a phase of the received signal based on the determined phase of the received signal. By using a variable replacement method, a known signal is used to replace part of unknown variables, and the original optimization problem is simplified into the following new optimization problem: The optimization objective is: ; The constraints are: ; ； wherein ; compared to the original optimization problem, the phase constraint of the new optimization problem involves only a subset of the variables reconstructed signal is replaced by 8. The method of claim 7, wherein the method further comprises: The closed-form optimal solution of the new optimization problem is: ； wherein, ； ； obtained i.e. the preliminary reconstructed signal.

9. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the amplitude and phase grouping modulation oriented received signal reconstruction method according to any one of claims 1-8.

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