A precoding method against power efficiency distortion in a multiple antenna system

Abstract

This invention discloses a precoding method for power amplifier distortion-resistant multi-antenna systems, belonging to the field of wireless communication and radar sensing fusion technology. This invention is mainly applied to integrated sensing systems. Compared with traditional integrated sensing systems that do not consider power amplifier nonlinearity, this invention incorporates the power amplifier nonlinearity into the system performance, providing a received signal model and sensing and rate indices under power amplifier distortion conditions. Compared with classical precoding algorithms, this invention considers the impact of power amplifier distortion, resulting in superior performance in practical systems. Furthermore, this invention uses alternating optimization and manifold optimization to solve the non-convex problem of rate maximization, and employs a two-stage solution, enabling its application to hybrid beamforming arrays and making it suitable for real-time applications.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and radar sensing fusion technology, specifically relating to a precoding method for resisting power amplifier distortion in a multi-antenna system. Background Technology

[0002] With the advancement of 6G mobile communication, massive MIMO (Multi-Tap) systems, as a core means to improve spectrum efficiency and spatial multiplexing capabilities, have become a research focus in academia and industry. Compared to traditional single antennas or small-scale arrays, multi-antenna technology can support more users and services with the same time and frequency resources, and achieve stronger directional gain and interference suppression through beamforming. Therefore, it has broad application prospects in various scenarios such as mobile communication, satellite communication, and positioning sensing. In terms of physical layer implementation, the combination of millimeter-wave bands and massive MIMO arrays is considered an important path to meet the requirements of high data rates and low latency. On the other hand, although all-digital precoding has the best performance in theory, each antenna requires an independent RF link and digital-to-analog converter. Hardware costs and energy consumption increase exponentially with the array size, and challenges are also faced in system calibration and thermal management. Hybrid precoding, through a limited number of RF links and a large-scale phase-shift network, approaches the performance of all-digital systems with controllable hardware complexity. Some connection structures are considered more engineering-feasible solutions due to their simple wiring, low loss, and ease of calibration and implementation.

[0003] In real transmitters, power amplifiers (PAs) typically operate near their saturation high-efficiency range to balance energy efficiency and coverage. However, the inherent nonlinearity of power amplifiers introduces distortion in-band and adjacent channels. In multi-antenna systems, this distortion is not independent random noise for each antenna, but exhibits significant spatial correlation with the precoding matrix and signal statistical characteristics, thus forming a directional "distortion beam" in the far field. Spatially correlated nonlinear leakage degrades reception quality in the user direction, reduces communication rates, and generates interference in other directions, affecting the overall system energy efficiency and reliability. Especially under conditions of high signal-to-noise ratio, strong directivity, or large array gain, noise components are effectively suppressed, and the proportion of nonlinear distortion increases, becoming a key bottleneck limiting performance.

[0004] Existing research on multi-antenna precoding largely relies on the assumption of ideal linear amplification, primarily focusing on optimization under the objectives of maximizing rate, suppressing interference, or controlling power. A few studies have addressed power amplifier nonlinearity, but these are mostly concentrated on energy efficiency modeling, power allocation, or compensation methods in single-user scenarios, lacking in-depth utilization and suppression of the spatial characteristics of nonlinear distortion in multi-antenna environments. Overall, engineering solutions that simultaneously meet the following requirements remain scarce: first, incorporating power amplifier nonlinearity into system performance analysis with sufficient accuracy; second, using the actual transmit output power as a constraint, rather than merely approximating the energy of the preceding signal stage; third, the optimization results can be directly mapped to partially connected hybrid precoding hardware, satisfying structural constraints such as amplitude constant mode or phase quantization; and fourth, providing an adjustable trade-off between communication and sensing performance indicators, and explicitly reducing distortion leakage in both user and interference directions.

[0005] In summary, multi-antenna precoding designs that rely solely on the assumption of ideal linearity are unlikely to achieve the expected performance on real hardware platforms. Joint design at the precoding level to address nonlinear distortion, while considering hardware constraints and actual output power, suppressing spatial domain distortion leakage and optimizing overall system performance, represents a more engineering-feasible research direction that aligns with future communication needs. This approach can be integrated with necessary linearization techniques and is easily promoted across different hardware platforms and array sizes, providing a methodological and implementation foundation for the large-scale application of multi-antenna systems. Summary of the Invention

[0006] This invention provides a precoding method for resisting power amplifier distortion in multi-antenna systems, aiming to solve the practical power amplifier nonlinearity problem of multi-antenna systems under partially connected hybrid precoding (HBF) architecture.

[0007] The technical solution adopted in this invention is: a precoding method for resisting power amplifier distortion in a multi-antenna system, the method comprising the following steps:

[0008] The base station transmitter employs a partially connected hybrid beamforming architecture, integrating a fully digital precoding matrix. Decomposed into analog beamforming matrix With digital beamforming matrix ,Right now ,in The dimension is , The dimension of is , This refers to the number of antennas at the base station. For the number of radio frequency chains, Number of users;

[0009] By employing a polynomial-based nonlinear modeling of the power amplifier, an equivalent expression for the power amplifier output signal is obtained.

[0010] An optimization problem with a weighted sum of communication rate and perceived mutual information as the objective function is established and solved under the constraint of total transmit power. During the solution process, manifold optimization and alternating optimization algorithms are used to obtain the all-digital beamforming matrix. That is, the all-digital precoding matrix, and then the partial connection structure is obtained through a decomposition algorithm. and .

[0011] The method of this invention can reduce the impact of nonlinear distortion on communication and sensing performance in multi-antenna systems, and achieve data rate optimization. Compared with random beamforming (RBF), maximum ratio transmission (MRT), and zero-forcing-zero (ZF) algorithms, the method of this invention significantly improves communication sensing and data rate under high signal-to-noise ratio and strong nonlinear conditions.

[0012] Furthermore, the nonlinear modeling of the power amplifier adopts a third-order polynomial model. The relationship between the power amplifier input and output signals, that is, the equivalent expression of the power amplifier output signal, is:

[0013]

[0014] in, Let be the input vector of the power amplifier in a multi-antenna system, satisfying ; It is an all-digital precoding matrix; The original signal vector transmitted by the base station; It is the equivalent linear gain matrix; This is an additive distortion vector that is unrelated to the signal;

[0015] Where the equivalent linear gain matrix Distortion vector covariance matrix for:

[0016]

[0017]

[0018] in, These are the third-order nonlinear coefficients of the power amplifier model. for An identity matrix of order 1. This represents the Hadamard product (element-by-element product). This indicates taking the square of the modulus of each element of the matrix, and the superscript H indicates the conjugate transpose.

[0019] Furthermore, the objective function is:

[0020]

[0021] in, These are the weighting coefficients for communication and sensing, respectively. ; For users The weights; and The first The communication rate of each user and the perception rate of the target, and , ; and The first The signal-to-interference distortion-to-noise ratio of the individual user and the signal-to-distortion-to-noise ratio of the target.

[0022] Furthermore, the first The signal-to-interference distortion-to-noise ratio (SINDR) for each user is defined as:

[0023]

[0024] in, For digital precoding matrix The List, For multi-antenna systems to users The channel coefficient, For the first The power of additive white Gaussian noise for each user.

[0025] Furthermore, the signal-to-distortion-to-noise ratio of the sensing link is:

[0026]

[0027] in, The complex reflection coefficient of the target (including RCS information); For the target at the azimuth angle The array response vector at that location; To sense the additive noise power at the receiver.

[0028] Furthermore, the optimization problem satisfies the following constraints:

[0029]

[0030]

[0031] in, For the total power constraint, This refers to the raw signal that has not yet been pre-encoded, i.e., the raw signal vector transmitted by the base station. For mathematical expectation, This is the equivalent output of the power amplifier. It is a family of block matrices, where each block is a A dimensional vector with a unit modulus element; and These represent the number of antennas and the number of radio frequency chains in the hybrid beamforming architecture, respectively.

[0032] Furthermore, the optimization problem can be rewritten as:

[0033]

[0034] in, For all-digital precoding matrix The List, and For the introduced auxiliary variables, for The fourth-order mapping term, for The sixth-order mapping term, and and ; The penalty coefficient is... users respectively The expressions for the expected signal power, multi-user interference power, nonlinear distortion power, and the expected signal power and distortion power of the sensing link are as follows:

[0035]

[0036] in, For all-digital precoding matrix The List, Let be the trace of the matrix.

[0037] Furthermore, an algorithm combining alternating optimization and manifold optimization is employed to solve the optimization problem, wherein the solution... The iterative update formula is:

[0038]

[0039]

[0040] in, for and When determined, the objective function is about The Riemann gradient, In the manifold gradient descent method, the first... The iteration yielded The value, The Fletcher-Reeves coefficient, Let the step size be determined by the Armijo linear search. For the first The update direction of the next iteration, where proj is the projection operator. For the manifold containing the power constraint, For corresponding The tangent space of the manifold, the revert function retr is used to map the updated points back to the manifold itself;

[0041] Auxiliary variables and The updates are obtained by applying the Karush-Kuhn-Tucker conditions to obtain closed-form solutions, and their optimal solutions are as follows:

[0042]

[0043]

[0044] in, , To obtain a Lange multiplier, the optimal solution is:

[0045]

[0046] in, , for A 1-dimensional matrix of all ones. For element-wise division, the superscript " " indicates the optimal solution, indicated by the superscript " "Indicates conjugate, and The constant coefficients in the solution of the Karush-Kuhn-Tucker conditions are as follows:

[0047]

[0048] in, Let be the trace of the matrix.

[0049] The technical solution provided by this invention brings at least the following beneficial effects:

[0050] (1) Compared with traditional integrated systems that do not consider power amplifier nonlinearity, this invention incorporates the power amplifier nonlinearity into the system performance. The received signal model and inductance and rate performance under power amplifier distortion conditions are given.

[0051] (2) Compared with the classic precoding algorithm, the present invention takes into account the influence of power amplifier distortion and has better performance in practical systems. In addition, the present invention uses alternating optimization and manifold optimization to solve the non-convex problem of maximizing sum and rate, and uses a two-stage solution to make it applicable to hybrid beamforming arrays, which is suitable for real-time applications. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a schematic diagram of an integrated anti-power amplifier distortion sensing system considered in this invention;

[0054] Figure 2 The convergence curves of the manifold optimization sub-algorithm proposed in this invention are shown under different signal-to-noise ratio conditions.

[0055] Figure 3 This is a performance comparison chart of the precoding proposed in this invention and three traditional precoding methods. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described in detail and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Generally, the components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the present invention.

[0057] This invention addresses the practical power amplifier nonlinearity problem in multi-antenna systems with partially connected hybrid precoding (HBF) architectures, proposing a precoding method robust to power distortion in multi-antenna systems. This method explicitly models the impact of power amplifier (PA) nonlinearity on the communication and sensing links in the multi-antenna system during the precoding stage, incorporating distortion into joint performance metrics and constraints. This addresses: the decrease in user SINDR and sensing SNDR caused by correlation leakage of PA nonlinearity in the spatial domain; the requirement that true radiated power constraints should be based on amplifier output signals rather than input signals; the strong non-convex coupling between the structural constraints of partially connected HBF and joint metrics; and the adjustable trade-offs and robust convergence issues caused by communication and sensing metrics sharing the same transmit resources.

[0058] In one embodiment, in a precoding method for resisting power distortion in a multi-antenna system provided in this embodiment, a configuration with root antenna and A base station with a radio frequency chain, of which This base station simultaneously serves A single-antenna communication user, and for an azimuth angle of To detect point targets.

[0059] First, an equivalent linear decomposition is performed on the array-level nonlinear output. Let the original signal vector transmitted by the base station be... It satisfies a cyclically symmetric complex Gaussian distribution. The pre-encoded signal enters the power amplifier group, and the nonlinear output vector of the PA group... According to Bussgang's decomposition theory, this can be expressed as:

[0060]

[0061] in, Let be the input vector of the power amplifier in a multi-antenna system, satisfying . It is a fully digital precoding matrix. It is the equivalent linear gain matrix. It is an additive distortion vector that is unrelated to the signal.

[0062] In a hybrid beamforming architecture, the precoding matrix It can be decomposed into a digital precoding matrix. With analog precoding matrix The product of:

[0063]

[0064] user ( ) received signal for:

[0065]

[0066] in, It is from base station to user The conjugate transpose of the channel vector. Represents the digital precoding matrix The List. User Additive white noise at the location satisfies , This represents noise power.

[0067] Under the third-order nonlinear model, the equivalent linear gain matrix With distortion vector covariance matrix They are represented as follows:

[0068]

[0069]

[0070] in, For the third-order nonlinear coefficients of the power amplifier model. for An identity matrix of order 1. This represents the Hadamard product (element-by-element product). This represents taking the square of the modulus of each element of the matrix.

[0071] From this, we can obtain the... Signal-interference-distortion-noise ratio for each user:

[0072]

[0073] And the signal-distortion-noise ratio of the sensing link:

[0074]

[0075] in, The complex reflection coefficient (including RCS information) represents the target. Represents the target at the azimuth angle The array response vector at that location. This represents the additive noise power at the sensing receiver.

[0076] To maximize the inductive weighted sum and rate of a multi-antenna system, the optimization objective function is defined as follows:

[0077]

[0078] in, These are the weighting coefficients for communication and sensing, respectively. . For users The weight. and The first The communication rate of each user and the perceived mutual information of the target. That is... and The first The communication rate of each user and the perception rate of the target, among which and The first The signal-to-interference distortion-to-noise ratio of the individual user and the signal-to-distortion-to-noise ratio of the target.

[0079] Partial connection structure and total radiated power equality constraints:

[0080]

[0081]

[0082] in, For the total power constraint, The raw signal that has not yet been pre-encoded. Represents a family of block matrices, where each block is a A dimensional vector with elements having a unit modulus. and These represent the number of antennas and the number of RF chains in the hybrid beamforming architecture, respectively. The optimization problem is written as:

[0083]

[0084] in, Total power budget. (Set) A family of block diagonal matrices representing partially connected structures: , where each sub-block vector

[0085] And its elements satisfy the unit modulus constraint. .

[0086] To balance solution efficiency and engineering feasibility, this invention adopts a two-stage design: first, solving for the optimal all-digital precoding matrix in the all-digital domain. Then, it is decomposed and mapped to a hybrid shaping structure. For example... Figure 1 As shown, the specific implementation steps include:

[0087] S1, Joint Optimization of the Entire Digital Domain

[0088] Due to the nonlinear distortion of the power amplifier, the original optimization objective function and the power equality constraints include information about the matrix. Higher-order nonlinear terms (involving fourth-order terms) and sixth-order terms To address the aforementioned non-convex, high-order coupling problem, this invention introduces auxiliary variables. and The higher-order operators are extracted from the precoding matrix using the penalty function method. Decoupling in the middle. Introducing and Afterwards, regarding the original The sixth-order optimization problem is reconstructed as about The problem involves a second-order coupled optimization of the three elements. Simultaneously, the complex nonlinear power equality constraints are transformed into a problem concerning the trace of variables (…). The linear combination form of the auxiliary variables significantly reduces computational complexity and gives the problem an alternating optimization structure. The spatial correlation characteristics are used for approximation. Variables Physical representation The fourth-order mapping term This reflects the amplitude compression effect of the power amplifier's nonlinearity on the baseband signal. (Variable) Physical representation The sixth-order mapping term (When converged, it is equivalent to) This directly corresponds to the nonlinear distortion power generated by the power amplifier and its spatial distribution characteristics. The following reconstruction optimization problem is constructed. :

[0089]

[0090] in, This is the penalty coefficient. All are real scalars, and their physical meanings are respectively user The expected signal power, multi-user interference power, nonlinear distortion power, and the expected signal power and distortion power of the sensing link are specifically expressed as follows:

[0091]

[0092] In this embodiment, in order to solve An alternating optimization framework is adopted, and initialization and iterative optimization are completed through the following steps.

[0093] Step 0: Initialization

[0094] (1) Precoding matrix initialization: The basic matrix is ​​constructed using the zero-forcing or maximum ratio transmission criteria. And based on total power constraints Normalization is performed to obtain initial values. .

[0095] (2) Auxiliary variable initialization: Let , This ensures that the initial penalty is zero.

[0096] (3) Parameter initialization: setting (like Initialize the iteration counter .

[0097] Step 1: Fix and ,renew

[0098] With a fixed auxiliary variable, the subproblem is about The manifold optimization problem. Calculate the Riemann gradient at point The search direction is calculated using the manifold conjugate gradient method. The step size is determined by searching the Armijo line. Finally, an update was performed using a rollback operation:

[0099]

[0100]

[0101] in, It is an auxiliary and When determined, the objective function is about The Riemann gradient, where It is the first in the manifold gradient descent method The iteration yielded The value, It is the Fletcher-Reeves coefficient. The step size is determined by the Armijo linear search. It is the first The update direction of the next iteration. Proj is the projection operator and the pullback function. Used to map the updated points back to the manifold itself.

[0102] Step 2: Fix and Update auxiliary variables

[0103] fixed and , The subproblem is a quadratic programming problem with trace constraints. By solving its KKT conditions, a closed-form solution is obtained:

[0104]

[0105] in, , For Lagrange multipliers, the corresponding solutions are:

[0106]

[0107] in, , , yes A 1-dimensional matrix of all ones. This represents element-wise division. and These are the constant coefficients in the Karush-Kuhn-Tucker condition solution, respectively:

[0108]

[0109]

[0110] Step 3: Fix and Update auxiliary variables

[0111] fixed and , The subproblem can be viewed as a projection problem onto the hyperplane, and its closed-form update is:

[0112]

[0113] Step 4: Convergence Determination and Iteration Termination

[0114] After each round of alternating optimization (steps 1-3), check if any of the following stopping criteria are met:

[0115] Objective function convergence: The relative rate of change of the objective function value between two adjacent iterations is less than a preset threshold. :

[0116]

[0117] Physical constraint consistency: The residual between the auxiliary variable and its physical definition is less than the preset tolerance. :

[0118]

[0119] Maximum number of iterations: the current total number of alternating optimization rounds Reaching the preset maximum value (For example ).

[0120] If any condition is met, stop the iteration and output the optimal solution of the all-digital precoding matrix. Proceed to step S2. Otherwise, update the iteration counter. And optionally update the penalty coefficient. and ( Then return to Step 1 and continue the loop.

[0121] S2, Partial Connection Decomposition Implementation

[0122] The converged result Decompose into the HBF structure space and solve

[0123]

[0124]

[0125] The solution can be obtained using a greedy algorithm based on column matching (such as OMP) or a closed / iterative update method, under the constraints of constant modulus and submatrix connectivity. and .

[0126] Figure 2 The convergence curves of the manifold optimization sub-algorithm in this embodiment are shown under different signal-to-noise ratio conditions; Figure 3 This is a performance comparison chart of the precoding in this embodiment and three traditional precoding methods; from Figure 2 It can be seen that under different signal-to-noise ratios, the method proposed in this embodiment exhibits faster convergence speed and higher convergence performance, especially at medium to high signal-to-noise ratios, where its advantages are more pronounced. Compared with the comparative algorithms, it has better stability and optimization efficiency. Figure 3 It can be seen that the performance of each algorithm improves with the increase of signal-to-noise ratio. However, the method proposed in this embodiment is always superior to the maximum ratio transmission precoding, beamforming algorithm and the comparative methods with or without power amplifier models in the entire signal-to-noise ratio range, demonstrating better inductive rate performance.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the foregoing embodiments have described the present invention in detail, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the embodiments of the present invention.

[0128] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A precoding method for resisting power distortion in a multi-antenna system, characterized in that, Includes the following steps: The base station transmitter employs a partially connected hybrid beamforming architecture, integrating a fully digital precoding matrix. Decomposed into analog beamforming matrix With digital beamforming matrix ,Right now ,in The dimension is , The dimension of is , This refers to the number of antennas at the base station. For the number of radio frequency chains, Number of users; By employing a polynomial-based nonlinear modeling of the power amplifier, an equivalent expression for the power amplifier output signal is obtained. An optimization problem with a weighted sum of communication rate and perceived mutual information as the objective function is established and solved under the constraint of total transmit power. During the solution process, manifold optimization and alternating optimization algorithms are used to obtain the all-digital beamforming matrix. That is, the all-digital precoding matrix, and then the partial connection structure is obtained through a decomposition algorithm. and .

2. The method as described in claim 1, characterized in that, The nonlinear modeling of the power amplifier uses a third-order polynomial model, and the equivalent expression of the power amplifier output signal is as follows: in, Let be the input vector of the power amplifier in a multi-antenna system, satisfying ; It is an all-digital precoding matrix; The original signal vector transmitted by the base station; It is the equivalent linear gain matrix; The distortion vector; Equivalent linear gain matrix Distortion vector covariance matrix for: in, These are the third-order nonlinear coefficients of the power amplifier model. for An identity matrix of order 1. Represents the Hadamard product. This indicates taking the square of the modulus of each element of the matrix, and the superscript H indicates the conjugate transpose.

3. The method as described in claim 2, characterized in that, The objective function is: in, These are the weighting coefficients for communication and sensing, respectively. ; For users The weights; and The first The communication rate of each user and the perception rate of the target, and , ; and The first The signal-to-interference distortion-to-noise ratio of the individual user and the signal-to-distortion-to-noise ratio of the target.

4. The method as described in claim 3, characterized in that, No. Signal-to-interference distortion-to-noise ratio for individual users for: in, , For digital precoding matrix The , List, For multi-antenna systems to users The channel coefficient, For the first The power of additive white Gaussian noise for each user.

5. The method as described in claim 3, characterized in that, No. Signal-to-distortion-to-noise ratio for individual users for: in, The complex reflection coefficient of the target; For the target at the azimuth angle The array response vector at that location; This is the additive noise power.

6. The method as described in claim 1, characterized in that, The optimization problem satisfies the following constraints: in, For the total power constraint, It is a family of block matrices, where each block is a A dimensional vector with a unit modulus element; Let be the mathematical expectation.

7. The method as described in claim 3, characterized in that, The optimization problem is: in, For all-digital precoding matrix The List, and For the introduced auxiliary variables, for The fourth-order mapping term, for The sixth-order mapping term, and and ; The superscript " represents the penalty coefficient. "Indicates conjugate, users respectively The expressions for the expected signal power, multi-user interference power, nonlinear distortion power, and the expected signal power and distortion power of the sensing link are as follows: in, For all-digital precoding matrix The List, Let be the trace of the matrix.

8. The method according to any one of claims 3 to 7, characterized in that, An algorithm combining alternating optimization and manifold optimization is used to solve the optimization problem. The iterative update formula is: in, for and When determined, the objective function is about The Riemann gradient, In the manifold gradient descent method, the first... The iteration yielded The value, The Fletcher-Reeves coefficient, Let the step size be determined by the Armijo linear search. For the first The update direction of the next iteration, where proj is the projection operator. For the manifold containing the power constraint, For corresponding The tangent space, the retraction function `retr` is used to map the updated points back to the manifold itself; auxiliary variables and The updates are obtained by using the Karush-Kuhn-Tucker conditions to obtain closed-form solutions.

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