A neural network-based prediction LMS power inversion adaptive step size adjustment method

Abstract

The application discloses a neural network-based LMS power inversion adaptive step size adjustment method, and relates to the technical fields of satellite navigation and signal processing. By constructing and training a neural network model, the input is the current frame input signal power and the maximum eigenvalue, and the output is the current frame predicted step size. Compared with the fixed step size LMS power inversion algorithm, the application introduces a neural network to dynamically predict the optimal step size, solves the problem of non-adaptive step size adjustment in the traditional experience formula, and combines the covariance matrix and the maximum eigenvalue of the input signal to reflect the interference intensity, realize interference sensing adjustment, increase the step size in the case of strong interference, accelerate convergence and enhance tracking ability, reduce the step size in the case of weak interference, reduce the steady-state imbalance, and improve the anti-interference performance. The application can solve the problem that the step size parameter in the existing LMS power inversion algorithm is difficult to adaptively adjust, especially the slow convergence or system divergence problem caused by improper step size setting in a multi-interference channel or a dynamic environment.

Description

Technical Field

[0001] This invention relates to the fields of satellite navigation and signal processing technology, and in particular to a method for adaptive step size adjustment based on neural network-predicted LMS power inversion. Background Technology

[0002] The Least Mean Squares (LMS) algorithm, a typical adaptive filtering algorithm, is widely used in communication systems, radar signal processing, and GNSS anti-jamming. To improve its robustness in strong interference environments, the LMS Power Inverse algorithm is proposed, with a step size that is a function of the input signal power. However, power estimation suffers from problems such as time delay and nonlinear response, leading to a decrease in convergence performance under variable interference scenarios.

[0003] In practical applications, especially under conditions of strong or sudden interference, the performance of the fixed-step LMS power inversion algorithm is severely limited. On the one hand, setting the step size too small will result in slow algorithm convergence and an inability to adapt to sudden changes in channel conditions in a timely manner; on the other hand, setting the step size too large will cause weight oscillations or even algorithm divergence, impairing the stability and robustness of the system.

[0004] Existing variable step-size methods primarily update the step-size parameter based on the magnitude of the error signal, the gradient change trend, or the signal autocorrelation characteristics. However, these algorithms still exhibit slow response and poor suppression when faced with sudden strong interference. In high-precision positioning and high-speed communication scenarios, the system's anti-interference capability is subject to higher requirements. Therefore, there is an urgent need for a technique that can sense the interference intensity in real time and dynamically adjust the step-size of the LMS power inversion algorithm accordingly to improve the algorithm's robustness and adaptability under strong interference conditions. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a neural network-based method for predicting LMS power inversion and adaptive step size adjustment. This method involves constructing and training a neural network model, with the current frame input signal power P as the input. x and the largest eigenvalue λ max The output is the prediction step size μ of the current frame, which solves the problem of non-adaptive adjustment of traditional empirical step size.

[0006] To achieve the above objectives, the present invention adopts the following technical solution, including:

[0007] A method for adaptive step size adjustment based on neural network-based prediction of LMS power inversion includes the following steps:

[0008] S1, the input signal X(n)=[x1(n),x2(n),...] is the signal vector received by the array antenna of the multi-element linear array, and the first input signal x1(n) is fixed as the desired signal d(n=x1(n); where n represents the sampling time;

[0009] S2, the remaining input signals [x2(n),...] constitute the vector X. a (n), calculate vector X a The covariance matrix of (n) E[·] represents the mathematical expectation, Let X be a vector a The conjugate transpose of (n);

[0010] S3, calculate the input signal power P at the current sampling time, i.e., the current frame. x (n) and the largest eigenvalue λ max (n):

[0011] Input signal power P x (n)=E[||X a (n)|| 2 ] = tr(R aa (n));

[0012] Among them, ||·|| 2 E[·] represents the square of the norm; E[·] represents the mathematical expectation; tr(·) represents the trace of the matrix;

[0013] Initialize random vector (||v (0) ||2=1);

[0014] Iterative computation Where the superscript t = 1, 2, ..., T represents the iteration number; norm(·) represents the normalization function;

[0015] Maximum eigenvalue λ max (n)=(v (T) ) H R aa (n)v (T) ;

[0016] S4, Build and train a neural network, with the network input being the input signal power P of the current frame. x (n) and the largest eigenvalue λ max (n), the output is the prediction step size μ of the current frame in the LMS power inversion algorithm. pred (n).

[0017] Preferably, in step S4, the training process of the neural network is as follows:

[0018] S41, generate simulation signals with different interference intensities, noise power, and abrupt change frequencies, and construct a simulation dataset;

[0019] Set step size range [μ] min ,μ max For each scene, a series of steps μ∈[μ min ,μ max The LMS power inversion algorithm is executed, and the performance index J(μ) corresponding to all step sizes μ is compared. The step size that minimizes J(μ) is selected as the optimal step size μ for the current scenario. opt ; where μ min μ max These are the minimum and maximum values ​​of the step size, respectively.

[0020] The formula for calculating the performance index J(μ) is:

[0021]

[0022] Where T is the number of iterations to reach steady state; N s denoted as the number of sampling points; α and β are weighting coefficients; N0 is the start time of steady-state evaluation; J(μ) is the performance index; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm.

[0023] Optimal step size μ opt The calculation formula is as follows:

[0024]

[0025] S42, Use a simulation dataset to train the neural network, with the loss function being:

[0026]

[0027] Where N is the total number of samples; This represents the prediction step size of the neural network output for the i-th sample; This represents the optimal step size for the i-th sample.

[0028] The preferred LMS power inversion algorithm is as follows:

[0029] W a (n+1)=W a (n)+μ(n)X a (n)e H (n);

[0030] e(n)=d(n)-Y a (n);

[0031]

[0032] Among them, W a (n) is X a The weight vector of d(n); e(n) is the weight vector of d(n) and Y. a Error signal between (n); e H (n) is the conjugate transpose of e(n); The weight vector W a The conjugate transpose of (n); μ is the iteration step size; n is the sampling time.

[0033] Preferably, in subsequent iterations, the covariance matrix is ​​recursively updated, as shown in the following formula:

[0034]

[0035] Where α is the forgetting factor, 0 < α < 1.

[0036] Preferably, the output signal is obtained until the error signal e(n) converges.

[0037] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned method for adaptive step size adjustment of LMS power inversion based on neural network prediction.

[0038] The present invention also provides a readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the aforementioned method for adaptive step size adjustment of LMS power inversion based on neural network prediction.

[0039] The present invention also provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned method for adaptive step size adjustment of LMS power inversion based on neural network prediction.

[0040] The advantages of this invention are:

[0041] (1) This invention constructs and trains a neural network model, with the input being the input signal power P of the current frame. x and the largest eigenvalue λ max The output is the predicted step size μ for the current frame. Compared with the LMS power inversion algorithm with a fixed step size, this invention introduces a neural network to dynamically predict the optimal step size, solving the problem of non-adaptive adjustment of the traditional empirical step size. It also combines the covariance matrix and the maximum eigenvalue of the input signal to reflect the interference intensity, realizing interference-aware adjustment. Under strong interference, the step size can be increased to accelerate convergence and enhance tracking ability; under weak interference, the step size can be decreased to reduce steady-state misalignment and improve anti-interference performance.

[0042] (2) The present invention can solve the problem that the step size parameter is difficult to adaptively adjust in the existing LMS power inversion algorithm, especially the problem of slow convergence or system divergence caused by improper step size setting in multi-interference channels or dynamic environments. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the LMS power inverted array;

[0044] Figure 2 This is a schematic diagram of a quaternion linear array;

[0045] Figure 3 This is a flowchart of the method of the present invention;

[0046] Figure 4 This is a diagram of the neural network structure;

[0047] Figure 5 This is a three-dimensional beam diagram of an embodiment of the method of the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Reference Figure 1 The power inverted array shown and Figure 2 The principle of the LMS power inversion algorithm for the shown quadruple linear array is as follows:

[0050] The input signal X(n) = [x1(n), x2(n), ...] is the signal vector received by the array antenna of the four-element linear array. The first input signal x1(n), i.e., the received signal of the first array element, is fixed as the desired signal d(n) = x1(n); the received signal vectors of the other array elements are X... a x2(n), x3(n), x4(n)] is used as the input signal of the filter (i.e. the input signal of the LMS power inversion algorithm) to estimate d(n), and the difference is calculated to achieve the purpose of interference cancellation.

[0051] W a (n+1)=W a (n)+μ(n)X a (n)e H (n);

[0052]

[0053] e(n)=d(n)-Ya (n);

[0054] Among them, X a (n) is the vector formed by the received signals of the 2nd, 3rd, and 4th array elements, that is, the vector formed by the 2nd, 3rd, and 4th input signals, X a (n)=[x2(n),x3(n),x4(n)];W a (n) is a vector X a The weight vector of (n); n is the sampling time; The weight vector W a The conjugate transpose of d(n); μ is the iteration step size; e(n) is the sum of d(n) and Y. a Error signal between (n); e H (n) is the conjugate transpose of e(n); Y a (n) is the filter output signal (i.e., the output signal of the LMS power inversion algorithm).

[0055] like Figure 3 As shown, the specific steps of the LMS power inversion adaptive step size adjustment method based on neural network prediction of the present invention are as follows:

[0056] Step 1: The input signal X(n) = [x1(n), x2(n), x3(n), x4(n)] is the signal vector received by the array antenna of the four-element linear array. The first input signal x1(n) is fixed as the desired signal d(n) = x1(n).

[0057] Step 2: The remaining input signals, namely the 2nd, 3rd, and 4th input signals, constitute vector X. a (n), calculate vector X a The covariance matrix of (n) E[·] represents the mathematical expectation, Let X be a vector a The conjugate transpose of (n);

[0058] In subsequent iterations, the covariance matrix can be updated recursively, as shown in the following formula:

[0059]

[0060] Where α is the forgetting factor, 0 < α < 1.

[0061] Step 3: Calculate the input signal power P of the current frame. x (n) and the largest eigenvalue λ max (n), the specific method is as follows:

[0062] Input signal power P x (n)=E[||X a (n)|| 2] = tr(R aa (n));

[0063] Among them, ||·|| 2 E[·] represents the square of the norm; E[·] represents the mathematical expectation; tr(·) represents the trace of the matrix;

[0064] Maximum eigenvalue λ max To characterize the projected power of the received signal in the interference subspace, λ can be approximated using the power iteration method to reduce computational complexity. max The specific process is as follows:

[0065] Initialize random vector (||v (0) ||2=1);

[0066] Iterative computation Where the superscript t = 1, 2, ..., T represents the iteration number; norm(·) represents the normalization function;

[0067] Estimate the largest eigenvalue λ max (n)≈(v (T) ) H R aa (n)v (T) .

[0068] Step 4: Build and train a neural network. The network input is the input signal power P of the current frame. x (n) and the largest eigenvalue λ max (n), the output is the current frame prediction step size μ used to update the weight vector in the LMS power inversion algorithm. pred (n).

[0069] The neural network sets the output activation function to the Sigmoid function, first mapping the output to [0,1], and then linearly scaling it to [μ]. min ,μ max This ensures that the prediction step size is within a reasonable range. min μ max These are the minimum and maximum values ​​of the step size, respectively.

[0070] The neural network training process is as follows:

[0071] S41, using an offline simulation dataset, generate simulation signals with different interference intensities, noise power, and abrupt change frequencies, and set the step size range [μ]. min ,μ max For each scene, iterate through the scene with a step size μ∈[μ min ,μ maxTry a series of different step size values, execute the LMS power inversion algorithm, compare the performance index J(μ) corresponding to all step sizes μ, and select the step size that minimizes J(μ) as the optimal step size μ for the current scenario. opt ;

[0072] The formula for calculating the performance index J(μ) is:

[0073]

[0074] Where T is the number of iterations to reach steady state; N s α is the number of sampling points; β is the weighting coefficient; N0 is the starting time of steady-state evaluation, N0>T; J(μ) is the performance index; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm;

[0075] Optimal step size μ opt The calculation formula is as follows:

[0076]

[0077] S42, Use a simulation dataset to train the neural network, with the loss function being:

[0078]

[0079] Where N is the total number of samples; This represents the prediction step size of the neural network output for the i-th sample; This represents the optimal step size corresponding to the i-th sample (obtained through offline simulation).

[0080] The goal of this loss function is to minimize the prediction step size for each sample output by the neural network. Get as close as possible to the optimal step size

[0081] Step 5: Calculate the prediction step size μ output by the neural network. pred (n) is used for updating the weight vector in the LMS power inversion algorithm. The update formula is:

[0082] W a (n)=W a (n-1)+μ pred (n)X a (n-1)e H (n-1).

[0083] Step 6: Compare the desired signal d(n) with the filter output signal Y. a (n) Subtraction yields the error signal:

[0084] e(n)=d(n)-Y a (n);

[0085]

[0086] Step 7: Perform the calculations iteratively according to steps 2 to 6. Subsequent iterations do not require iterative training of the neural network; only the weight vector of the LMS power inversion algorithm needs to be updated and iterated until the error e(n) converges. The final output signal Y(n) of the entire array is the error signal, as shown in the following formula:

[0087] Y(n)=e(n)=x1(n)-Y a (n).

[0088] Example 1

[0089] In this embodiment, the antenna array in the simulation is as follows: Figure 2 The shown quadruple linear array has a signal-to-noise ratio (SNR) of -35 dB, an interference-to-noise ratio (INR) of 20 dB, and an element spacing of half a wavelength. A narrowband interference signal is incident at an angle of (60°, 30°) and originates from (0°, 30°). c is the speed of light, which is 3 × 10⁻⁶. 8 m / s, the carrier frequency of the satellite signal is f0 = 1575.42MHz. For example... Figure 5 As shown, the neural network-based LMS power inversion adaptive step size adjustment method can achieve a null depth of about 50dB in the interference angle direction, and the null position is also relatively accurate and narrow, reducing the suppression of useful signals.

[0090] Example 2

[0091] An electronic device includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method of Embodiment 1 described above.

[0092] The electronic device in this application embodiment may be the mobile device itself, or a standalone device independent of it. The standalone device may communicate with the mobile device to receive the collected input signals from it and send the selected target decision behavior to it.

[0093] An electronic device includes one or more processors and memory. The processor may be a central processing unit (CPU) or other processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor may execute the program instructions to implement the decision-making behavior and decision-making methods of the various embodiments of this application described above, and / or other desired functions.

[0094] Electronic devices may also include input devices and output devices.

[0095] Example 3

[0096] In addition to the methods and devices described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the decision-making behavior method according to various embodiments of this application as described in Embodiment 1 above.

[0097] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this application. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0098] Example 4

[0099] Embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application described in Embodiment 1 above.

[0100] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0101] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for adaptive step size adjustment based on neural network-predicted LMS power inversion, characterized in that, Includes the following steps: S1, Input signal The signal vector received by the array antenna of the multi-element linear array is fixed with the first input signal as the basis. Desired signal Where n represents the sampling time; S2, the remaining input signals are Constructing vectors Calculate vector covariance matrix ; Represents the mathematical expectation. For vectors The conjugate transpose of; S3, calculate the input signal power at the current sampling time, i.e., the current frame. and the largest eigenvalue : Input signal power ; in, Represents the square of the norm; E ⋅ Represents the mathematical expectation; Represents the trace of a matrix; Initialize random vector ; Iterative computation ; where superscript , indicating the number of iterations; ( ) represents the normalization function; Maximum eigenvalue ; S4, Build and train a neural network, with the network input being the input signal power of the current frame. and the largest eigenvalue The output is the prediction step size of the current frame in the LMS power inversion algorithm. ; In step S4, the training process of the neural network is as follows: S41, generate simulation signals with different interference intensities, noise power, and abrupt change frequencies, and construct a simulation dataset; Set step size range For each scene, a series of steps are traversed. Execute the LMS power inversion algorithm and compare all step sizes. Corresponding performance indicators , choose to The minimum step size is taken as the optimal step size in the current scenario. ;in, These are the minimum and maximum values ​​of the step size, respectively. Performance indicators The calculation formula is: ； Where T is the number of iterations to reach a steady state; This represents the number of sampling points; , These are the weighting coefficients; This marks the starting point of the steady-state assessment. Here, represents the performance metric; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm. Optimal step size The calculation formula is as follows: ； S42, Use a simulation dataset to train the neural network, with the loss function being: ； Where N is the total number of samples; This represents the prediction step size of the neural network output for the i-th sample; This represents the optimal step size for the i-th sample.

2. The method for adaptive step size adjustment based on neural network prediction LMS power inversion according to claim 1, characterized in that, The LMS power inversion algorithm is as follows: ； ； ； in, for The weight vector; e(n) is the weight vector of d(n) and... Error signals between; It is the conjugate transpose of e(n); weight vector The conjugate transpose of ; μ is the iteration step size; n is the sampling time.

3. The method for adaptive step size adjustment based on neural network prediction of LMS power inversion according to claim 1, characterized in that, In subsequent iterations, the covariance matrix is ​​recursively updated, as shown in the following formula: ； in, Forgetting factor, .

4. The method for adaptive step size adjustment based on neural network prediction of LMS power inversion according to claim 2, characterized in that, The output signal is obtained when the error signal e(n) converges.

5. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the neural network-based predictive LMS power inversion adaptive step size adjustment method as described in any one of claims 1 to 4.

6. A readable storage medium, characterized in that, It stores a computer program, which, when executed, implements the method for adaptive step size adjustment of LMS power inversion based on neural network prediction as described in any one of claims 1 to 4.

7. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for adaptive step size adjustment of LMS power inversion based on neural network prediction as described in any one of claims 1 to 4.

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