A frequency domain channel equalization method and system based on ALS

Abstract

This invention provides a frequency domain channel equalization method and system based on ALS (Alternating Frequency Optimization), relating to the field of digital signal processing. The ALS-based frequency domain channel equalization method includes: acquiring a broadband signal as a reference signal, wherein the broadband signal is a linearly modulated (LFM) signal; using a broadband signal generated by a channel mismatch model as the signal to be calibrated; dividing the discrete frequency domain responses of the reference signal and the signal to be calibrated to obtain the discrete frequency response of the desired equalizer; fixing the filter order to obtain the discrete frequency response of the actual equalizer; subtracting the discrete frequency response of the desired equalizer from the discrete frequency response of the actual equalizer to obtain an error expression; solving for the optimal weight vector using the least squares method based on the error expression, and obtaining the optimal solution by direct inversion. Regularization techniques are used to handle the ill-conditioned nature of the matrix, and then multiple iterations are used to calculate the weight coefficients, thereby improving the accuracy of the equalizer.

Description

Technical Field

[0001] This invention relates to the field of digital signal technology, specifically to a frequency domain channel equalization method and system based on ALS. Background Technology

[0002] Channel simulators have multiple channels, each containing numerous amplifiers, mixers, filters, and analog devices such as A / D or D / A converters. These analog devices, due to environmental and temperature variations, can introduce various noise contaminations into the channel, such as amplitude and phase modulation noise and quantization noise. This contamination can cause amplitude and phase inconsistencies between channels, known as channel mismatch, thus affecting the characteristics and performance of the communication channel. To accurately simulate the characteristics and performance of real-world communication channels, especially multipath propagation simulation and coherence effects, high attention must be paid to amplitude and phase consistency between and within channels. However, achieving amplitude and phase consistency between channels is often a difficult task in practical applications because stringent system performance requirements must be met. To address this issue, channel equalization techniques are needed to ensure consistency between channels. Summary of the Invention

[0003] (a) Technical problems to be solved

[0004] To address the shortcomings of existing technologies, this invention provides a frequency domain channel equalization method and system based on ALS. First, regularization techniques are used to handle the ill-conditioned nature of the matrix. Then, multiple iterations are employed to calculate the weighting coefficients, thereby improving the equalizer's accuracy. This method effectively solves the channel mismatch problem, ensuring that signal transmission is unaffected by channel mismatch. Furthermore, real-time channel equalization can be achieved through hardware transmission.

[0005] (II) Technical Solution

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

[0007] Firstly, an ALS-based frequency domain channel equalization method is provided, including:

[0008] A broadband signal is acquired as a reference signal, wherein the broadband signal is a linear frequency modulated signal;

[0009] The broadband signal generated using the preset channel mismatch model is used as the signal to be calibrated;

[0010] The discrete frequency response of the desired equalizer is obtained by dividing the discrete frequency domain responses of the reference signal and the signal to be calibrated.

[0011] By fixing the order of the filter, the discrete frequency response of the actual equalizer is obtained;

[0012] The error expression is obtained by subtracting the discrete frequency response of the desired equalizer from the discrete frequency response of the actual equalizer.

[0013] The optimal weight vector is solved using the least squares method based on the error expression. The optimal solution is obtained by direct inversion. The ill-conditioned matrix is ​​solved by using regularization parameters.

[0014] By adding regularization parameters to the direct inverse method using alternating least squares and performing multiple iterations, the optimal equalizer coefficients are obtained.

[0015] The equalizer coefficients obtained after the selected number of iterations are multiplied with the signal to be calibrated to obtain the calibrated frequency domain signal.

[0016] Preferably, the linear frequency modulated signal includes a reference signal D. ref The signal to be calibrated, D i and disturbance signals:

[0017]

[0018]

[0019] Where t is the time variable, K is the linear frequency modulation, and T is the pulse duration;

[0020] The frequency response of the channel mismatch model is:

[0021]

[0022] Where a0, a1, b0, b1, c0, and c1 are constant coefficients that can be configured by the user to change the amplitude and frequency of the mismatched channel, and ω is the angular frequency.

[0023] Preferably, the calculation formula for the desired equalizer is:

[0024]

[0025] Among them, H i (ω) represents the frequency response of the equalizer.

[0026] Preferably, the calculation formula for the actual equalizer is:

[0027]

[0028] N is the number of discrete signal points, a(k) is the frequency factor matrix, and h i These are the filter coefficients.

[0029] Preferably, the error expression is:

[0030]

[0031] Preferably, the cost function of the regularization parameter is:

[0032]

[0033] Where λ is the regularization coefficient.

[0034] Preferably, the formula for solving the optimal equalizer coefficient is:

[0035] h k+1 =((A) T ) (k) A (k) +λE) -1 (A T ) (k) H

[0036] A k+1 =H(h) T ) (k) (h (k) (h T ) (k) +λE) -1 .

[0037] Where k is the number of iterations and E is the identity matrix.

[0038] Secondly, an ALS-based frequency domain channel equalization system is provided, including:

[0039] An acquisition module is used to acquire a broadband signal as a reference signal, wherein the broadband signal is a linear frequency modulated signal;

[0040] The generation module is used to generate a broadband signal using a preset channel mismatch model as the signal to be calibrated.

[0041] The first preprocessing module is used to divide the discrete frequency domain responses of the reference signal and the signal to be calibrated to obtain the discrete frequency response of the desired equalizer.

[0042] The second preprocessing module is used to fix the order of the filter and obtain the discrete frequency response of the actual equalizer.

[0043] The calculation module is used to obtain the error expression by subtracting the discrete frequency response of the desired equalizer from the discrete frequency response of the actual equalizer.

[0044] The solution module is used to solve for the optimal weight vector using the least squares method based on the error expression. It obtains the optimal solution by directly inverting the matrix and uses regularization parameters to solve the ill-conditioning of the matrix.

[0045] The iterative module is used to add regularization parameters to the direct inverse method using alternating least squares and perform multiple iterations to obtain the optimal equalizer coefficients.

[0046] The output module is used to multiply the equalizer coefficients obtained after a selected number of iterations with the signal to be calibrated to obtain the calibrated frequency domain signal.

[0047] Thirdly, a computer-readable storage medium is provided for storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the methods described.

[0048] Fourthly, a computing device is provided, comprising:

[0049] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing any of the methods described.

[0050] (III) Beneficial Effects

[0051] This invention presents a frequency domain channel equalization method and system based on ALS. On the one hand, it can solve the ill-conditioned problem of the matrix during the iteration process; on the other hand, each iteration makes the result of the actual equalizer get closer and closer to the result of the desired equalizer, resulting in a better calibrated signal. Furthermore, it can be implemented in real-time hardware. Attached Figure Description

[0052] Figure 1 This is a flowchart of the frequency domain channel equalization method based on ALS of the present invention;

[0053] Figure 2 This is a model diagram of channel equalization in an embodiment of the present invention;

[0054] Figure 3 A hardware implementation step diagram provided for one embodiment of the present invention;

[0055] Figure 4 A step diagram of a channel equalization signal processing module provided in an embodiment of the present invention;

[0056] Figure 5 This is a comparison chart of different channels before calibration, according to an embodiment of the present invention.

[0057] Figure 6 This is a comparison chart of different channels after calibration, according to one embodiment of the present invention.

[0058] Figure 7 This is a comparison diagram of amplitude mismatch before and after calibration according to an embodiment of the present invention;

[0059] Figure 8 This is a comparison diagram of phase mismatch before and after calibration, according to an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions in the embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0061] Example

[0062] like Figure 1-4 As shown, this embodiment of the invention provides a frequency domain channel equalization method based on ALS, including the following steps:

[0063] S101. Obtain a broadband signal as a reference signal, wherein the broadband signal is a linear frequency modulated signal;

[0064] S102. Use the broadband signal generated by the preset channel mismatch model as the signal to be calibrated;

[0065] S103. Divide the discrete frequency domain responses of the reference signal and the signal to be calibrated to obtain the discrete frequency response of the desired equalizer.

[0066] S104. Fix the order of the filter to obtain the discrete frequency response of the actual equalizer;

[0067] S105. Subtract the discrete frequency response of the desired equalizer from the discrete frequency response of the actual equalizer to obtain the error expression.

[0068] S106. Solve for the optimal weight vector using the least squares method based on the error expression, obtain the optimal solution by direct inversion, and solve the ill-conditioning of the matrix using the regularization parameter.

[0069] S107. By adding regularization parameters to the direct inverse method using alternating least squares and performing multiple iterations, the optimal equalizer coefficients are obtained.

[0070] S108. Multiply the equalizer coefficients obtained after the selected number of iterations with the signal to be calibrated to obtain the calibrated frequency domain signal.

[0071] S109. Hardware implementation: Perform channel equalization on the physical channel simulator.

[0072] Furthermore, in S101 and S102, the linear frequency modulation signal includes the reference signal D. ref The signal to be calibrated, Di and disturbance signals:

[0073]

[0074]

[0075] Where t is the time variable, K is the linear frequency modulation, and T is the pulse duration;

[0076] A linear frequency modulated (LFM) signal is used as the broadband signal. To more closely approximate actual operating conditions, a sinusoidal perturbation model is adopted for the channel mismatch model. The LFM signal bandwidth is 100MHz, the sampling frequency is 400MHz, and the number of sampling points N is 4096.

[0077]

[0078] Where a0, a1, b0, b1, c0, and c1 are constant coefficients that can be configured by the user to change the amplitude and frequency of the mismatched channel, and ω is the angular frequency.

[0079] From the above equation, it can be seen that the amplitude frequency response undergoes cosine motion around a0, and the phase frequency response undergoes sinusoidal perturbation around -b0ω. The amplitudes and spectra of the reference signal and the signal to be calibrated are as follows: Figure 5 As shown.

[0080] Furthermore, the formula for calculating the desired equalizer is:

[0081]

[0082] Among them, D delay (ω) is a delay network inserted in the reference channel to align the output sequence after mismatch channel correction with the center of the output sequence of the reference channel.

[0083] Furthermore, the actual calculation formula for the equalizer is as follows:

[0084]

[0085] N is the number of discrete signal points, a(k) is the frequency factor matrix, and h i These are the filter coefficients.

[0086] Furthermore, the error expression is as follows:

[0087]

[0088] The minimum error is always when Ah is minimized. i =H i When the error is found, the problem of finding the error becomes solving the overdetermined system of equations.

[0089] Furthermore, in this embodiment S106, one common solution to an overdetermined system of equations is to find the pseudo-inverse, i.e., the generalized inverse:

[0090] h i =A + H i

[0091] Among them, A + It is represented as the pseudoinverse of A.

[0092] To avoid finding the pseudo-inverse of a matrix, we can solve the system of equations using matrix decomposition. Multiplying both sides of the above equation by the conjugate transpose gives us:

[0093] A H Ah i =A H H i

[0094] Then for A H The optimal solution is obtained by directly inverting A:

[0095] h i =(A H A) -1 A H H i

[0096] like Figure 7 and Figure 8 The lines marked with 'x' and 'o' represent the errors obtained after calculating the pseudo-inverse and the direct inverse.

[0097] First, add a regularization term. The core idea of ​​regularization is to adjust the covariance matrix A of the rank-deficient matrix A. H Adding a weak smoothing constraint λ to each diagonal element of A results in a singular covariance matrix A. H The inverse of A is transformed into a nonsingular matrix A H Finding the inverse of A+λI greatly improves the stability of solving the rank-deficient matrix equation Ah=H. The cost function can be written as:

[0098]

[0099] In the formula, λ≥0 is the regularization parameter.

[0100] The conjugate gradient of the cost function with respect to the weight vector h is as follows:

[0101]

[0102] make Solution:

[0103]

[0104] Next, we use the ALS alternating least squares method. The loss function for the equalizer coefficients can be written as:

[0105]

[0106] As shown in the formula, the optimization objective of the alternating least squares method is the loss function mentioned above. Since the objective function is non-convex and matrices A and h are coupled together, it is an NP-hard problem. However, if one of the frequency factor matrix A and the weight coefficient matrix h is fixed, the problem is transformed into a convex, separable problem, and then the optimal value can be found using the least squares method. The steps of the alternating least squares method are as follows:

[0107] First, initialize the expected equalizer matrix H, which is usually known. Then, initialize the frequency factor matrix A and the weight coefficient matrix h. These two matrices are usually obtained by using the global mean, random values, or by providing a given input matrix.

[0108] Then, by fixing the frequency factor matrix A, we can find the filter coefficient matrix h. Then, the vector at this point... Since these are known constants, the loss function can be written as:

[0109]

[0110] Where, vector The superscript 0 indicates the first iteration.

[0111] Since the above equation only has one vector h left. j Since the problem of finding the optimal loss function is unknown, it is transformed into a least squares problem. The least squares method is used to solve for the optimal solution. First, h... j Taking the partial derivative, we get:

[0112]

[0113] make have to:

[0114]

[0115] Similarly, this time we fix the attribution matrix h to find the preference matrix A. Since the first filter coefficient matrix h has already been found in the previous step, the vector at this time... Since these are known constants, the loss function can be written as:

[0116]

[0117] Where, vector The superscript 0 indicates the first iteration.

[0118] For A iTaking the partial derivative, we get:

[0119]

[0120] make have to:

[0121]

[0122] Repeat the above steps alternately until the loss function L(A, h) converges or the set number of iterations is reached. The final frequency factor matrix A and weight coefficient matrix h are the optimal solution. The result is:

[0123] h k+1 =((A) T ) (k) A (k) +λE) -1 (A T ) (k) H

[0124] A k+1 =H(h) T ) (k) (h (k) (h T ) (k) +λE) -1

[0125] Substituting the frequency factor matrix A and weight coefficient matrix h obtained above, we obtain the actual equalizer coefficients. Multiplying the actual equalizer coefficients by the signal to be equalized yields the equalized signal, such as... Figure 6 As shown.

[0126] Furthermore, the formula for calculating the optimal equalizer coefficient is:

[0127] h k+1 =((A) T ) (k) A (k) +λE) -1 (A T ) (k) H

[0128] A k+1 =H(h) T ) (k) (h (k) (h T ) (k) +λE) -1 .

[0129] Where k is the number of iterations and E is the identity matrix.

[0130] Furthermore, such as Figure 3As shown, S109 is implemented using FPGA hardware:

[0131] Since the channel simulator is multi-channel, a data acquisition unit is connected to the channel simulator to receive the data from the channel simulator and send it to the signal processing module. The algorithm of the signal processing module is the ALS iterative equalization algorithm proposed in this paper.

[0132] The equalizer coefficients are obtained from the signal processing module and processed with the signal to be calibrated to obtain the calibrated signal.

[0133] The solution provided by this invention offers a method for equalizing the signal to be calibrated. By simulating channel mismatch, various factors can be considered and processed in the simulation environment, thereby solving the problem of inconsistent signal amplitude and phase, and better simulating problems that may occur in actual transmission.

[0134] Specifically:

[0135] First, use the data acquisition module to collect data from each channel.

[0136] The collected data is first buffered. Since there will be a certain delay in the collection time of each channel, a synchronization clock module is needed to align the data. A FIFO module can be used here.

[0137] Perform a Discrete Fourier Transform on the aligned data; this can be done using an FFT IP kernel.

[0138] The discrete signal is sent to the signal processing module to calculate the equalization coefficient, with the data of the first channel as the reference signal and the other channels as the channels to be calibrated.

[0139] The equalizer coefficients are calculated using MATLAB's data processing capabilities and then converted to fixed-point values. The results are then transmitted to the RAM module in the signal simulator for data storage using the feedback module.

[0140] The cached data is multiplied by the equalizer coefficients in the RAM module to obtain the equalized channel output. Here, the built-in FIR IP core can be used for convolution operation.

[0141] Embodiments of this application may be provided as methods or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application may be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0142] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0143] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0144] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0145] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method for frequency domain channel equalization based on ALS, characterized in that, The method comprises the following steps: acquiring a wideband signal as a reference signal, wherein the wideband signal adopts a linear frequency modulation signal; generating a wideband signal generated by a preset channel mismatch model as a signal to be calibrated; dividing discrete frequency domain responses of the reference signal and the signal to be calibrated to obtain a discrete frequency response of an expected equalizer; fixing an order of a filter to obtain a discrete frequency response of an actual equalizer; subtracting the discrete frequency response of the expected equalizer from the discrete frequency response of the actual equalizer to obtain an error expression; solving an optimal weight vector by using a least square method according to the error expression, obtaining an optimal solution by using a direct inversion method, and solving a matrix illness by using a regularization parameter; adding the regularization parameter to the direct inversion method by using an alternating least square method and performing multiple iterations to obtain optimal equalizer coefficients; multiplying the equalizer coefficients obtained after the selected number of iterations with the signal to be calibrated to obtain a calibrated frequency domain signal.

2. The method of claim 1, wherein the ALS-based frequency domain channel equalization method is characterized by: The chirp signal comprises a reference signal D ref , a signal to be calibrated D i and a perturbation signal: Wherein, t is a time variable, K is a linear frequency modulation, T is a pulse duration time; The channel mismatch model frequency response is: Wherein, a0, a1, b0, b1, c0, c1 are constant coefficients, configured by oneself, which can change the amplitude and frequency of the mismatch channel respectively, and ω is an angular frequency.

3. The method of claim 2, wherein the ALS-based frequency domain channel equalization method is characterized by: The calculation formula of the expected equalizer is: where H i (ω) is the frequency response of the equalizer.

4. The method of claim 3, wherein the ALS-based frequency domain channel equalization method is characterized by: The calculation formula of the actual equalizer is: N is the number of discrete signal points, a(k) is the frequency factor matrix, h i are the filter coefficients.

5. The method of claim 4, wherein the ALS-based frequency domain channel equalization method is characterized by: The error expression is:

6. The method of claim 5, wherein: The cost function of the regularization parameter is: Wherein, λ is a regularization parameter.

7. The method of claim 6, wherein the ALS-based frequency domain channel equalization method is characterized by: The solving formula of the optimal equalizer coefficient is: h k+1 = ((A T ) (k) A (k) + λE) -1 (A T ) (k) H A k+1 = H(h T ) (k) (h (k) (h T ) (k) + λE) -1 . Wherein, k is the number of iterations, and E is a unit matrix.

8. An ALS-based frequency domain channel equalization system, characterized by, The method comprises the following steps: An acquisition module is configured to acquire a wideband signal as a reference signal, wherein the wideband signal adopts a linear frequency modulation signal; A generation module is configured to generate a wideband signal generated by a preset channel mismatch model as a signal to be calibrated; A first preprocessing module is configured to divide discrete frequency domain responses of the reference signal and the signal to be calibrated to obtain a discrete frequency response of an expected equalizer; A second preprocessing module is configured to fix an order of a filter to obtain a discrete frequency response of an actual equalizer; A calculation module is configured to subtract the discrete frequency response of the expected equalizer from the discrete frequency response of the actual equalizer to obtain an error expression; A solving module is configured to solve an optimal weight vector by using a least square method according to the error expression, obtain an optimal solution by using a direct inversion method, and solve a matrix illness by using a regularization parameter; An iteration module is configured to add the regularization parameter to the direct inversion method by using an alternating least square method and perform multiple iterations to obtain optimal equalizer coefficients; An output module is configured to multiply the equalizer coefficients obtained after the selected number of iterations with the signal to be calibrated to obtain a calibrated frequency domain signal.

9. A computer-readable storage medium storing one or more programs, the one or more programs comprising instructions that when executed by a computer cause the computer to perform a method of any of claims 1-8. The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any of the methods of claims 1-7.

10. A computing device, comprising: The method comprises the following steps: One or more processors, memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods of claims 1-7.

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