A method, apparatus and medium for estimating signal periodicity based on off-grid interface

Abstract

This invention belongs to the field of periodic signal parameter estimation, and discloses a method, device, and medium for estimating the periodicity of a signal based on off-grid. The method includes: Step 1, constructing a cost function; Step 2, performing p=0 iterations to initialize the fundamental frequency f of the periodic signal; Step 3, performing the (p+1)th iteration, substituting the estimated value of f from the p-th iteration into J(f,u), and optimizing u to obtain an estimated value of u; Step 4, substituting the estimated value of u from the (p+1)th iteration into J(f,u), and using Newton's method to optimize the fundamental frequency f; Step 5, obtaining the period estimate from the (p+1)th iteration; Step 6, repeating steps 3-5 until the number of iterations P. This invention can be applied to practical communication or signal processing hardware systems to solve the problem of inaccurate period estimation caused by crystal oscillator frequency drift in the hardware system, thereby improving the performance of subsequent communication or signal processing algorithms.

Description

Technical Field

[0001] This invention relates to the field of periodic signal parameter estimation, specifically to a method, apparatus, and medium for estimating signal periodicity based on off-grid. Background Technology

[0002] Due to frequency drift of the hardware crystal oscillator or the sampling rate not being an integer multiple of the period, signal resampling is necessary to ensure the accuracy of period estimation. However, this grid-based period estimation method is limited by the grid, and its accuracy is related to the fineness of the grid division. Therefore, it is necessary to break away from the limitation of grid precision in traditional grid-based period estimation methods. By treating the fundamental frequency of the periodic signal as a continuous value, a more accurate fundamental frequency estimate can be obtained, thereby improving the performance of subsequent communication or signal processing algorithms. Summary of the Invention

[0003] The purpose of this invention is to provide a method, apparatus, and medium for estimating the periodicity of signals based on off-grid structures, in order to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for estimating signal periodicity based on off-grid locations includes:

[0006] Step 1: Construct the cost function J(f,u), where f is the fundamental frequency of the periodic signal and u is a complex number that contains both amplitude and phase information;

[0007] Step 2: Perform p=0 iterations to initialize the fundamental frequency f of the periodic signal;

[0008] Step 3: Perform the (p+1)th iteration, substitute the estimated value of f from the pth iteration into J(f,u), optimize u, and obtain the estimated value of u;

[0009] Step 4: Substitute the estimated value of u in the (p+1)th iteration into J(f,u) and use Newton's method to optimize the fundamental frequency f.

[0010] Step 5: Obtain the period estimate for the (p+1)th iteration;

[0011] Step 6: Repeat steps 3-5 until the number of iterations P.

[0012] Furthermore, the cost function J(f,u) in step 1 is:

[0013] ,

[0014] Where y is the acquired signal with length K, and a(f) is a column vector whose elements are the values ​​of a complex exponential function at different time points.

[0015] Furthermore, in step 3, u is optimized, specifically by taking the frequency estimate obtained in the p-th iteration. Substituting the cost function and setting its partial derivative with respect to u to zero, we obtain the estimated value of u for the (p+1)th iteration. for:

[0016] ,

[0017] The superscript H represents the conjugate transpose operation.

[0018] Furthermore, step 4 specifically includes:

[0019] The estimated value of u in the (p+1)th iteration Substituting J(f,u), and using Newton's method to iteratively calculate the fundamental frequency f, we have...

[0020] ,

[0021] in Find the first derivative of J(f,u) with respect to the fundamental frequency f, where u is the estimate from the (p+1)th iteration. For J(f,u), take the second derivative with respect to the fundamental frequency f when u is fixed as the estimate of the (p+1)th iteration, i.e.:

[0022]

[0023] ,

[0024] in, Operators that represent the real part of complex numbers.

[0025] Furthermore, the estimated period value for the (p+1)th iteration in step 5 is:

[0026] .

[0027] The present invention also provides an off-grid-based signal periodicity estimation device, comprising one or more processors for implementing the off-grid-based signal periodicity estimation method described above.

[0028] The present invention also provides a readable storage medium having a program stored thereon, which, when executed by a processor, implements a signal periodicity estimation method based on off-grid as described above.

[0029] Compared with the prior art, the beneficial effects of the present invention are:

[0030] 1) The method of this invention breaks the limitation of traditional grid-based period estimation methods by grid accuracy.

[0031] 2) This invention treats the fundamental frequency of a periodic signal as a continuous value and uses Newton's method to iteratively estimate the fundamental frequency, ultimately obtaining an accurate period estimate.

[0032] 3) This invention can be applied to actual communication or signal processing hardware systems to solve the problem of inaccurate period estimation caused by crystal oscillator frequency drift in hardware systems, thereby improving the performance of subsequent communication or signal processing algorithms. Attached Figure Description

[0033] Figure 1 This is a flowchart of a signal periodicity estimation method based on off-grid according to the present invention.

[0034] Figure 2 It is a curve showing the estimated period as a function of the number of iterations.

[0035] Figure 3 It is the convergence curve of the cost function.

[0036] Figure 4 This is a schematic diagram of the structure of a signal periodicity estimation device based on off-grid according to the present invention. Detailed Implementation

[0037] 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.

[0038] This invention provides a method for estimating signal periodicity based on off-grid conditions, such as... Figure 1 As shown, this paper addresses the problem of inaccurate period estimation caused by crystal oscillator frequency drift in hardware systems. By treating the period as a continuous value and using Newton's method to iteratively estimate the period, an accurate period estimate is obtained, breaking the limitation of traditional grid-based period estimation methods on grid precision.

[0039] The problem of inaccurate period estimation caused by crystal oscillator frequency drift in the hardware system refers to the original signal period being... The number of cycles is When the crystal oscillator frequency is stable, the number of signal samples acquired by the hardware system is When the crystal oscillator frequency drifts, it causes the sampling rate to increase or decrease, which in turn causes the number of signal samples acquired by the hardware system to decrease or increase. The period at this time is It is no longer the original cycle. In this embodiment, it is assumed that the original signal has a period of A single-pulse periodic signal, with the number of periods being Because the crystal oscillator frequency drift causes a slower sampling rate, the number of signal samples acquired by the hardware system decreases, resulting in a reduction of the number of samples. Therefore, the number of signal samples acquired by the hardware is .

[0040] The fundamental frequency of a periodic signal is iteratively estimated using Newton's method to obtain an accurate estimate of the period. This process includes the following steps:

[0041] Step 1: Construct the cost function J(f,u), where f is the fundamental frequency of the periodic signal, and u is a complex number that contains both amplitude and phase information. The cost function J(f,u) is:

[0042]

[0043] Where y is the signal acquired by the hardware system, with a length of K. , It is a column vector whose elements are the values ​​of a complex exponential function at different points in time, i.e.:

[0044]

[0045] In the formula, exp(·) is an exponential function, the superscript T indicates the transpose operation, and the symbol j is the imaginary unit, which is the complex number representation commonly used in mathematics and engineering. U is a complex number that contains both amplitude and phase information. The relationship between the fundamental frequency f of a periodic signal and the period L of the signal is as follows: .

[0046] Step 2: In the next iteration, the fundamental frequency of the periodic signal is initialized. In this embodiment, the initialization base frequency for the 0th iteration is set to... .

[0047] Step 3: In the next iteration, u is optimized, and the p-th iteration... The estimated value Substituting J(f,u), we get Let the cost function be... Set the partial derivative to zero, i.e. We obtain the (p+1)th iteration. The estimated value is:

[0048]

[0049] The superscript H represents the conjugate transpose operation.

[0050] Step 4: [Regarding...] Optimize and make the first The estimated value of u in the next iteration Substituting J(f,u), we get The calculation is performed using Newton's method.

[0051]

[0052] Among them, Let J(f,u) be the estimated value of the (p+1)th iteration with u fixed. Take the first derivative with respect to the fundamental frequency f. Let J(f,u) be the estimated value of the (p+1)th iteration with u fixed. When the second derivative with respect to the fundamental frequency f is taken, that is...

[0053]

[0054] Step 5: Based on the relationship between the fundamental frequency and the period of the periodic signal, obtain the estimated period value for the (p+1)th iteration.

[0055]

[0056] Step 6: Repeat steps 3-5 until the specified number of iterations is reached. In this embodiment, the number of iterations is set. To obtain an estimate of the period. With the number of iterations The curve is as follows Figure 2 The convergence curve of the cost function is as follows: Figure 3 As shown, the cost function converges when the number of iterations is greater than 25. The final accurate period estimate is obtained.

[0057]

[0058] In this embodiment, the estimated value of the period is respectively... The period value of the signal taken by the actual hardware In comparison, the two are basically the same, with a relative error of [missing information]. By using the off-grid-based signal periodicity estimation method proposed in this invention, an accurate period estimate is obtained, solving the problem of inaccurate period estimation caused by crystal oscillator frequency drift in the hardware system, and improving the performance of subsequent communication or signal processing algorithms.

[0059] See Figure 4 The present invention provides an off-grid-based signal periodicity estimation device, which includes one or more processors for implementing an off-grid-based signal periodicity estimation method in the above embodiments.

[0060] An embodiment of the off-grid signal periodicity estimation device of the present invention can be applied to any device with data processing capabilities, such as a computer or other equipment. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 4 The diagram shown is a hardware structure diagram of any device with data processing capabilities, including the off-grid signal periodicity estimation device of the present invention. (Except for...) Figure 4 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing-capable manufacturing process in which the device is located in the embodiment may also include other hardware depending on the actual function of the data processing-capable device, which will not be described in detail here.

[0061] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0062] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0063] This invention also provides a readable storage medium storing a program that, when executed by a processor, implements an off-grid-based signal periodicity estimation method as described in the above embodiments.

[0064] The readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the readable storage medium can include both internal storage units of any data processing device and external storage devices. The readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0065] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the periodicity of signals based on off-grid interfaces, characterized in that, include: Step 1: Construct the cost function J(f,u), where f is the fundamental frequency of the periodic signal and u is a complex number that contains both amplitude and phase information; Step 2: Perform p=0 iterations to initialize the fundamental frequency f of the periodic signal; Step 3: Perform the (p+1)th iteration, substitute the estimated value of f from the pth iteration into J(f,u), optimize u, and obtain the estimated value of u; Step 4: Substitute the estimated value of u in the (p+1)th iteration into J(f,u) and use Newton's method to optimize the fundamental frequency f. Step 5: Obtain the period estimate for the (p+1)th iteration; Step 6: Repeat steps 3-5 until the number of iterations P.

2. The signal periodicity estimation method based on off-grid as described in claim 1, characterized in that, The cost function J(f,u) in step 1 is: ， Where y is the acquired signal with length K, and a(f) is a column vector whose elements are the values ​​of a complex exponential function at different time points.

3. The signal periodicity estimation method based on off-grid as described in claim 1, characterized in that, In step 3, u is optimized, specifically by taking the frequency estimate obtained in the p-th iteration. Substituting the cost function and setting its partial derivative with respect to u to zero, we obtain the estimated value of u for the (p+1)th iteration. for: ， The superscript H represents the conjugate transpose operation.

4. The signal periodicity estimation method based on off-grid as described in claim 1, characterized in that, Step 4 specifically includes: The estimated value of u in the (p+1)th iteration Substituting J(f,u), and using Newton's method to iteratively calculate the fundamental frequency f, we have... ， in Find the first derivative of J(f,u) with respect to the fundamental frequency f, where u is the estimate from the (p+1)th iteration. For J(f,u), take the second derivative with respect to the fundamental frequency f when u is fixed as the estimate of the (p+1)th iteration, i.e.: ， in, Operators that represent the real part of complex numbers.

5. The signal periodicity estimation method based on off-grid as described in claim 1, characterized in that, The estimated period value for the (p+1)th iteration in step 5 is: 。 6. A signal periodicity estimation device based on off-grid interface, characterized in that, It includes one or more processors for implementing the off-grid-based signal periodicity estimation method according to any one of claims 1-5.

7. A readable storage medium, characterized in that, It stores a program that, when executed by a processor, implements a signal periodicity estimation method based on any one of claims 1-5.

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