Signal periodicity estimation method and device based on off-grid, and medium

Abstract

The invention belongs to the field of periodic signal parameter estimation, and discloses an off-grid-based signal periodic estimation method and device and a medium, and the method comprises the steps: 1, constructing a cost function; step 2, performing p = 0 iteration, and initializing the fundamental frequency f of the periodic signal; step 3, performing the (p + 1) th iteration, substituting the estimated value of the p th iteration f into J (f, u), and optimizing u to obtain the estimated value of u; 4, substituting the estimated value of the (p + 1) th iteration u into J (f, u), and optimizing the optimized fundamental frequency f by adopting a Newton method; step 5, obtaining a period estimation value of the (p + 1) th iteration; and step 6, repeating the steps 3-5 until the number of iterations P. The method can be applied to an actual communication or signal processing hardware system, the problem of inaccurate period estimation caused by crystal oscillator frequency drift of the hardware system is solved, and the performance of a subsequent communication or signal processing algorithm is improved.

Description

Technical Field

[0001] The present invention relates to the field of periodic signal parameter estimation, and in particular to a signal periodicity estimation method, device and medium based on an off-grid. Background Art

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

[0003] The object of the present invention is to provide a method, device and medium for estimating signal periodicity based on an off-grid basis, so as to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A signal periodicity estimation method based on an off-grid, comprising:

[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 containing 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+1th iteration, substitute the estimated value of f at 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 at the p+1th iteration into J(f,u) and use Newton's method to optimize the optimal fundamental frequency f;

[0010] Step 5, obtain the estimated value of the period of the p+1th iteration;

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

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

[0013] ,

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

[0015] Furthermore, in step 3, u is optimized, specifically by subtracting the estimated value of the frequency obtained in the pth iteration from Substitute the cost function and set the partial derivative of the cost function with respect to u to zero to obtain the estimated value of u for the p+1th iteration. for:

[0016] ,

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

[0018] Furthermore, the step 4 specifically includes:

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

[0020] ,

[0021] in Find the first-order derivative of J(f,u) with respect to the fundamental frequency f when u is fixed to the estimated value of the p+1th iteration, Find the second-order derivative of J(f,u) with respect to the fundamental frequency f when u is fixed to the estimated value of the p+1th iteration, that is:

[0022]

[0023] ,

[0024] in, Represents the real part operator of a complex number.

[0025] Furthermore, the estimated period value of the p+1th 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 as described above.

[0028] The present invention also provides a readable storage medium having a program stored thereon. When the program is executed by a processor, the above-mentioned signal periodicity estimation method based on off-grid is implemented.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

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

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

[0032] 3) The present 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 the hardware system, thereby improving the performance of subsequent communication or signal processing algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of a signal periodicity estimation method based on off-grid in the present invention.

[0034] Figure 2 is a curve of the estimated value of the period versus the number of iterations.

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

[0036] Figure 4 This is a schematic structural diagram of a signal periodicity estimation device based on an off-grid in the present invention. DETAILED DESCRIPTION

[0037] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0038] The present invention is a method for estimating signal periodicity based on off-grid, such as Figure 1 As shown in the figure, the problem of inaccurate period estimation caused by the crystal oscillator frequency drift of the hardware system is solved. By considering the period as a continuous value and using the Newton method to iteratively estimate the period, an accurate period estimate is finally obtained, breaking the limitation of the traditional grid-based period estimation method on grid accuracy.

[0039] The problem of inaccurate period estimation caused by the crystal oscillator frequency drift of the hardware system refers to the period of the original signal being , the number of cycles is , when the crystal oscillator frequency is stable, the number of samples of the signal collected by the hardware system is When the crystal oscillator frequency drifts, the sampling rate will become faster or slower, which will further cause the number of signal samples collected by the hardware system to become smaller or larger, that is, , the cycle at this time 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 the sampling rate to slow down, which further leads to a decrease in the number of samples of the signal collected by the hardware system. The number of samples reduced is , so the number of signal samples collected by the hardware is .

[0040] The Newton method is used to iteratively estimate the fundamental frequency of a periodic signal, ultimately obtaining an accurate period estimate. This involves 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 containing both amplitude and phase information. The cost function J(f,u) is:

[0042]

[0043] Among them, y is the signal collected by the hardware system, with a length of K. , is a column vector whose elements are the values ​​of the complex exponential function at different time points, that is:

[0044]

[0045] Where exp(·) is the exponential function, the superscript T represents the transposition 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: .

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

[0047] Step 3: Iterations, optimize u, and the pth iteration Estimated value of Substituting into J(f,u), we get , let the cost function be Find the partial derivative and set it to zero, that is , get the p+1th iteration The estimated value of is:

[0048]

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

[0050] Step 4: To optimize, The estimated value of iteration u Substituting into J(f,u), we get , calculated using Newton's method, we have

[0051]

[0052] Among them, is the estimated value of J(f,u) at the p+1th iteration when u is fixed When the first derivative of the fundamental frequency f is taken, is the estimated value of J(f,u) at the p+1th iteration when u is fixed When the second-order derivative of the fundamental frequency f is obtained,

[0053]

[0054] Step 5: Based on the relationship between the fundamental frequency and period of the periodic signal, the estimated period of the p+1th iteration is

[0055]

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

[0057]

[0058] In this embodiment, the estimated value of the period is and the actual hardware-taken signal period value For comparison, the two are basically consistent, with a relative error of By using the off-grid based signal periodicity estimation method proposed in the present invention, an accurate period estimation value is finally obtained, which solves the problem of inaccurate period estimation caused by the crystal oscillator frequency drift of the hardware system and improves the performance of subsequent communication or signal processing algorithms.

[0059] See also Figure 4 An embodiment of the present invention provides a signal periodicity estimation device based on an off-grid, including one or more processors for implementing a signal periodicity estimation method based on an off-grid in the above embodiment.

[0060] An embodiment of the signal periodicity estimation device based on off-grid in the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Figure 4 As shown in the figure, it is a hardware structure diagram of any device with data processing capability where the signal periodicity estimation device based on the grid is located. Figure 4 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in the embodiment may also include other hardware according to the actual function of the device with data processing capabilities, which will not be described in detail.

[0061] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0062] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned 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] An embodiment of the present invention further provides a readable storage medium having a program stored thereon. When the program is executed by a processor, the method for estimating signal periodicity based on off-grid in the above embodiment is implemented.

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

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

Claims

1. A signal periodicity estimation method based on an off-grid, 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 containing 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+1th iteration, substitute the estimated value of f at the pth iteration into J(f,u), optimize u, and obtain the estimated value of u; Step 4: Substitute the estimated value of u at the p+1th iteration into J(f,u) and use Newton's method to optimize the optimal fundamental frequency f; Step 5, obtain the estimated value of the period of the p+1th iteration; Step 6: Repeat steps 3 to 5 until the number of iterations P is reached.

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

3. The method for estimating signal periodicity based on an off-grid basis according to claim 1, wherein: In step 3, u is optimized, specifically by taking the estimated value of the frequency obtained in the pth iteration Substitute the cost function and set the partial derivative of the cost function with respect to u to zero to obtain the estimated value of u for the p+1th iteration. for: ， The superscript H represents the conjugate transpose operation.

4. The method for estimating signal periodicity based on an off-grid basis according to claim 1, wherein: The step 4 specifically includes: The estimated value of u at the p+1th iteration Substitute J(f,u) and use Newton's method to iteratively calculate the fundamental frequency f, and we have ， in Find the first-order derivative of J(f,u) with respect to the fundamental frequency f when u is fixed to the estimated value of the p+1th iteration, Find the second-order derivative of J(f,u) with respect to the fundamental frequency f when u is fixed to the estimated value of the p+1th iteration, that is: ， in, Represents the real part operator of a complex number.

5. The method for estimating signal periodicity based on an off-grid basis according to claim 1, wherein: The estimated period of the p+1th iteration in step 5 is: 。 6. A signal periodicity estimation device based on an off-grid, characterized in that: The method comprises one or more processors for implementing the off-grid based signal periodicity estimation method according to any one of claims 1 to 5.

7. A readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, the method for estimating signal periodicity based on off-grid according to any one of claims 1 to 5 is implemented.

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