A pipeline ADC variable step size LMS calibration system based on inverse hyperbolic sine function

Abstract

The application claims a pipeline ADC variable step size LMS calibration system based on inverse hyperbolic sine function, comprising a high-speed pipeline ADC module to be calibrated, a low-speed system clock module, a low-speed high-precision sigma-delta ADC, a variable step size adaptive filter, a digital frequency reducer and a subtractor. On the basis of the traditional LMS algorithm, the inverse hyperbolic sine function arcsinh x is introduced, the improved step size factor updating mode, and the step size factor E(n) is updated according to the square sum of the error and the square difference of the input signal. Accordingly, the mathematical model of the step size, the input signal and the error is established as mu(n)=p·arcsinh(beta·E(n)), the step size is updated in real time according to the error signal size, and the minimum error and the corresponding filter weight and output result are saved at each time of updating the filter weight. In this way, the optimal filter weight and the corresponding output result can be obtained after the algorithm is run. The algorithm has the advantages of high calibration accuracy, fast convergence speed and the like.

Description

Technical Field

[0001] This invention belongs to the field of mixed-signal integrated circuit design technology, and specifically relates to a pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function. Background Technology

[0002] In today's electronic systems, analog-to-digital converters (ADCs) play a crucial role in digital signal processing (DSP), especially in portable devices where data processing primarily occurs in the digital domain. However, the ADC is a bottleneck in DSP-based systems. To improve ADC performance, digital auxiliary circuitry can be employed. Digitally assisted ADCs aim to enhance ADC performance while mitigating its analog limitations using digital circuitry.

[0003] Pipeline ADCs are the best candidates for relatively high-bandwidth intermediate frequency applications, including telecommunications systems. High-resolution pipelined ADCs typically consume high power due to the stringent limitations imposed by operational amplifier and capacitor mismatch. Therefore, high-precision pipelined ADCs often employ digital auxiliary circuitry to compensate for their errors, including the finite open-loop gain of operational amplifiers, input parasitic capacitance, comparator offset, and capacitor mismatch. These non-ideal factors often degrade the final conversion rate and resolution of the pipelined ADC.

[0004] When the accuracy of an ADC reaches 12 bits or higher, various errors, such as capacitor mismatch, limited operational amplifier gain, charge injection, comparator offset, and process errors, limit its performance. Traditional analog circuit design struggles to overcome this accuracy bottleneck. Therefore, calibration techniques are employed in the design of high-speed, high-precision ADCs. Calibration techniques can be categorized into digital calibration and analog calibration based on their implementation methods. Digital calibration, based on whether it affects normal output, can be divided into front-end calibration and back-end calibration. Compared to analog calibration, digital calibration offers greater flexibility, avoids the need for additional analog circuit modules, describes mismatch errors in the circuit in the digital domain, and then adjusts them in the digital domain to normal values ​​without concern for analog domain values. This is currently the most widely used calibration technique and, to some extent, represents the future direction of ADC development.

[0005] Digital background calibration technology is a method for calibrating digital systems. It improves the accuracy and performance of the system by performing compensation and correction in the background of the signal processing process. It is widely used in pipeline ADCs when combined with adaptive filtering algorithms.

[0006] Traditional LMS algorithms used for pipelined ADC calibration update tap weight coefficients with a fixed step size. They utilize the steepest descent algorithm to adjust the filter weight vector W(n) along the steepest descent direction (negative gradient direction) of the performance surface, searching for the minimum point on the performance surface and solving for the optimal weight vector W. opt The updated weights are fed back into the adaptive filter to improve the accuracy of the pipelined ADC output, making the output of the pipeline to be calibrated gradually approach the output of the low-speed but high-precision ADC.

[0007] CN115118282A discloses a pipelined ADC variable step-size LMS calibration system based on the hyperbolic tangent function, comprising an ADC to be calibrated, a down-conversion unit, a low-speed, high-precision ADC, an LMS adaptive filter, and a subtractor. Based on the traditional LMS algorithm, a hyperbolic tangent function tanhx is introduced, establishing a nonlinear relationship between step size and error: u(n) = αu(n-1) + β. 2 tanh(e(n-1)) is used to update the step size in real time based on the magnitude of the error signal. Simultaneously, a perturbation factor r(n) related to the error is added when updating the tap weight coefficients to offset some of the excessively large iteration increments and reduce the oscillation amplitude of the tap weight coefficients. The output of the ADC to be calibrated is connected to the input of a variable step-size LMS adaptive filter. The output is down-converted by a frequency downconverter and connected to one input of a subtractor. The other input of the subtractor is connected to the output of a low-speed, high-precision ADC, and the output is connected to the control terminal of the filter, allowing the output of the pipeline ADC to be calibrated to gradually approach the output of the low-speed, high-precision ADC.

[0008] Analysis of patent CN115118282A reveals that the nonlinear relationship between the step size and error in the aforementioned algorithm is: u(n) = αu(n+1) + β²tanh(e(n+1)). The step size variation in this algorithm is based on the step size of the previous time step, further iterated using the hyperbolic tangent function tanhx to control the error. Since the update of the weight coefficients is influenced by the step size of the previous time step, in some cases, this reduces the convergence of the weight coefficient iterations. With a high number of iterations, this can exceed the maximum step size range of LMS, leading to the failure of the entire LMS algorithm. While introducing the hyperbolic tangent function can establish a nonlinear relationship between the step size and error to some extent, the characteristics of this function are not explained in detail.

[0009] This invention is based on the characteristics and curve of the inverse hyperbolic sine function. Through analysis and manipulation of this function, the curve's variation is made to conform to the step size of the adaptive filtering algorithm. This curve conforms to the algorithm's step size adjustment mechanism; its slope gradually decreases as the independent variable increases, meaning the step size is larger in the early stages of convergence, smaller during the convergence process, and slowly adjusted as the error approaches zero. A mathematical model is established for the step size, input signal, and error as μ(n) = ρ·arcsin h(β·E(n)), where the parameter factor ρ always controls the step size's variable range within the allowable range of the LMS algorithm. During the step size approximation process, the inverse hyperbolic sine function is used to approximate the step size factor, reducing step size jitter and improving the algorithm's stability and convergence performance.

[0010] In this patented variable step-size algorithm, the step-size factor improves the algorithm's convergence, stability, and anti-interference capability. The adjustment principle of the factor is to adjust the step-size relationship by establishing the magnitude of the error and the square of the input signal. The adaptive step-size adjustment factor E(n) is:

[0011]

[0012] The step size factor is adjusted based on the magnitude of the error and the square of the input signal. This allows for the use of different step sizes at different stages of the algorithm to achieve rapid convergence and maintain stable accuracy. Summary of the Invention

[0013] This invention aims to solve the problems of the prior art. It proposes a pipelined ADC variable step-size LMS calibration system method based on an inverse hyperbolic sine function. The technical solution of this invention is as follows:

[0014] A pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function includes: a high-speed pipeline ADC module to be calibrated, a low-speed system clock module, a low-speed high-precision Sigma-Delta ADC, a variable step size adaptive filter, a digital down-conversion unit, and a subtractor.

[0015] The input signal is electrically connected to a calibrated pipeline ADC, and the input signal is converted into a calibrated digital code D by the ADC. est (n), this digital code D est (n) The initial filtering is performed by the LMS system, and the filtered result D is... out D is obtained after passing through a digital frequency down converter. in (n) is passed to the subtractor module; the input signal is also connected to the low-speed system clock module, and the frequency-reduced signal is converted into a high-precision reference signal D by a low-speed high-precision Sigma-Delta ADC. refThe output of the subtractor is the system error e(n), which is connected to the control terminal of the variable step size LMS adaptive filter. The error e(n) is introduced into the FIR filter to correct its coefficients, thereby realizing the tracking of the system error. The gradient steepest descent adaptive method is used to track the error. The inverse hyperbolic sine function arcsinh x is introduced to update the step size u(n) and the desired signal. The nonlinear relationship between the step size and the error is established and the FIR coefficients are updated.

[0016] Furthermore, in a variable step-size adaptive filter, the system error is e(n) = D. ref (n)-D in (n), employing the steepest gradient descent adaptive method, introduces the inverse hyperbolic sine function arcsinh x to update the step size u(n) and the desired signal. By establishing a nonlinear relationship between the step size and the error, μ(n) = ρ·arcsinh(β·E(n)), where μ(n-1) is the iteration step size of the previous time step, and E(n-1) is the step size adjustment adaptive factor of the previous time step, the magnitude of which is related to the input signal D. in The square of the error is related to the sum of the squares of the error en. E(n-1) is processed in segments according to the magnitude of the error e(n-1) at the previous time step, which can achieve adaptive adjustment. The operation iterates to obtain the updated tap weight coefficients. With the tap coefficients updated, the output of the pipeline ADC to be calibrated gradually approaches the output of the low-speed, high-precision pipeline Sigma-Delta ADC.

[0017] Furthermore, in the process of adaptively updating the tap coefficients, a nonlinear relationship between the step size and the error is established. An initial value for the step size is taken at the beginning of the algorithm, and the adaptive factor E(n) for step size adjustment is used.

[0018]

[0019] γ is the control factor in the iteration of the step size adaptive factor, used to control the range of variation of the step size factor;

[0020] The step size u(n) is updated based on the inverse hyperbolic sine function arcsinh x, and parameters ρ and β are introduced to jointly control the shape of the step size curve, resulting in the following relationship between the step size factor and the error function:

[0021]

[0022] When the error previousError at the previous time step is greater than the set error Δ, an improved step size factor update strategy is adopted. The step size factor is adjusted according to the magnitude of the error and the square of the input signal by calculating the increment of the step size factor. When the step size is approximated, the step size factor is approximated by an inverse hyperbolic sine function.

[0023] Furthermore, the LMS adaptive filter is a Wiener filter that optimizes its transmission characteristics. Let the order of the LMS adaptive filter be M, and let the input signal of the LMS adaptive filter be represented as X(n) = [x(n), x(n-1), ..., x(nM)]. T The weight vector of the LMS adaptive filter is represented as W(n)=[ω0(n),ω1(n),…ω M (n)] T Let the output of the LMS adaptive filter be y(n), then we have

[0024]

[0025] Let the error signal be e(n) and the desired signal be d(n), then we have:

[0026] e(n)=d(n)-y(n)=d(n)-W T (n)X T (n)

[0027] Taking the minimum mean square value of the error signal e(n) as the optimal statistical criterion, the cost function J(n) is defined as: J(n) = E[e 2 (n)]

[0028] The change of J(n) over time characterizes the convergence speed and convergence accuracy of the filter; when J(n) reaches its minimum value, the weight coefficients of the filter can reach the optimal value.

[0029] Step size update μ(n):

[0030]

[0031] Using the steepest descent algorithm, the filter weight vector W(n) is adjusted along the direction of the steepest descent on the performance surface, i.e., the negative gradient direction, to search for the minimum point on the performance surface and solve for the optimal weight vector W. opt :

[0032]

[0033] Update of LMS adaptive filter weight vector:

[0034] w(n+1)=w(n)+μ(n)e(n)x(n)

[0035] Furthermore, in the step size update mathematical model, the parameter ρ is a positive number, and the value of ρ determines the changing trend of the error factor and the step size factor. The range of the inverse hyperbolic sine function is controlled within {-ρ, ρ}, and β is used to limit the adaptive size of the step size factor.

[0036] Furthermore, the initial value of the step size μ(n) is any value between the maximum step size and half of the maximum step size in the traditional LMS algorithm.

[0037] Furthermore, the adaptive gradient descent method is a commonly used optimization algorithm for finding the minimum point of a function in the function space. Its basic idea is to iteratively adjust the search direction based on the gradient direction at the current position, gradually approaching the optimal solution. The values ​​of variables are updated according to the gradient direction and step size. The core of the gradient descent rule is to find the fastest descent direction based on the gradient direction.

[0038] The updated formula is: w(n+1)=w(n)+μ(n)e(n)x(n)

[0039] In the model, step size μ(n) = ρ·arcsinh(β·E(n)) represents the learning rate updated in each iteration.

[0040] The advantages and beneficial effects of this invention are as follows:

[0041] 1. To meet the key requirements of algorithm design, balancing convergence speed, steady-state error, and tracking performance, this invention uses the characteristics and curve of the inverse hyperbolic sine function as a basis. Through analysis and manipulation of this function, the curve's variation is made to conform to the step size of the adaptive filtering algorithm. This curve conforms to the algorithm's step size adjustment mechanism; its slope gradually decreases as the independent variable increases, meaning the step size is larger in the early stages of convergence, smaller during the convergence process, and slowly adjusted as the error approaches zero. A mathematical model is established for the step size, input signal, and error as μ(n) = ρ·arcsinh(β·E(n)). During the step size approximation process, the inverse hyperbolic sine function is used to approximate the step size factor, reducing step size jitter and improving the algorithm's stability and convergence performance. Traditional variable step size LMS algorithms focus more on step size and convergence speed in the initial stage, neglecting the impact of step size jitter on algorithm stability.

[0042] 2. In the variable step-size algorithm, the step-size factor improves the algorithm's convergence, stability, and anti-interference ability to a certain extent. The principle of adjusting the step-size factor is to adjust the step-size relationship by establishing the magnitude of the error and the square of the input signal. The adaptive step-size adjustment factor E(n) is:

[0043]

[0044] Update the step size u(n), and introduce parameters ρ, β, and γ to jointly control the shape of the step size curve. The relationship between the step size factor and the error function is obtained as follows:

[0045]

[0046] The maximum step size is determined by ρ, while the rate of change of the step size factor can be adjusted by the simultaneous action of β and γ. Within the range of values ​​that satisfy the algorithm's convergence, as the values ​​of β and γ increase, the value of the step size factor also increases, and the convergence speed of the algorithm increases accordingly.

[0047] At the beginning of the algorithm, a large step size is used in the initial stage, and the filter weights are randomly initialized, which may be far from the true optimal solution. To quickly approach the optimal solution, a large step size speeds up the weight adjustment, allowing the algorithm to converge quickly in the initial stage and find the neighborhood of the optimal solution more rapidly. In subsequent stages, a smaller step size is used, and as the algorithm iterates, the weights gradually approach the optimal solution. At this point, a large step size may cause the weights to fluctuate around the optimal solution, preventing convergence. Reducing the step size allows for more precise and detailed weight adjustment, resulting in higher accuracy and stability. This is based on the error e(n) and the input signal D. in When choosing the step size factor using the square of (n), the magnitude of the error and the input signal D are considered. in The square of (n). The magnitude of the error e(n) reflects the degree to which the current weight adjustment is needed; a larger error e(n) indicates that the magnitude of the weight adjustment should be larger. The input signal D... in The square of (n) represents the energy of the signal. Larger input signal energy typically requires a smaller step size factor to avoid excessive weight adjustment. Therefore, based on the magnitude of the error e(n) and the input signal D... in The step size factor is adjusted by the square of error e(n), allowing for flexible selection of the step size based on actual conditions and balancing convergence speed and stability at different stages of the algorithm. Therefore, based on the magnitude of the error e(n) and the input signal D... in The step size factor is adjusted by squared (n), which allows for the use of a larger step size in the initial stage of the algorithm to achieve fast convergence, while a smaller step size is used in subsequent stages to maintain stability and accuracy. Attached Figure Description

[0048] Figure 1 This invention provides a preferred embodiment of a Pipeline ADC calibration system based on a variable step-size algorithm.

[0049] Figure 2 System block diagram of an adaptive filter;

[0050] Figure 3 Schematic diagram of the adaptive filter algorithm;

[0051] Figure 4 Comparison of algorithm convergence speed;

[0052] Figure 5 Comparison of algorithm convergence errors;

[0053] Figure 6 FFT results of an ideal 14-bit Pipeline ADC;

[0054] Figure 7 FFT results of the Pipeline ADC to be calibrated;

[0055] Figure 8 The fixed-step LMS algorithm is used to calibrate the FFT results of the Pipeline ADC;

[0056] Figure 9 The variable step size LMS algorithm is used to calibrate the FFT results of the Pipeline ADC. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0058] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0059] A Pipeline ADC variable step size LMS calibration system based on an inverse hyperbolic sine function mainly includes: a high-speed Pipeline ADC module to be calibrated, a low-speed system clock module, a low-speed high-precision Sigma-Delta ADC, a variable step size adaptive filter, a digital down-conversion unit, and a subtractor.

[0060] The first path of the input signal is to the Pipeline ADC to be calibrated, where the signal is converted into the digital code D to be calibrated. est (n), this digital code D est (n) The initial filtering is performed by the LMS system, and the filtered result D is... out D is obtained after passing through a digital frequency down converter. in (n) is passed to the subtractor module; the second path of the input signal is passed to the low-speed system clock module. The signal with reduced frequency is converted into a high-precision reference signal D by a low-speed, high-precision Sigma-Delta ADC. ref (n). The output of the subtractor obtains the system error e(n), which is connected to the control terminal of the variable step size LMS adaptive filter. The error e(n) is introduced into the FIR filter to correct its coefficients, thereby realizing the tracking of the system error. The steepest gradient descent adaptive method is used to track the error and update the FIR coefficients.

[0061] In the LMS adaptive filter system, the system error is e(n) = D ref (n)-D in(n), employing the steepest gradient descent adaptive method, introduces the inverse hyperbolic sine function arcsinh x to update the step size u(n) and the desired signal. By establishing a nonlinear relationship between the step size and the error, μ(n) = ρ·arcsinh(β·E(n)), where μ(n-1) is the iteration step size of the previous time step, and E(n-1) is the step size adjustment adaptive factor of the previous time step, the magnitude of which is related to the input signal D. in The square of the error is related to the sum of the squares of the errors en. E(n-1) is processed piecewise according to the magnitude of the error e(n-1) at the previous time step, thus enabling adaptive adjustment. The operation iterates to obtain updated tap weight coefficients. With the tap coefficients updated, the output of the pipeline ADC to be calibrated gradually approaches the output of the high-precision pipeline ADC.

[0062] In the process of adaptively updating the tap coefficients, a non-linear relationship between the step size and the error is established, allowing the step size to take a single value in the early stages of the algorithm. This enables the algorithm to perform rapid iterations, and the step size is adjusted by an adaptive factor E(n).

[0063]

[0064] γ is the control factor in the iteration of the step size adaptive factor, which is used to control the range of change of the step size factor. It mainly controls the range of values ​​of the step size curve and affects the convergence speed of the algorithm. Within the range of γ values ​​that satisfy the convergence of the algorithm, the larger the value of γ, the larger the value of the step size factor, and the faster the convergence speed of the algorithm.

[0065] Therefore, the step size u(n) update is based on the inverse hyperbolic sine function arcsinh x, and the parameters ρ and β are introduced to jointly control the shape of the step size curve, resulting in the following relationship between the step size factor and the error function:

[0066]

[0067] When the previous error (previousError) exceeds the set error Δ, an improved step size factor update strategy is employed. The step size factor is adjusted based on the magnitude of the error and the square of the input signal by calculating its increment. This allows for faster convergence using a larger step size in the initial stages of the algorithm, while smaller step sizes are used in later stages to maintain stability and accuracy. During the approximation process, an inverse hyperbolic sine function is used to approximate the step size factor, better handling its range. Introducing parameters ρ and β to jointly control the shape of the step size curve effectively limits the magnitude of the step size factor, preventing excessively large or small step sizes from negatively impacting algorithm performance.

[0068] The LMS algorithm has a slow convergence speed, which can be improved using acceleration techniques. One such technique is to add an acceleration factor during tap weight coefficient updates: an error-related perturbation factor R(n), which is a linear combination of the historical update step size and historical weights. This allows the output of the pipelined ADC to be calibrated to gradually approximate the output of a low-speed, high-precision pipelined ADC. Specifically, this includes:

[0069] The LMS adaptive filter is essentially a Wiener filter that optimizes its transmission characteristics. Let the order of the LMS adaptive filter be M, and the input signal of the LMS adaptive filter can be expressed as X(n) = [x(n), x(n-1), ..., x(nM)]. T The weight vector of the LMS adaptive filter can be represented as W(n)=[ω0(n),ω1(n),…ω M (n)] T Let the output of the LMS adaptive filter be y(n), then we have

[0070]

[0071] Let the error signal be e(n) and the desired signal be d(n), then we have:

[0072] e(n)=d(n)-y(n)=d(n)-W T (n)X T (n)

[0073] The cost function J(n) is defined by taking the minimum mean square value of the error signal e(n) as the optimal statistical criterion:

[0074] J(n)=E[e 2 (n)]

[0075] The change of J(n) over time characterizes the convergence speed and convergence accuracy of the filter. When J(n) reaches its minimum value, the weight coefficients of the filter can reach their optimal value.

[0076] Step size update μ(n):

[0077]

[0078] Using the steepest descent algorithm, the filter weight vector W(n) is adjusted along the steepest descent direction (negative gradient direction) of the performance surface to search for the minimum point of the performance surface and solve for the optimal weight vector W. opt :

[0079]

[0080] Update of LMS adaptive filter weight vector:

[0081] w(n+1)=w(n)+μ(n)e(n)x(n)

[0082] This application example employs a 14-bit 1G / S pipelined ADC, a 14-bit 2M / S Sigma-delta ADC, a low-speed system clock module, a variable-step adaptive filter, a digital down-conversion unit, and a subtractor.

[0083] like Figure 1 As shown: The first path of the input signal is to the Pipeline ADC to be calibrated, where the signal is converted into a digital code D with the code to be calibrated. est (n), this digital code D est (n) The initial filtering is performed by the LMS system, and the filtered result D is... out D is obtained after passing through a digital frequency down converter. in (n) is passed to the subtractor module; the second path of the input signal is passed to the low-speed system clock module. The signal with reduced frequency is converted into a high-precision reference signal D by a low-speed, high-precision Sigma-Delta ADC. ref (n). The output of the subtractor obtains the system error e(n), which is connected to the control terminal of the variable step size LMS adaptive filter. The error e(n) is introduced into the FIR filter to correct its coefficients, thereby realizing the tracking of the system error. The steepest gradient descent adaptive method is used to track the error and update the FIR coefficients.

[0084] like Figure 2 The diagram shows the system principle of the adaptive filter used in this algorithm, which is essentially a Wiener filter that optimizes its transmission characteristics. Using the steepest descent algorithm, the filter weight vector W(n) is adjusted along the steepest descent direction (negative gradient direction) of the performance surface to search for the minimum point of the performance surface and solve for the optimal weight vector.

[0085] like Figure 3 The diagram shows the principle of the adaptive filter algorithm used in this paper. The red part in the diagram illustrates the difference between the variable step size LMS algorithm and the traditional algorithm. In the traditional algorithm, the step size parameter is a constant value. In the variable step size LMS algorithm, the adaptive step size factor is calculated by the square of the input signal and the square of the error. By establishing a nonlinear relationship between the step size, the adaptive factor, and the error, based on the inverse hyperbolic sine function of the step size selection function, the step size changes as: μ(n)=ρ·arcsin h(β·E(n)). The step size can be updated in real time according to these information values.

[0086] like Figure 4As shown in (a) and (b): This compares the convergence speed of the traditional fixed-step LMS algorithm with the variable-step LMS algorithm based on the inverse hyperbolic sine function in this design. It can be seen that... Figure 4 In (a), when the input frequency Fin is (63 / 1024)*1G, the convergence speed of the two algorithms with variable step size is better than that of the traditional fixed step size algorithm. Figure 4 In (b), when the input frequency Fin is (501 / 1024)*1G, which is closer to the Nyquist sampling frequency, the calibration algorithm is significantly better than the fixed step size.

[0087] like Figure 5 The figure shows a comparison of the convergence error and step size relationship between the traditional fixed-step-size LMS algorithm and the variable-step-size LMS algorithm based on the inverse hyperbolic sine function in this design. It can be seen that the algorithm in the figure has a smaller error reduction during iteration compared to the traditional fixed-step-size LMS algorithm, and its iteration rate is also faster.

[0088] like Figure 6 Figures 7, 8, and 9 show a comparison of the results before and after variable step size LMS adaptive filtering calibration for a 14-bit 1G / s non-ideal Pipeline ADC. Figure 6 The FFT test of the output of an ideal 14-bit Pipeline ADC is performed when the input signal frequency Fin is (501 / 1024)*1GHz. The effective number of bits (ENOB) is 14 bits, the SNDR is 86dB, and the SFDR is 102.5dB. Figure 7 The image shows the FFT test results of an uncalibrated, non-ideal pipelined ADC. It can be seen that due to errors such as capacitor mismatch, interstage gain error, and comparator offset, the effective bit depth decreased from 14 bits to 8.9 bits, the SNDR was 55.6 dB, and the SFDR was 57.8 dB. Figure 8 The FFT test results after calibration using the traditional variable step size LMS algorithm are shown in the simulation results. It can be seen from the simulation results that the effective number of bits has increased from 8.9 bits before calibration to 11.4 bits, the SNDR has increased from 55.6dB to 70.5dB, and the SFDR has increased to 70.7dB. However, it is still some distance from the accuracy of a 14-bit ADC. The continuous oscillation of the tap weight coefficients will bring error fluctuations. Figure 9 This invention presents the calibration effect of the variable step size LMS based on the inverse hyperbolic sine function. The effective bit depth is increased from 8.9 bits to 13.8 bits, the SNDR is improved from 55.6 dB to 84.9 dB, and the SFDR is increased to 85.6 dB, which can effectively improve the accuracy of pipelined ADCs.

[0089] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0090] It should also be noted that 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 limitation, 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.

[0091] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A pipelined ADC variable step-size LMS calibration system based on an inverse hyperbolic sine function, characterized in that, include: High-speed pipeline ADC module to be calibrated, low-speed system clock module, low-speed high-precision Sigma-Delta ADC, variable step size adaptive filter, digital down-conversion unit and subtractor; The input signal is electrically connected to the Pipeline ADC module to be calibrated. The input signal is converted into the digital code D to be calibrated by the AD converter. est (n), this digital code D est (n) The initial filtering is performed by the LMS system, and the filtered result D is... out D is obtained after passing through a digital frequency down converter. in (n) is passed to the subtractor module; the input signal is also connected to the low-speed system clock module, and the frequency-reduced signal is converted into a high-precision reference signal D by a low-speed, high-precision Sigma-Delta ADC. ref The output of the subtractor is the system error e(n), which is connected to the control terminal of the variable step size LMS adaptive filter. The error e(n) is introduced into the FIR filter to correct its coefficients, thereby realizing the tracking of the system error. The gradient steepest descent adaptive method is used to track the error. The inverse hyperbolic sine function arcsinh x is introduced to update the step size μ(n) and the desired signal. The nonlinear relationship between the step size and the error is established and the FIR coefficients are updated.

2. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 1, characterized in that, In a variable step size adaptive filter, the system error is The steepest gradient descent adaptive method is adopted, and the inverse hyperbolic sine function arcsinh x is introduced to update the step size. And the desired signal, by establishing a nonlinear relationship between step size and error, , It is the iteration step size of the previous time step. It is the adaptive factor for step size adjustment at the previous time step, and its magnitude is related to the input signal D. in The square of is related to the sum of the squares of the errors en. It processes the error e(n-1) from the previous moment in segments, enabling adaptive adjustment; it iterates to obtain updated tap weight coefficients, and then updates the tap coefficients again, so that the output of the pipeline ADC to be calibrated gradually approaches the output of the low-speed, high-precision pipeline Sigma-Delta ADC.

3. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 2, characterized in that, In the process of adaptively updating the tap coefficients, a nonlinear relationship between the step size and the error is established. An initial value for the step size is taken at the beginning of the algorithm, and the adaptive factor E(n) for step size adjustment is used. This is a control factor in the iteration of the step size adaptive factor, used to control the range of variation of the step size factor; Update step size Based on the inverse hyperbolic sine function arcsinh x, parameters are introduced. β and β jointly control the shape of the step size curve, and the relationship between the step size factor and the error function is as follows: When the error from the previous time step (previousError) is greater than the set error... The improved step size factor update strategy is implemented; the step size factor is adjusted based on the magnitude of the error and the square of the input signal by calculating the increment of the step size factor; during the approximation process of the step size factor, the inverse hyperbolic sine function is used to approximate the step size factor.

4. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 3, characterized in that, The LMS adaptive filter is a Wiener filter that optimizes its transmission characteristics. Let the order of the LMS adaptive filter be M, and the input signal of the LMS adaptive filter be expressed as... The weight vector of LMS adaptive filtering is represented as: Let the output of the LMS adaptive filter be y(n), then we have Let the error signal be e(n) and the desired signal be d(n), then we have: The minimum mean square value of the error signal e(n) is used as the optimal statistical criterion, and the cost function is defined. : The change of J(n) over time characterizes the convergence speed and convergence accuracy of the filter; When J(n) reaches its minimum value, the weight coefficients of the filter can reach their optimal value. Step-by-step update : Using the steepest descent algorithm, the filter weight vector W(n) is adjusted along the direction of the steepest descent on the performance surface, i.e., the negative gradient direction, to search for the minimum point on the performance surface and solve for the optimal weight vector W. opt : Update of LMS adaptive filter weight vector: 。 5. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 3, characterized in that, Step size update parameters in mathematical model The value of is a positive number. The value of determines the changing trends of the error factor and the step size factor, and the range of the inverse hyperbolic sine function is controlled within {- , }, β is used to limit the adaptive size of the step size factor.

6. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 3, characterized in that, The step size The initial value is any value between the maximum step size and half of the maximum step size in the traditional LMS algorithm.

7. The pipelined ADC variable step size LMS calibration system based on an inverse hyperbolic sine function according to claim 1, characterized in that, The gradient steepest descent adaptive method is used to find the minimum point of a function in the function space. Its basic idea is to iteratively adjust the search direction according to the gradient direction at the current position, gradually approaching the optimal solution; and to update the value of the variable according to the gradient direction and step size. The core of the gradient steepest descent rule is to find the fastest descent direction according to the gradient direction. The updated formula is: The step size is a variable step size used in the algorithm. The model represents the learning rate updated in each iteration.

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