Statistical eye diagram reconstruction method based on ber confidence and non-local total variation

Abstract

The application discloses a statistical eye diagram reconstruction method based on BER confidence and non-local total variation, and belongs to the technical field of high-speed serial communication link signal integrity testing. The method comprises the following steps: obtaining a two-dimensional BER matrix; performing data cleaning and lower limit correction on the BER matrix, and then performing logarithmic domain mapping and normalization; constructing a confidence weight matrix; performing initial up-sampling with different scales in the horizontal and vertical directions; performing non-local self-similarity structure compensation; constructing a joint objective function which fuses data consistency, edge-preserving total variation regularization, non-local prior and eye diagram physical monotonicity constraint for iterative solution, and simultaneously performing data consistency back-projection correction in combination with the confidence weight matrix; inversely transforming the high-resolution logarithmic domain result into a BER diagram, extracting contour lines and calculating eye diagram indexes. The application can reconstruct a statistical eye diagram with high resolution, clear boundaries and consistency with original data without increasing sampling time.

Description

Technical Field

[0001] This invention relates to the field of high-speed serial communication link signal integrity testing and eye diagram analysis technology, and in particular to a statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation. Background Technology

[0002] Signal integrity assessment of high-speed serial communication links typically relies on eye diagram analysis. Traditional oscilloscope eye diagrams are obtained by acquiring time-domain waveforms and performing clock recovery, waveform segmentation, and persistence superposition. While offering high resolution, this method is dependent on high-speed oscilloscope hardware. In embedded testing environments such as FPGA high-speed transceivers, IBERT, ChipScoPy, and high-speed cable testers, limitations in on-chip storage resources and testing time often prevent the acquisition of long-term waveform data with high sampling rates. In practice, a common approach is to perform bit error rate (BER) statistics under different horizontal sampling offsets and vertical sampling thresholds to generate a two-dimensional BER statistical eye diagram. This type of statistical eye diagram can be used to observe the eye opening, estimate eye height, eye width, opening area, and link margin, serving as a crucial basis for high-speed link debugging and compliance testing.

[0003] In existing technologies, the following processing flow is typically used for an acquired two-dimensional BER matrix: linear or logarithmic mapping is applied to the BER or error count; nearest neighbor interpolation, bilinear interpolation, cubic spline interpolation, or pseudo-color interpolation is used for magnification and display; and the open-eye region is extracted based on a threshold, with indicators such as eye height and eye width output. This type of method is simple to implement and computationally fast, and is widely used in existing host computer software. In addition, there are methods that generate eye diagrams by overlaying waveforms acquired by an oscilloscope using software CDR and persistence, and methods that predict eye diagrams based on link parameters using machine learning. However, the former has high hardware resource requirements, and the latter relies on training data and has weak interpretability.

[0004] The aforementioned existing technical solutions have the following main drawbacks: First, due to time constraints, the number of horizontal and vertical sampling points in FPGA / ChipScoPy statistical eye scans is usually small. For low-resolution matrices such as 31×9 and 31×17, ordinary interpolation can easily cause blockiness and boundary breaks.

[0005] Second, the BER spans multiple orders of magnitude, and displaying it linearly directly will compress the details of the low BER eye area; simply taking the logarithm can easily mistake the detection lower limit point for the real high confidence area.

[0006] Third, the absence of error sampling points in eye scans represents the minimum BER lower limit, but is not equivalent to the true BER; high BER closed-eye areas may have saturation or strong noise, and ordinary interpolation cannot distinguish the reliability of different measurement points.

[0007] Fourth, while bilinear and cubic interpolation can magnify the image, they do not utilize the structural features of the eye diagram, which can easily blur the BER contour lines and affect the accuracy of the calculation of eye height, eye width, and opening area.

[0008] Fifth, ordinary image interpolation does not reflect the physical law that the BER of the eye diagram generally increases from the center of the eye to the boundary, which may produce false textures in the central eye area or near the boundary.

[0009] Sixth, although some smoothing or super-resolution algorithms can generate visually better images, they cannot maintain consistency with the measured BER matrix after downsampling back to the original matrix, affecting the reliability of the test.

[0010] Therefore, there is an urgent need for a super-resolution reconstruction method for two-dimensional BER statistical eye diagrams. This method should be able to reconstruct low-resolution BER matrices with high definition without increasing eye scanning sampling time or changing FPGA hardware and transceiver configuration. The reconstruction results should simultaneously possess high display resolution, continuous eye diagram boundaries, and distribution characteristics that conform to the physical laws of eye diagrams. Furthermore, the downsampling should maintain data consistency with the original measured BER matrix. This would provide more reliable image reconstruction results and index extraction basis for high-speed serial link eye diagram analysis and high-speed cable tester host computer display. Summary of the Invention

[0011] To address the aforementioned technical problems, this invention provides a statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation. The aim is to reconstruct a low-resolution two-dimensional BER statistical eye diagram matrix into a high-resolution statistical eye diagram without increasing eye scanning sampling time or changing hardware configuration. This method provides the eye diagram with high display resolution, continuous and clear eye diagram boundaries, and reconstruction reliability consistent with the original measured data. It can also stably extract eye diagram indicators such as eye height, eye width, opening area, and center margin.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows: 1. A statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation, comprising the following steps: Step 1: Obtain the two-dimensional BER statistical eye diagram matrix and related coordinate information generated during the high-speed serial communication link test; Step 2: Perform data cleaning and lower bound correction on the two-dimensional BER statistical eye diagram matrix, and then perform logarithmic domain mapping and normalization on the corrected matrix; Step 3: Construct a confidence weight matrix based on BER measurement characteristics, and perform initial upsampling of the normalized logarithmic domain matrix at different scales in both the horizontal and vertical directions; Step 4: Using the initial upsampling result as input, perform nonlocal self-similar structure compensation, and construct a joint objective function that integrates data consistency, edge-preserving total variational regularization, nonlocal prior, and eye diagram physical monotonic constraints for iterative solution; during the iteration process, perform data consistency back projection correction in conjunction with the confidence weight matrix until the preset stopping condition is met; Step 5: Transform the high-resolution logarithmic domain result obtained after iterative convergence into a high-resolution BER map, extract contour lines under a specified threshold based on the high-resolution BER map, and calculate the eye map index.

[0013] In the above scheme, in step two, the lower limit correction uses a lower limit correction constant. Replace zero, missing, or non-positive values; the lower limit correction constant Determine as follows: ; in, The first BER in the original two-dimensional matrix Line number The element values ​​of the column, The lower limit of computer floating-point precision; the corrected BER matrix. for: ; in, For the corrected BER matrix, the first Line number The element values ​​of the column.

[0014] In the above scheme, in step two, the logarithmic field mapping is to map the corrected BER matrix. Mapped to: Obtain the low-resolution log-domain eye map matrix before normalization. ; The normalization process is to... Linear mapping to the following formula The interval is used to obtain the normalized low-resolution log-domain eye diagram matrix. : ; in, The first normalized low-resolution logarithmic field eye map matrix is ​​the... Line number The element values ​​of the column, for The global minimum value, for The global maximum value.

[0015] In the above scheme, step three, the method for constructing the confidence weight matrix includes: Identify BER points that are close to the detection lower limit, when Assign weights at time ,in, This is the lower limit tolerance coefficient; Identify high BER saturation regions, when Assign weights at time ,in, According to the test system settings; Identify valid transition regions and assign weights. ; To identify isolated mutation points, a neighborhood window centered on the pixel is selected, and the local median and local median absolute deviation are calculated. If the deviation of a point from the local median exceeds a preset multiple, it is determined to be an isolated mutation point and assigned a weight. ; The weights satisfy the following: .

[0016] In the above scheme, in step three, the high-resolution target size is set as follows in the initial upsampling with different horizontal and vertical scales: ; in, This represents the number of vertical sampling points. This represents the number of horizontal sampling points. This refers to the lateral magnification. This is the vertical magnification, and and For different positive integers; initial high-resolution image Through the upsampling operator get: .

[0017] In the above scheme, step four, the non-local self-similar structure compensation specifically involves: for any pixel in the current high-resolution image... ,by Select image patch centered Search for candidate pixels within the search window. ,by Select image patch centered Weighted fusion based on similarity weights, followed by normalization, yields the nonlocal compensation result. The similarity weight calculation formula is as follows: ; in, For pixels With candidate pixels Similarity weights between them For smooth control parameters.

[0018] In the above scheme, in step four, the edge-preserving total variation regularization is: ; in, The edge-guided total variational regularization term is used to smooth flat regions while preserving the boundaries. For the horizontal gradient, For the vertical gradient, For pixels Edge guiding weights at: ; in, The edge sensitivity coefficient, For pixels The gradient magnitude at point A is calculated as follows: .

[0019] In the above scheme, step four, the physical monotonic constraint of the eye diagram is: first, determine the geometric center of the logarithmic domain maximum point or the low BER eye opening region as the eye diagram center point. ,by Starting from a point, construct several ray directions in the horizontal and vertical directions, and for adjacent points on the same ray direction that are farther from the center... and neighboring points closer to the center Expected to be satisfied That is, it decreases monotonically from the center of the eye opening to the boundary; define the monotonic penalty term: ; in, This is a penalty term for the physical monotonicity constraint of the eye diagram. These are adjacent pixels that are closer to the center along the same ray direction. These are adjacent pixels that are farther from the center along the same ray direction. Image values ​​near the endpoint, The image value at the far endpoint.

[0020] In the above scheme, in step four, the joint objective function is: ; in, To optimize the obtained high-resolution logarithmic field eye diagram matrix; The optimization variable represents the high-resolution image currently being solved; For downsampling operators, This represents the norm weighted by the confidence weight matrix. This is a low-resolution logarithmic field eye diagram matrix. For non-local enhancement images, For total variation regularization, This is a penalty term for the physical monotonicity constraint of the eye diagram. , , These are the corresponding regularization parameters; Solve using an iterative approach, with the initial value being... In the In each iteration, updates are performed based on the gradient of the objective function, and the numerical values ​​are constrained to [value missing]. Interval.

[0021] In the above scheme, step four, the data consistency backprojection correction, specifically involves: adjusting the current high-resolution image... Downsampling Calculate the error matrix: ; Using the confidence weight matrix The error correction yielded: ; Will Upsampling to high resolution size : ; Perform back projection correction using the following formula: ; in, For upsampling operators, Correct the step size for back projection.

[0022] Through the above technical solution, the statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation provided by this invention has the following beneficial effects: (1) Improved display resolution. This invention does not require increasing the number of eye scanning sampling points and the testing time, nor does it require changing the FPGA hardware and transceiver configuration. It can reconstruct a low-resolution statistical eye map into a high-resolution image simply by post-processing the acquired two-dimensional BER matrix, thus solving the block effect and boundary breakage problems caused by sparse sampling points in the prior art. (2) Enhanced boundary continuity. This invention compensates and repairs broken boundaries by using the structural similarity of the upper and lower boundaries, left and right transition areas and central eye opening area of ​​the eye diagram through non-local self-similar structure compensation; combined with edge-preserving total variational regularization, the smoothing intensity is adaptively controlled according to the gradient magnitude, which protects the boundary while denoising, and significantly improves the continuity and stability of BER contour lines; (3) Improved measurement reliability. The present invention uses a data consistency back projection mechanism to repeatedly compare and correct errors between the downsampled high-resolution image and the original BER matrix during the iterative optimization process, ensuring that the reconstructed result after downsampling is consistent with the original measured data, thus avoiding the problem of excessive image retouching in the prior art that is "only good but not reliable"; (4) It conforms to the statistical characteristics of BER. This invention constructs a confidence weight matrix that distinguishes between the detection lower limit point, the saturated high BER point, the effective transition region and the isolated mutation point, so that the measurement points with different confidence levels play different roles in the reconstruction, effectively solving the problems unique to statistical eye diagrams in the prior art, such as the inability to distinguish between the detection lower limit point and the true BER and the low confidence of the high BER saturation region; (5) Physical laws are interpretable. This invention introduces physical monotonic constraints on eye diagrams, constraining the logarithmic domain value to decrease monotonically from the center of the eye diagram towards the boundary in each direction, starting from the center of the eye diagram. This makes the reconstruction result conform to the physical law that the BER of the high-speed link eye diagram gradually increases from the center to the boundary, reducing false textures and improving the physical interpretability of the reconstruction result; (6) More stable index extraction. The BER contour lines reconstructed in this invention are more continuous. Based on this, the eye diagram indices such as eye height, eye width, opening area, opening ratio, and center margin are less affected by sampling grid quantization error, providing a more reliable quantitative basis for link quality assessment and consistency testing; (7) It does not depend on training samples. Unlike eye diagram prediction methods based on machine learning, this invention does not require a training dataset. The calculation process has a clear mathematical and physical meaning, is highly interpretable, and is easy to deploy in the host computer software of high-speed cable testers and FPGA transceivers. (8) Strong compatibility. This invention can process two-dimensional BER matrices of different formats exported from ChipScoPy, IBERT, FPGA high-speed transceivers and other test systems, and has good versatility and portability. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0024] Figure 1 This is a schematic diagram of a statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation disclosed in an embodiment of the present invention; Figure 2 The images show the statistical eye diagram reconstruction results obtained by different methods, where (a) is the original low-resolution eye diagram, (b) is the bilinear interpolation result, (c) is the cubic interpolation result, and (d) is the reconstruction result obtained by the method of this invention. Figure 3These are BER contour lines extracted based on the reconstruction results of this invention. Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0026] This invention provides a statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation. This method can be deployed in the host computer software of a high-speed cable tester, or in the supporting debugging software of an FPGA transceiver test system.

[0027] This embodiment uses a two-dimensional BER matrix exported by an FPGA eye-scanning module of a high-speed cable tester as input data for detailed explanation. For example... Figure 1 As shown, the process includes the following: I. Obtaining the 2D BER matrix During implementation, the two-dimensional BER matrix is ​​first obtained from the high-speed transceiver eye-scanning module, ChipScoPy, IBERT, or the host computer of the high-speed cable tester via a data interface. .in, This represents the number of vertical sampling threshold points. This represents the number of lateral sampling phase points. Simultaneously, the lateral offset coordinate sequence is acquired. ( ) and vertical offset coordinate sequence ( If the data comes from a CSV file, it is parsed through the file reading interface; if it comes from a database or shared memory on a host computer, it is read directly through the corresponding data interface.

[0028] II. Data Cleaning and Lower Bound Correction After obtaining the raw BER matrix, the first step is data cleaning. This involves removing CSV headers, blank rows, empty columns, and descriptive fields, retaining only the valid numerical range to form a normalized matrix. .

[0029] For matrix Check each element in: (1) If If the value is null or not numeric, mark the point as a missing point. (2) If Mark as invalid point; (3) If a point undergoes a significant abrupt change relative to its neighborhood, it is marked as a local outlier.

[0030] The validity markers mentioned above are recorded in the anomaly marker matrix.

[0031] Let the set of all BER points greater than 0 in the original matrix be: ; To calculate the minimum non-zero BER value, the lower limit correction constant is calculated using the following formula: ; in, The first BER in the original two-dimensional matrix Line number The element values ​​of the column, This is a lower bound correction constant used to replace zero and invalid values ​​to prevent errors in logarithmic operations. It represents the lower limit of floating-point precision in computers and is related to specific computer hardware and programming languages.

[0032] for Null values, missing points, or non-numerical points are used. By performing substitution, we obtain the corrected BER matrix: ; in, For the corrected BER matrix, the first Line number The element values ​​of the column.

[0033] For example, suppose a certain eye scan yields a 31×17 BER matrix, where the smallest non-zero BER is... Machine precision ,but: ; all Or missing points are all adopted Replacement.

[0034] III. BER Logarithmic Field Mapping and Normalization To expand the dynamic range of the low BER region, the modified BER matrix is ​​subjected to a negative logarithmic transformation to obtain a low-resolution logarithmic domain eye diagram matrix, denoted as... : ;

[0035] To facilitate subsequent image processing, Normalization to The interval, the normalized matrix is ​​denoted as : ; in, The first normalized low-resolution logarithmic field eye map matrix is ​​the... Line number The element values ​​of the column, for The global minimum value, for The global maximum value.

[0036] IV. Construction of Confidence Weight Matrix The measurement confidence level differs for each BER point in the statistical eye diagram. This embodiment constructs a confidence weight matrix. To distinguish the credibility of different points.

[0037] (a) Identifying BER points close to the detection lower limit When the BER value at a certain point satisfies When the point is close to the detection lower limit, a weight is assigned. . As the lower limit tolerance coefficient, this embodiment preferably uses... Although no errors were detected for these types of points within a finite sampling time, this does not mean that the true BER is equal to that value, and therefore they are not assigned the highest weight.

[0038] (ii) Identifying high BER saturation regions when When the point is determined to be in a high BER saturation region, a weight is assigned. . Depending on the test system settings, this embodiment is preferably configured as follows. Alternatively, it can be adaptively determined based on the original maximum BER value.

[0039] (iii) Identifying effective transition areas Points located near the eye-opening boundary best reflect the location of BER contour lines. These points are typically within the effective BER range, neither the detection lower limit nor saturation points, and are therefore assigned the highest weight. .

[0040] (iv) Identifying isolated mutation points by Select a neighboring window centered on the target window, with the window size preferably selected from the specified values. or Calculate the local median. and local median absolute deviation If the following conditions are met: ; in, The preferred value is If the point is considered an isolated mutation point, it is assigned the lowest weight. .

[0041] (v) Weighting In this embodiment, the preferred values ​​for each weight are: ; satisfy .

[0042] This weight matrix will be used as a weighting coefficient in the data fidelity term of the subsequent total variation optimization, controlling the strength of the correction of the original measurement error to the high-resolution image in the data consistency back projection.

[0043] V. Initial Super-Resolution Interpolation at Different Horizontal and Vertical Scales Statistical eye scan data typically have fewer horizontal sampling points and a relatively larger number of vertical sampling points. Let the original number of horizontal sampling points be... The number of original sampling points in the vertical direction is This embodiment sets the horizontal magnification. Vertical magnification The high-resolution target size is: ; in, This represents the vertical pixel count (number of rows) of a high-resolution image. This represents the number of horizontal pixels (columns) in a high-resolution image. This represents the number of vertical sampling points in the original BER matrix. This represents the number of horizontal sampling points in the original BER matrix. This is the vertical magnification. This represents the horizontal magnification.

[0044] For example, for an original matrix of 31×17, the reconstructed size is... (OK), (List).

[0045] Using upsampling operators For the normalized low-resolution logarithmic field matrix Perform interpolation: ;

[0046] in, This is the initial high-resolution logarithmic field eye diagram matrix. For upsampling operators, Lanczos interpolation, Bicubic interpolation, B-spline interpolation, or cubic spline interpolation can be used. This is the normalized low-resolution logarithmic field eye diagram matrix. Lanczos interpolation is preferred in this embodiment.

[0047] At the same time, the confidence weight matrix is ​​upsampled by the same size: ; in, This is the high-resolution confidence weight matrix after upsampling. For upsampling operators, This is the original low-resolution confidence weight matrix.

[0048] Generate high-resolution coordinate sequences: .

[0049] VI. Compensation for Nonlocal Self-Similar Structures Ordinary interpolation only utilizes local neighborhood information, making it difficult to recover the continuous structure of the eye diagram boundary. Statistical eye diagrams exhibit structural similarity in their upper and lower boundaries, left and right transition regions, and central open eye region. This embodiment introduces nonlocal self-similarity compensation.

[0050] For high-resolution initial image any pixel in ,by Select image patch centered In this embodiment, the preferred image block size is... or In the search window (preferred) or Search for candidate pixels within ) ,by Select image patch centered .

[0051] Calculate the similarity weight between the two: ; in, For pixels With candidate pixels Similarity weights between them For The image patch matrix centered on the image, For The image patch matrix centered on the image, For image blocks and The square of the Euclidean distance between them To smooth the control parameters and control the weight decay rate, this embodiment preferably sets the value to [value to be filled in]. ,in This represents the standard deviation of the initial high-resolution image.

[0052] Normalize the weights of all candidate points so that the sum of the weights is 1: ; in, This represents the normalized similarity weights.

[0053] The nonlocal compensation result is obtained: ; in, For pixels The nonlocal self-similarity compensation result at the location, Candidate pixels The initial high-resolution image value at that location.

[0054] Repeat the above process for all pixels to obtain the complete nonlocal enhancement image. .

[0055] VII. Constructing edge-guided total variational regularization terms To smooth noise while protecting the eye diagram boundary, this embodiment constructs an edge-guided total variation regularization term.

[0056] First calculate Lateral and longitudinal gradients: ; in, For high-resolution images at pixel points lateral gradient at the location, For high-resolution images at pixel points The longitudinal gradient at that point For the current high-resolution image at the pixel level The value at that location.

[0057] Calculate the gradient magnitude: ; in, For pixels The gradient magnitude at a point reflects the edge strength at that point.

[0058] Construct edge-guided weights based on gradient magnitude: ; in, For pixels The edge guide weights are set to be smaller when the gradient is large at the boundary to reduce the smoothing intensity, and larger when the gradient is small in flat regions to enhance the smoothing effect. This is the edge sensitivity coefficient, which controls the sensitivity of the gradient magnitude to the weights. In this embodiment, a preferred value is [value to be inserted here]. .

[0059] The edge-guided total variation term is defined as: ; in, The edge-guided total variational regularization term is used to smooth flat regions while preserving the boundaries. For pixels Edge-guided weights at the location, For the horizontal gradient, This represents the vertical gradient.

[0060] 8. Constructing Physical Monotonic Constraints for Eye Diagrams In statistical eye diagrams, the open-eye center region typically has a low BER and a high logarithmic value; as you move from the open-eye center to the upper, lower, left, and right boundaries, the BER increases overall, and the logarithmic value decreases overall. This embodiment introduces a physical monotonic constraint for the eye diagram.

[0061] First, determine the center point of the eye opening; we can take the point where the logarithmic field has the maximum value: ; in, Here are the pixel coordinates of the eye map center point. To enhance the image at the pixel level The value at that location. Alternatively, the geometric center of the low BER eye region can be taken.

[0062] With the center point Starting from the center, construct several ray directions in both the horizontal and vertical directions. For adjacent points further from the center along the same ray direction... and neighboring points closer to the center Expected to be met: ; That is, it decreases monotonically from the center of the eye opening towards the boundary.

[0063] Define the monotonic penalty term: ; in, This is a penalty term for the physical monotonicity constraint of the eye diagram. These are adjacent pixels that are closer to the center along the same ray direction. These are adjacent pixels that are farther from the center along the same ray direction. Image values ​​near the endpoint, Image values ​​at the far endpoint. This is the positive penalty value generated when the value at the far endpoint is greater than the value at the near endpoint.

[0064] This penalty term is added to the joint optimization objective function to constrain the reconstruction result to conform to the physical trend of the eye diagram gradually closing from the center to the boundary.

[0065] IX. Nonlocal Total Variational Joint Optimization by As initial values, solve for high-resolution logarithmic domain eye diagrams. The joint optimization objective of this embodiment is: ; in, To optimize the obtained high-resolution logarithmic field eye diagram matrix; The optimization variable represents the high-resolution image currently being solved; This is a downsampling operator used to restore a high-resolution image to its original low-resolution size; This is the original low-resolution logarithmic field eye diagram matrix. This is a data consistency term that ensures the downsampled high-resolution image closely approximates the original measurement data, and is determined by the confidence weight matrix. Weighted, The norm of the confidence weight matrix is: ; in, The confidence weight matrix at the pixel point The value at that location, To preserve the total variation regularization term at the edges, The regularization parameter for the total variation regularization term is preferably set to a value of in this embodiment. , For non-local enhancement images, Nonlocal structural priors are used to constrain the reconstruction results to not deviate from the nonlocal enhancement results. For the regularization parameter of the nonlocal prior, the preferred value in this embodiment is [value]. , This is a penalty term for the physical monotonicity constraint of the eye diagram. For the regularization parameter of the monotonic constraint term, the preferred value in this embodiment is [value to be filled in]. The optimal ranges for each regularization parameter are as follows: , , .

[0066] The gradient descent method is used for iterative solution, with the initial value set to... That is, in the 0th iteration, the image is enhanced nonlocally. As the starting point, in the... In this iteration, updates are performed according to the gradient of the objective function: ; in, As the initial value for iteration, For the first High-resolution image at the next iteration For the first High-resolution image at the next iteration The preferred iteration step size in this embodiment is [value to be inserted here]. , For the objective function in The gradient at that point. After each update, the value is limited to... The interval. In this embodiment, the total number of iterations is preferably selected as... Second-rate.

[0067] 10. Data Consistency Backprojection To avoid high-resolution images becoming visually smoother and deviating from the measured BER data, this embodiment performs data consistency backprojection after each iteration.

[0068] Current high-resolution image Downsampling back to original size: ; in, This is the low-resolution image after downsampling. For downsampling operators, For the first High-resolution image at the next iteration.

[0069] Compared with the original low-resolution logarithmic field matrix By comparison, the error matrix is ​​obtained: ; in, This is the error matrix, reflecting the difference between the downsampled high-resolution image and the original low-resolution data. This is the original low-resolution logarithmic field eye diagram matrix. This is a low-resolution image after downsampling.

[0070] Error correction using the confidence matrix: ; in, This is the weighted error matrix. This is the confidence weight matrix. This is the error matrix.

[0071] Upsample the error to a high-resolution size: ; in, This is the high-resolution error matrix after upsampling. For upsampling operators, This is the weighted error matrix.

[0072] Perform backprojection correction on the current high-resolution image: ; in, This is the high-resolution image after back projection correction. The image is a high-resolution image before backprojection correction. To control the magnitude of each correction in the back projection correction step, this embodiment preferably uses a step size of [missing value]. , This is the high-resolution error matrix after upsampling.

[0073] XI. Determining the Iteration Stopping Condition Determine whether the current high-resolution reconstruction result has converged. This embodiment uses the following stopping condition: (1) The number of iterations reaches the maximum value. In this embodiment, the preferred choice is... At this point, the iteration stops. (2) The change between two consecutive high-resolution images is less than the threshold. : ; in, For the first High-resolution images from the next iteration. For the first High-resolution images from the next iteration. The square of the Frobenius norm of the matrix. As the image change threshold, this embodiment preferably selects [value]. ; (3) Calculate the eye height every 5 iterations. If the change in eye height is less than In this embodiment, the preferred choice is... You can also stop the iteration.

[0074] If the stopping condition is not met, continue iterating; if the stopping condition is met, output the final high-resolution logarithmic domain eye diagram. .

[0075] 12. Normalized logarithmic domain inverse transform to high-resolution BER image First of all Anti-normalization: ; in, This is the high-resolution logarithmic field eye diagram matrix after inverse normalization. The final output is a high-resolution logarithmic field eye diagram matrix (normalized to...). (interval) This represents the maximum value of the original low-resolution logarithmic field eye diagram matrix. This represents the minimum value of the original low-resolution logarithmic field eye diagram matrix.

[0076] Then, the logarithmic field is inversely transformed back to the BER space: ; in, For the high-resolution BER image, the first Line number The element values ​​of the column, The third high-resolution logarithmic field eye map matrix after inverse normalization Line number The element values ​​of the column.

[0077] To prevent non-physical values ​​from appearing after the inverse transformation, the range of the results is limited: ; in, As the lower limit of BER, this embodiment takes... ; This is the upper limit of BER, which is taken in this embodiment. .

[0078] XIII. Image Normalization and Pseudocolor Rendering To display the reconstruction results on the host computer interface, Perform display mapping. This embodiment preferably uses... As a display of intensity, this form is able to highlight the low BER open-eye area.

[0079] Normalize the display intensity to the display grayscale or pseudocolor range: ; in, To display the image at pixels The intensity value at that location, This is a mapping function that maps the display intensity to a grayscale or pseudocolor range. For the high-resolution BER image, the first Line number The element values ​​of the column, This is a lower limit correction constant to prevent errors in logarithmic calculations.

[0080] The x-axis uses the original horizontal offset coordinate. The vertical axis uses the original vertical offset coordinate. This allows the displayed image to have true coordinate meaning.

[0081] XIV. BER Contour Extraction Extract contour lines at a specified BER threshold from the reconstructed high-resolution BER map. Let the set of BER thresholds to be extracted be: ; For threshold ,exist Seeking satisfaction The location of contour lines. The MarchingSquares algorithm was used to obtain continuous contour lines for contour line extraction.

[0082] 15. BER Eye-Opening Region Recognition Given a BER threshold Below, regions with a BER less than or equal to the threshold are defined as candidate regions for opening eyes: ; in, The candidate region for opening the eye includes all pixels with a BER value less than or equal to the threshold. For the high-resolution BER image, the first Line number The element values ​​of the column.

[0083] right Perform connected component analysis and select components containing the eye diagram center point. Connected regions as effective eye-opening regions .

[0084] Extract the boundaries of the effective eye-opening area: ; in, To effectively define the boundary outline of the eye opening area, Extract operators for boundaries.

[0085] Used for subsequent indicator calculations and image annotation.

[0086] XVI. Calculation of eye height, eye width, opening area, and central margin Based on effective eye-opening area Calculate key parameters of the eye diagram.

[0087] Determine the coordinates of the eye-opening center ,Pick Geometric center: ; in, To determine the vertical pixel coordinates of the center of the effective eye-opening region, To determine the horizontal pixel coordinates of the center of the effective eye-opening area, The total number of pixels contained in the effective eye area.

[0088] Wide eyes: In On the horizontal line, find the leftmost and rightmost boundaries where the eye-opening area intersects with this horizontal line, and denote them as... and Convert to actual time units: ; in, This is the eye width value, in units of UI or seconds. The horizontal coordinates corresponding to the rightmost boundary. This represents the horizontal coordinate corresponding to the leftmost boundary.

[0089] High standards: In On the vertical line, find the lower and upper boundaries where the opening region intersects with this vertical line, and denote them as follows: and Convert to actual voltage units: ; in, This is the highest value for the eye, measured in volts. The vertical coordinates corresponding to the upper boundary. This represents the vertical coordinate corresponding to the lower boundary.

[0090] Opening area: ; in, This represents the area of ​​the opening. The number of pixels contained in the effective eye area. The horizontal coordinate interval for high-resolution images. The vertical coordinate interval of the high-resolution image.

[0091] Opening ratio: ; in, The aperture ratio refers to the proportion of the open-eye area to the total scanned area. This represents the number of horizontal pixels (columns) in a high-resolution image. This represents the vertical pixel count (number of rows) of a high-resolution image.

[0092] Central Margin: Represented using the central margin of the logarithm field: ; in, The margin value represents the center of the eye diagram in the normalized logarithmic domain, reflecting the margin level of the eye diagram center in the normalized logarithmic domain. This represents the value of the high-resolution logarithmic field eye diagram matrix after inverse normalization at the center of the open eye region.

[0093] Alternatively, the BER ratio can be used: ; in, The center margin value is represented logarithmically as the BER level at the center of the eye diagram. This represents the value at the center of the open-eye region in the high-resolution BER image.

[0094] 17. Annotation drawing, result output and saving Display high-resolution images BER contour lines Boundary of the eye-opening area It also displays parameters such as eye height, eye width, opening area, and center margin in an overlay.

[0095] The annotation content includes: horizontal sampling coordinate axis, vertical sampling coordinate axis, BER contour line label, eye opening region boundary, eye height label line, eye width label line, opening area text label, opening ratio text label, and center point margin text label.

[0096] The final output includes: (1) High-resolution statistical eye diagram pseudocolor image; (2) BER contour map; (3) Eye diagram index chart with annotations; (4) Eye diagram parameter table (including eye height, eye width, opening area, opening ratio, center point Margin_log, center point Margin_BER, etc.).

[0097] The results are saved as PNG image files, CSV table files, or MAT data files, and simultaneously displayed directly on the host computer interface of the high-speed cable tester.

[0098] The two-dimensional BER eye diagram matrix used in this embodiment of the invention originates from the actual test results of high-speed cable testing equipment. The test data is directly collected and exported by the eye scanning module of the FPGA high-speed transceiver, representing the raw measurement data obtained under real working conditions, rather than simulation data or artificially constructed data. This data includes the BER distribution under different horizontal sampling phases and vertical decision thresholds, which can realistically reflect the signal integrity status of the high-speed cable link in the current test environment. Since the test data comes directly from the FPGA hardware test platform, it has strong engineering authenticity and reliability. Therefore, conducting eye diagram reconstruction experiments based on this data can more effectively verify the applicability of the algorithm in actual high-speed cable testing systems. The BEAR-Eye statistical eye diagram super-resolution reconstruction algorithm proposed in this invention does not rely on additional training samples, nor does it require changes to the original FPGA hardware structure and eye scanning sampling process. It only performs post-processing reconstruction on the raw BER matrix exported by the device, thus possessing good engineering deployment value and practical application significance.

[0099] To verify the effectiveness of the proposed BEAR-Eye statistical eye diagram super-resolution reconstruction algorithm, this invention selects the original two-dimensional BER eye diagram matrix as input data and performs eye diagram reconstruction using bilinear interpolation, cubic interpolation, and the method of this invention, respectively. Experimental results are as follows: Figure 2 As shown.

[0100] from Figure 2As shown in (a), the original eye diagram results exhibit a noticeable blocky effect due to the limited number of sampling points in the original two-dimensional BER matrix, with the eye diagram boundary displaying a stepped distribution. While this type of low-resolution display can reflect the approximate location of the eye diagram opening, it is difficult to accurately describe the continuous changes in the eye opening boundary. When directly calculating parameters such as eye height, eye width, and opening area based on the original matrix, the results are easily affected by sampling interval and grid quantization errors, leading to insufficient stability of the measurement results.

[0101] like Figure 2 As shown in (b), bilinear interpolation improves the continuity of the image to some extent, alleviating the blocky phenomenon in the original eye map and making the transition of the eye map boundary smoother. However, bilinear interpolation essentially only uses local neighboring pixels for linear weighting, without considering the physical distribution characteristics and boundary structure features of the BER statistical eye map. Therefore, although this method improves the visual display effect, it is prone to causing blurring of the eye map boundary and making the local shape of the BER contour lines unstable.

[0102] like Figure 2 As shown in (c), cubic interpolation offers better smoothness and continuity compared to bilinear interpolation, resulting in a more natural eye diagram contour and finer boundary transitions. However, cubic interpolation remains a traditional image interpolation method, primarily relying on the mathematical fitting relationship of pixel neighborhoods for magnified display. It lacks confidence differentiation for BER detection lower limits, saturation error points, and effective transition regions, and cannot guarantee that the reconstructed result remains consistent with the original BER measurement matrix after downsampling. Therefore, while cubic interpolation outperforms bilinear interpolation in terms of display effect, it still falls short in terms of measurement reliability and boundary physical consistency.

[0103] In comparison, such as Figure 2 As shown in (d), the method proposed in this invention introduces BER logarithmic domain mapping, confidence weight modeling, nonlocal self-similar structure compensation, TV edge preservation constraints, and data consistency back projection mechanism during image reconstruction. While eliminating the blocky effect of the original eye diagram, it also maintains the continuity of the eye diagram boundary and the stability of the central open-eye region.

[0104] like Figure 3 As shown, compared with ordinary interpolation methods, the eye map reconstructed by the method of this invention has clearer boundaries, a more complete outline of the open eye region, and no obvious over-smoothing phenomenon. The BER contour map further demonstrates that the method of this invention can obtain a relatively continuous and stable contour distribution, which is beneficial for the accurate extraction of subsequent parameters such as eye height, eye width, and opening area.

[0105] To further quantitatively evaluate the reconstruction effects of different methods, this invention uses BER=10 -5As the threshold for determining the open eye region, the eye height, eye width, opening area, opening ratio, and center BER obtained by different methods were statistically analyzed, and the results are shown in Table 1.

[0106] Table 1. Reconstruction effects of different methods

[0107] As shown in Table 1, regarding the comparison of quantitative indicators, the original low-resolution eye diagram has an eye height of 43.3333. Bilinear interpolation and cubic interpolation improve this to 44.1296 and 44.5344 respectively, while the method of this invention further improves it to 44.9393, the highest among all methods. Compared to the original eye diagram, the eye height improvement of the method of this invention is approximately 3.71%. This indicates that the method of this invention can more fully recover the vertical opening boundary, making the upper and lower boundaries of the eye diagram more continuous.

[0108] Regarding eye width, the original eye diagram has an eye width of 0.5000 UI, which is significantly limited by the original sampling resolution. After reconstruction, the bilinear interpolation result improves to 0.5734 UI, while cubic interpolation and the method of this invention both reach 0.5804 UI. Compared with the original eye diagram, the eye width of the method of this invention is improved by approximately 16.08%. This indicates that high-resolution reconstruction can improve the problem of inaccurate positioning of the left and right opening boundaries under low sampling density conditions. Although the method of this invention and cubic interpolation are close in eye width value, the method of this invention, through confidence modeling and data consistency back projection constraints, makes the result not only have better display continuity but also stronger measurement reliability.

[0109] Regarding the opening area, the original eye diagram has an opening area of ​​20.0000, which is higher than that of all reconstruction methods. It should be noted that the opening area in the original low-resolution matrix is ​​directly obtained from coarse grid statistics, and the boundaries are distributed in a stepped manner, making it susceptible to grid quantization errors. Therefore, its larger value does not necessarily indicate more accurate opening region estimation. When comparing reconstruction methods, the opening area of ​​the method in this invention is 17.6609, higher than 17.0380 for bilinear interpolation and 17.5703 for cubic interpolation, indicating that the method in this invention can obtain a more complete and effective opening region while maintaining boundary continuity.

[0110] Regarding the aperture ratio, the method of this invention achieves a highest value of 0.1747, which is higher than the original eye diagram's 0.1720, bilinear interpolation's 0.1685, and cubic interpolation's 0.1738. The aperture ratio is a normalized index of the open-eye region relative to the overall scan area, and it can effectively reflect the proportion of the open-eye region. The improved aperture ratio of the method of this invention indicates that its reconstruction results maintain better aperture integrity across the entire scan range.

[0111] Regarding the center point BER metric, the center point BER of the original eye diagram, bilinear interpolation, and cubic interpolation were all 1.9074e-07, while the center point BER of the method in this invention was 1.8778e-07, the lowest among all methods. A smaller center point BER indicates a lower BER in the central region of the eye diagram. This result demonstrates that the method in this invention can effectively maintain the low BER characteristics of the central open-eye region and, to some extent, suppress the distortion in the central region that may be caused by ordinary interpolation and smoothing processes.

[0112] The combined image display results and quantization metrics show that while the original low-resolution eye diagram retains direct measurement data, it exhibits significant blockiness and boundary quantization errors. Bilinear and cubic interpolation can improve display continuity, but they lack constraints on BER statistical characteristics and the physical laws of the eye diagram, easily leading to boundary blurring or insufficient measurement stability. The statistical eye diagram reconstruction method proposed in this invention, through BER confidence modeling, nonlocal structure compensation, TV edge preservation, and data consistency backprojection, enhances eye diagram display resolution while improving boundary continuity and parameter extraction stability. Experimental results demonstrate that this method outperforms ordinary interpolation methods in key metrics such as eye height, eye width, aperture area, aperture ratio, and center point BER, providing more reliable image reconstruction results for high-speed serial link eye diagram analysis and high-speed cable tester host computer display.

[0113] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A statistical eye diagram reconstruction method based on BER confidence and nonlocal total variation, characterized in that, Includes the following steps: Step 1: Obtain the two-dimensional BER statistical eye diagram matrix and related coordinate information generated during the high-speed serial communication link test; Step 2: Perform data cleaning and lower bound correction on the two-dimensional BER statistical eye diagram matrix, and then perform logarithmic domain mapping and normalization on the corrected matrix; Step 3: Construct a confidence weight matrix based on BER measurement characteristics, and perform initial upsampling of the normalized logarithmic domain matrix at different scales in both the horizontal and vertical directions; Step 4: Using the initial upsampling result as input, perform nonlocal self-similar structure compensation, and construct a joint objective function that integrates data consistency, edge-preserving total variational regularization, nonlocal prior, and eye diagram physical monotonic constraints for iterative solution; during the iteration process, perform data consistency back projection correction in conjunction with the confidence weight matrix until the preset stopping condition is met; Step 5: Transform the high-resolution logarithmic domain result obtained after iterative convergence into a high-resolution BER map, extract contour lines under a specified threshold based on the high-resolution BER map, and calculate the eye map index.

2. The method according to claim 1, characterized in that, In step two, the lower limit correction uses a lower limit correction constant. Replace zero, missing, or non-positive values; the lower limit correction constant Determine as follows: ； in, The first BER in the original two-dimensional matrix Line 1 The element values ​​of the column, The lower limit of computer floating-point precision; the corrected BER matrix. for: ； in, For the corrected BER matrix, the first... Line 1 The element values ​​of the column.

3. The method according to claim 1, characterized in that, In step two, the logarithmic field mapping is to map the corrected BER matrix. Mapped to: Obtain the low-resolution log-domain eye diagram matrix before normalization. ; The normalization process is to... Linear mapping to the following formula The interval is used to obtain the normalized low-resolution log-domain eye diagram matrix. : ； in, The first normalized low-resolution logarithmic field eye map matrix is ​​the... Line 1 The element values ​​of the column, for The global minimum value, for The global maximum value.

4. The method according to claim 1, characterized in that, In step three, the method for constructing the confidence weight matrix includes: Identify BER points that are close to the detection lower limit, when Assign weights at time ,in, This is the lower limit tolerance coefficient; Identify high BER saturation regions, when Assign weights at time ,in, According to the test system settings; Identify valid transition regions and assign weights. ; To identify isolated mutation points, a neighborhood window centered on the pixel is selected, and the local median and local median absolute deviation are calculated. If the deviation of a point from the local median exceeds a preset multiple, it is determined to be an isolated mutation point and assigned a weight. ; The weights satisfy the following: .

5. The method according to claim 1, characterized in that, In step three, during the initial upsampling at different horizontal and vertical scales, the high-resolution target size is set as follows: ； in, This represents the number of vertical sampling points. This represents the number of horizontal sampling points. This refers to the lateral magnification. This is the vertical magnification, and and For different positive integers; initial high-resolution image Through the upsampling operator get: 。 6. The method according to claim 1, characterized in that, In step four, the non-local self-similar structure compensation specifically involves: for any pixel in the current high-resolution image... ,by Select image patch centered Search for candidate pixels within the search window. ,by Select image patch centered Weighted fusion based on similarity weights, followed by normalization, yields the nonlocal compensation result. The similarity weight calculation formula is as follows: ； in, For pixels With candidate pixels Similarity weights between them For smooth control parameters.

7. The method according to claim 1, characterized in that, In step four, the edge-preserving total variation regularity is: ； in, The edge-guided total variational regularization term is used to smooth flat regions while preserving the boundaries. For the horizontal gradient, For the vertical gradient, For pixels Edge guiding weights at: ； in, The edge sensitivity coefficient, For pixels The gradient magnitude at point A is calculated as follows: 。 8. The method according to claim 1, characterized in that, In step four, the physical monotonic constraint of the eye diagram is as follows: First, determine the geometric center of the logarithmic domain maximum point or the low BER eye opening region as the eye diagram center point. ,by Starting from a point, construct several ray directions in the horizontal and vertical directions, and for adjacent points on the same ray direction that are farther from the center... and neighboring points closer to the center Expected to be satisfied That is, it decreases monotonically from the center of the eye opening to the boundary; define the monotonic penalty term: ； in, This is a penalty term for the physical monotonicity constraint of the eye diagram. These are adjacent pixels that are closer to the center along the same ray direction. These are adjacent pixels that are farther from the center along the same ray direction. Image values ​​near the endpoint, The image value at the far endpoint.

9. The method according to claim 1, characterized in that, In step four, the joint objective function is: ； in, To optimize the obtained high-resolution logarithmic field eye diagram matrix; The optimization variable represents the high-resolution image currently being solved; For downsampling operators, This represents the norm weighted by the confidence weight matrix. This is a low-resolution logarithmic field eye diagram matrix. For non-local enhancement images, For total variation regularization, This is a penalty term for the physical monotonicity constraint of the eye diagram. , , These are the corresponding regularization parameters; Solve using an iterative approach, with the initial value being... In the In each iteration, updates are performed based on the gradient of the objective function, and the numerical values ​​are constrained to [value missing]. Interval.

10. The method according to claim 1, characterized in that, In step four, the data consistency backprojection correction specifically involves: adjusting the current high-resolution image... Downsampling Calculate the error matrix: ； Using the confidence weight matrix The error correction yielded: ； Will Upsampling to high resolution size : ； Perform back projection correction using the following formula: ； in, For the upsampling operator, Correct the step size for back projection.

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