CN115941129B - High-speed link eye diagram implementation method based on linear fitting error matrix - Google Patents
High-speed link eye diagram implementation method based on linear fitting error matrix Download PDFInfo
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Abstract
The invention provides a high-speed link eye diagram implementation method based on a linear fitting error matrix, which is used for solving the problems of long simulation time and inaccurate calculation result of calculating a nonlinear high-speed link statistical eye diagram. The implementation steps are as follows: (1) constructing a response waveform matrix of a nonlinear high-speed link; (2) constructing an input sample matrix of the nonlinear high-speed link; (3) Performing linear fitting on the response waveform matrix to generate a linear fitting error matrix; (4) Generating probability density vectors of the linear fitting error matrix; (5) The statistical eye diagram of the high-speed link is calculated using the probability density vector of the linear fit error matrix. The invention can evaluate the statistical eye diagram of the nonlinear link efficiently and accurately, and can be used for signal integrity analysis.
Description
Technical Field
The invention belongs to the technical field of electricity, and further relates to a high-speed link eye diagram implementation method based on a linear fitting error matrix in the technical field of digital information transmission. The invention can be applied to the design analysis of signal integrity in the technical field of electric digital data processing and provides a reference for evaluating a nonlinear high-speed link channel.
Background
With the innovative development and popularization and application of electronic design and integrated circuit technology, electronic components are developed towards multifunction, miniaturization and rapidness. The bandwidth requirements of the industry on signal transmission are higher and higher, and the signal transmission speed is higher and higher. In this background, phenomena such as Signal reflection, crosstalk, ringing and the like frequently occur, which severely restricts the development of electronic products, so Signal Integrity (SI) analysis has become an indispensable link in high-speed links. In the design process of the high-speed link, analysis of signal waveforms in products and even superposition of output signal waveforms into an eye diagram are considered, and the analysis is very important for performance evaluation of the high-speed link and solving of the signal integrity problem. Currently, the common eye patterns include a statistical eye pattern and a transient eye pattern, and the mainstream algorithm for calculating the eye pattern is based on the assumption that the linearity is unchanged. As the data rate increases, ignoring the nonlinear factors in the link can lead to relatively large errors, and it is highly necessary to evaluate how accurately the nonlinear factors affect the high speed link.
The Xiuqin Chu et al publication, "Statistical Eye Diagram Analysis Based on Double-Edge Responses for Coding Buses" (volume IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY,2020,62) discloses a statistical eye diagram implementation method based on double edge responses. The method comprises the following implementation steps: establishing a probability distribution model of the coded bus bit vector based on the constraint of the coding rule, wherein the bus bit of the previous time interval possibly affects the numerical value of the current time interval due to the influence of the coding scheme, and different bus values have different probability values; then, the implementation method of the PDA and the BER eye diagram is deduced according to the bus bit transition probability and the rising and falling edge response calculation system response of the superposition shift. The method can accurately calculate the statistical eye diagram of the coding bus, and solves the problem of influence of asymmetric rising and falling edges. However, this approach still suffers from the disadvantage that significant errors are still introduced due to imperfections in the covered nonlinearities when the nonlinearities extend beyond the edge transitions of the response waveform.
An eye diagram measuring and calculating method under the interference of additive noise and a device and a storage medium thereof (patent application number CN202210103888.6, application publication number CN 114124318A) of Shenzhen city Ding yang science and technology Co-Ltd are disclosed in patent literature applied by Shenzhen city Ding yang science and technology Co-Ltd. The method comprises the following implementation steps: the method comprises the steps of firstly, obtaining unit impulse response and outputting sampling data; step two, processing to obtain a first signal probability density function; thirdly, generating an output noise probability density function; fourthly, processing to obtain a second signal probability density function; and fifthly, generating a statistical eye diagram, wherein the statistical eye diagram comprises contour information of an eye diagram with any error rate. The method can simplify the test operation flow of the tested transmission system and improve the efficiency of output signal acquisition and statistical analysis in the statistical eye diagram test process. However, this method still has two disadvantages: firstly, because the predicted statistical eye diagram output by the method only considers unit impulse response, but ignores jitter contained in a high-speed link, if the high-speed link contains jitter, the predicted eye height and eye width data of the statistical eye diagram have at least 5% of relative errors with transient simulation results, and the predicted outline of the statistical eye diagram also has larger deviation with the transient simulation results; secondly, if the high-speed link contains a nonlinear factor, both the current and subsequent code bits are affected by the nonlinear factor. Because the statistical eye diagram output by the method only considers the unit impulse response, and the influence of the saturation nonlinearity on the subsequent code bits is ignored, the predicted eye height and eye width data of the statistical eye diagram and the transient simulation result have at least more than 5% of relative errors, and the predicted outline of the statistical eye diagram also has larger deviation from the transient simulation result. Meanwhile, the predicted statistical eye diagram output by the method only considers the unit impulse response, the edge response of the unit impulse response is completely symmetrical, the situation that the rising edge response and the falling edge response are not symmetrical is ignored, and then the predicted eye height and eye width data of the statistical eye diagram and the transient simulation result have relative errors of more than 5%, and the predicted outline of the statistical eye diagram also has larger deviation with the transient simulation result.
Disclosure of Invention
The invention aims to provide a high-speed link eye diagram implementation method based on a linear fitting error matrix aiming at the defects of the prior art, which is used for solving the problems that the eye diagram calculation is inaccurate and the simulation time is overlong because the influence of jitter, rising and falling edge asymmetry in a high-speed link on a subsequent code bit is ignored only by considering the unit impulse response of a current bit and the simulation of a large number of response waveforms of different code patterns is needed for simulating a high-nonlinearity link in the prior art.
The specific idea for realizing the purpose of the invention is as follows: the data used in the present invention consists of a series of Pseudo random binary sequence PRBS (Pseudo-Random Binary Sequence) and response waveforms output after the Pseudo random binary sequence PRBS is input into the high speed link. Since the present invention uses a complete response waveform, both the current code bit and the subsequent code bit are considered. Meanwhile, the invention only uses a group of PRBS response waveform data for statistical analysis, thereby solving the problem of overlong simulation time caused by simulating a large number of response waveforms with different code patterns. The invention carries out linear fitting on the response waveform, calculates the error between the linear fitting waveform and the actual response waveform, and the linear fitting error matrix obtained by calculation reflects the jitter and nonlinear factors in the high-speed link and the influence of asymmetrical rising edge response and falling edge response on the response waveform. By carrying out statistical analysis on the linear fitting error matrix, error probability density vectors at different sampling points can be obtained. In the process of obtaining a statistical eye diagram by using a unit impulse response algorithm, the probability density vector of the obtained error is convolved, and nonlinear factors in a link are added into the statistical eye diagram, so that the problem of inaccurate eye diagram calculation caused by insufficient nonlinear factors considered in the prior art is solved.
The technical scheme adopted by the invention comprises the following steps:
step 1, constructing a response waveform matrix of a nonlinear high-speed link:
step 1.1, constructing a binary sequence consisting of a start bit, a target code pattern 1, a target code pattern 2 and a tail bit in sequence;
step 1.2, inputting the binary sequence into a high-speed link to output a response waveform; sampling the output response waveform by utilizing the sampling frequency to obtain a response waveform sequence; wherein T is the time required for transmitting 1-bit binary symbols in the high-speed link, and M represents the total number of sampling points in each bit;
step 1.3, selecting from the (k+g+2) th in the response waveform sequence N ) X M to (k+g+2) N+1 ) Sampling point data in the X M position, k is the total number of code bits of the initial bit, g is the total number of code bits of the final bit, and N is the pseudo-random binary code order in the target code pattern 1 and the target code pattern 2; equally spaced apart of selected data into 2 N After the dividing, a response waveform moment Y is constructed, the total number of the matrix rows is equal to M, and the total number of the columns is equal to 2 N ；
Step 2, constructing an input sample matrix of the nonlinear high-speed link:
selecting the pseudo-random binary codes of the back f bits and the front f bits of the target code pattern 2 from the binary sequence to form an input code pattern sequence, wherein f is less than or equal to 2 N The method comprises the steps of carrying out a first treatment on the surface of the Circularly right-shifting the input code pattern sequence to obtain a preliminary sample matrix, and supplementing a row of '1' on the last row of the preliminary sample matrix to obtain a row total number of 2 N +1, total number of columns of 2 N Input sample matrix X of (a) 1 ；
Step 3, performing linear fitting on the response waveform matrix to generate a linear fitting error matrix:
step 3.1 according toThe formula, calculate the transfer matrix P, Y represents the response waveform matrix, X 1 Representing an input sample matrix, wherein an upper corner mark T represents transposition operation, and an upper corner mark-1 represents inversion operation;
step 3.2, according to Y 1 ＝PX 1 Formula, calculating a linear fitting response waveform matrix Y 1 The method comprises the steps of carrying out a first treatment on the surface of the Response waveform matrix Y by linear fitting 1 Subtracting the response waveform matrix Y to obtain a linear fitting error matrix E;
step 4, generating probability density vectors of the linear fitting error matrix:
step 4.1, generating a lineProbability density vector of each sampling point of error matrix is fit in a sex mode, the total number of rows of the probability density vector is 2, and the total number of columns is 2 N The method comprises the steps of carrying out a first treatment on the surface of the The first row elements of the probability density vector are voltage differences between the linear fitting response waveform matrix and each sampling point of the response waveform matrix, and the second row elements are probability values corresponding to the first row elements;
step 4.2, probability combination is carried out on probability density vectors of each sampling point of the linear fitting error matrix;
step 5, calculating a statistical eye diagram of the high-speed link by using probability density vectors of the linear fitting error matrix:
step 5.1, deleting the voltage difference element of the last column of the transfer matrix P to obtain a total number of rows M and a total number of columns 2 N Impulse response matrix of (a); generating a probability density vector of each sampling point of the impulse response matrix, wherein a first row element of the probability density vector is a voltage value of each sampling point of the impulse response matrix, and a second row element is a probability value corresponding to the first row element;
step 5.2, convolving the linear fitting error matrix and the probability density vector of the impulse response matrix at each sampling point position to obtain a statistical probability density vector of each sampling point; carrying out probability combination on the statistical probability density vector of each sampling point by adopting the same method as the step 4.2;
step 5.3, mapping the probability value in the statistical probability density vector with the RGB value of the color in the RGB color mode; and drawing a statistical eye diagram of the high-speed link according to the mapping relation between the probability value in the statistical probability density vector and the RGB value of the color in the RGB color mode.
Compared with the prior art, the invention has the following advantages:
firstly, the invention inputs the generated binary sequence into the high-speed link to obtain a response waveform matrix, and constructs an input sample matrix of the nonlinear high-speed link by utilizing the binary sequence. When calculating the statistical eye diagram of the high-speed link with high nonlinearity degree, a large number of response waveforms with different code patterns do not need to be simulated, so that the problem of overlong simulation time in the prior art is avoided. The method has the advantages of short time consumption, small simulation amount and high efficiency in calculating the statistical eye diagram of the high-speed link by using the probability density vector of the linear fitting error matrix.
Second, the invention generates a linear fitting error matrix by performing linear fitting on the response waveform matrix. The linear fitting error matrix used in the invention covers the influence of jitter, nonlinear factors and rising and falling edge response asymmetry in a high-speed link on an actual response waveform, and overcomes the defect of inaccurate eye calculation of a simulation method of unit impulse response in the prior art. Therefore, the invention considers the influence of all nonlinear factors in the link on the actual waveform, improves the accuracy of calculating the statistical eye diagram, and has the advantage of calculating the statistical eye diagram.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a diagram of a high-speed link constructed in ADS according to the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The specific steps of an implementation of the present invention will be further described with reference to fig. 1 and the embodiment.
Step 1, building a nonlinear high-speed link:
the high-speed link diagram built in the simulation software advanced design system ADS (Advanced Design System) of the present invention will be described in further detail with reference to fig. 2.
The bit rate of the nonlinear high-speed link built in the ADS in the embodiment of the invention is 16Gbps, and a simulation mode of transient simulation Transient simulation is used. The nonlinear high-speed link consists of a transmitting end, an IO port module, a transmission line and an I port module. The transmitting end and the receiving end are both realized by adopting an Input/output buffer information specification-algorithm modeling interface IBIS-AMI (Input/Output Buffer Information Specification-Algorithmic Modeling Interface) model, the transmission line is realized by adopting an S (scaling) parameter model with the insertion loss changing along with the frequency, the IO port module and the I port module are realized by adopting an Input/output buffer information specification-algorithm modeling interface IBIS-AMI (Input/model).
And 2, constructing a response waveform matrix of the nonlinear high-speed link.
Step 2.1, constructing a binary sequence consisting of a start bit, a target code pattern 1, a target code pattern 2 and a last bit. The initial bit of the binary sequence is composed of k '0' code bits, the final bit is composed of g '0' code bits, and the target code pattern 1 and the target code pattern 2 are both 2 with equal code patterns N A pseudo-random binary code; wherein k is more than or equal to 500, g is more than or equal to 500, and the values of k and g are correspondingly equal; n is the order of a pseudorandom binary code randomly selected within the range 3,5,7,9,11,13,15,31.
The initial bit of the binary sequence constructed by the embodiment of the invention consists of 1000 '0' code bits, and the final bit consists of 1000 '0' code bits. Target pattern 1 and target pattern 2 are both equal in pattern 2 13 Each pseudo-random binary code PRBS is composed of the order of the pseudo-random binary sequence PRBS 13. The start bit of the binary sequence of all "0" code bits preceding the target pattern 1, the target pattern 1 preceding the target pattern 2 is 2 13 Bit PRBS13 pattern.
Intersymbol interference ISI (Inter Symbol Interference) in the high-speed link is stretched by the nonlinear factors in the link, however ISI caused by all "0" code bits in the nonlinear link is small. Since the start bits before the target pattern 1 are all "0" code bits, the response waveform after the target pattern 1 passes through the nonlinear link does not include all nonlinear factors in the link. Since the target pattern 1 preceding the target pattern 2 is a PRBS code, the ISI caused by the PRBS code is long, and all nonlinear factors in the link can be provided for the response waveform sequence corresponding to the target pattern 2. Thus, the target pattern 1 and the target pattern 2 have the same pattern and bit number.
Step 2.2, inputting the constructed binary sequence into a high-speed link to output a response waveform, using the sampling frequencyAnd sampling the output response waveform to obtain a response waveform sequence consisting of 588288 sampling points. Where T is the time required to transmit a 1-bit binary symbol in the high-speed link and M represents the total number of sampling points in each bit. In this embodiment, m=32, +.>In ns.
And 2.3, selecting sampling point data from 326144 to 588288 positions in a response waveform sequence in order to ensure that nonlinear factors in the system can be completely overlapped on the output response waveform. The selected data is equally divided into 8192 parts, and a response waveform matrix Y with the total number of rows equal to 32 and the total number of columns equal to 8192 is constructed.
Step 3, constructing an input sample matrix of the nonlinear high-speed link:
step 3.1, selecting the pseudo-random binary codes of the last 8190 bit and the first 8190 bit of the target code pattern 2 from the binary sequence to form an input code pattern sequence x r
x r ＝[x 2 (3),...,x 2 (8192),x 2 (1),...,x 2 (8190)]
Wherein x is 2 (1) 1 st bit, x, representing target pattern 2 2 (3) The 3 rd bit, x, representing target pattern 2 2 (8190) 8190 th code bit, x, representing target pattern 2 2 (8192) Representing the last code bit of the target pattern 2. Pattern sequence x r X in the middle 2 (3) And x 2 (8192) The code bits between the two are continuous code bits from the 3 rd code bit to the 8192 nd code bit of the target code pattern 2; pattern sequence x r X in the middle 2 (1) And x 2 (8190) The code bits in between are consecutive code bits between the 1 st code bit and 8190 th code bit of the target code pattern 2.
Step 3.2, for the input pattern sequence x r A circular right shift is performed to form a preliminary sample matrix with dimensions 8192 x 8192. To ensure that the DC level between the response waveform of the linear fitting and the output response waveform is consistent, supplementing a row of '1' to the last row of the preliminary sample matrix to obtainAn input sample matrix X with a total of 8193 rows and 8192 columns 1 。
Will input pattern sequence x r Shifting 1 bit to the right, taking the last element before shifting the input code pattern sequence as the first element after shifting, replacing the input code pattern sequence before shifting by the input code pattern sequence after shifting, repeating the process until the input code pattern sequence shifts 8192 bits to the right, and obtaining a preliminary sample matrix. To ensure consistent DC levels between the linearly fitted response waveform and the output response waveform, a row of "1" is supplemented in the last row of the preliminary sample matrix to obtain an input sample matrix X with 8193 rows and 8192 columns 1 。
Wherein x is r Representing the sequence of input patterns, x r (1)、x r (8192) Representing the input pattern sequence x r Bit 1, 8192 code bits.
Step 4, performing linear fitting on the response waveform matrix to obtain a linear fitting error matrix:
step 4.1 according toThe formula calculates the transfer matrix P. The transfer matrix P is used to characterize the transmission characteristics of a linear time-invariant channel, and the last line element thereof represents the dc level value of the output response waveform at successive sampling points between the 1 st sampling point and the 32 nd sampling point. Wherein Y represents a response waveform matrix, X 1 The input sample matrix is represented, the upper-corner T represents the transpose operation, and the upper-corner-1 represents the inversion operation.
Step 4.2, using the transfer matrix P and the input sample matrix X 1 After matrix multiplication, a linear fitting response waveform matrix Y is obtained 1 The matrix has the same matrix dimensions as the response waveform matrix Y. Response waveform matrix Y by linear fitting 1 Subtracting the response waveform matrix Y matrix to obtain a linear fitting error matrix E, which representsNonlinear factors in the link are relative to x in the target pattern 2 The effect of the generation.
Step 5, generating probability density vectors of the linear fitting error matrix:
step 5.1, generating probability density vector of each sampling point of the linear fitting error matrix, wherein the total number of rows of the probability density vector is 2, and the total number of columns is 2 N The method comprises the steps of carrying out a first treatment on the surface of the The first row elements of the probability density vector are voltage differences between the linear fitting response waveform matrix and each sampling point of the response waveform matrix, and the second row elements are probability values corresponding to the first row elements.
Generating probability density vectors at each sampling point in the linear fit error matrix according to:
wherein e i A probability density vector representing a linear fitting response waveform matrix and an ith sampling point of the response waveform matrix, wherein i represents a serial number of the sampling point; v (V) 1 Representing the voltage difference between the linear fitting response waveform matrix and the 1 st code bit of the response waveform matrix at the i-th sampling point; v (V) 8192 Representing a voltage difference between the linear fit response waveform matrix and the 8192 nd code bit of the response waveform matrix at the i-th sample point; p is p 1 Represented in the probability density vector e i V is obtained from 8192 code bits of the voltage difference 1 Probability of (2); p is p 8192 Represented in the probability density vector e i V is obtained from 8192 code bits of the voltage difference 8192 Is a probability of (2).
And 5.2, carrying out probability combination on probability density vectors of each sampling point of the linear fitting error matrix. The probability merging refers to the selection of a target voltage difference value which is not repeated in each probability density vector; searching the voltage difference value which is the same as the target voltage in the rest voltage difference values of the probability density vectors, adding the probability value which corresponds to the voltage difference value which is the same as the target voltage to the probability value of the target voltage, and deleting the voltage difference value which is the same as the target voltage and the corresponding probability value in the probability density vectors.
The response waveform data used in the embodiments of the present invention is accurate to the last eight bits of the decimal point. When the voltage difference value of each probability density vector is combined, the more decimal places of the voltage difference value data are used, the higher the calculation accuracy is, the larger the calculated engineering quantity is, and little benefit is brought to the calculation result. Therefore, the voltage difference data used in the embodiment of the invention only needs to be reserved to the last five bits of the decimal point. In the embodiment of the invention, the whole voltage difference value of each probability density vector is amplified by 100000 times and the data remained after decimal point is rounded.
The probability values of the voltage differences for each probability density vector are combined as follows. Selecting the voltage difference V of the 1 st code bit in each probability density vector 1 Finding a sum V among the voltage differences of the remaining 8191 code bits in the probability density vector 1 The same voltage difference is recorded and the first and V 1 The code bit sequence number j corresponding to the same voltage difference. If sequence number j exists, V in the probability density vector 1 The corresponding probability p 1 Probability p corresponding to voltage difference of jth code bit j And adding and deleting the j-th element in the probability density vector. Then, the voltage difference value of the remaining code bits in the probability density vector is found again with V 1 The same voltage difference and the above procedure is repeated. If the sequence number j does not exist, selecting the voltage difference V of the 2 nd code bit of the probability density vector 2 The above procedure is repeated.
Step 6, calculating a statistical eye diagram of the high-speed link by using probability density vectors of the linear fitting error matrix:
and 6.1, deleting the last column of voltage difference elements of the transfer matrix P to obtain an impulse response matrix with the dimension of 32 multiplied by 8192. The probability density vector for each sample point in the impulse response matrix is generated in the same way as in step 4.1.
And 6.2, constructing a statistical probability density vector of each sampling point in the impulse response matrix, wherein the internal elements represent the voltage amplitude which can occur at the sampling point of the response waveform output by the nonlinear high-speed link and the probability that the response waveform appears as the voltage amplitude, and the vector is a vector convolution result of the impulse response matrix and the probability density vector of the linear fitting error matrix at the same sampling point position.
And obtaining a statistical probability density vector of each sampling point of the impulse response matrix according to the following formula. And (4) combining probability values of voltage difference values in the statistical probability density vectors of each sampling point of the impulse response matrix by adopting the same method as that of the step (4.2) to obtain the refreshed statistical probability density vector. In order to ensure that the voltage difference value of the statistical probability density vector of each sampling point is in the same magnitude as the voltage difference value in the linear fitting error matrix, the voltage difference value in the statistical probability density vector of each sampling point is reduced by 100000 times.
Wherein, es x A statistical probability density vector, ex, representing the x-th sample point in the impulse response matrix m Probability density vector, ey representing the mth sample point in the impulse response matrix n The probability density vector representing the position of the nth sampling point in the linear fitting error matrix, and the values of x, m and n are correspondingly equal; * Representing a convolution operation; v (V) 1 And V is equal to 2 The 1 st and 2 nd voltage differences, p, respectively, representing the probability density vector of the mth sample point in the impulse response matrix 1 And p 2 Respectively representing probability values corresponding to the 1 st and 2 nd voltage differences; v (V) 1 ' and V 2 ' the 1 st and 2 nd voltage differences, p, respectively, of the probability density vector of the nth sample point in the linear fit error matrix 1 'and p' 2 The probability values corresponding to the 1 st and 2 nd voltage differences are shown, respectively.
And 6.3, taking the maximum value and the minimum value of the probability in the statistical probability density vector as probability value intervals. Mapping the probability value in the probability value area with the RGB value of the color in the color change interval from red to black in the RGB color mode, wherein the minimum probability value and the maximum probability value in the probability value area correspond to the RGB value (0, 0) of black and the RGB value (255, 0) of red in the RGB color mode respectively. And drawing a statistical eye diagram of the high-speed link according to the mapping relation between the probability value in the statistical probability density vector of each sampling point and the RGB value of the color in the color change interval.
The invention is further described below with reference to simulation figures:
1. simulation conditions:
the hardware platform of the simulation experiment of the invention is: the CPU is Intel (R) Core (TM) i7-6700, and the main frequency of the CPU is 3.40GHZ and the memory is 8G.
The software platform of the simulation experiment of the invention is: windows 10 operating system, MATLAB R2021a software, and ADS2020 software.
2. Simulation content and result analysis:
the simulation experiment of the invention adopts the technology, the transient simulation technology and the prior art (based on the unit impulse response technology) to respectively calculate the statistical eye diagram of the nonlinear high-speed link.
Transient simulation is one of three simulation modes of ADS software, adopts a partial differential equation (kirchhoff voltage and current equation) to check the time domain characteristic (eye diagram) of a receiving end, represents the real state of data at the receiving end, and can be applied to linear and nonlinear circuits.
In the prior art, the method for predicting the eye pattern based on the unit impulse response refers to a method for predicting the eye pattern based on the unit impulse response technology used in an eye pattern measuring and calculating method under the interference of additive noise and a device and a storage medium thereof (patent application number CN202210103888.6, application publication number CN 114124318A) of Shenzhen Dingyang science and technology Co., ltd.
The simulation experiment of the invention builds a nonlinear high-speed link as shown in fig. 2 in software ADS2020, the data rate used for simulation is 3.2Gbps/s, and the sampling point number of each bit is 32. According to the simulation experiment, the input data of the transmitting end is a series of binary code, the voltage amplitude range of the data waveform transmitted by the transmitting end is 0-1V, and the rising time and the falling time of the data waveform are both 0.195ns. The transmission line in the simulation experiment of the invention uses four-port S parameter, the insertion loss of the S parameter at the frequency of 3.2Gbps/S is-29.4 dB, and the return loss is-29.76 dB.
The statistical eye diagram of the nonlinear high-speed link obtained by the simulation experiment contains rich information, the influence of inter-code crosstalk and noise can be observed from the eye diagram, and the integral characteristic of the digital signal is reflected, so that the system quality degree can be estimated, and therefore, the eye diagram analysis is the core of the signal integrity analysis of the high-speed interconnection system.
The eye height, eye width information in the eye diagram may characterize the magnitude of jitter and bit error rate in the high-speed nonlinear link. In engineering, the channel quality of the high-speed link is often further evaluated according to information such as eye height and eye width of an eye diagram under a specified error rate.
In order to verify the simulation experiment effect of the invention, the accuracy of the statistical eye diagram calculated by the three methods is respectively evaluated by using two evaluation indexes (eye height and eye width), the eye height and eye width values of the statistical eye diagram calculated by the three methods under the error rate of 1e-4 are counted, and the statistical eye diagram is drawn into a table 1.
The eye height and eye width values obtained by the transient simulation technology are obtained by simulation through ADS2020 software. The information of eye height, eye width and the like obtained through transient simulation is considered to be accurate in engineering, and a nonlinear high-speed link can be described.
Table 1 eye height and eye width comparison table of statistical eye diagrams calculated by three different methods
| Error rate | Eye height | Eye width | |
| The invention is that | 1e-4 | 626.7 millivolts | 27.81 nanoseconds |
| Transient simulation technology | 1e-4 | 626.0 millivolts | 27.81 nanoseconds |
| Unit impulse response technique | 1e-4 | 627.8 millivolts | 29.68 nanoseconds |
The comprehensive table 1 shows that by comparing the eye height and the eye width calculated by the transient simulation technology under the error rate of 1e-4, the error of the statistical eye diagram obtained by the transient simulation technology and the invention is within 0.11%, the error is extremely small, and the result obtained by the invention is accurate. By comparing the unit impulse response technique with the eye height and eye width calculated by the invention at the bit error rate of 1e-4, the invention can be seen to describe the nonlinear high-speed link more accurately than the unit impulse response technique.
The simulation experiment above shows that: the invention uses matrix operation to linearly fit the output response waveform of the nonlinear high-speed link, can obtain an error matrix containing the nonlinear information of the link, and uses the probability density vector of the linear fit error matrix to calculate the statistical eye diagram of the high-speed link, thereby solving the problem of inaccurate eye diagram calculation caused by ignoring the influence of jitter, rising and falling edge asymmetry in the high-speed link on the subsequent code bits due to considering only the unit impulse response of the current bit in the prior art.
Claims (4)
1. A high-speed link eye diagram implementation method based on a linear fitting error matrix is characterized in that a response waveform matrix of a nonlinear high-speed link is constructed, and the response waveform matrix is subjected to linear fitting to generate the linear fitting error matrix; the method comprises the following specific implementation steps:
step 1, constructing a response waveform matrix of a nonlinear high-speed link:
step 1.1, constructing a binary sequence consisting of a start bit, a target code pattern 1, a target code pattern 2 and a tail bit in sequence;
step 1.2, inputting the binary sequence into a high-speed link to output a response waveform; using sampling frequencySampling the output response waveform to obtain a response waveform sequence; wherein T is the time required for transmitting 1-bit binary symbols in the high-speed link, and M represents the total number of sampling points in each bit;
step 1.3, selecting from the (k+g+2) th in the response waveform sequence N ) X M to (k+g+2) N+1 ) Sampling point data in the X M position, k is the total number of code bits of the initial bit, g is the total number of code bits of the final bit, and N is the pseudo-random binary code order in the target code pattern 1 and the target code pattern 2; equally spaced apart of selected data into 2 N After the division, a response waveform matrix Y is constructed, the total number of matrix rows is equal to M, and the total number of columns is equal to 2 N ；
Step 2, constructing an input sample matrix of the nonlinear high-speed link:
selecting the pseudo-random binary codes of the back f bits and the front f bits of the target code pattern 2 from the binary sequence to form an input code pattern sequence, wherein f is less than or equal to 2 N The method comprises the steps of carrying out a first treatment on the surface of the Circularly right-shifting the input code pattern sequence to obtain a preliminary sample matrix, and supplementing a row of '1' on the last row of the preliminary sample matrix to obtain a row total number of 2 N +1, total number of columns of 2 N Input sample matrix X of (a) 1 ；
Step 3, performing linear fitting on the response waveform matrix to generate a linear fitting error matrix:
step 3.1 according toThe formula, calculate the transfer matrix P, Y represents the response waveform matrix, X 1 Representing an input sample matrix, wherein an upper corner mark T represents transposition operation, and an upper corner mark-1 represents inversion operation;
step 3.2, according to Y 1 ＝PX 1 Formula, calculating a linear fitting response waveform matrix Y 1 The method comprises the steps of carrying out a first treatment on the surface of the Response waveform matrix Y by linear fitting 1 Subtracting the response waveform matrix Y to obtain a linear fitting error matrix E;
step 4, generating probability density vectors of the linear fitting error matrix:
step 4.1, generating probability density vector of each sampling point of the linear fitting error matrix, wherein the total number of rows of the probability density vector is 2, and the total number of columns is 2 N The method comprises the steps of carrying out a first treatment on the surface of the The first row elements of the probability density vector are voltage differences between the linear fitting response waveform matrix and each sampling point of the response waveform matrix, and the second row elements are probability values corresponding to the first row elements;
step 4.2, probability combination is carried out on probability density vectors of each sampling point of the linear fitting error matrix;
step 5, calculating a statistical eye diagram of the high-speed link by using probability density vectors of the linear fitting error matrix:
step 5.1, deleting the voltage difference element of the last column of the transfer matrix P to obtain a total number of rows M and a total number of columns 2 N Impulse response matrix of (a); generating a probability density vector of each sampling point of the impulse response matrix, wherein a first row element of the probability density vector is a voltage value of each sampling point of the impulse response matrix, and a second row element is a probability value corresponding to the first row element;
step 5.2, convolving the linear fitting error matrix and the probability density vector of the impulse response matrix at each sampling point position to obtain a statistical probability density vector of each sampling point; carrying out probability combination on the statistical probability density vector of each sampling point by adopting the same method as the step 4.2;
step 5.3, mapping the probability value in the statistical probability density vector with the RGB value of the color in the RGB color mode; and drawing a statistical eye diagram of the high-speed link according to the mapping relation between the probability value in the statistical probability density vector and the RGB value of the color in the RGB color mode.
2. The method according to claim 1, wherein the start bit in the binary sequence in step 1.1 is composed of k "0" code bits, the end bit is composed of g "0" code bits, and the target pattern 1 and the target pattern 2 are both equal in pattern 2 N A pseudo-random binary code; wherein k is more than or equal to 500, g is more than or equal to 500, and the values of k and g are correspondingly equal; n is the order of a pseudorandom binary code randomly selected within the range 3,5,7,9,11,13,15,31.
3. The method for implementing a high-speed link eye diagram based on a linear fitting error matrix as claimed in claim 1, wherein in the step 2, the cyclic right shift of the input pattern sequence means that the input pattern sequence is shifted right by 1 bit, the last element before shifting the input pattern sequence is used as the first element after shifting, the shifted input pattern sequence replaces the input pattern sequence before shifting, and the above process is repeated until the input pattern sequence is shifted right by 2 bits N After the bits, a preliminary sample matrix is obtained.
4. The method according to claim 1, wherein the probability combination in step 4.2 refers to a selection of target voltage differences that are not repeated in each probability density vector; searching the voltage difference value which is the same as the target voltage in the rest voltage difference values of the probability density vectors, adding the probability value which corresponds to the voltage difference value which is the same as the target voltage to the probability value of the target voltage, and deleting the voltage difference value which is the same as the target voltage and the corresponding probability value in the probability density vectors.
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