CN117240427A - TIADC system time skew error calibration method based on AGA algorithm - Google Patents

Abstract

The invention belongs to the technical field of signal sampling and processing, and specifically relates to a TIADC system time skew error calibration method based on the AGA algorithm. The invention includes: S1: Evaluate the impact of time skew on the performance of the TIADC system; S2: Randomly select a group of time skew τ _i and the ratio r of the sampling period T _S as the chromosomes in the population; S3: Calculate the adaptation of the chromosomes in the population value to promote the crossover and mutation of chromosomes; S4: Select the excellent chromosomes in the population for reproduction and inherit their excellent genes; S5: Exchange the genetic information of the chromosomes in the population to obtain better chromosomes; S6: According to the fitness value of the chromosomes Adaptively adjust the mutation probability; S7: Find the optimal chromosome in the population; S8: Calibrate the channel using a variable delay line. The method of the present invention has fast detection speed for time skew, high estimation accuracy and calibration accuracy, and also has good calibration effect when the input signal is close to the Nyquist frequency.

Description

TIADC system time skew error calibration method based on AGA algorithm

Technical field

The invention belongs to the technical field of signal sampling and processing, and specifically relates to a TIADC system time skew error calibration method based on an AGA algorithm.

Background technique

Many applications of modern communication technology, such as radar communications, oscilloscopes, etc., require high-speed and high-precision analog-to-digital converters (ADCs). Due to the mutual constraints between accuracy and sampling rate, it is difficult for a single ADC to meet high accuracy and high sampling rate at the same time. The emergence of time-sharing alternating sampling technology solves this problem. This technology uses multiple high-precision ADCs to cyclically alternate sampling to achieve high accuracy and high sampling rate at the same time. These ADCs form a time-sharing alternating analog-to-digital converter (TIADC). )system.

However, due to the non-ideal characteristics of the circuit and the mismatch characteristics between different TIADC channels, additional errors will be caused, resulting in a degradation of the performance of the TIADC system. Therefore, in order to better play the role of TIADC, it is of great significance to study how to calibrate various mismatch errors in the TIADC system and improve the overall performance of the TIADC system.

Channel mismatch can be divided into offset mismatch, gain mismatch and time mismatch. The calibration of offset mismatch and gain mismatch is relatively simple, while the calibration of time offset mismatch is more difficult, and calibration methods exist. Many limitations and flaws. Document Z.Lu, 4, doi:10.1109/ASICON52560.2021.9620473. Use the cross-correlation between channel outputs to estimate the time skew of the sub-ADC, and use the delay line for calibration. This method has low complexity, but this method relies too much on the statistics of the input signal. Characteristics,In practice, the amplitude, bandwidth, and statistical,characteristics of the input change over time. Document M.V.N.Chakravarthi and C.M.Bhuma, "Detection and Correction ofSampling-Time-Errors in an N-ChannelTime-Interleaved ADC using Genetic Algorithm," 201714th IEEE India Council International Conference (INDICON), 2017, pp.1-6, doi: 10.1109/INDICON.2017.8487561. A genetic algorithm is used to detect the time skew of the sub-ADC, and calibration is achieved through a fractional delay filter. The disadvantage is that this method requires the introduction of multiple reference channels to complete the time skew detection, hardware resources Consumption is large. Document Y.X.Zou andX.J.Xu, "Blind Timing Skew Estimation Using SourceSpectrum Sparsity in Time-Interleaved ADCs," in IEEE Transactions on Instrumentation and Measurement, vol.61, no.9, pp.2401-2412, Sept.2012, doi :10.1109/TIM.2012.2192337. The sparse characteristics of the input signal are used to estimate the time skew through the spectrum information of the channel output. This method uses the spectrum information of the sub-channel output to detect the time skew, so there is a problem of spectrum leakage. Most calibration methods have problems such as dependence on input signal characteristics, high hardware resource consumption, slow time skew estimation, and poor estimation accuracy.

Contents of the invention

The purpose of the present invention is: the present invention proposes a TIADC system time skew error calibration method based on the AGA algorithm, which solves the most difficult time skew problem in estimation and calibration in the TIADC system. In addition, the method proposed by the present invention has faster detection speed of time skew, higher estimation accuracy and calibration accuracy, and has good calibration effect when the input signal is close to the Nyquist frequency.

In order to achieve the above-mentioned object, the technical solutions adopted by the present invention are as follows:

The TIADC system time skew error calibration method based on the AGA algorithm includes the following steps:

S1: Evaluate time skew: evaluate the impact of time skew τ _i on TIADC system performance;

S2: Establish the initial population: Randomly select a group of time skew τ _i and the ratio r of the sampling period T _S as the chromosomes in the population, then multiply it by 1000 and convert it into a 10-digit binary number, increasing before the highest bit One binary bit represents the positive or negative of the time skew; the highest bit is 1, which means the time skew is leading, and 0, which is lagging;

S3: Calculate the fitness value of chromosomes in the population: select the average absolute difference between the channel output calibrated by the variable delay line and the output of adjacent channels as the fitness value function to promote the crossover and mutation of chromosomes;

S4: Chromosome selection: Use the exponential sorting selection algorithm as the selection strategy of AGA to select excellent chromosomes in the population for reproduction and inherit their excellent genes;

S5: Adaptive crossover: According to the crossover probability P _c, the genetic information of the chromosomes in the population is exchanged to obtain better chromosomes;

S6: Adaptive mutation: Adaptively adjust the mutation probability P _m according to the fitness value f of the chromosome, retain the excellent chromosomes, and use the multi-point mutation method to mutate the chromosomes to make the population more diverse;

S7: Find the optimal chromosome: find the chromosome with the smallest fitness value in the population;

S8: Calibration: After completing the time skew detection of the channel, use the variable delay line to calibrate the channel.

As a further preferred technical solution of the present invention, step S1 specifically includes the following steps:

S1.1: Use a sinusoidal signal as the input signal of the TIADC system. The expression of the sinusoidal signal is:

x(t)=sin(ω _in t)

Among them, ω _in is the frequency of the sinusoidal signal;

S1.2: The expression of the sinusoidal signal input in S1.1 after sampling by the TIADC system is:

Among them, M is the number of channels in the TIADC system, T _S is the sampling period of a single ADC in the TIADC system, and τ _i is the time skew of the i-th channel in the TIADC system;

S1.3: Perform Fourier transform FT on the expression of the input signal in S1.1 to obtain:

S1.4: Perform discrete Fourier transform DFT on the expression of the sinusoidal signal sampled by the TIADC system in S1.2 to obtain its expression in the frequency domain:

Among them, ω _S is the sampling frequency of the TIADC system;

S1.5: In step S1.4, the impact of time skew error in the frequency domain was obtained. In any M-channel TIADC system, the harmonic component caused by time skew error is located at:

S1.6: Time skew and spurious-free dynamic range SFDR are used to measure the performance of the TIADC system. The functional relationship between the two is:

As a further preferred technical solution of the present invention, step S3 specifically includes the following steps:

S3.1: For the TIADC system, select the average absolute difference between the channel output after variable delay line calibration and the adjacent channel output as the fitness value function:

F _i =|E(|x _{i_d} -x _ref1 |-|x _ref2 -x _{i_d} |)|

Among them, x _ref1 and x _ref2 are adjacent reference channels, and x _{i_d} is the channel output after being delayed by the variable delay line;

S3.2: Select two channels in the four-channel TIADC system as fitness value calculation objects. Assume that channel 0 is ideal and channel 1 only contains time skew. Establish |x ₁ -x ₀ | and |x ₂ -x ₁ |Relationship with time skew;

S3.3: In S3.2, x ₁ represents the sample value of channel 1, x ₀ represents the sample value of channel 0, and x ₂ represents the next sample value of channel 0. From a statistical point of view, when the number of samples is large, The average difference between |x ₁ -x ₀ | and |x ₂ -x ₁ | is proportional to the time skew. The relationship between the average difference and the time skew is:

E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]∝τ ₁

Among them, τ ₁ represents the time skew of a single ADC channel in the TIADC system;

S3.4: Expand the correlation function E[(x ₁ -x ₀ ) ² ] between the sampling value x ₁ of channel 1 and the sampling value x ₀ of channel 0 in S3.3 to get:

Among them, σ ² represents the average power;

S3.5: Expand the correlation function E[(x ₂ -x ₁ ) ² ] between the next sample value x ₂ of channel 0 and the sample value x ₁ of channel 1 in S3.3 to get:

S3.6: Subtract the expansion of the time skew function and the average power in S3.4 and S3.5 to get:

E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]＝-2R(T _S +τ ₁ )

+2R(T _S -τ ₁ )

S3.7: Based on the time skew obtained in S3.6 is usually small, and R(T _S ±τ ₁ ) can be approximately equal to R(T _S )±τ ₁ dR/dτ, convert the time skew obtained in step S3.6 The expression changes to:

S3.8: It can be seen from step S3.7 that the time skew is proportional to the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ]. When the time skew is calibrated , the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ] is close to 0; when the fitness value of the chromosome is smaller, the chromosome is better, and the time skew it represents is closer The actual time skew, and the larger the fitness value, the worse the chromosome, and the time skew it represents deviates further from the actual time skew.

Further, as a preferred technical solution of the present invention, step S4 specifically includes the following steps:

S4.1: Use the exponential sorting selection algorithm as the selection strategy of AGA, and assign the selection probability according to the ranking level; in step S3 time skew detection, the smaller the fitness value, the better the chromosome, and the descending order is based on the fitness value of the chromosome. Sort so that the chromosome with the largest fitness value is 1 and the chromosome with the smallest fitness value is N;

S4.2: Calculate the probability of being selected based on the sorting of chromosomes in step S4.1. The formula is as follows:

Among them, i represents the i-th chromosome, c is the set parameter, and its value must be between 0 and 1. The closer the value is to 1, the lower the "exponentiality" of the selection method;

S4.3: Cumulatively sum the probabilities of chromosomes according to the sequence of chromosomes, obtain the probability sum _i of the cumulative sum, and randomly generate a random number σ from 0 to 1;

S4.4: If the random number σ is greater than sum _i-1 and less than sum _i , then the i-th chromosome is selected.

Further, as a preferred technical solution of the present invention, step S5 specifically includes the following steps:

S5.1: The crossover operation can exchange the genetic information of chromosomes in the population, and better chromosomes will appear in the population after crossover; the execution of the crossover operation depends on the set crossover probability P _c . The larger the P _c , the more excellent chromosomes will be introduced. The faster the population, when the crossover probability P _c is too large, high-performance chromosomes will be discarded faster than selection can produce improvements;

S5.2: Use the adaptive crossover method, which generates crossover probability based on the fitness value of the chromosome. The formula is:

Among them, f _min is the minimum fitness value of the chromosome; f′ is the smaller fitness value of the two chromosomes to be crossed; f _mean is the average fitness value of the chromosome, thus ensuring that all chromosomes with fitness values greater than the average are Perform a crossover operation; set k ₁ and k ₃ to 1 to prevent falling into a local optimum during the optimal solution search process;

S5.3: Select a pair of chromosomes and calculate their crossover probability according to the crossover probability formula in S5.2. At the same time, a random number is randomly generated. If the random number is less than the crossover probability, a crossover operation is performed.

As a further preferred technical solution of the present invention, step S6 specifically includes the following steps:

S6.1: Adaptive mutation is used to solve the problem that the genetic algorithm becomes a pure random search algorithm when the mutation probability P _m is large, and the genetic algorithm may converge prematurely when P _m is small. The adaptive mutation formula is: :

Among them, k ₂ and k ₄ are set to 0.5 to prevent the AGA algorithm from falling into local optimum;

S6.2: After completing the calculation of mutation probability, use the multi-point mutation method to mutate the chromosome to make the population more diverse; this method randomly selects multiple mutation points to mutate the information at that point. If the If the information of the point is 1, it mutates to 0; if the information is 0, it mutates to 1.

As a further preferred technical solution of the present invention, step S7 specifically includes the following steps:

S7.1: According to step S3, find the chromosome with the smallest fitness value, and determine whether its fitness value meets the set condition F _best <F _set ;

S7.2: If the conditions in S7.1 are met, the time skew corresponding to the chromosome is the time skew of the i-th channel. If the condition is not met, return to step S4 and repeat subsequent steps until the condition is met. .

Further, as a preferred technical solution of the present invention, step S8 specifically includes the following steps:

S8.1: For a 4-channel TIADC system, use channel 0 as the reference channel, detect the time skew of channel 2 and calibrate it;

S8.2: Use channel 0 and channel 2 as reference channels, detect the time skew of channel 1 and channel 3 and calibrate them.

The TIADC system time skew error calibration method based on the AGA algorithm of the present invention adopts the above technical solution and has the following technical effects compared with the existing technology:

(1) The TIADC system time skew error calibration method proposed by the present invention based on the AGA algorithm adopts a fully digital estimation and calibration scheme, which is easy to implement.

(2) The present invention uses the adaptive genetic algorithm AGA to calibrate the time skew. Compared with the traditional LMS and GA algorithms, it solves the problems of large population size, low accuracy of time skew estimation, and time skew convergence. The problem of requiring a relatively large number of iterations; and the calibration method adopted in the present invention has a good calibration effect on input signals in almost the entire Nyquist band.

(3) The TIADC channel time skew calibration method proposed by the present invention is suitable for low-frequency input calibration of the 18-bit high-resolution TIADC system, further improving the scope of application.

(4) The algorithm of the present invention has low computational difficulty, can be extended to any M-channel TIADC system, and has broad application prospects.

Description of drawings

Figure 1 is a schematic diagram of the method steps of the present invention;

Figure 2 is the working principle diagram of the M-channel time-sharing alternating analog-to-digital converter;

Figure 3 is a schematic diagram showing the error caused by the time skew of a single ADC in the TIADC system in the time domain;

Figure 4 is a schematic diagram of using the AGA algorithm to detect time skew in each sub-ADC in the TIADC system in the present invention;

Figure 5 is a schematic diagram of fitness value calculation for the internal sub-ADC of the TIADC system in the present invention;

Figure 6(a) is a schematic diagram of multi-point crossover of two pairs of chromosomes in the present invention;

Figure 6(b) is a schematic diagram of multi-point mutation of two pairs of chromosomes in the present invention;

Figure 7 is a schematic diagram for calibrating the internal sub-ADC of the 4-channel TIADC system in the present invention;

Figure 8(a) is a comparison diagram of the convergence of time skew detection on channel 1 using the AGA algorithm in the present invention under different sizes of Fset;

Figure 8(b) is a comparison diagram of the convergence of time skew detection on channel 2 using the AGA algorithm in the present invention under different sizes of Fset;

Figure 8(c) is a comparison diagram of the convergence of time skew detection on channel 3 using the AGA algorithm in the present invention under different sizes of Fset;

Figure 9 is a comparison chart of the number of iterations of the three algorithms GA, LMS, and AGA in time skew detection;

Figure 10 is a performance comparison chart of the AGA algorithm, GA algorithm, and LMS algorithm after calibrating the time skew error of the same TIADC system;

Figure 11(a) is the corresponding output spectrum diagram of the four-channel TIADC system of the present invention before error calibration through the variable delay line;

Figure 11(b) is the corresponding output spectrum diagram of the four-channel TIADC system of the present invention after error calibration through a variable delay line;

Figure 12(a) is a comparison chart of the SNDR of the four-channel TIADC system of the present invention before and after error calibration through the variable delay line;

Figure 12(b) is a comparison chart of the SFDR of the four-channel TIADC system of the present invention before and after error calibration through the variable delay line;

Figure 12(c) is a comparison chart of the ENOB of the four-channel TIADC system of the present invention before and after error calibration through the variable delay line.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings for further explanation, so that those skilled in the art can have a deeper understanding of the present invention and be able to implement it. However, the following reference examples are only used to explain the present invention and do not serve as the basis for the present invention. restrictions.

Example 1

During specific implementation, as shown in Figure 1, the TIADC system time skew error calibration system and method based on the AGA algorithm includes: S1: Evaluate the impact of time skew on TIADC system performance; S2: Randomly select a set of time skew τ _i The ratio r to the sampling period T _S is used as the chromosome in the population; S3: Calculate the fitness value of the chromosome in the population to promote the crossover and mutation of the chromosome; S4: Select the excellent chromosomes in the population to reproduce and inherit its excellent genes; S5: Exchange the genetic information of chromosomes in the population to obtain better chromosomes; S6: Adaptively adjust the mutation probability according to the fitness value of the chromosome; S7: Find the optimal chromosome in the population; S8: Use variable delay lines to calibrate the channel.

As shown in Figure 2, time-sharing alternating sampling technology uses multiple high-precision ADCs to cyclically alternate sampling to achieve high accuracy and high sampling rate at the same time. Multiple sub-ADCs form a time-sharing alternating analog-to-digital converter (TIADC) system. .

As shown in Figure 3, due to the time skew mismatch of each sub-ADC within the TIADC system, the actual sampling time of the sampling clock circuit deviates from the ideal sampling time, which in turn causes errors in the sampling values. In Figure 3, τi is the i-th sub-ADC. time skew, Error is the sampling value deviation caused by time skew.

Figure 4 to Figure 7, the TIADC system time skew error calibration system and method based on the AGA algorithm of this embodiment specifically includes the following steps:

The TIADC system time skew error calibration system and method based on the AGA algorithm includes the following steps:

S1: Evaluate time skew: evaluate the impact of time skew τ _i on TIADC system performance;

S2: Establish the initial population: Randomly select a group of time skew τ _i and the ratio r of the sampling period T _S as the chromosomes in the population, then multiply it by 1000 and convert it into a 10-digit binary number, increasing before the highest bit One binary bit represents the positive or negative time skew;

The highest bit is 1, which represents the time skew leading, and 0, which represents lagging;

S3: Calculate the fitness value of chromosomes in the population: select the average absolute difference between the channel output calibrated by the variable delay line and the output of adjacent channels as the fitness value function to promote the crossover and mutation of chromosomes;

S4: Chromosome selection: Use the exponential sorting selection algorithm as the selection strategy of AGA to select excellent chromosomes in the population for reproduction and inherit their excellent genes;

S5: Adaptive crossover: According to the crossover probability P _c, the genetic information of the chromosomes in the population is exchanged to obtain better chromosomes;

S6: Adaptive mutation: Adaptively adjust the mutation probability P _m according to the fitness value f of the chromosome, retain the excellent chromosomes, and use the multi-point mutation method to mutate the chromosomes to make the population more diverse;

S7: Find the optimal chromosome: find the chromosome with the smallest fitness value in the population;

S8: Calibration: After completing the time skew detection of the channel, use the variable delay line to calibrate the channel.

Step S1 specifically includes the following steps:

S1.1: Use a sinusoidal signal as the input signal of the TIADC system. The expression of the sinusoidal signal is:

x(t)=sin(ω _in t)

Among them: ω _in is the frequency of the sinusoidal signal;

S1.2: The expression of the sinusoidal signal input in S1.1 after sampling by the TIADC system is:

Among them: M is the number of channels in the TIADC system, T _S is the sampling period of a single ADC in the TIADC system, τ _i is the time skew of the i-th channel in the TIADC system;

S1.3: Perform Fourier transform (FT) on the expression of the input signal in S1.1 to obtain:

S1.4: Perform discrete Fourier transform DFT on the expression of the sinusoidal signal sampled by the TIADC system in S1.2 to obtain its expression in the frequency domain:

Among them: ω _S is the sampling frequency of the TIADC system;

S1.5: In step S1.4, the impact of time skew error in the frequency domain was obtained. In any M-channel TIADC system, the harmonic component caused by time skew error is located at:

S1.6: Time skew and spurious-free dynamic range SFDR are used to measure the performance of the TIADC system. The functional relationship between the two is:

Step S3 specifically includes the following steps:

S3.1: For the TIADC system, select the average absolute difference between the channel output after variable delay line calibration and the adjacent channel output as the fitness value function:

F _i =|E(|x _{i_d} -x _ref1 |-|x _ref2 -x _{i_d} |)|

Among them: x _ref1 and x _ref2 are adjacent reference channels, and x _{i_d} is the channel output after being delayed by the variable delay line.

S3.2: Select two channels in the four-channel TIADC system as fitness value calculation objects. Assume that channel 0 is ideal and channel 1 only contains time skew. Establish |x ₁ -x ₀ | and |x ₂ -x ₁ |Relationship with time skew;

S3.3: In S3.2, x ₁ represents the sample value of channel 1, x ₀ represents the sample value of channel 0, and x ₂ represents the next sample value of channel 0. From a statistical point of view, when the number of samples is large, The average difference between |x ₁ -x ₀ | and |x ₂ -x ₁ | is proportional to the time skew. The relationship between the average difference and the time skew is:

E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]∝τ ₁

Among them: τ ₁ represents the time skew of a single ADC channel in the TIADC system;

S3.4: Expand the correlation function E[(x ₁ -x ₀ ) ² ] between the sampling value x ₁ of channel 1 and the sampling value x ₀ of channel 0 in S3.3 to get:

Among them: σ ² represents the average power;

S3.5: Expand the correlation function E[(x ₂ -x ₁ ) ² ] between the next sample value x ₂ of channel 0 and the sample value x ₁ of channel 1 in S3.3 to get:

S3.6: Subtract the expansion of the time skew function and the average power in S3.4 and S3.5 to get:

E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]＝-2R(T _S +τ ₁ )

+2R(T _S -τ ₁ )

S3.7: Based on the time skew obtained in S3.6 is usually small, and R(T _S ±τ ₁ ) can be approximately equal to R(T _S )±τ ₁ dR/dτ, convert the time skew obtained in step S3.6 The expression changes to:

S3.8: It can be seen from step S3.7 that the time skew is proportional to the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ]. When the time skew is calibrated , the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ] is close to 0; the smaller the fitness value of the chromosome, the better the chromosome, and the closer the time skew it represents The actual time skew, and the larger the fitness value, the worse the chromosome, and the time skew it represents deviates further from the actual time skew.

Step S4 specifically includes the following steps:

S4.1: Use the exponential sorting selection algorithm as the selection strategy of AGA, and assign the selection probability according to the ranking level; in step S3 time skew detection, the smaller the fitness value, the better the chromosome, and the descending order is based on the fitness value of the chromosome. Sort so that the chromosome with the largest fitness value is 1 and the chromosome with the smallest fitness value is N;

S4.2: Calculate the probability of being selected based on the sorting of chromosomes in step S4.1. The formula is as follows:

Among them: i represents the i-th chromosome, c is the set parameter, and its value must be between 0 and 1. The closer the value is to 1, the lower the "exponentiality" of the selection method;

S4.3: Cumulatively sum the probabilities of chromosomes according to the sequence of chromosomes, obtain the probability sum _i of the cumulative sum, and randomly generate a random number σ from 0 to 1;

S4.4: If the random number σ is greater than sum _i-1 and less than sum _i , then the i-th chromosome is selected.

Step S5 specifically includes the following steps:

S5.1: The crossover operation can exchange the genetic information of chromosomes in the population, and better chromosomes will appear in the population after crossover; the execution of the crossover operation depends on the set crossover probability P _c . The larger the P _c , the more excellent chromosomes will be introduced. The faster the population, but if the crossover probability P _c is too large, high-performance chromosomes will be discarded faster than selection can produce improvements;

S5.2: The TIADC system time skew error calibration system based on the AGA algorithm uses the adaptive crossover method to solve the problems in S5.1. This method generates crossover probability based on the fitness value of the chromosome. The formula is:

Among them: f _min is the minimum fitness value of the chromosome; f′ is the smaller fitness value of the two chromosomes to be crossed; f _mean is the average fitness value of the chromosome, so as to ensure that all chromosomes with fitness values greater than the average are Perform a crossover operation; set k ₁ and k ₃ to 1 to prevent falling into a local optimum during the optimal solution search process;

S5.3: Select a pair of chromosomes and calculate their crossover probability according to the crossover probability formula in S5.2, and randomly generate a random number. If the random number is less than the crossover probability, perform a crossover operation;

Step S6 specifically includes the following steps:

S6.1: Adaptive mutation is used to solve the problem that the genetic algorithm becomes a pure random search algorithm when the mutation probability P _m is large, and the genetic algorithm may converge prematurely when P _m is small. The adaptive mutation formula is: :

Among them: set k ₂ and k ₄ to 0.5 to prevent the AGA algorithm from falling into local optimal;

S6.2: After completing the calculation of mutation probability, use the multi-point mutation method to mutate the chromosome to make the population more diverse; this method randomly selects multiple mutation points to mutate the information at that point. If the If the information of the point is 1, it mutates to 0; if the information is 0, it mutates to 1.

Step S7 specifically includes the following steps:

S7.1: According to step S3, find the chromosome with the smallest fitness value, and determine whether its fitness value meets the set condition F _best <F _set ;

S7.2: If the conditions in S7.1 are met, the time skew corresponding to the chromosome is the time skew of the i-th channel. If the condition is not met, return to step S4 and repeat subsequent steps until the condition is met. ;

Step S8 specifically includes the following steps:

S8.1: For a 4-channel TIADC system, use channel 0 as the reference channel, detect the time skew of channel 2 and calibrate it;

S8.2: Use channel 0 and channel 2 as reference channels, detect the time skew of channel 1 and channel 3 and calibrate them.

Example 2

In order to verify that the present invention can realize the estimation and calibration of the time skew error of the 18-bit high-resolution TIADC system, the following is a verification using a four-channel TIADC system model as an example, and a detailed description is given in combination with the TIADC system and simulation results.

Verification steps include:

First, let’s explain the TIADC system for this verification. This verification example takes a four-channel TIADC simulation system as an example. The overall sampling rate of this system is 1GS/s and it is composed of four identical 18-bit single-channel ADCs. In order to facilitate the analysis of time skew error, it is assumed that the TIADC system is not affected by offset mismatch error and gain mismatch error, and then configure the time skew of each channel of the TIADC system. It is assumed that channel 0 has no time skew, and channel 0 has no time skew. 1. The time skew of channel 2 and channel 3 are τ ₁ =2e-11, τ ₂ =-5e-11, and τ ₃ =1e-11 respectively. This verification example uses a sinusoidal signal with a frequency of 47.71MHz as the input signal, and the parameter c of the AGA's exponential sorting selection method is set to 0.9.

Figure 8 shows the convergence of AGA’s time skew detection for each channel under different sizes of F _set in this verification example. t _c is the convergence time of time skew detection. The smaller the F set value, the better the AGA’s time skew detection. The higher the accuracy of the skew estimation, but the number of iterations of the convergence time increases. Taking comprehensive considerations into account, this verification example sets Fset to 2.6e-4 to obtain an approximate estimate of the actual time skew. It can be seen from Figure 8(a), Figure 8(b), and Figure 8(c) that the time skew of channel 1 converges to 0.02T _S after 10 iterations, and the time skew of channel 2 and channel 3 is estimated after 10 iterations. It converges to -0.05T _S and 0.01T _S after 10 and 9 iterations respectively.

Figure 9 shows a comparison chart of the three algorithms GA, LMS, and AGA in terms of time skew detection. It can be seen from the figure that under the premise of the same time skew error, the number of iterations of the AGA algorithm is 10, and that of the GA algorithm is 10. The number of iterations of the and LMS algorithms are 29 and 117 respectively. It can be seen that the calibration method proposed by the present invention has a faster detection speed of time skew.

Figure 10 is a performance comparison chart of the three methods of LMS, GA, and AGA algorithms under the same time skew error. As can be seen from the figure, the time skew error detected by the AGA algorithm for the four-channel TIADC system in this verification example is 0.02, which is more accurate than the 0.0199 and 0.0210 detected by the LMS algorithm and GA algorithm; the number of iterations and convergence time of the AGA algorithm Compared with the traditional LMS and GA algorithms, there are significant improvements; the number of samples that the LMS, GA, and AGA algorithms need to collect are 42.5K, 72.5K, and 25K respectively. It can be seen that the AGA algorithm needs to collect fewer samples; AGA The running time of the algorithm is 0.13092 seconds, which is faster than the detection speed of the LMS algorithm and GA algorithm;

Figure 11(a) shows the frequency domain diagram of the TIADC model with time skew error in this verification example, in which the input signal produces a peak spectrum at 47.71MHz, and the remaining peaks are the noise spectrum generated by the time skew error; Figure 11( b) shows the output spectrum of the TIADC system after calibrating the variable delay line. The glitches caused by the time skew error are effectively suppressed, the signal-to-noise ratio is increased from 40.7dB to 106.6dB, and the effective number of bits is increased from 6.4 bits. To 17.4bit.

Figure 12 shows the correlation between SNDR, SFDR, ENOB and the input signal frequency before and after calibration. It can be seen that the SNDR, SFDR, and ENOB of the TIADC system have been greatly improved after the TIADC system time skew error calibration system based on the AGA algorithm. , and this calibration method has good calibration effects on input signals in almost the entire Nyquist band.

Adopting the above technical solution, the present invention proposes a fully digital calibration method for the time skew error of the TIADC system, using the AGA algorithm to calibrate the time skew error of the TIADC system, and is suitable for any M-channel TIADC system.

The TIADC system mismatch error calibration method proposed by the present invention is suitable for calibrating the time skew error in the channel, and significantly improves the dynamic performance of TIADC such as SNR and SFDR. The invention has a simple structural design, low algorithm operation difficulty, and is independent of the number of channels. limitations and broad application prospects.

The above-mentioned specific embodiments further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above-mentioned are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (8)

1. The TIADC system time skew error calibration method based on the AGA algorithm is characterized by including the following steps: S1: Evaluate time skew: evaluate the impact of time skew τ _i on TIADC system performance; S2: Establish the initial population: Randomly select a group of time skew τ _i and the ratio r of the sampling period T _S as the chromosomes in the population, then multiply it by 1000 and convert it into a 10-digit binary number, increasing before the highest bit One binary bit represents the positive or negative of the time skew; the highest bit is 1, which means the time skew is leading, and 0, which is lagging; S3: Calculate the fitness value of chromosomes in the population: select the average absolute difference between the channel output calibrated by the variable delay line and the output of adjacent channels as the fitness value function to promote the crossover and mutation of chromosomes; S4: Chromosome selection: Use the exponential sorting selection algorithm as the selection strategy of AGA to select excellent chromosomes in the population for reproduction and inherit their excellent genes; S5: Adaptive crossover: According to the crossover probability P _c, the genetic information of the chromosomes in the population is exchanged to obtain better chromosomes; S6: Adaptive mutation: Adaptively adjust the mutation probability P _m according to the fitness value f of the chromosome, retain the excellent chromosomes, and use the multi-point mutation method to mutate the chromosomes to make the population more diverse; S7: Find the optimal chromosome: find the chromosome with the smallest fitness value in the population; S8: Calibration: After completing the time skew detection of the channel, use the variable delay line to calibrate the channel. 2. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S1 specifically includes the following steps: S1.1: Use a sinusoidal signal as the input signal of the TIADC system. The expression of the sinusoidal signal is: x(t)=sin(ω _in t) Among them, ω _in is the frequency of the sinusoidal signal; S1.2: The expression of the sinusoidal signal input in S1.1 after sampling by the TIADC system is: Among them, M is the number of channels in the TIADC system, T _S is the sampling period of a single ADC in the TIADC system, and τ _i is the time skew of the i-th channel in the TIADC system; S1.3: Perform Fourier transform FT on the expression of the input signal in S1.1 to obtain: S1.4: Perform discrete Fourier transform DFT on the expression of the sinusoidal signal sampled by the TIADC system in S1.2 to obtain its expression in the frequency domain: Among them, ω _S is the sampling frequency of the TIADC system; S1.5: In step S1.4, the impact of time skew error in the frequency domain was obtained. In any M-channel TIADC system, the harmonic component caused by time skew error is located at: S1.6: Time skew and spurious-free dynamic range SFDR are used to measure the performance of the TIADC system. The functional relationship between the two is: 3. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S3 specifically includes the following steps: S3.1: For the TIADC system, select the average absolute difference between the channel output after variable delay line calibration and the adjacent channel output as the fitness value function: F _i =|E(|x _{i_d} -x _ref1 |-|x _ref2 -x _{i_d} |)| Among them, x _ref1 and x _ref2 are adjacent reference channels, and x _{i_d} is the channel output after being delayed by the variable delay line; S3.2: Select two channels in the four-channel TIADC system as fitness value calculation objects. Assume that channel 0 is ideal and channel 1 only contains time skew. Establish |x ₁ -x ₀ | and |x ₂ -x ₁ |Relationship with time skew; S3.3: In S3.2, x ₁ represents the sample value of channel 1, x ₀ represents the sample value of channel 0, and x ₂ represents the next sample value of channel 0. From a statistical point of view, when the number of samples is large, The average difference between |x ₁ -x ₀ | and |x ₂ -x ₁ | is proportional to the time skew. The relationship between the average difference and the time skew is: E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]∝τ ₁ Among them, τ ₁ represents the time skew of a single ADC channel in the TIADC system; S3.4: Expand the correlation function E[(x ₁ -x ₀ ) ² ] between the sampling value x ₁ of channel 1 and the sampling value x ₀ of channel 0 in S3.3 to get: Among them, σ ² represents the average power; S3.5: Expand the correlation function E[(x ₂ -x ₁ ) ² ] between the next sample value x ₂ of channel 0 and the sample value x ₁ of channel 1 in S3.3 to get: S3.6: Subtract the expansion of the time skew function and the average power in S3.4 and S3.5 to get: E[(x ₁ -x ₀ ) ² ]-E[(x ₂ -x ₁ ) ² ]＝-2R(T _S +τ ₁ ) +2R(T _S -τ ₁ ) S3.7: Based on the time skew obtained in S3.6 is usually small, and R(T _S ±τ ₁ ) can be approximately equal to R(T _S )±τ ₁ dR/dτ, convert the time skew obtained in step S3.6 The expression changes to: S3.8: It can be seen from step S3.7 that the time skew is proportional to the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ]. When the time skew is calibrated , the difference between E[(x ₁ -x ₀ ) ² ] and E[(x ₂ -x ₁ ) ² ] is close to 0; when the fitness value of the chromosome is smaller, the chromosome is better, and the time skew it represents is closer The actual time skew, and the larger the fitness value, the worse the chromosome, and the time skew it represents deviates further from the actual time skew. 4. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S4 specifically includes the following steps: S4.1: Use the exponential sorting selection algorithm as the selection strategy of AGA, and assign the selection probability according to the ranking level; in step S3 time skew detection, the smaller the fitness value, the better the chromosome, and the descending order is based on the fitness value of the chromosome. Sort so that the chromosome with the largest fitness value is 1 and the chromosome with the smallest fitness value is N; S4.2: Calculate the probability of being selected based on the sorting of chromosomes in step S4.1. The formula is as follows: Among them, i represents the i-th chromosome, c is the set parameter, and its value must be between 0 and 1. The closer the value is to 1, the lower the "exponentiality" of the selection method; S4.3: Cumulatively sum the probabilities of chromosomes according to the sequence of chromosomes, obtain the probability sum _i of the cumulative sum, and randomly generate a random number σ from 0 to 1; S4.4: If the random number σ is greater than sum _i-1 and less than sum _i , then the i-th chromosome is selected. 5. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S5 specifically includes the following steps: S5.1: The crossover operation can exchange the genetic information of chromosomes in the population, and better chromosomes will appear in the population after crossover; the execution of the crossover operation depends on the set crossover probability P _c . The larger the P _c , the more excellent chromosomes will be introduced. The faster the population, when the crossover probability P _c is too large, high-performance chromosomes will be discarded faster than selection can produce improvements; S5.2: Use the adaptive crossover method, which generates crossover probability based on the fitness value of the chromosome. The formula is: Among them, f _min is the minimum fitness value of the chromosome; f′ is the smaller fitness value of the two chromosomes to be crossed; f _mean is the average fitness value of the chromosome, thus ensuring that all chromosomes with fitness values greater than the average are Perform a crossover operation; set k ₁ and k ₃ to 1 to prevent falling into a local optimum during the optimal solution search process; S5.3: Select a pair of chromosomes and calculate their crossover probability according to the crossover probability formula in S5.2. At the same time, a random number is randomly generated. If the random number is less than the crossover probability, a crossover operation is performed. 6. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S6 specifically includes the following steps: S6.1: Adaptive mutation is used to solve the problem that the genetic algorithm becomes a pure random search algorithm when the mutation probability P _m is large, and the genetic algorithm may converge prematurely when P _m is small. The adaptive mutation formula is: : Among them, k ₂ and k ₄ are set to 0.5 to prevent the AGA algorithm from falling into local optimum; S6.2: After completing the calculation of mutation probability, use the multi-point mutation method to mutate the chromosome to make the population more diverse; this method randomly selects multiple mutation points to mutate the information at that point. If the If the information of the point is 1, it mutates to 0; if the information is 0, it mutates to 1. 7. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S7 specifically includes the following steps: S7.1: According to step S3, find the chromosome with the smallest fitness value, and determine whether its fitness value meets the set condition F _best <F _set ; S7.2: If the conditions in S7.1 are met, the time skew corresponding to the chromosome is the time skew of the i-th channel. If the condition is not met, return to step S4 and repeat subsequent steps until the condition is met. . 8. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, characterized in that the step S8 specifically includes the following steps: S8.1: For a 4-channel TIADC system, use channel 0 as the reference channel, detect the time skew of channel 2 and calibrate it; S8.2: Use channel 0 and channel 2 as reference channels, detect the time skew of channel 1 and channel 3 and calibrate them.