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 particularly relates to a time skew error calibration method of a TIADC system based on an AGA algorithm. The invention comprises the following steps: s1: evaluating the effect of time skew on TIADC system performance; s2: randomly selecting a set of time skews τ _i And sampling period T _S The ratio r is taken as the chromosome in the population; s3: calculating fitness values of chromosomes in the population to promote crossover and mutation of the chromosomes; s4: selecting excellent chromosomes in the population for reproduction and inheriting excellent genes thereof; s5: exchanging chromosome genetic information in the population to obtain more excellent chromosomes; s6: self-adaptively adjusting mutation probability according to the adaptive value of the chromosome; s7: searching out an optimal chromosome in the population; s8: the channels are calibrated using a variable delay line. The method has higher detection speed for time deflection, higher estimation precision and calibration precision, and when the input signal approaches the Nyquist frequencyGood calibration results are also obtained.

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 particularly relates to a time skew error calibration method of a TIADC system based on an AGA algorithm.

Background

Many applications of modern communication technologies, such as radar communication, oscilloscopes, etc., require high-speed and high-precision analog-to-digital converters (ADCs), and it is difficult for a single ADC to meet both high precision and high sampling rate due to the constraints between precision and sampling rate. The advent of time-sharing interleaved sampling techniques that utilize multiple high-precision ADCs that make up a time-sharing interleaved analog-to-digital converter (TIADC) system to cyclically interleaved samples to achieve both high precision and high sampling rate.

However, due to non-ideal characteristics of the circuit and mismatch between the different channels of the TIADC, additional errors are created, resulting in degradation of the performance of the TIADC system. Therefore, in order to better play the role of TIADC, it is important to research how to calibrate various mismatch errors in the TIADC system and improve the overall performance of the TIADC system.

Channel mismatch can be classified into bias mismatch, gain mismatch and time mismatch, wherein calibration for bias mismatch and gain mismatch is simpler, and calibration for time bias mismatch is more difficult, and the calibration method has many limitations and drawbacks. Document Z.Lu, X.Peng, Z.Ren, H.Tang and b.guo, "A Timing Mismatch Background Calibration Technique with High-Precision Skew Estimation,"2021IEEE 14th International Conference on ASIC (ASICON), 2021, pp.1-4, doi:10.1109/ASICON52560.2021.9620473. Using cross-correlation between channel outputs to estimate the time skew of sub-ADCs and using delay lines for calibration, the method is less complex, but the method is too dependent on the statistics of the input signal, in practice the amplitude, bandwidth and statistics of the input will vary over time. Document m.v. chakravarthi and c.m. bhuma, "Detection and Correction ofSampling-Time-error in an N-Channel Time-Interleaved ADC using Genetic Algorithm,"201714th IEEE India Council International Conference (indication), 2017, pp.1-6, doi: 10.1109/indication.2017.8487561. A genetic algorithm is used to detect the Time skew of the sub-ADC, and calibration is implemented by a fractional delay filter, which has the disadvantage that the method needs to introduce multiple reference channels to complete the Time skew detection, and the hardware resource consumption is large. Literature y.x.zou and x.j.xu, "Blind Timing Skew Estimation Using Source Spectrum 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.2012.219237. The sparse characteristics of the input signal are used and the time skew is estimated from the spectral information output by the channel, which has a problem of spectral leakage because the spectral information output by the sub-channels is used to detect the time skew. Most calibration methods have the problems of dependence on input signal characteristics, high hardware resource consumption, low time skew estimation speed, poor estimation accuracy and the like.

Disclosure of Invention

The invention aims at: the invention provides a time deflection error calibration method of a TIADC system based on an AGA algorithm, which solves the problem of the time deflection which is most difficult to estimate and calibrate in the TIADC system. In addition, the method provided by the invention has the advantages of higher detection speed of time deflection, higher estimation precision and calibration precision, and good calibration effect when the input signal approaches the Nyquist frequency.

In order to achieve the aim of the invention, the technical scheme adopted by the invention is as follows:

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

s1: time skew was evaluated: evaluating time skew τ _i Influence on TIADC system performance;

s2: establishing an initial population: randomly selecting a set of time skews τ _i And sampling period T _S The ratio r is taken as the chromosome in the population, and then multiplied by 1000 and transformedFor 10-bit binary numbers, adding one bit binary bit before the highest bit to represent the positive and negative of time skew; the time skew represented by the highest bit of 1 is the advanced case, and 0 represents the lagged case;

s3: calculating fitness values of chromosomes in the population: selecting the average absolute difference between the channel output calibrated by the variable delay line and the adjacent channel output as an adaptive value function, and pushing the intersection and variation of the chromosome;

s4: chromosome selection: using an exponential ranking selection algorithm as a selection strategy of AGA, selecting excellent chromosomes in the population for reproduction and inheriting excellent genes thereof;

s5: adaptive crossover: according to the crossover probability P _c Exchanging the genetic information of the chromosomes in the population to obtain more excellent chromosomes;

s6: adaptive variation: adaptive adjustment of mutation probability P according to chromosome adaptation value f _m The excellent chromosome is reserved, and meanwhile, the chromosome is mutated by adopting a multipoint mutation method, so that the population is more diversified;

s7: searching for optimal chromosomes: finding out the chromosome with the minimum adaptation value in the population;

s8: and (3) calibrating: after the time skew detection of the channel is completed, the channel is calibrated by using a variable delay line.

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

s1.1: the sine signal is used as an input signal of a TIADC system, and the expression of the sine signal is as follows:

x(t)＝sin(ω _in t)

wherein omega _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:

wherein M is TIADC systemNumber of channels, T _S For the sampling period, τ, of a single ADC within a TIADC system _i Time skew for the ith channel in the TIADC system;

s1.3: fourier transform FT is performed on the expression of the input signal in S1.1 to obtain:

s1.4: performing Discrete Fourier Transform (DFT) on the expression of the sinusoidal signal sampled by the TIADC system in the S1.2 to obtain the expression of the sinusoidal signal in a frequency domain, wherein the expression is as follows:

wherein omega _S Sampling frequency of the TIADC system;

s1.5: in step S1.4, the influence of the time skew error in the frequency domain is obtained, and in any M-channel TIADC system, the harmonic component caused by the time skew error is located:

s1.6: the performance of the TIADC system is measured by adopting time skew and spurious-free dynamic range SFDR, and the function relationship established for the time skew and spurious-free dynamic range SFDR is:

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

s3.1: for a TIADC system, selecting the average absolute difference between the channel output after the calibration of the variable delay line and the adjacent channel output as an adaptive value function:

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

wherein x is _ref1 And x _ref2 For adjacent reference channels, x _{i_d} Is output by the channel delayed by the variable delay line;

s3.2: two channels in a four-channel TIADC system are selected as adaptive value calculation objects, and assuming that a channel 0 is ideal, the channel 1 only contains time skew, and |x is established ₁ -x ₀ I and I x ₂ -x ₁ Relationship of i to time skew;

s3.3: in S3.2 x ₁ Representing the sample value, x, of channel 1 ₀ Represents the sample value of channel 0, x ₂ Representing the next sample value of channel 0, from a statistical point of view, |x, when the number of samples is large ₁ -x ₀ I and I x ₂ -x ₁ The average difference of i is proportional to time skew, and the average difference is related to time skew as:

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

wherein τ ₁ Representing the amount of time skew of a single ADC channel within a TIADC system;

s3.4: sample value x of channel 1 in S3.3 ₁ Sample value x with channel 0 ₀ The correlation function E [ (x) ₁ -x ₀ ) ² ]And (3) unfolding to obtain:

wherein sigma ² Representing the average power;

s3.5: the next sample value x of channel 0 in S3.3 ₂ Sample value x of channel 1 ₁ The correlation function E [ (x) ₂ -x ₁ ) ² ]And (3) unfolding to obtain:

s3.6: subtracting the expansion including the time skew function from the average power in S3.4 and S3.5 yields:

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

+2R(T _S -τ ₁ )

s3.7: the time skew based on that obtained in S3.6 is typically small, and R (T _S ±τ ₁ ) Can be approximately equal to R (T _S )±τ ₁ dR/dτ, the expression obtained in step S3.6 is changed to:

s3.8: from step S3.7, the time skew and E [ (x) can be seen ₁ -x ₀ ) ² ]And E [ (x) ₂ -x ₁ ) ² ]Is proportional to the difference in (x) after the time skew is calibrated ₁ -x ₀ ) ² ]With E [ (x) ₂ -x ₁ ) ² ]Is close to 0; the smaller the fitness value of the chromosome, the more excellent the chromosome, the more closely the time skew it represents to the actual time skew, and the worse the fitness value, the more the time skew it represents to the actual time skew.

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

s4.1: taking an exponential ranking selection algorithm as a selection strategy of AGA, and distributing selection probability according to ranking; in the step S3 of time skew detection, the smaller the adaptation value is, the more excellent the chromosome is, the descending order is ordered according to the adaptation value of the chromosome, so that the maximum adaptation value of the chromosome is 1, and the minimum adaptation value is N;

s4.2: calculating the probability of being selected according to the sorting of the chromosomes in the step S4.1, wherein the formula is as follows:

where i denotes the ith chromosome, c is a set parameter, the value of which must be between 0 and 1, the closer the value is to 1, the lower the "exponential" of the selection method;

s4.3: accumulating the probabilities of the chromosomes according to the chromosome sequence to obtain the accumulated probability sum _i And randomly generating a random number sigma of 0 to 1;

s4.4: if the random number sigma is greater than sum _i-1 And is smaller than sum _i The ith chromosome is selected.

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

s5.1: the crossing operation can enable the genetic information of the chromosomes in the population to be exchanged, and more excellent chromosomes appear in the crossed population; the crossover operation is performed depending on the set crossover probability P _c ，P _c The larger the new chromosome is, the faster the new chromosome is introduced into the population, when the crossover probability P is _c Too large, it occurs that high performance chromosomes are discarded faster than the selection yields improvement;

s5.2: the adaptive crossing method is adopted, and the method generates the crossing probability according to the adaptive value of the chromosome, and the formula is as follows:

wherein f _min Is the minimum of the chromosome fitness values; f' is the smaller fitness value of the two chromosomes to be crossed; f (f) _mean The average fitness value of the chromosomes is ensured, so that all chromosomes with fitness values larger than the average value are crossed; will k ₁ And k ₃ Setting to 1 to prevent the situation of falling into local optimum in the optimum solution searching process;

s5.3: selecting a pair of chromosomes, calculating the crossover probability according to the crossover probability formula in S5.2, randomly generating a random number, and performing crossover operation if the random number is smaller than the crossover probability.

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

s6.1: solving variation probability P by adaptive variation _m The larger resulting genetic algorithm becomes a pure random search algorithm, and P _m Less phenomena that might cause premature convergence of the genetic algorithm, the adaptive variation formula is:

wherein k is ₂ And k ₄ Setting to 0.5 to prevent the AGA algorithm from falling into local optimum;

s6.2: after the calculation of the mutation probability is completed, a multi-point mutation method is adopted to mutate the chromosome, so that the population is more diversified; the method comprises the steps of randomly selecting a plurality of mutation points, mutating information of the points, wherein if the information of the points is 1, the mutation points are 0, and if the information of the points is 0, the mutation points are 1.

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

s7.1: according to step S3, find the chromosome with the minimum adaptation value, judge whether its adaptation value meets the set condition F _best <F _set ；

S7.2: if the condition in S7.1 is satisfied, the time skew corresponding to the chromosome is the time skew of the ith channel, and if the condition is not satisfied, returning to step S4 and repeating the subsequent steps until the condition is satisfied.

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

s8.1: for a 4-channel TIADC system, channel 0 is used as a reference channel, and the time skew of channel 2 is detected and calibrated;

s8.2: using channel 0 and channel 2 as reference channels, the time skew of channel 1 and channel 3 is detected and calibrated.

Compared with the prior art, the TIADC system time deflection error calibration method based on the AGA algorithm has the following technical effects:

(1) The TIADC system time deflection error calibration method based on the AGA algorithm adopts a full-digital estimation and calibration scheme, and is easy to realize.

(2) Compared with the traditional LMS and GA algorithms, the method solves the problems of large population scale, low estimation accuracy of time deflection and relatively more iteration times required by time deflection convergence; the calibration method adopted by the invention has good calibration effect on the input signals in the almost entire Nyquist frequency band.

(3) The TIADC channel time skew calibration method provided by the invention is suitable for low-frequency input calibration of an 18bit high-resolution TIADC system, and further improves the application range.

(4) The algorithm of the invention has low operation difficulty, can be popularized to any M-channel TIADC system, and has wide application prospect.

Drawings

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

FIG. 2 is a schematic diagram of the operation of an M-channel time-sharing alternating analog-to-digital converter;

FIG. 3 is a schematic diagram of a time skew of a single ADC within a TIADC system causing errors in the time domain;

FIG. 4 is a schematic diagram of the time skew detection of each sub-ADC in a TIADC system using an AGA algorithm in the present invention;

FIG. 5 is a schematic diagram of adaptive value calculation for sub-ADCs in a TIADC system according to the present invention;

FIG. 6 (a) is a schematic diagram of the multi-point crossing of two pairs of chromosomes according to the present invention;

FIG. 6 (b) is a schematic diagram of the multi-point mutation of two pairs of chromosomes according to the present invention;

FIG. 7 is a schematic diagram of the calibration of a sub-ADC within a 4-channel TIADC system according to the present invention;

FIG. 8 (a) is a graph comparing convergence of time skew detection of channel 1 with Fset of different sizes using AGA algorithm in the present invention;

FIG. 8 (b) is a graph comparing convergence of time skew detection of channel 2 using AGA algorithm under different size Fset;

FIG. 8 (c) is a graph comparing convergence of time skew detection of channel 3 with Fset of different sizes using AGA algorithm in the present invention;

FIG. 9 is a graph of iteration count versus time skew detection for three algorithms GA, LMS, AGA;

FIG. 10 is a graph showing the performance of the AGA algorithm, the GA algorithm, and the LMS algorithm after time skew error calibration for the same TIADC system;

FIG. 11 (a) is a graph of the output spectrum of the four-channel TIADC system of the present invention before error calibration via a variable delay line;

FIG. 11 (b) is a graph of the output spectrum of the four-channel TIADC system according to the present invention after error calibration by the variable delay line;

FIG. 12 (a) is a graph showing SNDR comparison of a four-channel TIADC system of the present invention before and after error calibration via a variable delay line;

FIG. 12 (b) is a graph showing the SFDR comparison of the four channel TIADC system of the present invention before and after error calibration via the variable delay line;

fig. 12 (c) is a diagram showing the comparison of ENOB corresponding to the four-channel TIADC system of the present invention before and after error calibration via the variable delay line.

Detailed Description

The invention is further explained in the following detailed description with reference to the drawings so that those skilled in the art can more fully understand the invention and can practice it, but the invention is explained below by way of example only and not by way of limitation.

Example 1

In specific implementation, as shown in fig. 1, the TIADC system time skew error calibration system and method based on the AGA algorithm include: s1: evaluating the effect of time skew on TIADC system performance; s2: randomly selecting a set of time skews τ _i And sampling period T _S The ratio r is taken as the chromosome in the population;s3: calculating fitness values of chromosomes in the population to promote crossover and mutation of the chromosomes; s4: selecting excellent chromosomes in the population for reproduction and inheriting excellent genes thereof; s5: exchanging chromosome genetic information in the population to obtain more excellent chromosomes; s6: self-adaptively adjusting mutation probability according to the adaptive value of the chromosome; s7: searching out an optimal chromosome in the population; s8: the channels are calibrated using a variable delay line.

As shown in fig. 2, the time-sharing alternating sampling technique uses a plurality of high-precision ADCs to cyclically and alternately sample, thereby achieving both high precision and high sampling rate, and the plurality of sub-ADCs form a time-sharing alternating analog-to-digital converter (TIADC) system.

As shown in fig. 3, due to the mismatch of the time skew of each sub-ADC in the TIADC system, the actual sampling time of the sampling clock circuit deviates from the ideal sampling time, so that the sampling value is in Error, where τi is the time skew of the ith sub-ADC in fig. 3, and Error is the sampling value deviation generated by the time skew.

Fig. 4 to fig. 7 show a TIADC system time skew error calibration system and method based on an AGA algorithm according to the present embodiment specifically includes the following steps:

TIADC system time deflection error calibration system and method based on AGA algorithm, comprising the following steps:

s1: time skew was evaluated: evaluating time skew τ _i Influence on TIADC system performance;

s2: establishing an initial population: randomly selecting a set of time skews τ _i And sampling period T _S The ratio r is used as a chromosome in the population, then the chromosome is multiplied by 1000 and converted into a 10-bit binary number, and one bit of binary bit is added before the highest bit to represent the positive and negative of time skew;

the time skew represented by the highest bit of 1 is the advanced case, and 0 represents the lagged case;

s3: calculating fitness values of chromosomes in the population: selecting the average absolute difference between the channel output calibrated by the variable delay line and the adjacent channel output as an adaptive value function, and pushing the intersection and variation of the chromosome;

s4: chromosome selection: using an exponential ranking selection algorithm as a selection strategy of AGA, selecting excellent chromosomes in the population for reproduction and inheriting excellent genes thereof;

s5: adaptive crossover: according to the crossover probability P _c Exchanging the genetic information of the chromosomes in the population to obtain more excellent chromosomes;

s6: adaptive variation: adaptive adjustment of mutation probability P according to chromosome adaptation value f _m The excellent chromosome is reserved, and meanwhile, the chromosome is mutated by adopting a multipoint mutation method, so that the population is more diversified;

s7: searching for optimal chromosomes: finding out the chromosome with the minimum adaptation value in the population;

s8: and (3) calibrating: after the time skew detection of the channel is completed, the channel is calibrated by using a variable delay line.

The step S1 specifically comprises the following steps:

s1.1: the sine signal is used as an input signal of a TIADC system, and the expression of the sine signal is as follows:

x(t)＝sin(ω _in t)

wherein: omega _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:

wherein: m is the channel number of the TIADC system, T _S For the sampling period, τ, of a single ADC within a TIADC system _i Time skew for the ith channel in the TIADC system;

s1.3: fourier Transforming (FT) the expression of the input signal in S1.1 gives:

s1.4: performing Discrete Fourier Transform (DFT) on the expression of the sinusoidal signal sampled by the TIADC system in the S1.2 to obtain the expression of the sinusoidal signal in a frequency domain, wherein the expression is as follows:

wherein: omega _S Sampling frequency of the TIADC system;

s1.5: in step S1.4, the influence of the time skew error in the frequency domain is obtained, and in any M-channel TIADC system, the harmonic component caused by the time skew error is located:

s1.6: the performance of the TIADC system is measured by adopting time skew and spurious-free dynamic range SFDR, and the function relationship established for the time skew and spurious-free dynamic range SFDR is:

the step S3 specifically comprises the following steps:

s3.1: for a TIADC system, selecting the average absolute difference between the channel output after the calibration of the variable delay line and the adjacent channel output as an adaptive value function:

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

wherein: x is x _ref1 And x _ref2 For adjacent reference channels, x _{i_d} Is the channel output delayed by the variable delay line.

S3.2: two channels in a four-channel TIADC system are selected as adaptive value calculation objects, and assuming that a channel 0 is ideal, the channel 1 only contains time skew, and |x is established ₁ -x ₀ I and I x ₂ -x ₁ Relationship of i to time skew;

s3.3: in S3.2 x ₁ Representing the sample value, x, of channel 1 ₀ Represents the sample value of channel 0, x ₂ Representation ofThe next sample value of channel 0, statistically, is |x when the number of samples is large ₁ -x ₀ I and I x ₂ -x ₁ The average difference of i is proportional to time skew, and the average difference is related to time skew as:

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

wherein: τ ₁ Representing the amount of time skew of a single ADC channel within a TIADC system;

s3.4: sample value x of channel 1 in S3.3 ₁ Sample value x with channel 0 ₀ The correlation function E [ (x) ₁ -x ₀ ) ² ]And (3) unfolding to obtain:

wherein: sigma (sigma) ² Representing the average power;

s3.5: the next sample value x of channel 0 in S3.3 ₂ Sample value x of channel 1 ₁ The correlation function E [ (x) ₂ -x ₁ ) ² ]And (3) unfolding to obtain:

s3.6: subtracting the expansion including the time skew function from the average power in S3.4 and S3.5 yields:

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

+2R(T _S -τ ₁ )

s3.7: the time skew based on that obtained in S3.6 is typically small, and R (T _S ±τ ₁ ) Can be approximately equal to R (T _S )±τ ₁ dR/dτ, the expression obtained in step S3.6 is changed to:

s3.8: from step S3.7, the time skew and E [ (x) can be seen ₁ -x ₀ ) ² ]And E [ (x) ₂ -x ₁ ) ² ]Is proportional to the difference in (x) after the time skew is calibrated ₁ -x ₀ ) ² ]With E [ (x) ₂ -x ₁ ) ² ]Is close to 0; the smaller the fitness value of the chromosome, the more excellent the chromosome, the more closely the time skew it represents to the actual time skew, and the worse the fitness value, the more the time skew it represents to the actual time skew.

The step S4 specifically comprises the following steps:

s4.1: taking an exponential ranking selection algorithm as a selection strategy of AGA, and distributing selection probability according to ranking; in the step S3 of time skew detection, the smaller the adaptation value is, the more excellent the chromosome is, the descending order is ordered according to the adaptation value of the chromosome, so that the maximum adaptation value of the chromosome is 1, and the minimum adaptation value is N;

s4.2: calculating the probability of being selected according to the sorting of the chromosomes in the step S4.1, wherein the formula is as follows:

wherein: i represents the ith chromosome, c is a set parameter, the value of which must be between 0 and 1, the closer the value is to 1, the lower the "exponential" of the selection method;

s4.3: accumulating the probabilities of the chromosomes according to the chromosome sequence to obtain the accumulated probability sum _i And randomly generating a random number sigma of 0 to 1;

s4.4: if the random number sigma is greater than sum _i-1 And is smaller than sum _i The ith chromosome is selected.

The step S5 specifically comprises the following steps:

s5.1: crossover operations can exchange genetic information of chromosomes in the population, and the crossed population is more developedAdding excellent chromosomes; the crossover operation is performed depending on the set crossover probability P _c ，P _c The larger the new chromosome is, the faster the new chromosome is introduced into the population, but if the crossover probability P is _c Too large, it may occur that high performance chromosomes are discarded more quickly than the selection yields improvement;

s5.2: the TIADC system time skew error calibration system based on the AGA algorithm adopts a self-adaptive crossing method to solve the problem existing in S5.1, and the method generates crossing probability according to the adaptive value of a chromosome, and the formula is as follows:

wherein: f (f) _min Is the minimum of the chromosome fitness values; f' is the smaller fitness value of the two chromosomes to be crossed; f (f) _mean The average fitness value of the chromosomes is ensured, so that all chromosomes with fitness values larger than the average value are crossed; will k ₁ And k ₃ Setting to 1 to prevent the situation of falling into local optimum in the optimum solution searching process;

s5.3: selecting a pair of chromosomes, calculating the crossover probability according to the crossover probability formula in S5.2, randomly generating a random number, and performing crossover operation if the random number is smaller than the crossover probability;

the step S6 specifically comprises the following steps:

s6.1: solving variation probability P by adaptive variation _m The larger resulting genetic algorithm becomes a pure random search algorithm, and P _m Less phenomena that might cause premature convergence of the genetic algorithm, the adaptive variation formula is:

wherein: will k ₂ And k ₄ Setting to 0.5 to prevent the AGA algorithm from falling into local optimum;

s6.2: after the calculation of the mutation probability is completed, a multi-point mutation method is adopted to mutate the chromosome, so that the population is more diversified; the method comprises the steps of randomly selecting a plurality of mutation points, mutating information of the points, wherein if the information of the points is 1, the mutation points are 0, and if the information of the points is 0, the mutation points are 1.

The step S7 specifically includes the following steps:

s7.1: according to step S3, find the chromosome with the minimum adaptation value, judge whether its adaptation value meets the set condition F _best <F _set ；

S7.2: if the condition in S7.1 is satisfied, the time skew corresponding to the chromosome is the time skew of the ith channel, if the condition is not satisfied, returning to the step S4 and repeating the subsequent steps until the condition is satisfied;

the step S8 specifically comprises the following steps:

s8.1: for a 4-channel TIADC system, channel 0 is used as a reference channel, and the time skew of channel 2 is detected and calibrated;

s8.2: using channel 0 and channel 2 as reference channels, the time skew of channel 1 and channel 3 is detected and calibrated.

Example 2

In order to verify that the invention can realize the estimation and calibration of the time skew error of the 18bit high-resolution TIADC system, a four-channel TIADC system model is taken as an example for verification, and the invention is described in detail by combining the TIADC system and a simulation result.

The verification step comprises the following steps:

firstly, a TIADC system is described, the four-channel TIADC simulation system is taken as an example, and the whole sampling rate of the system is 1GS/s and consists of four identical 18bit single-channel ADCs. In order to facilitate analysis of the time skew errors, it is assumed that the TIADC system is not affected by the bias mismatch error and the gain mismatch error, then the time skew of each channel of the TIADC system is configured, and it is assumed that channel 0 has no time skew, and the time skew of channel 1, channel 2, and channel 3 are τ respectively ₁ ＝2e-11，τ ₂ ＝-5e-11,τ ₃ =1e-11. The verification example uses the frequency of 47.71MHzThe sinusoidal signal is used as the input signal, and the parameter c of the exponential ordering selection method of the AGA is set to 0.9.

FIG. 8 shows the different sizes of F for AGA in this verification example _set Convergence of time skew detection for each channel, t _c For convergence time of time skew detection, where the smaller the Fset value, the higher the accuracy of the AGA to time skew estimation, but the number of iterations of the convergence time increases, comprehensively considering that the present verification example sets Fset to 2.6e-4 to obtain an approximate estimate of actual time skew. From FIGS. 8 (a), 8 (b) and 8 (c), it can be seen that the time skew of the channel 1 converges to 0.02T after 10 iterations _S The time skew estimates for lanes 2 and 3 converge to-0.05T after 10 and 9 iterations, respectively _S And 0.01T _S 。

Fig. 9 shows a comparison diagram of GA, LMS, AGA algorithms in terms of time skew detection, and it can be seen from the diagram that, under the premise of the same time skew error, the iteration number of the AGA algorithm is 10 times, and the iteration numbers of the GA algorithm and the LMS algorithm are 29 times and 117 times, respectively, so that the calibration method provided by the invention has a higher speed in time skew detection.

Fig. 10 is a graph showing the performance of the LMS, GA, AGA algorithm in comparison to the three methods under the same time skew error. The graph shows that the time skew error detected by the AGA algorithm on the four-channel TIADC system of the verification example is 0.02, and is more accurate than 0.0199 and 0.0210 detected by the LMS algorithm and the GA algorithm; the iteration times and the convergence time of the AGA algorithm are greatly improved compared with those of the traditional LMS and GA algorithms; the number of samples required to be collected by the LMS, GA, AGA algorithm is 42.5K, 72.5K and 25K respectively, and the number of samples required to be collected by the AGA algorithm is less; the running time of the AGA algorithm is 0.13092 seconds, which is faster than the detection speed of the LMS algorithm and the GA algorithm;

FIG. 11 (a) shows a frequency domain plot of the TIADC model with time skew error in this verification example, where the input signal produced a peak spectrum at 47.71MHz, the remaining peaks being noise spectra produced by the time skew error; fig. 11 (b) shows the output spectrum of a TIADC system after a variable delay line level, in which the glitch due to time skew error is effectively suppressed, the signal-to-noise ratio is increased from 40.7dB to 106.6dB, and the effective number of bits is increased from 6.4bit to 17.4bit.

Fig. 12 shows the correlation between the frequency of the input signal and the pre-calibration and post-calibration SNDR, SFDR, ENOB, and it can be seen that SNDR, SFDR, ENOB of the TIADC system is significantly improved by the TIADC system time skew error calibration system based on the AGA algorithm, and the calibration method has a good calibration effect on the input signal in almost the entire nyquist band.

By adopting the technical scheme, the invention provides a full-digital calibration method for the time skew error of the TIADC system, and the time skew error of the TIADC system is calibrated by adopting an AGA algorithm, so that the method is suitable for any M-channel TIADC system.

The TIADC system mismatch error calibration method provided by the invention is suitable for calibrating time skew errors in channels, remarkably improves the dynamic performances of the TIADC, such as SNR, SFDR and the like, has simple structural design and low algorithm operation difficulty, is not limited by the number of channels, and has wide application prospect.

While the foregoing is directed to embodiments of the present invention, other and further details of the invention may be had by the present invention, it should be understood that the foregoing description is merely illustrative of the present invention and that no limitations are intended to the scope of the invention, except insofar as modifications, equivalents, improvements or modifications are within the spirit and principles of the invention.

Claims (8)

1. The TIADC system time skew error calibration method based on the AGA algorithm is characterized by comprising the following steps of:

s1: time skew was evaluated: evaluating time skew τ _i Influence on TIADC system performance;

s2: establishing an initial population: randomly selecting a set of time skews τ _i And sampling period T _S The ratio r is used as a chromosome in the population, then the chromosome is multiplied by 1000 and converted into a 10-bit binary number, and one bit of binary bit is added before the highest bit to represent the positive and negative of time skew; at its most, it isThe time skew represented by the high order 1 is the leading case, and 0 is the lagging case;

s3: calculating fitness values of chromosomes in the population: selecting the average absolute difference between the channel output calibrated by the variable delay line and the adjacent channel output as an adaptive value function, and pushing the intersection and variation of the chromosome;

s4: chromosome selection: using an exponential ranking selection algorithm as a selection strategy of AGA, selecting excellent chromosomes in the population for reproduction and inheriting excellent genes thereof;

s5: adaptive crossover: according to the crossover probability P _c Exchanging the genetic information of the chromosomes in the population to obtain more excellent chromosomes;

s6: adaptive variation: adaptive adjustment of mutation probability P according to chromosome adaptation value f _m The excellent chromosome is reserved, and meanwhile, the chromosome is mutated by adopting a multipoint mutation method, so that the population is more diversified;

s7: searching for optimal chromosomes: finding out the chromosome with the minimum adaptation value in the population;

s8: and (3) calibrating: after the time skew detection of the channel is completed, the channel is calibrated by using a variable delay line.

2. The TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, wherein the step S1 specifically includes the steps of:

s1.1: the sine signal is used as an input signal of a TIADC system, and the expression of the sine signal is as follows:

x(t)＝sin(ω _in t)

wherein omega _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:

wherein M is TIADC systemChannel number T of (1) _S For the sampling period, τ, of a single ADC within a TIADC system _i Time skew for the ith channel in the TIADC system;

s1.3: fourier transform FT is performed on the expression of the input signal in S1.1 to obtain:

s1.4: performing Discrete Fourier Transform (DFT) on the expression of the sinusoidal signal sampled by the TIADC system in the S1.2 to obtain the expression of the sinusoidal signal in a frequency domain, wherein the expression is as follows:

wherein omega _S Sampling frequency of the TIADC system;

s1.5: in step S1.4, the influence of the time skew error in the frequency domain is obtained, and in any M-channel TIADC system, the harmonic component caused by the time skew error is located:

s1.6: the performance of the TIADC system is measured by adopting time skew and spurious-free dynamic range SFDR, and the function relationship established for the time skew and spurious-free dynamic range SFDR is:

3. the TIADC system time skew error calibration method based on the AGA algorithm according to claim 1, wherein the step S3 specifically includes the steps of:

s3.1: for a TIADC system, selecting the average absolute difference between the channel output after the calibration of the variable delay line and the adjacent channel output as an adaptive value function:

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

wherein x is _ref1 And x _ref2 For adjacent reference channels, x _{i_d} Is output by the channel delayed by the variable delay line;

s3.2: two channels in a four-channel TIADC system are selected as adaptive value calculation objects, and assuming that a channel 0 is ideal, the channel 1 only contains time skew, and |x is established ₁ -x ₀ I and I x ₂ -x ₁ Relationship of i to time skew;

s3.3: in S3.2 x ₁ Representing the sample value, x, of channel 1 ₀ Represents the sample value of channel 0, x ₂ Representing the next sample value of channel 0, from a statistical point of view, |x, when the number of samples is large ₁ -x ₀ I and I x ₂ -x ₁ The average difference of i is proportional to time skew, and the average difference is related to time skew as:

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

wherein τ ₁ Representing the amount of time skew of a single ADC channel within a TIADC system;

s3.4: sample value x of channel 1 in S3.3 ₁ Sample value x with channel 0 ₀ The correlation function E [ (x) ₁ -x ₀ ) ² ]And (3) unfolding to obtain:

wherein sigma ² Representing the average power;

s3.5: the next sample value x of channel 0 in S3.3 ₂ Sample value x of channel 1 ₁ The correlation function E [ (x) ₂ -x ₁ ) ² ]And (3) unfolding to obtain:

s3.6: subtracting the expansion including the time skew function from the average power in S3.4 and S3.5 yields:

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

+2R(T _S -τ ₁ )

s3.7: the time skew based on that obtained in S3.6 is typically small, and R (T _S ±τ ₁ ) Can be approximately equal to R (T _S )±τ ₁ dR/dτ, the expression obtained in step S3.6 is changed to:

s3.8: from step S3.7, the time skew and E [ (x) can be seen ₁ -x ₀ ) ² ]And E [ (x) ₂ -x ₁ ) ² ]Is proportional to the difference in (x) after the time skew is calibrated ₁ -x ₀ ) ² ]With E [ (x) ₂ -x ₁ ) ² ]Is close to 0; the smaller the fitness value of the chromosome, the more excellent the chromosome, the more closely the time skew it represents to the actual time skew, and the worse the fitness value, the more the time skew it represents to the actual time skew.

4. The TIADC system time skew error calibration method according to claim 1, wherein the step S4 specifically comprises the steps of:

s4.1: taking an exponential ranking selection algorithm as a selection strategy of AGA, and distributing selection probability according to ranking; in the step S3 of time skew detection, the smaller the adaptation value is, the more excellent the chromosome is, the descending order is ordered according to the adaptation value of the chromosome, so that the maximum adaptation value of the chromosome is 1, and the minimum adaptation value is N;

s4.2: calculating the probability of being selected according to the sorting of the chromosomes in the step S4.1, wherein the formula is as follows:

where i denotes the ith chromosome, c is a set parameter, the value of which must be between 0 and 1, the closer the value is to 1, the lower the "exponential" of the selection method;

s4.3: accumulating the probabilities of the chromosomes according to the chromosome sequence to obtain the accumulated probability sum _i And randomly generating a random number sigma of 0 to 1;

s4.4: if the random number sigma is greater than sum _i-1 And is smaller than sum _i The ith chromosome is selected.

5. The TIADC system time skew error calibration method according to claim 1, wherein the step S5 specifically comprises the steps of:

s5.1: the crossing operation can enable the genetic information of the chromosomes in the population to be exchanged, and more excellent chromosomes appear in the crossed population; the crossover operation is performed depending on the set crossover probability P _c ，P _c The larger the new chromosome is, the faster the new chromosome is introduced into the population, when the crossover probability P is _c Too large, it occurs that high performance chromosomes are discarded faster than the selection yields improvement;

s5.2: the adaptive crossing method is adopted, and the method generates the crossing probability according to the adaptive value of the chromosome, and the formula is as follows:

wherein f _min Is the minimum of the chromosome fitness values; f' is the smaller fitness value of the two chromosomes to be crossed; f (f) _mean Is the average fitness value of the chromosomes, thereby ensuring that all chromosomes with fitness values greater than the average value are subjected toPerforming cross operation; will k ₁ And k ₃ Setting to 1 to prevent the situation of falling into local optimum in the optimum solution searching process;

s5.3: selecting a pair of chromosomes, calculating the crossover probability according to the crossover probability formula in S5.2, randomly generating a random number, and performing crossover operation if the random number is smaller than the crossover probability.

6. The TIADC system time skew error calibration method according to claim 1, wherein the step S6 specifically includes the steps of:

s6.1: solving variation probability P by adaptive variation _m The larger resulting genetic algorithm becomes a pure random search algorithm, and P _m Less phenomena that might cause premature convergence of the genetic algorithm, the adaptive variation formula is:

wherein k is ₂ And k ₄ Setting to 0.5 to prevent the AGA algorithm from falling into local optimum;

s6.2: after the calculation of the mutation probability is completed, a multi-point mutation method is adopted to mutate the chromosome, so that the population is more diversified; the method comprises the steps of randomly selecting a plurality of mutation points, mutating information of the points, wherein if the information of the points is 1, the mutation points are 0, and if the information of the points is 0, the mutation points are 1.

7. The TIADC system time skew error calibration method according to claim 1, wherein the step S7 specifically comprises the steps of:

s7.1: according to step S3, find the chromosome with the minimum adaptation value, judge whether its adaptation value meets the set condition F _best <F _set ；

S7.2: if the condition in S7.1 is satisfied, the time skew corresponding to the chromosome is the time skew of the ith channel, and if the condition is not satisfied, returning to step S4 and repeating the subsequent steps until the condition is satisfied.

8. The TIADC system time skew error calibration method according to claim 1, wherein the step S8 specifically comprises the steps of:

s8.1: for a 4-channel TIADC system, channel 0 is used as a reference channel, and the time skew of channel 2 is detected and calibrated;

s8.2: using channel 0 and channel 2 as reference channels, the time skew of channel 1 and channel 3 is detected and calibrated.