CN105811980A - TIADC time error mismatch self-adaption blind correction method based on differentiator and average time error - Google Patents

Abstract

A TIADC(Time Interleaved Analog-to-digital Converter) time error mismatch self-adaption blind correction method based on differentiator and average time error belongs to the field of analog digital conversion. According to the invention, slope approximation and the average value of time errors of all slave ADCs of the TIADC are utilized for deducing a system unknown parameter to be estimated. The TIADC system is adopted for sampling output values practically, the differentiator and a high-pass filter are utilized, a certain degree of oversampling is required and a minimum mean squared error algorithm is utilized for realizing the self-adaption blind correction of the time error mismatch of the TIADC system. The to-be-estimated parameter of the correction system is a difference value between the relative time error of each slave ADC and the average value of the relative time error of all the slave ADCs. The parameter is used for error reconstruction and system compensation. By adopting the method provided by the invention, hardware complexity, hardware implementation difficulty and system power consumption are reduced effectively. The method can be applied to multiple channels. The more the channel number is, the more obvious the advantage of the method becomes.

Description

A kind of adaptive blind bearing calibration of the time error mismatch based on differentiator and the TIADC of mean timing error

Technical field

The present invention relates to a kind of TIADC (Time-InterleavedAnalog-to-digitalConverter based on differentiator and mean timing error, time-interleaved analog-digital converter) the adaptive blind bearing calibration of time error mismatch, belong to high-speed, high precision Analog-digital Converter technical field.

Background technology

The TIADC system that the high-precision single ADC parallel time of multiple relative low speeds sampling structure alternately forms is utilized to have become as the developing direction of current high speed, high-precision adc.But, in actual applications, due to the overall performance having influence on TIADC that error misfits (time error mismatch, gain error mismatch and the biased error mismatch) meeting between the TIADC system neutron ADC that the factors such as manufacturing process cause is serious.Wherein, gain error mismatch and biased error mismatch be easier to process, and time error mismatch be TIADC correction in the most scabrous technical barrier.The adaptive calibration device that the number of applying for a patent is 201010225056.9 time-interleaved analog-digital converter mismatch errors can gain and biased error mismatch between calibrated channel, time and frequency error mismatch can also be calibrated, but the method for this correction requires have signal generator to produce reference signal.The number of applying for a patent is the estimation of the 201210454365.2 time mismatch parameters giving TIADC system based on the TIADC time mismatch parameter Blind Test metering method that signal frequency domain is openness, this method requires that input signal is sparse on frequency domain, limits the type of input signal.US Patent No. 2008030387-A1 can only calibration-gain error；US2008024338-A1 can only calibration-gain error and biased error.

M sampling rate is f_sTotal sample frequency of the TIADC system of the sub-ADC composition of/M is f_s, along with the increase of port number M, total sampling rate of TIADC system can increase.Port number is more many, and correcting structure is more complicated and power consumption is also more big, it is achieved difficulty also more big.How ensureing that the less complexity of correcting structure, relatively low power consumption and reduction hardware realize difficulty is the purpose of the present invention.

Summary of the invention

It is an object of the invention to provide the adaptive blind bearing calibration of a kind of time error mismatch based on differentiator and the TIADC of mean timing error, it is possible not only to effectively time error mismatch is corrected, and its correcting structure reduces hardware complexity and realizes difficulty, and reduce the power consumption of correction system.

The present invention realizes by the following technical solutions:

A kind of adaptive blind bearing calibration of the time error mismatch based on differentiator and the TIADC of mean timing error, its thought is, for there is each sub-ADC of sampling time error, the time error finally making each sub-ADC all tends to identical value, the meansigma methods of the time error being sized to all sub-ADC of this value.The interchannel time error mismatch that result final after correction is TIADC system is reduced.Specifically comprise the following steps that

Step one: building the reconfiguration system of the time error mismatch of the TIADC of M passage, the error e [n] caused due to time error mismatch can be expressed as:

$e\[n\]=\frac{d(y\[n\])}{d\left(t\right)}(r_k-r_{ave}),k=\left(n\mathrm{mod}M\right)=0,1,2,\mathrm{...},M-1---\left(1\right)$

r_ave=(r₀+r₁+,...,+r_k+,...,+r_M-1)/M(2)

(1) in formula, the nonideal non-homogeneous digital sample values of TIADC when y [n] is for free error misfits, d (y [n])/d (t) represents and in t, y [n] is asked slope value, and its value can by y [n] by obtaining after a differentiator effect；r_kRepresent the relative time error of the sub-ADC of kth, i.e. r_kCorresponding Absolute timing errors t_kRelation be t_k=r_kT_s, wherein T_sTotal sampling period for TIADC.Because in (1), the value of k is the n value to M delivery, and M is the port number of TIADC, therefore r_k-r_aveWith the product of d (y [n])/d (t), d (y [n])/d (t) is corresponding in the slope value of t with the sampled value of the individual sub-ADC of kth (wherein k=nmodM) in TIADC.As k=0, the sampled value of sub-ADC-0 can obtain by d (y [n])/d (t) carries out M times down-sampled in the slope value of t.Work as k=1,2 ..., during M-1, the sampled value of the sub-ADC of kth can obtain by carrying out M times down-sampled after d (y [n])/d (t) first carries out the delay of M-k unit again in the slope value of t.

(2), in formula, M is the port number of TIADC；r_aveFor the meansigma methods of the relative time error of all sub-ADC, r₀,r₁,…,r_k,…,r_M-1Represent sub-ADC-0, ADC-1 respectively ..., ADC-k ..., the relative time error of ADC-(M-1).Because the change of the time error of passage is slowly in TIADC system, may be considered constant within a period of time, therefore r_k-r_aveThe unknown constant that needs are estimated can be regarded as within a period of time.If r_k-r_ave(wherein k=0,1,2 ..., M-1) value and M and each parameter r corresponding for sub-ADC_k-r_aveValue be estimated, then can be obtained the error e [n] of required reconstruct by (1) formula.

Step 2: to parameter r_k-r_aveThe estimation of value:

Analogue signal x to input_cT () is limited in certain bandwidth [0, β π] (herein representing by normalization bandwidth), wherein β is the parameter to input signal bandwidth size restriction, and β can in the scope value less than 1 more than 0.Without the existence of any error, then the signal spectrum of the output after TIADC processes is contained only in bandwidth [0, β π], in bandwidth [β π, π] and be absent from signal energy.And the existence of the error caused due to the mismatch of inter-channel time error, the signal energy of error can occur in bandwidth [β π, π], this portion of energy can be filtered off by a high pass filter, is expressed as [n].Parameter r_k-r_aveValue LMS (LeastMeanSquare, Minimum Mean Square Error) algorithm can be utilized by constantly reducing the value of [n], iteration convergence estimates.

Step 3: uncorrected output is compensated, estimates the parameter r obtained through step 2_k-r_aveValue can be obtained e [n] by formula (1), it is desirable to correction after output y_ave[n] is represented by:

y_ave[n]=y [n]-e [n] (3)

To sum up, this algorithm achieves the adaptive blind correction of the time error mismatch to TIADC.

The beneficial effects of the present invention is: the time error mismatch of TIADC system just can carried out adaptive school for the blind by method of the present invention, it is not required to introduce any test signal, only need the output data y [n] of TIADC system, input signal is required nothing more than certain bandwidth restriction, it is not necessary to know concrete information or parameter.Correcting structure is not required to any manipulator；Correction for the TIADC system of M passage, except a differentiator, a high pass filter, M-1 adder, a subtractor and [d+ (M-1)+3M (M-1)/2] (wherein d represents the delay of differentiator) individual unit delay, other parts (comprise M multiplier, (M-1+D) individual unit delay, wherein D is the delay of high pass filter and a LMS algorithm module) operating frequency, no matter port number M is how many, all it is only and is always total sample frequency f of TIADC_s1/M times, i.e. the operating frequency of sub-ADC.It reduce the complexity of correcting structure and realize difficulty, especially reducing power consumption.Method of the present invention can expand to arbitrarily many port numbers, and along with the increase of port number, its have the advantage that is all the more obvious.

Accompanying drawing explanation

Fig. 1 is the structural representation of time-interleaved analog-digital converter (TIADC) system；

Fig. 2 is the analysis chart of time error mismatch；

Fig. 3 is the principle assumption diagram of reconstruct and the compensation of uncorrected output containing error；

Fig. 4 is the overall structure figure of adaptively correcting；

Fig. 5 is the uncorrected output signal spectrum of TIADC system；

Fig. 6 is the output signal spectrum corrected of TIADC system；

Fig. 7 is the convergence result of the coefficient to estimate.

Detailed description of the invention

The specific embodiment of the present invention is described in detail below in conjunction with accompanying drawing.

It is illustrated in figure 1 the structural representation of time-interleaved analog-digital converter (TIADC) system, comprises M passage.Whole TIADC system is MT by the sampling time interval of M concurrent working_sSub-ADC composition, total operating frequency of TIADC is f_s=1/T_s, wherein T_sTotal sampling period for TIADC.r₀,r₁,…,r_k,…,r_M-1Represent sub-ADC-0, ADC-1 respectively ..., ADC-k ..., the relative time error of ADC-(M-1).Each work parallel for sub-ADC, the analogue signal x of input_c(t) by after the sub-ADC parallel sampling of M passage by being reduced to the nonideal non-homogeneous digital sample values y [n] of the TIADC of a uncorrected free error misfits after multiplexer MUX effect.Then the bearing calibration in the present invention is adopted to be corrected y [n].

It is illustrated in figure 2 the analysis chart of time error mismatch, ideal value when x [n] is suppose TIADC system not free error, the nonideal non-homogeneous digital sample values of the TIADC that y [n] is free error misfits.y_ave[n], for exporting after desired correction, its value is when the relative time error of each sub-ADC of TIADC system is all the meansigma methods r of the relative time error of all sub-ADC_ave=(r₀+r₁+,…,+r_k+,…,+r_M-1During)/M, the sampled value of TIADC.Relative time error if all of sub-ADC is all r_ave, then TIADC system is output as the output of not free error misfits.D (y [n])/d (t) represents and in t, y [n] is asked slope value.t_nRepresent the Absolute timing errors in the moment of the n-th sampled point, and t_aveRepresent r_aveCorresponding absolute value, i.e. t_ave=r_aveT_s.E [n] represents the error caused due to time error mismatch.As shown in Figure 2 it can be seen that e [n] can by slope d (y [n])/d (t) and t of y [n]_n-t_aveValue obtain, namely have:

$e\[n\]=\frac{d(y\[n\])}{d\left(t\right)}(t_n-t_{ave})=\frac{d(y\[n\])}{d\left(t\right)}(r_n{T}_s-r_{ave}{T}_s)---\left(1\right)$

Wherein, r_nFor t_nRelative value, i.e. t_n=r_nT_s.The value of d (y [n])/d (t) can by y [n] by obtaining after a differentiator effect, owing to such a differentiator can introduce a 1/T_sCoefficient, therefore e [n] can be expressed as:

$e\[n\]=\frac{d(y\[n\])}{d\left(t\right)}(r_n-r_{ave})---\left(2\right)$

Because in TIADC system, the time error of passage is slowly varying, i.e. r_n=r_(nmodM), so that

$e\[n\]=\frac{d(y\[n\])}{d\left(t\right)}(r_k-r_{ave}),k=\left(n\mathrm{mod}M\right)=0,1,2,\mathrm{...},M-1---\left(3\right)$

Owing in (3), the value of k is the n value to M delivery, M is the port number of TIADC, therefore r_k-r_aveWith the product of d (y [n])/d (t), d (y [n])/d (t) is corresponding in the slope value of t with the sampled value of the individual sub-ADC of kth (wherein k=nmodM) in TIADC.As k=0, the sampled value of sub-ADC-0 can obtain by d (y [n])/d (t) carries out M times down-sampled in the slope value of t.Work as k=1,2 ..., during M-1, the sampled value of the sub-ADC of kth can obtain by carrying out M times down-sampled after d (y [n])/d (t) first carries out the delay of M-k unit again in the slope value of t.

Formula (3) described in Fig. 2 can obtain needing the error e [n] of reconstruct, is therefore illustrated in figure 3 the principle assumption diagram of the compensation of reconstruct and the uncorrected output containing error, and wherein j ω represents differentiator.Convenient for representing, d (y [n])/d (t) is expressed as y_d[n]；r₀-r_ave,r₁-r_ave,r₂-r_ave,…,r_k-r_ave,…,r_M-1-r_aveIt is expressed as c₀,c₁,c₂,…,c_k,…,c_M-1.Known in formula described in Fig. 2 (3), r_k-r_aveWith the product of d (y [n])/d (t), d (y [n])/d (t) is corresponding in the slope value of t with the sampled value of the individual sub-ADC of kth (wherein k=nmodM) in TIADC.The sampled value of the sub-ADC of kth in TIADC can be obtained by the down-sampled module in Fig. 3 in the slope value of t, y_d[n] is by the y obtained after down-sampled module effect_d[nM+0], y_d+M-1[nM+1],y_d+M-2[nM+2],…,y_d+M-k[nM+k],…, y_d+1[nM+M-1] represents sub-ADC-0, ADC-1 respectively ..., ADC-k ..., ADC-(M-1) respective sampled value is in the slope value of t, and this slope value is respectively provided with d, d+M-1, d+M-2 ..., d+M-k ..., the delay of d+1 unit, wherein d represents the delay that differentiator is introduced.Through process M times down-sampled of down-sampled module, y_d[nM+0], y_d+M-1[nM+1],y_d+M-2[nM+2],…,y_d+M-k[nM+k],…,y_d+1The sample frequency of [nM+M-1] is f_s/M.The y obtained_d[nM+0], y_d+M-1[nM+1],y_d+M-2[nM+2],…,y_d+M-k[nM+k],…,y_d+1[nM+M-1] respectively with c₀,c₁,c₂,…,c_k,…,c_M-1Correspondence is multiplied then through the error amount y having d+M-1 unit delay obtaining reconstructing after liter sampling module process as described in Figure 3_d+M-1[n]c_n, wherein c_n=c_k=c_(nmodM).Uncorrected output y [n] obtains y [n-(d+M-1)] after d+M-1 unit delay processes, y [n-(d+M-1)] deduct y_d+M-1[n]c_nJust the output y after can being compensated_ave[n-(d+M-1)]。

If parameter c in Fig. 3₀,c₁,c₂,…,c_k,…,c_M-1Value it is known that then can method described in Fig. 3 uncorrected output y [n] be corrected, be therefore illustrated in figure 4 the overall structure figure containing the adaptively correcting to parameter estimation.For convenience of representing, the down-sampled module in Fig. 4 and liter sampling module are described in detail in figure 3, only use textual representation here.F [n] represents high pass filter, its role is to filter bandwidth restriction interior [0, β π] input signal (wherein β be to input signal bandwidth size restriction parameter, β can in the scope value less than 1 more than 0), and it is retained in the error energy [n] introduced due to time error mismatch in bandwidth restriction outer [β π, π].Down-sampled module after [n] is used for obtaining and y_d[nM+0], y_d+M-1[nM+1],y_d+M-2[nM+2],…,y_d+M-k[nM+k],…,y_d+1The down-sampled decimation value [nM+0] of [n] that [nM+M-1] is corresponding,_M-1[nM+1],_M-2[nM+2],…,_M-k[nM+k],…,₁[nM+M-1].For expressing simplicity in the drawings, the vector expression adopted is as follows:

$\begin{array}{c}{y}_{d+M-k}^v\[nM+k\]=\[y_d\[nM+0\],y_{d+M-1}\[nM+1\],\\ y_{d+M-2}\[nM+2\],\mathrm{...},y_{d+M-k}\[nM+k\],\mathrm{...},y_{d+1}\[nM+M-1\]\]\end{array}---\left(5\right)$

$\begin{array}{c}{\mathrm{\ϵ}}_{(M-k)}^v\[nM+k\]=\[\mathrm{\ϵ}\[nM+0\],{\mathrm{\ϵ}}_{M-1}\[nM+1\],\\ {\mathrm{\ϵ}}_{M-2}\[nM+2\],\mathrm{...},{\mathrm{\ϵ}}_{M-k}\[nM+k\],\mathrm{...},{\mathrm{\ϵ}}_1\[nM+M-1\]\end{array}---\left(6\right)$

WhereinFor c_kEstimated value.LMS (LeastMeanSquare) is lms algorithm module, and its effect is with y_d+M-k[nM+k] and_M-k[nM+k] is input, is estimated by iteration convergenceAs follows according to iterative formula:

Whereinμ is the step-length of iterative formula, 0 < μ≤1/ λ_max, wherein λ_maxFor the eigenvalue of maximum of the autocorrelation matrix of yd+M-k [(n-(M-1+D)/M) M+k], D is the delay of high pass filter f [n].When iteration convergence estimates coefficientValue, obtain actual error value by error reconstructing method as described in Figure 3(whereinFor c_nActual estimated value) and compensation method can finally give actual correction value output

As it is shown in figure 5, the uncorrected output signal spectrum of its TIADC system is obtained by MATLAB software emulation result.Adopt the four-way TIADC system being made up of the ADC of four desirable 14 bits, its simulation parameter is, the exponent number of differentiator and high pass filter is all 40 rank, normalization bandwidth is limited to [0,0.8 π], and the relative time error of its each subchannel is [-0.008,0.003,-0.004,0.009], the step size mu of iterative formula is set to 0.007.The SFDR of the frequency spectrum of uncorrected output signal is 36.36dB, and its SNR is 40.06dB.

As shown in Figure 6, the SFDR of the frequency spectrum of the output signal after its correction is 78.5dB, and its SNR is 65.84dB.Its SFDR and SNR improves 42.14dB and 25.78dB respectively.

As it is shown in fig. 7, the convergence result of the coefficient to estimate is consistent with the numerical value of theory calls, within 25000 iteration points, have converged to expected theoretical value.

Claims (1)

1. the adaptive blind bearing calibration based on the time error mismatch of differentiator and the TIADC of mean timing error, it is characterised in that comprise the following steps:

Step one: building the reconfiguration system of the time error mismatch of the TIADC of M passage, the error e [n] caused due to time error mismatch is expressed as:

$e\&lsqb;n\&rsqb;=\frac{d(y\&lsqb;n\&rsqb;)}{d\left(t\right)}(r_k-r_{ave}),k=\left(n\mathrm{mod}M\right)=0,1,2,...,M-1---\left(1\right)$

r_ave=(r₀+r₁+,...,+r_k+,...,+r_M-1)/M(2)

(1) in formula, the nonideal non-homogeneous digital sample values of TIADC when y [n] is for free error misfits, d (y [n])/d (t) represent y [n] is sought slope value in t, its value by y [n] by obtaining after a differentiator effect；r_kRepresent the relative time error of the sub-ADC of kth, i.e. r_kCorresponding Absolute timing errors t_kRelation be t_k=r_kT_s, wherein T_sTotal sampling period for TIADC；In (1), the value of k is the n value to M delivery, and M is the port number of TIADC, therefore r_k-r_aveWith the product of d (y [n])/d (t), d (y [n])/d (t) is corresponding in the slope value of t with the sampled value of the sub-ADC of the kth in TIADC；As k=0, the sampled value of sub-ADC-0 obtains by d (y [n])/d (t) carries out M times down-sampled in the slope value of t；Work as k=1,2 ..., during M-1, the sampled value of the sub-ADC of kth obtains by carrying out M times down-sampled after d (y [n])/d (t) first carries out the delay of M-k unit again in the slope value of t；

(2), in formula, M is the port number of TIADC；r_aveFor the meansigma methods of the relative time error of all sub-ADC, r₀,r₁,…,r_k,…,r_M-1Represent sub-ADC-0, ADC-1 respectively ..., ADC-k ..., the relative time error of ADC-(M-1)；

Step 2: to parameter r_k-r_aveThe estimation of value:

Analogue signal x to input_cT () is limited in bandwidth [0, β π], wherein β is in the scope value less than 1 more than 0；, can there is the signal energy of error in bandwidth [β π, π] in the existence of the error caused due to the mismatch of inter-channel time error, and this portion of energy is filtered off by a wave filter, is expressed as [n]；Parameter r_k-r_aveValue utilize lms algorithm to pass through constantly to reduce the value of [n], iteration convergence estimates；

Step 3: uncorrected output is compensated, estimates the parameter r obtained through step 2_k-r_aveValue obtained e [n] by formula (1), it is desirable to correction after output y_ave[n] is expressed as:

y_ave[n]=y [n]-e [n] (3).