时间交替采样系统的信号重建
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摘要
电子信息技术的快速发展使得各类电子系统的信号工作频率及信号复杂度剧增,作为信号数字化系统基础的高速高精度采样技术,是获取和分析复杂瞬态信号细微特征、进而完成有用信息提取的首要核心技术。受制于芯片技术的滞后,即使最新工艺制成的FLASH模数转换器(ADC),仍然无法满足实际系统实时采样的要求。时间交替采样(Time-Interleaved ADC,TIADC)系统通过多路ADC并行交替的方式对信号进行实时采样,以达到采样率倍增的目的。虽然该系统在速度上较单个ADC具有明显优势,然而各路ADC芯片以及时钟信号之间的差异使各个通道存在通道失配,这类失配通常包括增益失配、直流偏移失配及时钟延迟失配。通道失配的存在使TIADC系统的输出频谱产生失真,降低了系统的采样精度。因此,必须对系统输出进行信号重建,以减小通道失配,使TIADC系统在具有较高采样率的情况下,仍然具有较高的采样精度。
TIADC系统的信号重建一般包括通道失配的获取,以及通道失配的校准两个过程。其中,前者一般通过测量或估计两种方式进行,后者分为静态的离线及动态的在线两种校准方式。本文以最小二乘(Least Square,LS)法、期望最大化(Expectation-Maximum,EM)算法、插值拟合、多抽样滤波器组等理论和技术为基础,结合本人所参加的总装型号项目“×××宽带高精度数字化仪”的研制工作,研究通道失配的测量、估计以及动态校准。主要的工作及成果如下:
1.建立了TIADC系统通道采样模型,提出了一种采用最小二乘拟合法的通道失配测量方法。利用最小二乘法和插值滤波器对TIADC系统的输出数据进行处理,导出了TIADC系统通道失配的计算公式。为评估该方法的计算精度和性能,推导了当测试信号中含有谐波失真、采样通道含有量化误差及杂散失真时,通道失配的克拉美劳下限(Cramer-Rao Lower Bound—CRLB),以MonteCarlo仿真对该方法获取的通道失配方差与CRLB进行了分析比较,并进行了400MSPS、12-bit高速数字化仪通道失配的测量实验验证。仿真与实验表明,该方法对通道失配有较高的测量精度,并且其精度受量化误差、通道杂散及谐波失真影响较小,在实际系统中亦可执行有效测量。
2.为满足TIADC系统通道时钟延迟失配的动态校准的需要,提出了一种采用EM的TIADC系统时钟延迟估计方法。根据TIADC系统输入多音(Multitone)信号时,输入信号频率与时钟延迟失配引起的失真频率的关系,利用DFT变换和EM算法对输出信号进行分组,结合输出失真频谱的表达式获得时钟延迟失配。该算法对TIADC系统通道数量没有限制,运算复杂度低,并且可以实现通道时钟延迟失配的在线估计。仿真及实验表明,对于正弦信号或多音信号,该方法均能实现时钟延迟失配的有效估计。
3.通道失配动态校准方面,对于增益、直流偏移失配,可通过简单的乘法器和加法器完成校准,本文将研究重点放在了时钟延迟失配的动态校准上。TIADC系统时钟延迟失配的校准问题实为周期非均匀采样的重构问题。通常,重构滤波器的系数获取,需要对以时钟延迟为变量的时变滤波器进行求逆,运算复杂度较高。利用泰勒级数和DFT变换的性质,将时变滤波器的复杂求逆问题线性化,研究了一种采用重构滤波器的校准方法。利用前述估计方法获得时钟延迟的实时更新,无需改变滤波器系数,即可实现时钟延迟失配的自适应校准。
4.作为对重构滤波器校准方法的补充,将某个通道作为参考通道,在研究通道失配产生的采样点误差的基础上,建立了基于参考通道的校准模型,提出了一种TIADC系统通道失配的参考误差校准法。该方法不需要计算通道失配参数,也不需要滤波器,只需通过数值查表过程,即可实现通道失配的校准。在研究参考误差校准法的校准特点的基础上,针对参考误差校准法中地址覆盖不足的缺陷,进一步研究了改进方法。仿真与实验表明,改进后的参考误差校准法在全频带范围内都可实现TIADC系统通道失配的补偿校准。此外,该方法还可单独用于TIADC系统通道失配的动态校准。
The rapid development of electronics and information technology dramatically increases the operation frequency and complexity of signal in various electronic systems. As the basis of signal digitalization, high speed and accurate sampling technology is the key technique to obtain and analyze tiny characteristics of complex signal in order to distill useful information. Limited by lagged chip technology, even the speed of fastest flash analog to digital converter (ADC) falls far behind the pratical request. The time-interleaved ADC (TIADC) system achieves the multiplication of sampling rate by multiplexing a bank of slow ADCs operating in parallel. Though the sampling rate of TIADC is greatly higher than single ADC, the difference between ADC chips and clock signal in each channel generates the channel mismatches, which include the gain, offset and time mismatch. The channel mismatches produce distortions in the output spectrum of TIADC, and degrade significantly the resolution of the sampling system, which disbennifit the research of specific characteristics of complex transient signal. So the output signal should be properly reconstructed, in order to decrease channel mismatches and guarantee the high accuracy of high speed TIADC.
The signal reconstruction of TIADC usually was divided into two steps which contain obtaination and calibration of channel mismatches. Obtaination of channel mismatches could be carried out by measurenment or estimation. Calibration of channel mismatches includes two ways—off line static calibration and on line dynamic calibration. The measurement, estimation and dynamic calibration of channel mismatches are demonstrated and analyzed in this thesis. Based on theory and technology such as least square, expectation-maximum algorithm, interpolation fit and hybrid filter bank, uniting the pratical request and research work of project“×××wide band and high accurate digitaizer”, the main works and contributions of this thesis are as follows:
1. The hybrid filter bank (HFB) model of TIADC was built, and an approach using least square method (LS) to measure the channel mismatches of TIADC was proposed. Applying LS and interpolation filter to process output samples of TIADC, the formulas to measure the channel mismatches were deduced. Meanwhile, the Cramer-Rao Lower Bound (CRLB) was deduced when there were quantization error and spurious distortions in sample channel, in addition to harmonic distortions in the test signal. Accuracy of the method was verified by comparing channel mismatch variances to CRLB in MonteCarlo simulation. The effectiveness and accuracy of this method in actual applications were verified in the measurement of channel mismatches in 400MSPS 12-bit high speed digitizer.
2. To satisfy the requirement of time mismatch’s realtime calibration, estimation algorithm of time mismatch by expectation-maxmum algorithm (EM) was presented. According to the relationship between frequencies of input and distorted signals caused by time mismatch, DFT and EM were used to subgroup the output signal, and the expression of output spectrum was applied to obtain time mismatch. With no limitations on the channel number of TIADC, the algorithm can be implemented in the background. In the simulation and experiment, it was demonstrated that no matter the input signal was single tone or multi-tone, the algorithm can obtain time mismatch effectively.
3. To the dynamic calibration of channel mismatches, gain and offset mismatch can be simply calibrated by multiplier and adder, thus emphasis was focused on the dynamic calibration of time mismatch, which equalized to the reconstruction problem of periodic nonuniform sampling. Talor series were used to linearize the complex inversion of time varied filter in traditional reconstruction method to obtain coeffecients of reconstruction filter. In the case that timing mismatch was changed, the timing mismatch was updated by above mentioned calculation algorithm without recalculation of the filter coefficients.
4. Considering one channel as the reference channel, the calibration model based on reference channel was built, and reference error calibration method was proposed, as a compensation for reconstruction filter calibration method. Without estimating channel mismatches and using filters, the method can efficiently complete dynamic calibration by look-up-table. Aiming at the limitation that the coverage of address is inadequate, an improved sheme method was studied. Finally , simulations and experiments demonstrated that such approach can effectively compensated channel mismatches’calibration in the whole range of input frequency, furthermore, it can also independently be applied to dynamically calibrate the channel mismatches.
TIADC系统的信号重建一般包括通道失配的获取,以及通道失配的校准两个过程。其中,前者一般通过测量或估计两种方式进行,后者分为静态的离线及动态的在线两种校准方式。本文以最小二乘(Least Square,LS)法、期望最大化(Expectation-Maximum,EM)算法、插值拟合、多抽样滤波器组等理论和技术为基础,结合本人所参加的总装型号项目“×××宽带高精度数字化仪”的研制工作,研究通道失配的测量、估计以及动态校准。主要的工作及成果如下:
1.建立了TIADC系统通道采样模型,提出了一种采用最小二乘拟合法的通道失配测量方法。利用最小二乘法和插值滤波器对TIADC系统的输出数据进行处理,导出了TIADC系统通道失配的计算公式。为评估该方法的计算精度和性能,推导了当测试信号中含有谐波失真、采样通道含有量化误差及杂散失真时,通道失配的克拉美劳下限(Cramer-Rao Lower Bound—CRLB),以MonteCarlo仿真对该方法获取的通道失配方差与CRLB进行了分析比较,并进行了400MSPS、12-bit高速数字化仪通道失配的测量实验验证。仿真与实验表明,该方法对通道失配有较高的测量精度,并且其精度受量化误差、通道杂散及谐波失真影响较小,在实际系统中亦可执行有效测量。
2.为满足TIADC系统通道时钟延迟失配的动态校准的需要,提出了一种采用EM的TIADC系统时钟延迟估计方法。根据TIADC系统输入多音(Multitone)信号时,输入信号频率与时钟延迟失配引起的失真频率的关系,利用DFT变换和EM算法对输出信号进行分组,结合输出失真频谱的表达式获得时钟延迟失配。该算法对TIADC系统通道数量没有限制,运算复杂度低,并且可以实现通道时钟延迟失配的在线估计。仿真及实验表明,对于正弦信号或多音信号,该方法均能实现时钟延迟失配的有效估计。
3.通道失配动态校准方面,对于增益、直流偏移失配,可通过简单的乘法器和加法器完成校准,本文将研究重点放在了时钟延迟失配的动态校准上。TIADC系统时钟延迟失配的校准问题实为周期非均匀采样的重构问题。通常,重构滤波器的系数获取,需要对以时钟延迟为变量的时变滤波器进行求逆,运算复杂度较高。利用泰勒级数和DFT变换的性质,将时变滤波器的复杂求逆问题线性化,研究了一种采用重构滤波器的校准方法。利用前述估计方法获得时钟延迟的实时更新,无需改变滤波器系数,即可实现时钟延迟失配的自适应校准。
4.作为对重构滤波器校准方法的补充,将某个通道作为参考通道,在研究通道失配产生的采样点误差的基础上,建立了基于参考通道的校准模型,提出了一种TIADC系统通道失配的参考误差校准法。该方法不需要计算通道失配参数,也不需要滤波器,只需通过数值查表过程,即可实现通道失配的校准。在研究参考误差校准法的校准特点的基础上,针对参考误差校准法中地址覆盖不足的缺陷,进一步研究了改进方法。仿真与实验表明,改进后的参考误差校准法在全频带范围内都可实现TIADC系统通道失配的补偿校准。此外,该方法还可单独用于TIADC系统通道失配的动态校准。
The rapid development of electronics and information technology dramatically increases the operation frequency and complexity of signal in various electronic systems. As the basis of signal digitalization, high speed and accurate sampling technology is the key technique to obtain and analyze tiny characteristics of complex signal in order to distill useful information. Limited by lagged chip technology, even the speed of fastest flash analog to digital converter (ADC) falls far behind the pratical request. The time-interleaved ADC (TIADC) system achieves the multiplication of sampling rate by multiplexing a bank of slow ADCs operating in parallel. Though the sampling rate of TIADC is greatly higher than single ADC, the difference between ADC chips and clock signal in each channel generates the channel mismatches, which include the gain, offset and time mismatch. The channel mismatches produce distortions in the output spectrum of TIADC, and degrade significantly the resolution of the sampling system, which disbennifit the research of specific characteristics of complex transient signal. So the output signal should be properly reconstructed, in order to decrease channel mismatches and guarantee the high accuracy of high speed TIADC.
The signal reconstruction of TIADC usually was divided into two steps which contain obtaination and calibration of channel mismatches. Obtaination of channel mismatches could be carried out by measurenment or estimation. Calibration of channel mismatches includes two ways—off line static calibration and on line dynamic calibration. The measurement, estimation and dynamic calibration of channel mismatches are demonstrated and analyzed in this thesis. Based on theory and technology such as least square, expectation-maximum algorithm, interpolation fit and hybrid filter bank, uniting the pratical request and research work of project“×××wide band and high accurate digitaizer”, the main works and contributions of this thesis are as follows:
1. The hybrid filter bank (HFB) model of TIADC was built, and an approach using least square method (LS) to measure the channel mismatches of TIADC was proposed. Applying LS and interpolation filter to process output samples of TIADC, the formulas to measure the channel mismatches were deduced. Meanwhile, the Cramer-Rao Lower Bound (CRLB) was deduced when there were quantization error and spurious distortions in sample channel, in addition to harmonic distortions in the test signal. Accuracy of the method was verified by comparing channel mismatch variances to CRLB in MonteCarlo simulation. The effectiveness and accuracy of this method in actual applications were verified in the measurement of channel mismatches in 400MSPS 12-bit high speed digitizer.
2. To satisfy the requirement of time mismatch’s realtime calibration, estimation algorithm of time mismatch by expectation-maxmum algorithm (EM) was presented. According to the relationship between frequencies of input and distorted signals caused by time mismatch, DFT and EM were used to subgroup the output signal, and the expression of output spectrum was applied to obtain time mismatch. With no limitations on the channel number of TIADC, the algorithm can be implemented in the background. In the simulation and experiment, it was demonstrated that no matter the input signal was single tone or multi-tone, the algorithm can obtain time mismatch effectively.
3. To the dynamic calibration of channel mismatches, gain and offset mismatch can be simply calibrated by multiplier and adder, thus emphasis was focused on the dynamic calibration of time mismatch, which equalized to the reconstruction problem of periodic nonuniform sampling. Talor series were used to linearize the complex inversion of time varied filter in traditional reconstruction method to obtain coeffecients of reconstruction filter. In the case that timing mismatch was changed, the timing mismatch was updated by above mentioned calculation algorithm without recalculation of the filter coefficients.
4. Considering one channel as the reference channel, the calibration model based on reference channel was built, and reference error calibration method was proposed, as a compensation for reconstruction filter calibration method. Without estimating channel mismatches and using filters, the method can efficiently complete dynamic calibration by look-up-table. Aiming at the limitation that the coverage of address is inadequate, an improved sheme method was studied. Finally , simulations and experiments demonstrated that such approach can effectively compensated channel mismatches’calibration in the whole range of input frequency, furthermore, it can also independently be applied to dynamically calibrate the channel mismatches.
引文
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