Key Technologies For Sampling Of Wide-band Signals

The trend of modern communication and Radar systems are wideband andsoft-defined. Effective methods for sampling and reconstructing wideband signals areessentials to conform to the trend. However, the sampling systems based on traditionalschemes and theory become more and more difficult to meet requirements due to thelimitations of current IC processing and some especial application conditions. So,research of high efficient sampling schemes and general sampling theory are topics oftheoretical interest and also of great relevance to applications.Time-Interleaved ADC is a kind of high efficient parallel sampling scheme aimingat wideband signals with limited bandwidth, while the framework of finite rate ofinnovation (FRI) is the basic theory to sample a kind of non-bandlimited signalseffectively. It is a generalization of standard Shannon’s sampling theorem from the viewpoint of space projection. Based on non-linear filter bank (NLFB) model, two stateMarkov chains, differential filter bank and fractional delay filter, this dissertationstudies adaptive backward calibration method for channel mismatch errors. For theframework of FRI, studies are conducted in this dissertation, mainly on the internalconstraint relationship between sampling system and complex pulse shapes, and on therobustness of reconstruction in noisy scenario.The main contents of this dissertation are summarized as follows:1. Focus on the offset mismatch error of TIADC, an adaptive backward calibrationmethod based on data-randomizing operation is proposed. First, this part analyzesand verifies the defect of direct data-averaging method, and then, based on thereason of defect and the mechanism of offset error, we introduce a randomizingoperator to the data between sample-and-hold (S/H) and quantizer. When therandom series is zero-mean and uncorrelated with input signal, an unbiasedestimation of the channel offset error can be got by the best linear unbiasedestimator. In the light of high computational complexity of best linear unbiasedestimator, a suboptimal estimator based on data-averaging is proposed. Theasymptotic equivalence between the data-averaging estimator and the best linearunbiased estimator is proved. In order to implement easily and to provide moredegrees of freedom for design, the two state Markov chain is used as the randomseries generator. Analysis and simulation results verify that the performance ofcalibration will be improved by increasing the number of samples and setting the transition probability of Markov chain, and that the proposed method is effectiveeven if gain mismatch errors and timing mismatch errors are exist.2. Focus on the gain mismatch errors and timing mismatch errors, a digital adaptivebackward calibration method based on differential filter bank is proposed. First, bydesigning the sampling timing, each sub-channel is synchronized with the samereference channel periodically to sample input signals, and then, the samples of thereference channel can be expressed as the Taylor’s series of the samples ofsub-channels. According to this relationship, an adaptive calibration architecture isdesigned for both gain mismatch errors and timing mismatch errors. Therelationship between differential filter bank and fractional delay filter is analyzed,which provides a simple way to apply the proposed method to DSP platforms.Simulation results demonstrate that the proposed method is fit for both multi-tonesignals and bandlimited signals when they are slightly oversampled, and can workin both baseband and bandpass scenarios on the condition that we know the Nyquistband of input signal in advance. The performance of the proposed calibrationmethod is determined by the taps of differential filters and the length of Taylor’sexpansion. In order to improve precision of calibration and reduce the oversampling factor, the taps of differential filters must be increased, with the length ofTaylor expansion set properly.3. For the FRI signals with complex pulse shape, the constraint relationship betweensampling kernels and input signals is deduced from the reconstructing mechanismof FRI framework, and then, the design method of sampling system for periodicFRI signals and finite length FRI signals is proposed. For the periodic FRI signals,sinc or sum of sincs (SoS) sampling kernels should be chose, and frequency shiftoperation can be used to meet the constraint. For the finite length FRI signals, weshould choose SoS or exponential reproducing sampling kernels. When SoSsampling kernels are used, the constraint between sampling kernels and inputsignals is the same as that of the SoS sampling kernels used for the periodic signals.When exponential reproducing sampling kernels are chose, the constraint isdetermined by the parameters of sampling kernels, so we can set properly theparameters of sampling kernels for different complex pulse shape to satisfy theconstraint. In addition, we also analyze the constraint from the consideration ofrobustness of system and practical implement, and then, give the setting method ofsampling kernels. The simulations results demonstrate that the performance ofreconstruction can be improved by our design methods. 4. Focus on the robustness of reconstruction of FRI sampling system in noisyscenarios, two solutions are given out, which are modified exponential splinesampling kernels and subspace prewhitening method. When noise exists, robustreconstructing algorithms must be used. However, these algorithms require that thenoise components in samples are additive white noise. Due to the filtering ofsampling kernels, the samples may not meet this requirement. So, based on themechanism of action of sampling kernel on samples and the inherent convolutionproperty of exponential reproducing sampling kernels, we modify the originalexponential spline in frequency domain to keep the characteristic of noisecomponents. For the scenarios that the modified exponential spline samplingkernels are restricted, we can prewhiten the noise components by subspacewhitening method before reconstruction to satisfy the prerequisite. The simulationresults verify the validity of the proposed solutions, and demonstrate that themodified exponential spline sampling kernel gets better performance, while theprewhitening method has more applicability.