An efficient approximation for Maximum Likelihood estimation of ADC parameters

Maximum Likelihood (ML) estimation is applied for estimating ADC parameters in several papers. However, none of them provided an efficient way to calculate the code transition levels for sine wave excitation signals. Due to the vast amount of data points and parameters, the complexity of the estimation for high resolution ADCs is overwhelming. The general ML cost function is already published in [1] [14] for Gaussian noise where the algorithm involves calculations with the erf function. In order to be able to accelerate the algorithm, approximations are needed. An efficient approximation is proposed below which applies Laplacian noise model. In this case the likelihood function consists of only exponentials which simplifies the calculation. After finding the parameters, which are close to those for the Gaussian distribution, they can be adjusted to the Gaussian noise model. This approach not necessarily requires a Gaussian noise distribution. Simulation results show the the bias of the code transition level estimation is not necessarily dependent on the shape of the noise distribution.