Modified CRLB Based Optimal Sampling Frequency Selection in Phase and Frequency Estimation

The sampling process is an almost indispensable operation in signal processing. The sampling frequency is one of the factors in the sampling process and the selection of it is also important in the signal processing issues, such as detection, estimation, communication, and so on. In estimation theory, the Cramér-Rao lower bound (CRLB) provides an evaluation of the information contained in the observed data. Moreover, under unknown time shifting with known probability density function, the modified CRLB is a tighter lower bound than CRLB. Previously, the sampling frequency is often chosen as the Nyquist frequency, this frequency might not be optimal in some estimation issues. This paper proposes a strategy of sampling frequency selection, which is choosing the frequency for minimizing the determinant of modified CRLB. In this paper, the basic signal, single frequency signal, is considered. The proposed strategy is examined in the three cases, estimating the unknown phase, estimating the unknown frequency and jointly estimating the amplitude and phase. As the experimental results have shown, the performance of maximum likelihood estimator (MLE) under different frequencies corresponds to the relative values of modified CRLB under them. In addition, the estimator achieves bad performance under Nyquist frequency in all three scenes. Moreover, a bit of difference in sampling frequency would cause great different results, in the experiments. Therefore, choosing sampling frequency based on the proposed strategy is effective in the estimation issues.