Comparative Analysis of Resolution of Nonparametric BDS Criterion and Maximum Likelihood Criterion for Estimation of Delay and Doppler Frequency Shift of Pulse Signal

Abstract

The paper considers a potential resolution of BDS criterion that is used as a goal function in solving the problem of Doppler frequency estimation and the delay of a wideband phase-shift keying pulse signal. For the purpose of investigating the BDS criterion characteristics, BDS-criterion is compared with the maximum likelihood (ML) criterion. A comparative analysis is conducted using the sensitivity function (SF) of BDS criterion and the wideband ambiguity function (WAF) of BPSK signals that make it possible to determine the potential resolution of the methods under consideration. The results of numerical simulation of SF characteristics for BPSK signal were conducted for the cases of presence and absence of noise in observation. The resolution of above criteria was analyzed both with due regard for the signal carrier frequency and in terms of its complex envelope. It was shown that in solving the problem of Doppler frequency estimation and the delay of BPSK signal, the resolution of BDS criterion can be enhanced by taking into account the carrier frequency. The comparative analysis of the resolution of selected criteria depending on the level of additive Gaussian noise in observation was also conducted. It was shown that at low noise levels the potential resolution of BDS criterion is higher than that of ML criterion.