The time-domain maximum likelihood estimation of chirp signal parameters is investigated in this study. Three amplitude weighted phase-based estimators and two phase-unwrapping algorithms, that is, phase prediction and unwrapping algorithm (PP-UA) and differenced-phase prediction and unwrapping algorithm (DPP-UA) were proposed. The DPP-UA and PP-UA have their merits and drawbacks. The authors combine the merits of these two methods and propose a new phaseunwrapping algorithm, which outperforms PP-UA and DPP-UA under low signal-to-noise ratio (SNR) conditions. The authors' further study on the optimal number of initial data sample show that it is SNR-related and can be determined according to the '3σ' rule and the Cramer-Rao lower bound.
A novel method for solving Doppler ambiguous problem based on compressed sensing (CS) theory is proposed in this paper. A pulse train with the random and sparse transmitting time is transmitted. The received signals after matched filtering can be viewed as randomly sparse sampling from the traditional fixed-pulse repetition frequency (PRF) echo signals. The whole target echo could be reconstructed via CS recovery algorithms. Through refining the sensing matrix, which is equivalent to increase the sampling frequency of target characteristic, the Doppler unambiguous range is enlarged. In particular, Complex Approximate Message Passing (CAMP) algorithm is developed to estimate the unambiguity Doppler frequency. Cramer-Rao lower bound expressions are derived for the frequency. Numerical simulations validate the effectiveness of the proposed method. Finally, compared with traditional methods, the proposed method only requires transmitting a few sparse probing pulses to achieve a larger Doppler frequency unambiguous range and can also reduce the consumption of the radar time resources.
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