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Near-optimal estimation of radar pulse modulation waveform

In this study, the authors focus on pulse modulation waveform estimation based on a sequence of intercepted pulses from the same radar emitter. In general, modulation waveform estimators first perform pulse alignment in time and frequency separately, and then accumulate the aligned pulses to estimate the waveform. However, commonly used alignment methods may lead to considerable alignment errors which are difficult to detect and compensate, especially under low signal-to-noise ratio (SNR) conditions, resulting in non-ideal effects of accumulation. This study proposes a robust and nearly optimal modulation waveform estimation algorithm. The new algorithm first aligns pulses in time and frequency jointly via the cross-ambiguity function to avoid the transfer and accumulation of alignment errors. After that, an iterative maximum-likelihood estimator is invoked to achieve the waveform estimation. Theoretical analysis and extensive experiments show that the proposed algorithm has much smaller alignment errors and better modulation waveform and modulation parameter estimation ability than competing methods at low SNRs, and can approach the ideal case. Moreover, this algorithm does not make any assumption on the type of modulation and is computationally efficient, thus having broad applications.