Long-time coherent accumulation algorithms for reflected signal with non-zero higher derivatives of the range to radar target in the spectral domain

The purpose of the article is to present computationally economical algorithms for long-term coherent accumulation of signals reflected from a point target with compensation for range and frequency migration and accumulation of signals in the spectral region. The algorithms include intra-period processing with simultaneous correction of range and frequency migration and inter-period processing with coherent accumulation of signals at the output of intra-period processing. In the first variant of the algorithm, intra-period processing is implemented by calculating the spectra of the received signals in each repetition period, multiplying the samples of the spectra by the samples of the amplitude-phase-frequency characteristic of the matched filter of a single signal and correcting phase coefficients determined by the number of the repetition period and the values of the range derivatives, and the inverse Fourier transform of the transformed spectra. The difference between the second version of the algorithm at the stage of intraperiod processing is the correction of only the quadratic and subsequent components of the range and frequency migration and the use of the keystone transformation, which eliminates the linear range migration. Coherent accumulation for both variants is realized due to the fast Fourier transform of the signal samples over the repetition periods for all samples over the range. The concept of “rough speed resolutionˮ is introduced, which determines the arrangement of channels when compensating for range migration. The uncertainty function in the coordinates “velocity–acceleration” is obtained. The equivalence of the two variants of the algorithm is shown and estimates for the required number of receiver channels are given. The simulation results confirming the operability of the proposed algorithms are presented.

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