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On Application of Taper Windows for Sidelobe Suppression in LFM Pulse Compression

*Progress In Electromagnetics Research C*, Vol. 107, pp.259-271

**(2021)**

### V.G. Galushko

The efficiency of the standard tapered windows as applied to sidelobe suppression in compressed pulses with linear frequency modulation (LFM) or chirp pulses corresponds to the literature data only in the case of rather great values of the pulse duration-bandwidth product B ≥ 100. With
comparatively small values of B (several dozens or so), the side-lobe levels prove to be essentially greater than those announced in the literature. In the paper, the output signal of the chirp-pulse compression filter is analyzed in order to look into causes of the discrepancy between the sidelobe level obtainable using standard tapered windows and the literature data. Expressions are derived for estimating the maximum number of zeros and maxima in the response of the optimum filter of chirp-pulse compression and separation between adjacent and ?like? (with the same numbers) zeros and maxima in dependence on the signal duration-bandwidth product. The amount of loss in the signal-to-noise ratio due to the application of smoothing functions is determined. The case of applying window functions in the form of cosine harmonics of the Fourier series, which describes a rather great number of the standard windows, is analyzed in detail. Analytical expressions are presented for the output signal of the chirppulse compression filter on the basis of such windows and the amount of loss in the signal-to-noise ratio. A comparative analysis of the Hamming and Blackman windows is made in dependence on B.
It is shown that application of the Hamming window is more efficient up to B ≈ 80. For greater values of B, the Blackman window shows a higher efficiency. As B increases, the efficiency of both windows steadily increases asymptotically approaching the figure declared in the literature. Coefficients of window functions containing 2 cosine harmonics of the Fourier series have empirically been selected which made it possible to reduce the sidelobe level by approximately 0.34 dB for B = 21 and by more than 1 dB for B = 7 as compared with the Hamming window. The obtained results allow concluding that the optimization problem for the window function parameters in the case of small values of the pulse duration-bandwidth product should be solved individually for each specific value of B. Most likely it would be impossible to obtain the extremely low sidelobe level; however, a certain improvement of the characteristics of the chirp-pulse compression filter seems quite possible.

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