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Quasi-Optimal Processing of Coherent Quasi-Continuous Signals with Big Duration-Bandwidth Product in the Preselected Distance-Doppler Range


N.E. Bystrov, I.N. Zhukova, D.V. Chebotarev

Increase of noise immunity of radar systems often relate with increase of duration and duration-bandwidth product of complex-modulated probing signals. A quasi-continuous beaming mode is widely used utilizing one receive-transmit antenna. In this mode complex-modulated signals are transmitted as discrete modulated pulses and receiving of echo-signals is performed during silence interval. An alternative for modulated period pulses are complex-modulated signals with big duration and pseudo-random amplitude keying. In this case durations of discrete probing signals are relatively small and transmit intervals are not matched neither with distance, nor Doppler range of interest. Quasi-continuous signals ambiguity function has a pin-like appearance and provides unequivocal delay and Doppler frequency measurement of processed signals. Increasing of duration-bandwidth product for such signals aggravate its real time processing problems. Complex-modulated quasi-continuous signals processing can be performed by multichannel correlation methods. However in practice the number of correlation channels exceeds several millions. Therefore finding quasi-optimal processing methods of complex signals with big duration is reasonable and is a subject of consideration of this article. Mathematical model of complex quasi-continuous probing signal modulated by amplitude and phase with pseudorandom se-quences is described in the article. Classical correlation-filtering processing methods of echo signals are described. Limited working range of frequency-time delay shifts allows switching over to segment correlation-filtering processing. In this case signal with big duration is divided into segments with length which is matched with analyzed Doppler range. In the beginning a correlation processing of signal segments is performed in defined range of delays. Phase incursion in the processed signal during segment length is neglected. Then for each delay element a Doppler filtration over correlation processing results of all signal segments is performed. Doppler filtration is based on fast Fourier transform algorithm with size corresponding to analyzed frequency range. Analysis of correlation-filtering processing functional scheme modification is performed for segmented processed signal. An example of echo signal processing is given. A test signal at processing unit quadrature inputs and the results of processing after each stage of processing are shown. The results of echo signal processing with increase of Doppler frequency to maximum value are compared. Energy losses due to neglecting possible processed signal Doppler frequency shift during segment length time interval are ana-lyzed. An frequency shift energy losses function is introduced, which allows to estimate its value. It is noted that energy losses do not exceed 4dB when frequency shift is at its maximum. An analysis of processing costs in terms of number of complex multiply-add operations is performed. It is shown that for practical values of delay and Doppler frequency shift ranges implementation of segmented processing in time domain requires about 10 times less computing operations compared to implementation of classical methods based on calculation of fast Fourier transform with size equal to probe signal duration. Use of well known algorithms of fast convolution in correlation processing of segmented signal allows earning extra processing gain. For working parameters of processing this gain can be estimated as 16 times. Therefore research of quasi-optimal processing of complex signals with big duration in the limited delay-Doppler range and the methods of its implementation confirm reasonability and efficiency of its use.
June 24, 2020
May 29, 2020

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