31-45

UDC 621.37
DOI: 10.15350/2306-2819.2018.4.31

Introduction. Modern methods of processing of radar signals with the transmission of a coded sounding long-duration signal allow providing a comparatively narrow pulse of the reflected signal at the input of the receiver. As a result distance (time) radar resolution increases considerably while the whole energy of an echo signal within the compressed pulse is conserved. The processing requirement, necessary for the source signal is its energy spectrum uniformity. Only a small part of the known signals meets these requirements. One of the approaches, used nowadays, is inverse filtering. It allows obtaining high distance resolution for a wide spectrum of sounding signals. The cost of it is the decrease of signal-to-fluctuation noise ratio at the output of the compression device in case of close to zero components, called critical, in the signal spectrum. The purpose of the work is to ensure the stability of inverse filter operation in this situation by replacing the source input signal with the corrected signal, which does not contain critical components and simultaneously it has the high degree of similarity to the source signal. Component-wise spectral analysis of a vector signal. In order to solve the set task, the form of signal spectrum representation, called a component-wise spectrum, is used. This representation is in the form of a matrix, whose rows, considered as vectors, are the full family of elementary contours of the corresponding order, each of which is scaled and rotated by a certain angle relative to corresponding elementary contours. The sum of each column of the matrix is equal to the corresponding component of the signal spectrum. Such representation of the spectrum gives the possibility to control the value of the signal spectrum increment depending on the signal component variation. Correction of the critical component of the input signal spectrum. The procedure of component correction is made easier when the component-wise spectrum of the input signal is used. It allows representing components in the explicit form. With this signal representation, the correction of the critical spectrum component due to the variation of reduced numbers does not lead to the change of other elements of the component-wise spectrum. This approach provides the high value of the similarity measure of the source and corrected signals and it excludes the occurrence of new critical components. The estimate of efficiency of the correction of the critical component of the input signal spectrum.The similarity measure of the source and corrected signals, determined as the real part of their normalized scalar product serves as the preliminary estimate of the efficiency of input signal correction. The correction of the input signal of the inverse filter can be considered efficient enough if the value is more than 0.95. If this condition is not satisfied, the correction should be continued. Conclusion. The paper substantiates the signal compression algorithm, which allows carrying out signal resolution with zero or close to zero spectral components by inverse filtering replacing the critical spectrum component if the similarity measure ε of the source and corrected signals is close to one. Calculations showed that if ε > 0.95, the efficiency of corrected signal filtering by the filter, matched with the source signal, slightly decreases, by 5 %.  

1.   Vasilenko G.I. Golograficheskoe opoznavanie obrazov [Holographic Pattern Recognition]. Moscow: Sovetskoe radio, 1977. 328 p.
2. Zhang Y., Zhang Y., Li W. et al. Super-resolution surface mapping for scanning radar: Inverse filtering based on the fast iterative adaptive approach // IEEE Transactions on Geoscience and Remote Sensing. 2018. Vol. 56, Iss. 1, January. Pp. 127-144.
3.   Abramenkov V. V., Vasilchenko O.V., Semchenkov S.M. et al. Inversnaya fil`tratsiya impul`snykh signalov [Inverse Filtering of Impulse Signals]. Radiotekhnika [Radio Engineering]. 2017. No 4. Pp. 42 - 53.
4.   Furman Ya. A., Rozhentsov A. A., Krevetsky A. V. et al. Lineinoe preobrazovanie konechnomernogo vektornogo signala v signal s formoy simvola Kronekera [Linear Transformation of a Finite-Dimensional Vector Signal into the Signal with the Kronecker Symbol Shape]. Radiotekhnika [Radio Engineering]. 2017. No 1. Pp. 155-163.
5.   Semchenkov S. M., Savitsky F. L., Abramenkov A. V. et al. Povy`shenie razreshayushchey sposobnosti aktivnogo radara s signalom edinichnoy bazy` metodom inversnoy fil`tratsii [Resolution Enhancement of the Active Radar with the Singular Base Signal by the Inverse Filtering Method]. Matematicheskaya morfologiya [Mathematical Morphology]. 2015. Vol. 14. Iss 4. Pp. 43 - 62.
6.   Krevetsky A.V. Melnikov A.D. Evdokimov A.O. Obnaruzhenie periodicheskikh FM radio signalov s ispol`zovaniem sopryazhennogo soglasovannogo fil`tra [Detection of Periodic FM Radio Signals Using a Conjugate Matched Filter]. Radiotekhnika [Radio Engineering]. 2003. No 5. Pp.11-16.
7. Krevetsky A.V., Melnikov A.D. Razreshenie-obnaruzhenie signalov na baze sopryazhennykh soglasovannykh fil`trov [Signal Resolution-Detection Based on Conjugate Matched Filters]. Radiotekhnika [Radio Engineering]. 2007. No 4. Pp. 3-8.
8.   Furman Ya.A., Krevetsky A.V. Obespechenie nulevogo urovnya bokovykh lepestkov pri szhatii slaboogranichennykh po klassam signalov [Provision of the Zero Side-Lobe Level with the Compression of Weakly Class-Bounded Signals]. Radiotekhnika [Radio Engineering]. 2002. No 3. Pp. 9-18.
9. Furman Ya.A., Krevetsky A.V., Peredreev A.K. et al. Vvedenie v konturnyy analiz i ego prilozheniya k obrabotke izobrazheniy i signalov [Introduction to Contour Analysis and its Applications to Image and Signal Processing]. Moscow: Fizmatlit, 2002. 592 p.
10. Furman Ya.A., Hafizov D. G. Metody i sredstva obrabotki kompleksnoznachnykh i giperkompleksnykh signalov [Methods and Means of Complex Valued and Hypercomplex Signal Processing]. Yoshkar-Ola: Mari State Technical University, 2011. 388 p.
11.  LezinYu.S. Optimal`nye fil`try i nakopiteli impul`snykh signalov [Optimal Filters and Impulse Signals Accumulators]. Moscow: Sovetskoe radio, 1969. 448 p. 

For citation: Furman Ya. A., Kazarinov A. V., Gromyko D. S. Stabilization of the Inverse Filtering of a Signal by its Spectrum Reduction. Vestnik of Volga State University of Technology. Ser.: Radio Engineering and Infocommunication Systems. 2018. No 4 (40). Pp. 31-45. DOI: 10.15350/2306-2819.2018.4.31