|Article title||DISCRETE PHASE PROBLEM IN THE RECOVERY OF SIGNALS IN PRODUCTS OF ROCKET AND SPACE TECHNOLOGY|
|Authors||A. A. Kuleshova, E. A. Shchelokov|
|Section||SECTION II. DESIGNING MANAGEMENT INFORMATION AND AUTOMATED SYSTEMS|
|Month, Year||09, 2017 @en|
|Abstract||The problem of transmitting information via the wireless interface in the products of rocket and space technology is considered. The aim of the work is to study the main characteristics of receiving and transmitting devices in the products of rocket and space technology (namely, in the conditions of tight arrangement of equipment and metal structures). As a basis for determining the availability of receiving and transmitting devices in the dense configuration of selected devices such as Wi-fi with OFDM modulation, and modeling in 2D mode in metal structures using a CAD-based tamograph, as a result, it was proved that data can be transferred in dense configuration devices, as well as a complex electromagnetic environment, caused by metal crooks. The search for fast algorithms for signal reconstruction without phases is relevant at the present time. The main property of frames that makes them so useful in applied tasks is their redundancy. A well-chosen frame can provide numerical stability for signal recovery and important signal characteristics. The frame family restores the signal by the absolute value of the frame coefficients in polynomial time. It is shown that, in the actual case, a frame position consisting of (2m-1) -vectors can, under certain conditions, reconstruct a signal without phases. A similar result in complex space was obtained for (4m-2) vectors. With the change "reconstruction without phases," consideration of another version of the statement of the discrete phase problem is "phase reconstruction". The question of the equivalence of these variants has been put and partially solved. The restoration of information hidden in the phases of the vector-signal, does not lose relevance. A set of vectors , called frames, in space can be used to theoretically study the recovery of phases. Examples are considered for which sets of vectors are constructed that simultaneously perform phase restoration and recovery without phases. Examples of a signal in spaces of small dimension.|
|Keywords||Frame; recovery without phases; restoration of phases, alternative completeness; frames of general position.|
|References||1. Botelho-Andrade S., Casazza P., Van Nguyen H., Tremain J. Phase retrieval verses phaseless reconstruction [Electronic resource] arXiv:1507.05815 [math. FA] – 21 Jul 2015.
2. Shchelokov E.A. Application of technologies of wireless data transmission on aerospace hardware, The Bulletin of the Ryazan state radio engineering university, 2016, No. 56, pp. 131-135.
3. Bandeira A., Cahill J., Mixon D., Nelson A. Saving phase: Injectivity and stability for phase retrieval, Applied and Computational Harmonic Analysis (ACHA), 2014, Vol. 37, Issue 1, pp. 106-125.
4. Balan R., Bodmann B.G., Casazza P.G., Edidin D. Fast algorithems for signal reconstruction without phase, Proceedings of SPIE-Wavelets XII, San Diego 6701, 2007, 670111920-670111932.
5. Balan R.. Casazza P., Edidin D. On signal reconstruction without phase, Appl. Comput. Harmon. Anal., 2006, Vol. 20, pp. 345-356.
6. Holmes R., Paulsen V.I. Optimal frames for erasures, Lin. Alg. Appl., 2004, Vol. 377, pp. 31-51.
7. Balan R., Bodman B.G., Casazza P.G. and Edidin D. Painless reconstruction from magnitudes of frame coefficients, preprint.
8. Novikov S.Ya., Fedina M.E. Complete systems in problems of signal reconstruction, Proceedings of the International Scientific and Technical Conference. Vol. 1 "Perspective Information Technologies", 2015, pp. 280-283 (in Russian).
9. Cameron P.J., Seidel J.J. Quadratic forms over GF(2), Indag. Math., 1973, Vol. 35, pp. 1-8.
10. Cahill J., Mixon D.G. Full Spark Frames. Available online: arXiv:1110.3548.
11. Kuleshova A. Generic frame in problems for signal reconstruction without phase, ITNT 2016 Information Technology and Nanotechnology, 2016, pp. 364-372. Available at: http://ceur-ws.org/Vol-1638/.
12. Novikov S.Ya., Fedina M.E. Polnye sistemy v zadachakh vosstanovleniya signala [A complete system for the task of signal restoration,] Trudy Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii. T. 1 «Perspektivnye informatsionnye tekhnologii» [Proceedings of International scientific-technical conference. Vol. 1 "Promising information technologies"], 2015, pp. 280-283.
13. Balan R., Bodmann B.G., Casazza P.G., Edidin D. Fast algorithems for signal reconstruction without phase, Proceedings of SPIE-Wavelets XII, San Diego 6701 (2007) 670111920-670111932.
14. Novikov S.Ya. Vosstanovlenie signala po modulyam koeffitsientov [Signal recovery module of coefficients], Perspektivnye informatsionnye tekhnologii (PIT 2014): Trudy Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii [Advanced information technologies (AFT 2014): proceedings of the International scientific and technical conference], ed. by S.A. Prokhorova. Samara: Izd-vo Samarskogo nauchnogo tsentra RAN, 2014, pp. 223.
15. Planirovanie i obsluzhivanie Wi-Fi setey [Planning and maintenance of Wi-Fi networks]. Available at: http://www.tamos.ru/products/wifi-site-survey/.
16. Novikov S.Ya., Lihobabenko M.A. Frejmy konechnomernyh prostranstv. Samara: Samara University, 2013, 52 p.
17. Novikov S.Ya. Vosstanovlenie normy signala po normam proekcij, Perspective information technologies (PIT 2015): Proceedings of the International Scientific and Technical Conference. Vol. 1: Ed. S.A. Prokhorov. Samara: Publishing house of the Samara Scientific Center of the Russian Academy of Sciences, 2015, pp. 279.
18. Shchelokov E.A., Ovsyannikov A.N. Primenenie tekhnologiy besprovodnoy peredachi dannykh na izdeliyakh raketno-kosmicheskoy tekhnike [Use of technology for wireless transmission of data on rocket and space technology], Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta [Bulletin of Ryazan state Radiotechnical University], 2016, No. 56, pp. 144-148.
19. Semkin N.D., Kunikin S.A., Shchelokov E.A. Metod organizatsii i printsipy postroeniya abonentskoy apparatury retranslyatsii pri pomoshchi unifitsirovannoy analitiko-imitatsionnoy modeli sistemy funktsional'nogo kontrolya i diagnostirovaniya sistem kosmicheskikh apparatov [The method of organization and the principles of subscriber equipment relay with a unified analytical and simulation model of the system functional control and diagnosis of spacecraft systems], Konferentsiya «Sistemnyy analiz, navigatsiya i upravlenie», 2015: Cb. tezisov dokladov [Conference "System analysis, management and navigation", 2015: book of abstract].
20. Kunikin S.A. Analiz datchikovoy apparatury i sistem sbora informatsii, primenyaemykh na bortu kosmicheskogo apparata [Analysis of sensor equipment and data acquisition systems used on Board spacecraft ], Materialy Vserossiyskoy nauchno-tekhnicheskoy konferentsii
18-20 maya, 2016 g. [Materials of all-Russian scientific-technical conference may 18-20, 2016], pp. 146-148.