- Lecture Notes in Mathematics Journal
- June 2008
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
Electronic International Standard Serial Number (EISSN)
- These lecture notes provide a mathematical treatment of time-reversal experiments with a special emphasis on telecommunication. A direct link is established between time-reversal experiments and theadjoint imaging method. Based on this relationship, several iterative schemes are proposed for optimizing MIMO (multiple-input multiple-output) time-reversal systems in underwater acoustic and in wireless communication systems. Whereas in typical imaging applications these iterative schemes require the repeated solution of forward problems in a computer, the analogue in timereversal communication schemes consists of a small number of physical time-reversal experiments and does not require exact knowledge of the environment in which the communication system operates. The discussion is put in the general framework of wave propagation by symmetric hyperbolic systems, with detailed discussions of the linear acoustic system for underwater communication and of the time-dependent system of Maxwell's equations for telecommunication. Moreover, in its general form as treated here, the theory will also apply for several other models of wave-propagation, such as for example linear elastic waves.