Demonstration of time reversal methods in a multi-path environment

Abstract

INTRDDUCTIONTime reversal methods OK-B unique opportunity for solving the problem of e l s t r e magnetic (EM) wave propagation and focusing in a spatially varying (inhomogeneous) medium. While the concept of time reversal or applying time reversal mirrors to focus waves in spatially varying media is new to the field of EM wave propagation, it has been applied in the area of acoustics and ultrasonics for several years [I]. The basic premi~e is quite simple. Let an impulse source (in time and space) he transmitted into some general inhomogeneous medium, and consider the tangential surface fields determined on a closed surface surrounding the impulse. It can be shown mathematically that if these surface fidds are conjugated and re-radiated in time reversed sequence, that the incoming wave, generated by the surf-fields is identical to the outgoing wwe, and the returning energy focuses on the original source point. In the frequency domain, this is equivalent to simply taking the complex conjugate of the received field, and reradiating it. This can he shown to he an application of reciprocity, which can be viewed 68 a BpatiDtemporal matched filter, similar to temporal matched filters commonly applied in isdar and mmmmications.In practical applications of TRM, a source transmits through an inhomogeneous medium, to an a finite array. In the frequency domsln, it can be shown through reciprocity that the following relatiomhip holds:where EL, Ez are electric fields caused by current sources J,, J2, iespectively. Let E, represents the fields caused hy source J1, at the location of an array element, and E2 reprerent the fields caused hy reradiation of this element, at the location of the original source J1. If the reradiated fields from the array element are caused hy current source Jz, and Jz = E;. then the right side, and therefore the left side of (1) becomes purely real, and the received fields *om the array element a t the location of the original source thus are also purely real. Applying this to all elements in the array, the coherent sum of their fields at the original source point will add constructively, and focus the received energy at this point.In any b i t e size array that occupies B limited spatial area the system is diffraction limited. however in sousties, it has been shown that in m inhomogeneous medium a time reversal &may is not always diffraction limited and can achieve super-resolution 121. Basically xatterers near the transmitting army and/or focal point act as an extension of the array in the focusing process. In this paper the same phenomenon is show" to exist for EM waves J 1 . E x = . l . E l l

Electromagnetic Imaging Method Based on Time Reversal Processing Applied to Through-the-Wall Target Localization

“…It has been proved [13] that by reversing in time this data and radiating it from the same array, we focus on the source location. The focusing precision is imposed by the size of the array of transceivers and may even increase in presence of multipaths [14]. In this particular case, there is a source radiating a plane wave.…”

Multiple-Source Time-Reversal Transmissions in Random Media

“…There should be no confusion at this point that even though (13) is no more dependent on the effective heights {h m }, there is no such a thing as a single TRT field, but a set of fields, depending on the characteristics of each source. The TRT field W (r, ν) considered hereafter should therefore be regarded as an auxiliary function that makes sense only when considering its statistical moments, as those in (13). We need to recall that…”

Full-wave Characterization of Rough Terrain Surface Effects for Forward-looking Radar Applications: A Scattering and Imaging Study from the Electromagnetic Perspective

“…Then, a coherent field integration technique is employed to process the scattered signals to obtain an image of the illuminated scene. According to the time-reversal, or phase-conjugation, method (55,56), since the received scattered field can be written as…”