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Ref.: Proc. OCEANS MTS/IEEE ' 2007, (ISBN:), p., Vancouver, Canada, 2007. (to appear)
Abstract: In recent years active Time Reversal (TR) has
received particular attention from the
scientific community. After practical underwater demonstration of
focusing capabilities several applications of active TR (aTR),
from tomography to
communications, have been suggested. The passive version of TR
(pTR) uses a receive
only array, and the source sends a probe signal ahead of the data,
for Impulse Response
(IR) channel estimation. Such IR estimate is then used as a
synthetic channel for
temporal focusing of the data signal, which is equivalent
to deconvolving the multipath
generated by the real channel.
When applied to underwater digital coherent communications, due to the IR estimation error and the time variability of the channel, the achieved TR focus is not perfect resulting in uncompensated intersymbol interference (ISI). That problem is more relevant when applied to communications with a moving source and/or receiver. In such case it is intuitive that a rapid degradation of the passive TR temporal focusing capability will occur, due to the increased mismatch between the assumed and the actual channel. In order to guarantee a longer stability of the focal spot, threesolutions with advantages and disadvantages are usually suggested: one is to send probe signals more frequently; another is to use a high complexity adaptive algorithm to track the IR from the initial probe signal IR estimation; and finaly a third alternative is to use a low complexity equalizer for residual uncompensated ISI. A performance comparison between those adaptive pTR versions is presented in .
In the present paper, a physics-based adaptive algorithm for IR tracking is suggested. Such adaptive algorithm is based on the waveguide invariant properties of the shallow water channel. The waveguide invariant property has been applied to change the aTR range focus in , and to interpret a model for performance prediction of a time reversal communication system . In  the waveguide invariant property was extended to the compensation of geometric mismatch. This novel waveguide invariant property interpretation states that changes on geometric characteristics of the acoustic channel, such as source-receiver range, source depth and array depth, can be compensated by a frequency shift in the channel frequency response. The Frequency Shift compensation of the pTR (FSpTR), will guarantee a maximization of pTR output power and that results in a minimization of the mean square error between the detected and the transmitted symbol sequences. That will result in an underwater communications physics-based equalizer that is able to detect the transmitted data sequence and to simultaneously estimate the source-array range, source depth and array depth. The reliability of the physics-based waveguide invariant pTR equalizer is demonstrated using experimental data obtained during the MREA 2004 sea trial, where binary PSK signals at a data rate of 400 bits per second were transmitted with a carrier frequency of 3.6 kHz. Results obtained with the FSpTR, after Doppler compensation of the received signals, shows a long term compensation of the channel mismatch with the mean squared error between the transmitted and the received data symbols keeping stable up to a range mismatch of 40 m in presence of source depth varying between 71.6 m and 72.3 m and an array depth oscillation of approximately 0.63 m.
 J. Gomes, A. Silva, S.M. Jesus. Spatial combining for passive time-reversed communications. Submitted to J. Acoust. Soc. Am., 18 March 2007.
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 A. Silva, S.M. Jesus, J. Gomes. Passive time-reversal geometric mismatch compensation by using waveguide invariant properties. To be submitted to J. Acoust. Soc. Am.