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Physics-based passive time reversal equalizer using waveguide invariant properties

A. Silva,
S.M. Jesus
Institute for Systems and Robotics, University of Algarve
Campus de Gambelas, PT-8005-139 Faro, Portugal
J.P. Gomes,
Institute for Systems and Robotics, IST
Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

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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 its  spatial-temporal 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  [1].

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 [2], and to interpret a model for performance  prediction  of a time reversal communication system [3]. In [4] 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.

[1] J. Gomes, A. Silva, S.M. Jesus. Spatial combining for passive  time-reversed communications.  Submitted to J. Acoust. Soc. Am., 18  March 2007.
[2] H. C. Song, W. A. Kuperman, and W. S. Hodgkiss. Time-reversal mirror with variable range focusing. J. Acoust. Soc. Am., 103(6): 3234-3240, June 1998.
[3] D. Rouseff. Intersymbol interference in underwater acoustic communications using time-reversal signal processing. J. Acoust. Soc.   Am., 117(2), February 2005.
[4] 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.

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