Time-reversing array retrofocusing in noisy environments

Acoustic time reversal is a robust means of retrofocusing acoustic energy, in both time and space, to the original sound-source location. However, noi se may limit the performance of a time-reversing array (TRA) at long source -array ranges, or when the original-source or TRA-element power levels are low. The operation of a TRA requires two steps (reception and transmission) so both TRA-broadcast noise and ambient noise must be taken into account. In this paper, predictions are made for how a simple omnidirectional noise field influences the probability that the signal amplitude from a narrow-ba nd TRA will exceed the noise at the TRA's retrofocus. A general formulation for the probability of TRA retrofocusing, which can be used for TRA design , is developed that includes: the variance of the noise field, the original source strength, the TRA's element output power, the number of TRA element s (N), and the propagation characteristics of the environment. This formula tion predicts that a TRA's array gain tin dB) at the retrofocus may be as h igh as + 10 log(10)(N) to + 20 log(10)(N) depending on the relative strengt hs of the original source and the TRA's elements. Monte Carlo simulations i n both a free-space environment and a shallow-ocean sound-channel environme nt compare well to this probability formulation even when simple approximat e parametric relationships for the appropriate Green's functions are used. The dominant deviation between theory and simulation in the sound channel i s caused by acoustic absorption. (C) 2001 Acoustical Society of America.