Optimal time-reversal focusing by an iterative least-squares method

In this paper, an iterative least-squares prefiltering method is presented for the optimal time-reversal focusing of a random array. By adopting an iterative prefilter into the emitter end, the autocorrelation of Green's function can be compensated for optimal focusing to achieve an ideal Dirac delta function. The prefilter's impulse response is estimated iteratively by minimizing the square error between the focusing signal and the source signal. Then, using these estimated prefilters the time-reversed signal is filtered in series and successively re-emitted to achieve optimal focusing. Compared with previous optimal focusing methods, this method is simple and fast to implement. Moreover, the use of a random array permits the liberal placement of transducers in accordance with the actual need, and avoids the operation for the array response calibration. The optimal focusing experiment of a four-element random array is conducted in a reverberation chamber. The experimental results demonstrate the effectiveness of this method.