A comparison of filter design structures for multi-channel acoustic communication systems.

The application of inverse filter designs as a means of providing improved communication performance in acoustic environments is investigated. Tikhonov regularized inverse filters of channel transfer functions calculated in the frequency domain are used as a means of obtaining multi-channel filters. Three classifications of inverse filter structures have been considered using time-domain simulations. The performance of Tikhonov regularized inverse filters designed according to each of these classifications is compared with each other and against a filter design developed by Stojanovic [Stojanovic, M. (2005). "Retrofocusing techniques for high rate acoustic communications," J. Acoust. Soc. Am. 117, 1173-1185]. It is shown that the filter design developed by Stojanovic requires less regularization and outperforms the Tikhonov regularized inverse filter designs when communicating over a single channel. While the filter developed by Stojanovic is designed to use multiple transmitters to transmit to a single receiver, the filter was implemented in a multi-channel system and proposed to have a focusing similar to that obtained using time-reversal. It was found that for the scenario used in the simulation, the Tikhonov regularized inverse design for full multi-channel inversion achieved better focusing than the design by Stojanovic, where simulation results show 20 dB less cross-talk at the expense of around 2 dB loss in signal strength.

Transducer sensitivity compensation using diagonal preconditioning for time reversal and Tikhonov inverse filtering in acoustic systems.

Filters are commonly used in sound reproduction and communication systems as a means of compensating for the response of the electro-acoustic plant. Two commonly used filter designs in the field of acoustics are the time reversal filter and the Tikhonov inverse filter. In this paper the influence of transducer sensitivities on the performance of these filters is examined. It is shown that the sensitivity of the transducers can negatively affect the performance of the resulting filter. To compensate for the decrease in performance, diagonal preconditioning can be implemented in the system. It is shown that by using diagonal matrices, which minimize the condition number of the system, the loss in performance arising from unbalanced sensitivities is minimized. This paper proposes an algorithm to find such a set of diagonal matrices and results are presented showing the improvements in performance arising from the modified filter design.