There had been great interests in applying parametric arrays in sonar and underwater applications because they generate very narrow and low-frequency beams with almost no sidelobe. About parametric array or parametric acoustic array, it is generated due to the fact that the instantaneous sound speed (one of physical parameters) of an intense beam, for example, depends intrinsically on the sound pressure or particle velocity itself. It is not until 1973, when Bennett and Blackstock first demonstrated parametric array effect in air. During the years, several key researches and commercial products based on parametric acoustic array had been witnessed.

So YANG Jun from the Institute of Acoustics, Chinese Academy of Sciences, China, Woon-Seng Gan (Guest Editors) from the Nanyang Technological University, Singapore and Tamoo Kamakura from the University of Electro-Communications, Japan had compiled some of these key research works and report on new advances in the parametric acoustic array.

This special issue is composed of eleven contributions describing different aspects of Parametric Acoustic Array. Generally, the special issue can be classified into four sections: Theory, Measurement, Processing Method, and Application.

Under the theoretical development in Parametric Acoustic Array, two papers were selected: “A Cascaded Second-Order Approach to Computing Third-Order Scattering of Noncollinear Acoustic Beam” by Garner and Steer, looking into the theoretical development of the third-order scattering nonlinear scattering of sound from two noncollinear ultrasonic beams;  “Numerical Simulation of Parametric Sound Generation and its Application to Length-limited Sound Beam” by Nomura et al., proposing a simulation model for predicting the nonlinear sound propagation of ultrasonic beam over a few hundred wavelengths. 

Under the measurement section, two papers to describe the parametric acoustics array measurement techniques in underwater and air:  “Underwater Parametric Transmission with a Linear Array” by Marchal and Cervenka and “An alternative Method to Measure the On-axis Difference-Frequency sound in a Parametric Loudspeaker without using an Acoustic Filter” by Ji et al. 

The following digital signal processing methods and implementation techniques are the principal highlights in realizing parametric loudspeakers, in which“Identification of a Parametric Loudspeaker System Using an Adaptive Volterra Filter” by Ji and Gan and "Analysis and Calibration of System Error in Steerable Parametric Loudspeakers” by Shi and Gan were chosen.  The final set of papers is related to new applications of PAA. In this, the author opted for three papers to demonstrate it.

The authors believe that all of the above contributions in this Special Issue on Parametric Acoustic Array provide a useful guide for practitioners and researchers working in this field.

This research result will be published on the issued Applied Acoustics (Volume 73, Issue 12, December 2012, Pages 1209–1210).