Heller, A. J., Benjamin, E. M., & Lee, R. (2012, April). A toolkit for the design of ambisonic decoders. In Linux Audio Conference (pp. 1-12). Stanford.
Implementation of Ambisonic reproduction systems is limited by the number and placement of the loudspeakers. In practice, real-world systems tend to have insufficient loudspeaker coverage above and below the listening position. Because the localization experienced by the listener is a nonlinear function of the loudspeaker signals it is difficult to derive suitable decoders analytically. As an alternative, it is possible to derive decoders via a search process in which analytic estimators of the localization quality are evaluated at each search position. We discuss the issues involved and describe a set of tools for generating optimized decoder solutions for irregular loudspeaker arrays and demonstrate those tools with practical examples.