  A spatial active noise control (ANC) method based on kernel interpolation of
a sound field with exterior radiation suppression is proposed. The aim of
spatial ANC is to reduce incoming noise over a target region by using multiple
secondary sources and microphones. The method based on kernel interpolation of
a sound field allows noise attenuation in a regional space with an array of
arbitrary geometry. The cost function is defined as the acoustic potential
energy, i.e., the regional integral of the power distribution inside the target
region. However, this cost function does not take into consideration the
exterior radiation of secondary sources. Thus, the acoustic power in the
exterior region can be amplified by the output of the secondary sources. We
propose two spatial ANC methods with exterior radiation suppression. The first
approach is based on the minimization of the cost function formulated as a sum
of the interior acoustic potential energy and exterior radiation power. The
second approach is based on the minimization of the interior acoustic potential
energy with inequality constraints on the exterior radiation power. Adaptive
algorithms for minimizing the cost function are derived for the two approaches.
Numerical experimental results indicate that the proposed methods can reduce
the interior regional noise while suppressing the exterior radiation.
