  In this paper, a recently proposed approach to multizone sound field
synthesis, referred to as Joint Pressure and Velocity Matching (JPVM), is
investigated analytically using a spherical harmonics representation of the
sound field. The approach is motivated by the Kirchhoff-Helmholtz integral
equation and aims at controlling the sound field inside the local listening
zones by evoking the sound pressure and particle velocity on surrounding
contours. Based on the findings of the modal analysis, an improved version of
JPVM is proposed which provides both better performance and lower complexity.
In particular, it is shown analytically that the optimization of the tangential
component of the particle velocity vector, as is done in the original JPVM
approach, is very susceptible to errors and thus not pursued anymore. The
analysis furthermore provides fundamental insights as to how the spherical
harmonics used to describe the 3D variant sound field translate into 2D basis
functions as observed on the contours surrounding the zones. By means of
simulations, it is verified that discarding the tangential component of the
particle velocity vector ultimately leads to an improved performance. Finally,
the impact of sensor noise on the reproduction performance is assessed.
