Previously, Wave Field Synthesis (WFS), Near-field Compensated Higher-Order Ambisonics (NFC-HOA), Boundary Surface Control (BoSC), and the Spectral Division Method (SDM) have been proposed as sound field synthesis methods. These methods are based on matching the acoustic physical quantities at the boundary of the reproduced sound field with those of the desired sound field. Sound field synthesis techniques can be classified into data-based and model-based methods. The former aim at reproducing sound fields captured by microphone arrays, while the latter aim at synthesizing sound fields based on mathematical models. Most existing sound field reproduction methods only consider simple sound source models, such as static point sources, instead of sound sources with complex radiation properties. To generate a more realistic sound image, this study investigated the formulation of a sound field generated by a sound source with complex radiation properties moving along arbitrary trajectories in a spherical harmonic domain, and reproduced the sound field using loudspeaker arrays.