Analysis of 2D sound reproduction with fixed-directivity loudspeakers

The implementation of 3D sound reproduction is well founded theoretically, but the requirements for the number of loudspeakers and array geometry make it impractical using conventional technology. In practice, a 2D array of loudspeakers is commonly used which restricts the reproduction of sources to those in the horizontal plane and requires a restricted form for the free-field loudspeaker driving signals based on the sectorial spherical harmonics. However, reflections can impair reproduction quality when using the free-field solution. Since first-order loudspeakers are commercially available which increase the direct to reflected sound ratio, we extend the sectorial solution for the loudspeaker excitation signals to the first-order case. We also investigate the reproduction accuracy for both zeroth and first-order loudspeakers using numerical simulations.