Method and device for decoding a higher-order ambisonics (HOA) representation of an audio soundfield

An apparatus for decoding a Higher-Order Ambisonics (HOA) representation of a sound or sound field for audio playback, comprising:

• a decoder configured to decode coefficients of the HOA sound field representation, the decoder including:
• a receiver configured to receive a smoothed decode matrix {tilde over (D)} that is based on a mix matrix G and a mode matrix {tilde over (ψ)}, wherein the mix matrix G was determined based on L speakers and positions of a spherical modelling grid, wherein the mode matrix {tilde over (ψ)} was determined based on the spherical modelling grid and a HOA order N, and
• wherein the smoothed decode matrix {tilde over (D)} is determined based on smoothing a first decode matrix {circumflex over (D)} with smoothing coefficients, wherein the first decode matrix {circumflex over (D)} is determined U,V based on {circumflex over (D)}=V Ŝ UH, are based on Unitary matrices,
• wherein a compact singular value decomposition of a product of the mode matrix {tilde over (Ψ)} with a transposed mix matrix is determined based on U S VH={tilde over (ψ)}GT, wherein S was determined based on a diagonal matrix with singular value elements, wherein Ŝ is a truncated compact singular value decomposition matrix that is either an identity matrix or a modified diagonal matrix, the modified diagonal matrix being determined based on the diagonal matrix with singular value elements by replacing a singular value element that is larger or equal than a threshold by ones, and replacing a singular value element that is smaller than the threshold by zeros, wherein the smoothing of the decode matrix D is based on a first smoothing method L<O3D, wherein O3D=(N+1)2;
• and
• a renderer configured for rendering coefficients of the HOA representation from a time domain to a spatial domain based on the smoothed decode matrix domain {tilde over (D)}.