# Quality Enhancement of MPEG-H 3 DA Binaural Rendering Using a Spectral Compensation Technique
## 2 Spectral Distortions in the MPEG-H 3 DA BR  
Figure 1 illustrates the core decoding and rendering parts of the MPEG-H 3 DA. Dynamic range compression (DRC) and the HoA rendering block are omitted in the figure for brevity. The core decoder of MPEG-H 3 DA converts a compressed bit-stream to a waveform (e.g., channel-based object-based audio) and associated metadata (e.g., positions of objects and a loudspeaker geometry). During the rendering stage, the associated data are processed by the scene-displacement interface. It calculates and applies the rotation matrix to update the positions of audio objects and channels, both of which depend on user interaction (e.g., user's yaw, pitch, and roll movement). Using 3D VBAP, the object renderer then takes the object and channel signals and updated positions to produce virtual loudspeaker signals. Finally, the binaural renderer generates a binaural signal by filtering the channel signal by BRTFs/HRTFs that corresponds to the virtual loudspeaker position [13]. Figure 2 shows more detailed schematics of the VLR-based BR in MPEG-H 3 DA. For a given loudspeaker layout and head rotation information, the VLR system generates channel  
signals for all object signals. Following 3D VBAP, the \(i\)-th channel signal \(X_{i}(k)\) for input object signals \(S_{m}(l,k),m=1,2,...,N_{obj}\), is obtained as  
\[X_{i}(l,k)=\sum_{m=1}^{N_{obj}}\frac{S_{i,m}}{\|\mathbf{g}_{m}\|_{p}}S_{m}(l,k)= \sum_{m=1}^{N_{obj}}\tilde{g}_{i,m}S_{m}(k),\;\;i=1,2,...,N_{ch}, \tag{1}\]  
where \(l\) and \(k\) are the frame and frequency indices, respectively, and \(\|\mathbf{g}_{m}\|_{p}\) represents the \(p\) norm of the panning gain vector \(\mathbf{g}_{m}=[g_{1,m},\,g_{2,m},\,...,\,g_{N_{ch},m}]^{T}\). \(N_{obj}\), and \(N_{ch}\) denotes the total numbers of input sound objects and virtual loudspeakers. The normalized panning gain \(\xi_{i,m}(=g_{i,m}/\|\mathbf{g}_{m}\|_{p})\) allows the maintenance of a constant loudness regardless of the panning direction. The norm order \(p\) can be either 1 or 2 depending on the coherence between the binaural filters [8]. The ear signals are then obtained by filtering the channel signal with BRTFs/HRTFs that correspond to the virtual loudspeaker location. The binaural signal \(Y^{j}(l,k)\) in Figure 2 is obtained by summing the ear signals, as follows, where the frequency-transformed BRTFs/HRTFs are denoted as \(H_{i}^{j}(k)\), \(j\in\{L,R\}\). \[Y^{j}(l,k)=\sum_{i=1}^{N_{ch}}X_{i}(l,k)H_{i}^{j}(k),\;\;j\in\{L,R\}. \tag{2}\]  
The transfer function of the MPEG-H 3 DA BR system between the \(m\)-th sound object to the binaural signal, defined as \(H_{BR}^{j}(k)=Y^{j}(k)/S_{m}(k)\), can be expressed as  
\[H_{BR}^{j}(k)=\sum_{i=1}^{N_{ch}}\tilde{g}_{i}H_{i}^{j}(k)=\tilde{\mathbf{g}} ^{T}\mathbf{H}^{j}(k),\,j\in\{L,R\}, \tag{3}\]  
where \(\tilde{\mathbf{g}}\)\(=\)\([\tilde{g}_{1},...,\tilde{g}_{N_{ch}}]^{T}\) and \(\mathbf{H}^{j}(k)\)\(=\)\([H_{1}^{j}(k),...,H_{N_{ch}}^{j}(k)]^{T}\). Here, for simplicity, we omit the frame index \(l\) and assume \(m=1\). The comb filter effect occurs during the summing of the ear signals as Equation (2). The effect can be illustrated by calculating the transfer function between an object signal and the left ear signal, i.e., \(|H_{BR}^{1}|\), following the standard of MPEG-H 3 DA BR [1], as in  
Figure 1: A block diagram of the MPEG-H 3 DA 3 DoF rendering of audio objects and channel signals. Figure 2: Block diagram of the VLR-based BR in MPEG-H 3 DA. The transfer function in Figure 3, compared to true HRTFs, shows two main artifacts: broad spectral notches near 3.3 kHz as well as 12 kHz and a broad spectral boost below 1.5 kHz. These distortions are commonly observed in practical loudspeaker setups and directly affect the perceptual quality of the downmixed sound. A simple solution is active downmixing [11] that compensates for the spectral distortions during downmixing of the ear signals. However, the active downmixing applies gain to a downmixed binaural signal rather than an individual object signal.