# Quality Enhancement of MPEG-H 3 DA Binaural Rendering Using a Spectral Compensation Technique
## 4 Implementation and Complexity  
The proposed algorithm was implemented on the frequency-domain binaural rendering of the MPEG-H 3 DA reference software. Figure 5 shows block diagrams of the MPEG-H 3 DA BR comprising the PGC and BSC blocks. As illustrated, the PGC is applied to the output of object render (amplitude panning) before the binaural rendering block, while the BSC is applied to the downmixed binaural signal. In the figure, \(r\) denotes the QMF time slot, and \(l\) and \(r^{\prime}\) denote the index of the short-time segmented frame and the QMF time slot index of the segmented frame, respectively, i.e., \(r=l*N_{seg}+r^{\prime}\), where \(N_{seg}\) is the size of the short-time frame. In pursuit of the implementation, the compensated panning gains for the PGC, i.e., \(\hat{g}^{j}_{i}(k)\) in Equation (7), are calculated for all azimuth and elevation angles at 1-degree intervals and stored in a lookup table. The system was designed to refresh the panning gains at every time slot of the QMF subband. The PGC and BSC are selectively used in different QMF bands according to the bandwidth of the critical band and processing band, i.e., QMF bandwidth, as described in Section 3.3. The bands below 6 kHz are compensated using the PGC. For the bands below 750 Hz, PGC gains of the left and right ears are averaged to use for both ears signals. This is because the phase difference between the left and right ear's HRTFs is relatively insignificant. The BSC is employed for the bands above 6 kHz, where the critical bandwidth is wide enough to cover multiple QMF bands. To avoid artifacts, we limit the magnitude of BSC gain to have values within \(-4.8\) dB\(\sim\)4.8 dB, and \(A\{\cdot\}\) is implemented using a 1 st-order IIR low-pass filter with a time constant of 10 ms. Tables 1 and 2 summarize the computational complexities of the PGC and BSC blocks in the FD-BR in a unit of MOPS (million operations per second). In the tables, \(N_{obj}\) is the number of object signals as in Equation (1), and \(N_{punn}\) is the averaged number of loudspeakers involved in the amplitude panning, i.e., \(N_{punn}=3\) for 3D VBAP. \(N_{ch}\) is the total number of virtual loudspeakers, and \(N_{fft}=2*N_{seg}\) is the FFT size. Weight in the rightmost column of the tables is based on [17] and \(F\) accounts for the number of real operations of the butterfly in the FFT algorithm, i.e., \(F=2.5\)[13]. \(N_{bund}\) is the number of subbands over which the FD-BR is performed. \(N_{frm}\) is the number of FFT frames per second, calculated as \(N_{frm}=(F_{s}/64)/N_{seg}\), where \(F_{s}\) is the sampling frequency. Using Tables 1 and 2[13], the worst-case MOPS of the MPEG-H 3 DA BR can be counted using HRTFs as a virtual loudspeaker, with and without the proposed compensation method. For the calculation, we choose MPEG-H 3 DA low complexity (LC) profile level 4, which is a scenario of virtual loudspeaker rendering of 28 objects on the 22.2 channels, i.e., \(N_{ch}=22\), at a sampling rate of \(Fs=48\) kHz. We set the parameters considering a typical operating condition of FD-BR using HRTFs: \(N_{fft}=16,N_{bund}=48,N_{frm}=93.75\), and \(F_{s}=48\),000. The counted MOPS of the FD-BR are 71.4 and 61.4, respectively, for the cases with and without the proposed compensation algorithm. We can estimate the contribution of the proposed method to the total computation cost of the MPEG-H 3 DA decoding and binaural rendering process. The numbers areobtained under the condition that each QMF band selectively employs either PGC or BSC, as explained previously. Considering that, the proposed compensation algorithm takes about 3.1% and 16.3% of the worst-case complexity of the entire MPEG-H 3 DA decoding/rendering process [1] and the MPEG-H 3 DA BR, respectively. This means that the increase in complexity by employing the proposed method is marginal. In fact, the computational growth of 10 MOPS implies that the proposed method is affordable, even for low-power mobile devices.