# A Review of Sound Field Control
## 3 Personal Audio Systems
### Algorithm Improvements  
The ACC method focuses more on acoustic contrast performance, but the phase control and sound pressure distribution in the bright area are neglected, which affects the subjective perception of the listener. The PM method is concerned with the accurate reproduction of sound fields. If the two types of methods are combined, the system can take the advantages of both. The ACC-PM method [40] obtains the compromise effect between the reproduction error in the bright zone and the acoustic contrast by adjusting the weight factor. The SFR-ACC method [41] is to minimize the reproduction error with the acoustic contrast to not be lower than a given value. The latter can precisely adjust the acoustic contrast performance as needed. In practical applications, the acoustic transfer functions can be perturbed by such factors as inconsistencies in the sensitivities of loudspeaker, mismatch in positions of loudspeaker, and the scattering from the obstacles. Moreover, the performance of reproduction can be sensitive to errors in the acoustic transfer functions. Therefore, the robustness of reproduction systems is concerned. [PERSON] et al. [42] studied the robustness and regularization problem of the ACC method and increased the robustness by limiting the array effort. The regularization method is commonly used for robustness improvement, but it is difficult to select a good regularization parameter. The best regularization parameter can be found by Monte-Carlo simulations using the information about errors in the system, but the computational complexity is high. [PERSON] et al. [43] proposed a design framework for robust reproduction as shown in Figure 2 and provided a method to quickly estimate the regularization parameters. They modeled the acoustic transfer function as the superposition of the deterministic part (\(\mathbf{G}\)) and the perturbation part (\(\Delta\mathbf{G}\)):  
\[\widetilde{\mathbf{G}}=\mathbf{G}+\Delta\mathbf{G}. \tag{5}\]  
The perturbation part describes the transfer function variations due to possible errors. Based on the model, two strategies are provided. One is to estimate the bound of \(\Delta\mathbf{G}\) and achieve good performance in the worst acoustic situation. The other is to estimate the probability distribution of \(\Delta\mathbf{G}\) and establish the mean cost function to improve the average performance over all possible cases. Through such robust control, the ability of the system to resist disturbance is improved. The methods mentioned above are all designed to optimize the weight vectors at a set of discrete frequencies. However, the acoustic contrast can decrease significantly at non-control frequencies. Moreover, the designed method has the causality problem when transforming the weight vectors from the frequency domain to the time domain. To tackle these problems, [PERSON] and [PERSON] [44] presented a broadband acoustic contrast control (BACC) method by calculating the coefficients of the filters directly. However, the BACC method cannot control the consistency of frequency responses, which may not ensure a flat frequency response at a point in the bright zone and may lead to intolerable distortions. The BACC-RV method introduced a response variation (RV) term into the BACC method [45], which can effectively solve the frequency response consistency problem and improve the sound quality in the bright zone. In [45], a linear loudspeaker array consisting of eight loudspeaker units was used to generate the multi-zone sound field. The bright zone and dark zone were located at 45\({}^{\circ}\) and \(-45^{\circ}\), respectively, deviating from the loudspeaker array center. The sampling rate and the length of filter are set to 8000 Hz and 200, respectively, and thus the control frequency interval is 40 Hz. The weight vectors were computed according to traditional acoustic contrast control (TACC), BACC, and BACC-RV.