Study on the Cone Programming Reformulation of Active Noise Control Filter Design in the Frequency Domain

In the practice of active noise control, the control filter can be designed in either the time domain or the frequency domain. Compared with the former method category, it is more convenient to use frequency-domain methods to apply constraints such as stability, robustness, disturbance enhancement, input limit of loudspeakers, etc. Better noise reduction performance can usually be achieved by frequency-domain design as well. However, the computational complexity of designing a filter in the frequency domain is usually significant, especially for multichannel systems with multiple constraints. This is one of the challenges of using frequency-domain design in practical applications. In this paper, the traditional optimization problem used in frequency-domain filter design was modified and reformulated to a cone programming problem, where the inequality constraints were reformulated as second-order cones and positive semidefinite cones. Because of its convex nature, the global minimum solution to the problem can always be found. Another advantage of this cone programming reformulation is that algorithms with high computational efficiency can be used. It was demonstrated that, compared with using the traditional sequential quadratic programming method, the calculation is more efficient if the filter design problem is reformulated to cone programming and solved by the primal-dual interior-point method.