Numerical optimization of non-adaptive microphone arrays

The paper describes an application of the numerical optimization methods for the design of non-adaptive multisensor arrays. The parameters and the geometry of such arrays do not change with changes in the input signals, and must be chosen in advance, depending on the array application. Generally, the goal of a non-adaptive multisensor array may be numerically expressed through its pattern function which shows the gain for a signal coming from a particular direction in space. The real pattern function depends on the geometry of the array and on the processing which signals from every sensor undergo. The array pattern function is non-linear and it is frequency dependent. The difference between the goal pattern function and the real pattern function is the essence of numerical optimization. The geometry and the processing parameters of the multi-sensor array are optimized to provide the minimum difference over a specified frequency range. Such minimization is a difficult non-linear and multi-parameter problem . Optimization results for several goal functions for multi-microphone arrays are provided and discussed.