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Spatial analysis of room acoustics is an ongoing research topic. Microphonearrays have been employed for spatial analyses with an important objectivebeing the estimation of the direction-of-arrival (DOA) of direct sound andearly room reflections using room impulse responses (RIRs). An optimal methodfor DOA estimation is the multiple signal classification algorithm. When RIRsare considered, this method typically fails due to the correlation of roomreflections, which leads to rank deficiency of the cross-spectrum matrix.Preprocessing methods for rank restoration, which may involve averaging overfrequency, for example, have been proposed exclusively for spherical arrays.However, these methods fail in the case of reflections with equal time delays,which may arise in practice and could be of interest. In this paper, a methodis proposed for systems that combine a spherical microphone array and aspherical loudspeaker array, referred to as multiple-input multiple-outputsystems. This method, referred to as modal smoothing, exploits the additionalspatial diversity for rank restoration and succeeds where previous methodsfail, as demonstrated in a simulation study. Finally, combining modal smoothingwith a preprocessing method is proposed in order to increase the number of DOAsthat can be estimated using low-order spherical loudspeaker arrays.

Modal smoothing for analysis of room reflections measured with spherical microphone and loudspeaker arrays