Schätzung der Einfallsrichtung früher Reflexionen mittels Compressive Sensing
Bachelorarbeit von Förster, Jonas
Beamforming techniques are nowadays commonly used to detect the direction of arrival (DOA) of sound waves arriving at spherical microphone arrays (SMAs). The conventional plane-wave decomposition beamformer(PWD-BF) can be used to estimate the DOA with a maximal directivity function solving a ℓ2 - minimisation problem. However, since the number of microphones in SMAs is limited by physical constraints, the PWD-BF method suffers from low spatial resolution in the practical use case. The spatial resolution can be improved by applying compressive sensing, the so-called compress- ive beamforming(CB). The main requirement to apply compressive beamforming is sparsity in the solution of the problem. That means that the minimisation problem is underdetermined and can be solved with ℓ1 - minimisation. In reverberant room acoustic scenarios, the condition of sparsity is not fulfilled due to meas- urement noise and too many incoming reflections. Therefore, subspace-based preprocessing methods are used to divide the signals into two parts. The first part is assumed to consist of the direct sound and the early reflections whereas the second part includes late reverberation and measurement noise. The first part is then assumed to be sparse and the directions of arrival of the direct sound and the early reflections can be estimated using CB. In this work, the performance of CB with and without the subspace-based preprocessing methods is compared with the performance of PWD-BF and MUltiple SIgnal Classifica- tion(MUSIC). This is done in two simulation scenarios. In the first scenario, plane-wave sources are generated analytically and measurement noise is added. In the second, the methods are applied on directional room impulse responses. The focus of the analyses is on the influence of measurement noise and late reverberation to the simulations with respect to their effects on sparsity of the problem and the estimation of the DOA of the primary sources and reflections.