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In this paper, the integrated MVDR beamformer is extended for use with a microphone configuration where a microphone array, local to a speech processing device, has access to the signals from multiple external microphones (XMs) randomly located in the acoustic environment. The integrated MVDR beamformer is reformulated as a quadratically constrained quadratic program (QCQP) with two constraints, one of which is related to the maximum tolerable speech distortion for the imposition of the a priori RTF vector and the other related to the maximum tolerable speech distortion for the imposition of the data-dependent RTF vector. An analysis of how these maximum tolerable speech distortions affect the behaviour of the QCQP is presented, followed by the discussion of a general tuning framework. The integrated MVDR beamformer is then evaluated with audio recordings from behind-the-ear hearing aid microphones and three XMs for a single desired speech source in a noisy environment. In comparison to relying solely on an a priori RTF vector or a data-dependent RTF vector, the results demonstrate that the integrated MVDR beamformer can be tuned to yield different enhanced speech signals, which may be more suitable for improving speech intelligibility despite changes in the desired speech source position and imperfectly estimated spatial correlation matrices.<\/jats:p>","DOI":"10.1186\/s13636-020-00192-2","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T08:38:34Z","timestamp":1612946314000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An integrated MVDR beamformer for speech enhancement using a local microphone array and external microphones"],"prefix":"10.1186","volume":"2021","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-7826-1030","authenticated-orcid":false,"given":"Randall","family":"Ali","sequence":"first","affiliation":[]},{"given":"Toon","family":"van Waterschoot","sequence":"additional","affiliation":[]},{"given":"Marc","family":"Moonen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,10]]},"reference":[{"key":"192_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04619-7","volume-title":"Microphone Arrays: Signal Processing, Techniques and Applications","author":"M. 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