Microphone Array

Part of the Springer Handbooks book series (SHB)


This chapter deals with microphone arrays. It is arranged according to the different methods available to proceed through the different problems and through the different mathematical methods. After discussing general properties of different array types, such as plane arrays, spherical arrays, or scanning arrays, it proceeds to the signal processing tools that are most used in speech processing. In the third section, backpropagating methods based on the Helmholtz–Kirchhoff integral are discussed, which result in spatial radiation patterns of vibrating bodies or air.


Spherical Harmonic Sound Field Microphone Array Linear Equation System Minimum Variance Distortionless Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.





boundary-element method


Center for New Music and Audio Technologies


direction of arrival


finite-element method


generalized cross-correlation


generalized internal source density


Helmholtz equation least squares


linear constraint minimum variance


minimum variance distortionless response


signal-to-noise ratio


  1. 29.1.
    S. Gannot, D. Burshtein, E. Weinstein: Signal enhancement using beamforming and nonstationarity with applications to speech, IEEE Trans. Signal Process. 49, 1614–1626 (2001)ADSCrossRefGoogle Scholar
  2. 29.2.
    R. Bader: Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar, J. Acoust. Soc. Am. 131(1), 819–828 (2012)ADSCrossRefGoogle Scholar
  3. 29.3.
    M. Pollow, G.K. Behler, H. Pomberger, F. Zotter: Aufnahme und Wiedergabe von Schallfeldern mit Kugelarrays [Recording and Playback of sound fields using spherical arrays], DAGA 2011, Düsseldorf (2011)Google Scholar
  4. 29.4.
    E.G. Williams, J.D. Maynard, E. Skurdzyk: Sound source reconstructions using a microphone array, J. Acoust. Soc. Am. 6(1), 341–344 (1980)Google Scholar
  5. 29.5.
    D.L. Alon, B. Rafaely: Spindle-Torus Sampling for an Efficient-Scanning Spherical Microphone Array, Acust. Acta Acust. 98, 83–90 (2012)CrossRefGoogle Scholar
  6. 29.6.
    N. Epain, C.T. Jin: Independent Component Analysis Using Spherical Microphone Arrays, Acust. Acta Acust. 98, 91–102 (2012)CrossRefGoogle Scholar
  7. 29.7.
    I. Balmages, B. Rafaely: Open-sphere designs for spherical microphone arrays, IEEE Trans. Audio Speech Lang. Proc. 15, 727–732 (2007)CrossRefGoogle Scholar
  8. 29.8.
    B. Rafaely: The spherical-shell microphone array, IEEE Trans. Audio Speech Lang. Proc. 16, 740–747 (2008)CrossRefGoogle Scholar
  9. 29.9.
    J. Meyer, G.W. Elko: A highly scalable spherical microphone array based on an orthonormal decomposition of the sound field, ICASSP II Proc. (2002) pp. 1781–1784Google Scholar
  10. 29.10.
    T.D. Abhayapala, D.B. Ward: Theory and design of high order sound field microphones using spherical microphone array, ICASSP II Proc. (2002) pp. 1949–1952Google Scholar
  11. 29.11.
    B. Rafaely: Plane-wave decomposition of the pressure on a sphere by spherical convolution, J. Acoust. Soc. Am. 116, 2149–2157 (2004)ADSCrossRefGoogle Scholar
  12. 29.12.
    D. Alon, B. Rafaely: Efficient sampling for scanning spherical array, Proc. 2nd Int. Symp. Ambisonics and Spherical Acoustics (2010)Google Scholar
  13. 29.13.
    B. Rafaely: Analysis and design of spherical microphones arrays, IEEE Trans. Speech Audio Proc. 13, 135–143 (2005)CrossRefGoogle Scholar
  14. 29.14.
    D.N. Zotkin, R. Duraiswami, N.A. Gumerov: Sound field decomposition using spherical microphone arrays, IEEE ICASSP (2008) pp. 277–280Google Scholar
  15. 29.15.
    B. Rafaely: The spherical-shell microphone array, IEEE Trans. Audio Speech Lang. Process. 16(4), 740–747 (2008)CrossRefGoogle Scholar
  16. 29.16.
    E.G. Williams, N.P. Valdivia, P.C. Herdic, J. Kloss: Volumetric acoustic vector intensity imager, J. Acoust. Soc. Am. 120, 1887–1897 (2006)ADSCrossRefGoogle Scholar
  17. 29.17.
    J. Meyer, G. Elko: A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield, IEEE ICASSP II, Vol. 2 (2002) pp. 1781–1784Google Scholar
  18. 29.18.
    Z. Li, R. Duraiswami: A robust and self-reconfigurable design of spherical microhone array for multi-resolution beamforming, IEEE ICASSP 05, Vol. 4 (2005) pp. 1137–1140Google Scholar
  19. 29.19.
    M. Park, B. Rafaely: Sound-field analysis by plane-wave decomposition using spherical microphone array, J. Acoust. Soc. Am. 118, 3094–3103 (2005)ADSCrossRefGoogle Scholar
  20. 29.20.
    B. Rafaely: Plane-wave decomposition of the sound field on a sphere by spherical convolution, J. Acoust. Soc. Am. 116, 2149–2157 (2004)ADSCrossRefGoogle Scholar
  21. 29.21.
    Z. Li, R. Duraiswami: Flexible and optimal design of spherical microphone arrays for beamforming, IEEE Trans. Audio Speech Lang. Process. 15, 702–714 (2007)CrossRefGoogle Scholar
  22. 29.22.
    B. Rafaely: Analysis and design of spherical microphone arrays, IEEE Trans. Audio Speech Lang. Process. 13, 135–143 (2005)CrossRefGoogle Scholar
  23. 29.23.
    S.P. Applebaum: Adaptive arrays, IEEE Trans. Antennas Propag. 24, 585–598 (1976)ADSCrossRefGoogle Scholar
  24. 29.24.
    S. Gannot, D. Burshtein, E. Weinstein: Iterative and sequential Kalman filter-based speech enhancement algorithms, IEEE Trans. Speech Audio Process. 6, 373–385 (1998)CrossRefGoogle Scholar
  25. 29.25.
    K.K. Paliwal, A. Basu: A speech enhancement method based on Kalman filtering, Proc. IEEE ICASSP (1987) pp. 177–180Google Scholar
  26. 29.26.
    B. Lee, K.Y. Lee, S. Ann: An EM-based approach for parameter enhancement with an application to speech signals, Signal Process. 46, 1–14 (1995)CrossRefzbMATHGoogle Scholar
  27. 29.27.
    J.S. Lim (ed.): Speech Enhancement (Prentice-Hall, Englewood Cliffs 1983)Google Scholar
  28. 29.28.
    P. Loizou: Speech Enhancement: Theory and Practice (CRC, Boca Raton 2007)Google Scholar
  29. 29.29.
    P. Vary, R. Martin: Digital Speech Transmission: Enhancement, Coding, and Error Concealment (Wiley, New York 2006)CrossRefGoogle Scholar
  30. 29.30.
    J. Benesty, S. Makino, J. Chen (Eds.): Speech Enhancement (Springer, Heidelberg 2005)Google Scholar
  31. 29.31.
    S. Doclo, M. Moonen: GSVD-based optimal filtering for single and multimicrophone speech enhancement, IEEE Trans. Signal Process. 50, 2230–2244 (2002)ADSCrossRefGoogle Scholar
  32. 29.32.
    S. Doclo: Multi-Microphone Noise Reduction and Dereverberation Techniques for Speech Applications. Ph.D. Thesis (Katholieke Universiteit Leuven, Leuven 2003)Google Scholar
  33. 29.33.
    C.H. Knapp, G.C. Carter: The generalized correlation method for estimation of time delay, IEEE Trans. Acoust. Speech Signal Process. 24, 320–327 (1976)CrossRefGoogle Scholar
  34. 29.34.
    M. Brandstein, D.B. Ward (eds.): Microphone Arrays (Springer, Heidelberg 2001)Google Scholar
  35. 29.35.
    M. Omologo, P. Svaizer: Acoustic event localization using a crosspower-spectrum phase based technique, Proc. IEEE ICASSP II (1994) pp. 273–276Google Scholar
  36. 29.36.
    H. Wang, P. Chu: Voice source localization for automatic camera pointing system in videoconferencing, Proc. IEEE WASPAA (1997)Google Scholar
  37. 29.37.
    M.S. Brandstein: A pitch-based approach to time-delay estimation of reverberant speech, Proc. IEEE WASPAA (1997)Google Scholar
  38. 29.38.
    J. Benesty, J. Chen, Y. Huang: Microphone Array Signal Processing (Springer, Heidelberg 2008)Google Scholar
  39. 29.39.
    D.H. Johnson, D.E. Dudgeon: Array Signal Processing, Concepts and Techniques (Prentice-Hall, Englewood Cliffs 1993)zbMATHGoogle Scholar
  40. 29.40.
    D.E. Dudgeon: Fundamentals of digital array processing, Proc. IEEE 63, 898–904 (1977)CrossRefGoogle Scholar
  41. 29.41.
    X. Zhang, J.H.L. Hansen: CSA-BF: A constrained switched adaptive beamformer for speech enhancement and recognition in real car environments, IEEE Trans. Speech Audio Process 11, 733–745 (2003)CrossRefGoogle Scholar
  42. 29.42.
    J.L. Flanagan, J.D. Johnson, R. Zahn, G.W. Elko: Computer-steered microphone arrays for sound transduction in large rooms, J. Acoust. Soc. Am. 75, 1508–1518 (1985)ADSCrossRefGoogle Scholar
  43. 29.43.
    J.L. Flanagan, D.A. Berkley, G.W. Elko, J.E. West, M.M. Sondhi: Autodirective microphone systems, Acustica 73, 58–71 (1991)Google Scholar
  44. 29.44.
    S.A. Schelkunoff: A mathematical theory of linear arrays, Bell Syst. Tech. J. 22, 80–107 (1943)CrossRefzbMATHMathSciNetGoogle Scholar
  45. 29.45.
    A.V. Oppenheim, R.W. Schafer, J.R. Buch: Discrete-Time Signal Processing, 2nd edn. (Prentice Hall, Upper Saddle River 1998)Google Scholar
  46. 29.46.
    V.R. Algazi, M. Suk: On the frequency weighted least-square design of finite duction filters, IEEE Trans. Circuits Syst. 22, 943–953 (1975)CrossRefGoogle Scholar
  47. 29.47.
    S. Doclo, M. Moonen: Design of far-field and near-field braodband beamformers using eigenfilters, Signal Process. 83, 2641–2673 (2003)CrossRefzbMATHGoogle Scholar
  48. 29.48.
    M. Okuda, M. Ikehara, S. Takahashi: Fast and stable least-squares approach for the design of linear phase FIR filters, IEEE ICASSP II. Proc. (1994) pp. 273–276Google Scholar
  49. 29.49.
    S.P. Applebaum: Adaptive arrays, IEEE Trans. Antennas Propagat. 24, 585–598 (1976)ADSCrossRefGoogle Scholar
  50. 29.50.
    J. Capon: High resolution frequency-wavenumber spectrum analysis, Proc. IEEE 57, 1408–1418 (1969)CrossRefGoogle Scholar
  51. 29.51.
    O. Owsley: Sonar array processing. In: Array Signal Processing, ed. by S. Haykin (Prentice-Hall, Englewood Cliffs 1984)Google Scholar
  52. 29.52.
    L.C. Godara: Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations, Proc. IEEE 85, 1195–1245 (1997)CrossRefGoogle Scholar
  53. 29.53.
    O.L. Frost III: An algorithm for linearly constrained adaptive array processing, Proc. IEEE 60, 926–935 (1972)CrossRefGoogle Scholar
  54. 29.54.
    I. Cohen: Analysis of two-channel generalized sidelobe canceller (GSC) with post-filtering, IEEE Trans. Speech Audio Process. 11, 684–699 (2003)CrossRefGoogle Scholar
  55. 29.55.
    C. Marro, Y. Mahieux, K.U. Simmer: Analysis of noise reduction and dereverberation techniques based on microphone arrays with postfiltering, IEEE Trans. Speech Audio Process. 6, 240–259 (1998)CrossRefGoogle Scholar
  56. 29.56.
    R. Zelinksi: A microphone array with adaptive post-filtering for noise reduction in reverberant rooms, Proc. IEEE ICASSP (1988) pp. 2578–2581Google Scholar
  57. 29.57.
    W. Liu: Blind adaptive beamforming for wideband circular arrays, ICASSP Proc. (2009)Google Scholar
  58. 29.58.
    N. Epain, C. Jin, A. van Schaik: Blind source separation using independent component analysis in the spherical harmonic domain, Proc. 2nd Int. Symp. Ambisonics and Spherical Acoustics (2010)Google Scholar
  59. 29.59.
    M. Ochmann: The source simulation technique for acoustic radiation problems, Acustica 81, 512–527 (1995)zbMATHGoogle Scholar
  60. 29.60.
    M. Ochmann: The full-field equations for acoustic radiation and scattering, J. Acoust. Soc. Am. 105(5), 2574–2584 (1999)ADSCrossRefGoogle Scholar
  61. 29.61.
    L. Bouchet, T. Loyau: Calculation of acoustic radiation using equivalent-sphere methods, J. Acoust. Soc. Am. 170(5), 2387–2397 (2000)ADSCrossRefGoogle Scholar
  62. 29.62.
    M.B.S. Magalhães, R.A. Tenenbaum: Sound source reconstruction techniques: A review of their evolution and new trends, Acust. Acta Acust. 90, 199–220 (2004)Google Scholar
  63. 29.63.
    R. Jeans, C. Mathews: The wave superposition method as a robust technique for computing acoustic fields, J. Acoust. Soc. Am. 92(2), 1156–1166 (1992)ADSCrossRefGoogle Scholar
  64. 29.64.
    G.H. Koopmann, L. Song, J.B. Fahnline: A method for computing acoustic fields based on the principle of wave superposition, J. Acoust. Soc. Am. 86, 2433–2438 (1989)ADSCrossRefGoogle Scholar
  65. 29.65.
    P.R. Stepanishen: A gerneralized internal source density method for the forward and backward projection of harmonic pressure fields from complex bodies, J. Acoust. Soc. Am. 101, 3270–3277 (1997)ADSCrossRefGoogle Scholar
  66. 29.66.
    M.C. Junger, D. Feit: Sound, Structure, and Their Interaction (MIT Press, Cambridge 1972)Google Scholar
  67. 29.67.
    F. Fahy, P. Gardonio: Sound and Strucural Vibration, 2nd edn. (Elsevier, Amsterdam 2007)Google Scholar
  68. 29.68.
    A. Sommerfeld: Vorlesungen über theoretische Physik. Band IV: Optik (Akademische Verlagsgesellschaft, Heidelberg 1964) p. 170Google Scholar
  69. 29.69.
    A. Sommerfeld: Vorlesungen über theoretische Physik. Band II: Mechanik der deformierbaren Medien (Akademische Verlagsgesellschaft, Heidelberg 1976)Google Scholar
  70. 29.70.
    P. Morse, K.U. Ingard: Theoretical Acoustics (Princeton Univ. Press, Princeton 1986)Google Scholar
  71. 29.71.
    R. Kress: Linear Integral Equations (Springer, Heidelberg 1989)CrossRefzbMATHGoogle Scholar
  72. 29.72.
    A. Kirsch: An Introduction to the Mathematical Theory of Inverse Problems (Springer, Heidelberg 1996)CrossRefzbMATHGoogle Scholar
  73. 29.73.
    H. Schenck: Improved integral formulation for acoustic radiation problems, J. Acoust. Soc. Am. 44, 41–58 (1967)ADSCrossRefGoogle Scholar
  74. 29.74.
    A. Pierce: Acoustics (Acoust. Soc. of Am., New York 1991)Google Scholar
  75. 29.75.
    J. Hadamard: Lectures on Cauchyʼs Problem in Linear Partial Differential Equations (Yale Univ. Press, New Haven 1923)zbMATHGoogle Scholar
  76. 29.76.
    J.D. Meynard, E.G. Williams, Y. Lee: Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH, J. Acoust. Soc. Am. 78(4), 1395–1413 (1985)ADSCrossRefGoogle Scholar
  77. 29.77.
    J. Prager: Approximate reconstruction of sound fields close to the source sufrace using spherical nearfield acoustical holography, J. Acoust. Soc. Am. 122(4), 2067–2073 (2007)ADSCrossRefGoogle Scholar
  78. 29.78.
    W.A. Veronesi, J.D. Maynard: Digital holographic reconstruction of sources with arbitrarily shaped surfaces, J. Acoust. Soc. Am. 85(2), 588–598 (1988)ADSCrossRefGoogle Scholar
  79. 29.79.
    G. Bissinger, E.G. Williams, N. Valdivia: Violin f-hole contribution to far-field radiation via patch near-field acoustical holography, J. Acoust. Soc. Am. 121(6), 3899–3906 (2007)ADSCrossRefGoogle Scholar
  80. 29.80.
    E.G. Williams: Fourier Acouostics (Academic, San Diego 1999)Google Scholar
  81. 29.81.
    G.B. Arfken, H.J. Weber: Mathematical Methods for Physicists (Elsevier, Amsterdam 2005)zbMATHGoogle Scholar
  82. 29.82.
    D.L. Colton, R. Kress: Inverse Acoustic and Electromagnetic Scattering Theory (Springer, Heidelberg 1992)CrossRefzbMATHGoogle Scholar
  83. 29.83.
    E.G. Williams, B.H. Houston, P.C. Herdic: Fast Fourier transform and singular value decomosition formulations for patch nearfield acoustical holography, J. Acoust. Soc. Am. 144(3), 1322–1333 (2003)ADSCrossRefGoogle Scholar
  84. 29.84.
    J.B. Fahnline, G.H. Koopmann: A numerical solution for the general radiation problem based on the combined methods of superposition and singular-value decomposition, J. Acoust. Soc. Am. 90, 2808–2819 (1991)ADSCrossRefGoogle Scholar
  85. 29.85.
    W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling: Numerical Recipes (Cambridge Univ. Press, Cambridge 1986)Google Scholar
  86. 29.86.
    Z. Wang, S.F. Wu: Helmholtz equation-least-squares method for reconstructing the acoustic pressure field, J. Acoust. Soc. Am. 102(4), 2020–2032 (1995)ADSCrossRefGoogle Scholar
  87. 29.87.
    M.R. Bai: Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries, J. Acoust. Soc. Am. 92(1), 533–549 (1992)ADSCrossRefGoogle Scholar
  88. 29.88.
    R. Scholte, N.B. Roozen, I. Arteaga: Regularization in PNAH by means of L-curve, Proc. Forum Acusticum Budapest (2005) pp. 2579–2583Google Scholar
  89. 29.89.
    P.C. Waterman: Matrix formulation of electromagnetic scattering, Proc. IEEE 53, 805–812 (1965)CrossRefGoogle Scholar
  90. 29.90.
    P.C. Waterman: New formulation of acoustic scattering, J. Acoust. Soc. Am. 45, 1417–1429 (1969)ADSCrossRefzbMATHGoogle Scholar
  91. 29.91.
    P.A. Martin: On the null field equations for the exterior problems of acoustics, Quart. J. Mech. Appl. Math. 33, 385–396 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  92. 29.92.
    D. Colton, R. Kress: The unique solvability of the null field equations of acoustics, Quart. J. Mech. Appl. Math. 36, 87–95 (1983)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  93. 29.93.
    D. Colton, R. Kress: Integral Equation Methods in Scattering Theory (Wiley, New York 1983) p. 104zbMATHGoogle Scholar
  94. 29.94.
    P.A. Martin: Acoustic scattering and radiation problems, and the null-field method, Wave Motion 4, 391–408 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  95. 29.95.
    R.E. Kleinman, G.F. Roach, S.E.G. Ström: The null field method and modified Green function, Proc. R. Soc. London A 394, 121–136 (1984)ADSCrossRefzbMATHGoogle Scholar
  96. 29.96.
    M. Ochmann: Die Multipolstrahlersynthese – ein effektives Verfahren zur Berechnung der Schallabstrahlung von schwingenden Strukturen beliebiger Oberflächengestalt, Acustica 72, 233–246 (1990)Google Scholar
  97. 29.97.
    M. Ochmann: The complex equivalent source method for sound propagation over an impedance plane, J. Acoust. Soc. Am. 116(6), 3304–3311 (2004)ADSCrossRefMathSciNetGoogle Scholar
  98. 29.98.
    D. Wilton, I. Mathews, R. Jeans: A clarification of nonexistence problems with the superposition method, J. Acoust. Soc. Am. 94, 1676–1680 (1993)ADSCrossRefMathSciNetGoogle Scholar
  99. 29.99.
    L. Bouchet, T. Loyau, N. Hamzaoui, C. Boisson: Calculation of acoustic radiation using equivalent-sphere methods, J. Acoust. Soc. Am. 107, 2387–2397 (2000)ADSCrossRefGoogle Scholar
  100. 29.100.
    R. Bader: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology, Springer Series Current Research in Systematic Musicology, Vol. 2 (Springer, Heidelberg 2013)CrossRefGoogle Scholar
  101. 29.101.
    R. Bader: Characterizing classical guitars using top plate radiation patterns measured by a microphone array, Acust. Acta Acust. 97, 830–839 (2011)CrossRefGoogle Scholar
  102. 29.102.
    R. Bader: Reconstruction of radiating sound fields using minimum energy method, J. Acoust. Soc. Am. 127(1), 300–308 (2010)ADSCrossRefGoogle Scholar
  103. 29.103.
    N. Rayess, S.F. Wu: Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure, J. Acoust. Soc. Am. 107(6), 2955–2964 (1999)ADSCrossRefGoogle Scholar
  104. 29.104.
    S.F. Wu: On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method, J. Acoust. Soc. Am. 107(5), 2511–2522 (1999)ADSCrossRefGoogle Scholar
  105. 29.105.
    S.F. Wu, H. Lu, M.S. Bajwa: Reconstruction of transient acoustic radiation from a sphere, J. Acoust. Soc. Am. 117(4), 2065–2077 (2005)ADSCrossRefGoogle Scholar
  106. 29.106.
    S. Wu, J. Yu: Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method, J. Acoust. Soc. Am. 104, 2054–2060 (1998)ADSCrossRefGoogle Scholar
  107. 29.107.
    P.R. Stepanishen, S. Ramakrishna: Acoustic radiation from cylinders with a plane of symmetry using internal multi-pole line-source distributions, J. Acoust. Soc. Am. 93, 658–672 (1993)ADSCrossRefGoogle Scholar
  108. 29.108.
    P.R. Stepanishen, H.W. Chen: Surface pressure and harmonic loading on shells of revolution using an internal source density method, J. Acoust. Soc. Am. 92, 2248–2259 (1992)ADSCrossRefGoogle Scholar
  109. 29.109.
    S. Ramakrishna, P.R. Stepanishen: Acoustic scattering from cylinders with a plane of symmetry using internal multi-pole line-source distributions, J. Acoust. Soc. Am. 93, 673–682 (1993)ADSCrossRefGoogle Scholar
  110. 29.110.
    A. Sarkissian: Near-field acoustical holography for an axisymmetric source, J. Acoust. Soc. Am. 88, 199–209 (1990)ADSCrossRefMathSciNetGoogle Scholar
  111. 29.111.
    Z. Wang: Helmholtz equation-least squares (HELS) method for inverse acoustic radiation problems. Ph.D. Thesis (Wayne State Univ., Detroit 1995)Google Scholar
  112. 29.112.
    N. Rayess, S.F. Wu: Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure, J. Acoust. Soc. Am. 107(6), 2955–2964 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2014

Authors and Affiliations

  1. 1.Institute of MusicologyUniversity of HamburgHamburgGermany

Personalised recommendations