1. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
Office +82-2-2220-1795 | Fax +82-2-2220-4794
http://acoustics.hanyang.ac.kr
Plane wave decomposition and beamforming
for directional spatial sound localization
IBCAST
13th International Bhurban Conference on Applied Sciences & Technology
12 to 16 January, 2016
Muhammad Imran1, Jin Yong Jeon1, Akhtar Hussain2
1Department of Architectural Engineering Hanyang University, Seoul, Korea
2Centers of Excellence in Science and Technology (CESAT) Islamabad, Pakistan

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HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
2
Contents
o Introduction
o Background and motivation
o Potential application areas
o Spherical Harmonics and Spherical microphone arrays
o Methodology
o Plane wave decomposition and MVDR
o Computational Framework
o Verification
o Measurement setup
o Results
o Validation and experimental evaluation
o Results and discussion
o Conclusion and potential contribution

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ARCHITECTURAL ACOUSTICS LAB
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Introduction
o Plane wave decomposition (PWD) and Beamforming (using spherical microphone arrays) for
 Spatio-temporal analysis of the sound field in
 Room acoustics, Underwater technologies
• Estimation of the directional characteristics and localization of acoustic sources
 Spatial audio rendering applications
• Sound field reconstruction and virtual sound synthesis
o Propagation of sound is influenced by the reflections from surrounding
o Microphone arrays based processing to
o Emulate spatial and temporal behavior of the propagation of sound in spaces
o Different microphone array configurations
o The traditional methods
o Provide an approximation of spatial and temporal characteristics
o Result in limited spatial resolution and Limited capability for localization
o Low (SNR) Signal to noise ratio
o Propose PWD-MVDR framework (using optimum design of spherical microphone array)
o Spatio-temporal characterization
o Synthesizes the directional impulse responses (DIRs)
o Analyze the directional behavior and localization of the sound sources
o Improved spatial resolution and SNR

4. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Spherical Harmonics
o Spherical harmonics (SH) and spherical Fourier transform (base for sound field synthesis)
o Kirchoff Helmholz integral describes the sound pressure
o Enabling plane wave decomposition (PWD) and beamforming
o Orders and degrees of SH define the accuracy and detail of the resolution of the captured sound
o Higher SH orders, a higher directional selectivity
o A square integrable function at the surface of a unit sphere, its spherical Fourier transform and the
inverse transform are given as follows
𝑓𝑛𝑚 =
0
2𝜋
0
𝜋
𝑓 𝜃, 𝜑 𝑌𝑛
𝑚∗
𝜃, 𝜑 𝑠𝑖𝑛𝜃𝑑𝜃𝑑𝜑 (1)
𝑓(𝜃, 𝜑) =
𝑛=0
∞
𝑚=−𝑛
𝑛
𝑓𝑛𝑚 𝑌𝑛
𝑚
(𝜃, 𝜑) (2)
𝑌𝑛
𝑚
𝜃, 𝜑 =
2𝑛 + 1
4𝜋
(𝑛 − 𝑚)!
𝑛 + 𝑚
𝑃𝑛
𝑚
𝑐𝑜𝑠𝜃 𝑒 𝑖𝑚𝜑
(3)
Where, 𝑌𝑛
𝑚
are spherical harmonics of order 𝑛, and mode 𝑚, 𝑃𝑛
𝑚
are the
Legendre functions of order 𝑛, and mode 𝑚, 𝜃 and 𝜑 describe the azimuth
and elevation angles

5. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Spherical Microphone Arrays
o A spatially distributed array of microphones on a real or imaginary spherical surface
o Different configurations have been investigated
o Open Sphere with Pressure Transducers
o Open Sphere with Pressure Grad Transducers
o Rigid Sphere with Pressure Transducers
o Rigid Sphere with Pressure Grad Transducers
o Dual Open Sphere with Transducers
o Number of channel may vary from 8 to 128
o More channel, higher order spherical harmonic achieved
o Diameter of the Sphere
o Frequency band coverage

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ARCHITECTURAL ACOUSTICS LAB
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Eigenmike
o Eigenmike by mh-acoustics USA is used in this study
o Advantages of spherical surface geometries
o Easy mathematical handling
o Physical Design
o Implementing SH is convenient
o Eigenmike, a commercially available spherical microphone array from Gary Elko and Jens
Meyer (mh acoustics,USA)
o Diameter: 8.4cm
o Channels: 32 sensors
o Microphone: B&K Omni
o Real-time applications (spatial audio recordings/ room acoustics)
o Eigenmike can resolve a maximum order of SH to N=4

7. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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Computational Process
The computational process is represented in figure below
o Microphone Arrays and Sound Capturing System
• Spherical microphone capturing (32 channels, rigid body reflective surface, evenly embedded
transducers)
o Plane Wave Decomposition
o Adaptive Beamforming
• MVDR-Beamforming weighting filters
o DOA and Localization
o Visualization
o Direction signal synthesis

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ARCHITECTURAL ACOUSTICS LAB
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Methodology (Sound Capturing)
Step: 1
• Signal generation
• Dodecahedron omnidirectional sine swept signal (20Hz to 20KHz)
• Signal data acquisition
• Eigenmike microphone array
• Matlab, NI-cDAQ-9139
Step 2:
o Fourier transform of captured signals
o Adding signals
o Inverse Fourier transform
Step 3:
o Windowing (Hamming)
o 32 Impulse responses of the chamber

9. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Methodology (Plane Wave Decomposition) (01)
Mathematical model of PWD and MVDR-beamformer is presented
• Fourier transform of captured RIRs and subsequently converting into spherical harmonics
• Spatial Fourier coefficients computed using SH by considering the array grid weights and sound
pressure captured in the form of RIRs
• Radial part for the wave equation is incorporated including frequency dependencies
• Radial structure of the sound field is compensated as
• Complex-valued decomposed plane wave signal is computed
𝑃𝑛𝑚 =
𝑛=0
𝑁
𝛽𝑠 𝑝𝑠 𝑌𝑛
𝑚∗
(𝜗, 𝜑
Here, 𝑌𝑛
𝑚
are spherical harmonics of the order ‘n’ and mode ‘m’,
‘βs’ are the grid weights and ‘ps’ are the complex sound pressures
𝑃𝑛𝑚 = 𝑌𝑛
𝑚∗
𝜗 𝜔, 𝜑 𝜔 𝑏 𝑛
𝜔
𝑐
𝑟
𝑏 𝑛
𝜔
𝑐
𝑟 = 4𝜋𝑖 𝑛
𝑗 𝑛
𝜔
𝑐
𝑟 −
𝑗 𝑛
′ 𝜔
𝑐
𝑟
ℎ 𝑛
2 ′ 𝜔
𝑐
𝑟
ℎ 𝑛
2 𝜔
𝑐
𝑟
ℎ 𝑛
(2)
′ 𝜔
𝑐
𝑟
Bessel functions
Spherical Hankel
𝑗𝑛
′
𝜔
𝑐
𝑟
𝑑 𝑛 𝑘𝑟 =
1
)𝑏 𝑛(𝑘𝑟
𝑌 =
4
𝑁 + 1 2
𝑛=0
𝑁
𝑚=−𝑛
𝑛
𝑌𝑛
𝑚
(𝜗𝑙, 𝜑𝑙)𝑃𝑛𝑚 𝑑 𝑛 𝑐 𝑛

10. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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Limitations (Plane Wave Decomposition)
o A spatial-filter based beamformer (using PWD) is well characterized by a single
frequency
o Could not yield the same beamforming patterns for all frequency bands
o Limiting its utility for broadband frequency response
o The noise from the side lobes will not be attenuated uniformly over its entire spectrum
o Resulting in some disturbing artifacts in the array output
o Therefore
o A response-invariant broadband beamforming technique must be implemented
o A spatio-temporal filter to array outputs
o MVDR beamforming filters
o MVDR filters resolve the issues
o Effects of side lobes
o Noise attenuation along the steering directions
o Fixed array structures
o Thus they are widely used in adaptive beamformer methods in which the basic idea is to choose the
coefficients of filters to minimize the output power and the constraints without affecting the desired signal

11. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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o In this study, therefore
o MVDR beamforming weights for its certain advantages
o This technique was developed for direction of arrival estimation from a desired signal during
array processing
o The optimal filters are given
• Here 𝑆−1
is the matrix inverse
• These filters are reshaped by using a stability factor 𝛽(𝑘)
o Using in main Equation as 𝑐 𝑛
Methodology (MVDR beamforming weights) (02)
𝑌 =
4
𝑁 + 1 2
𝑛=0
𝑁
𝑚=−𝑛
𝑛
𝑌𝑛
𝑚
(𝜗𝑙, 𝜑𝑙)𝑃𝑛𝑚 𝑑 𝑛 𝑐 𝑛
𝐶 𝑇
𝑘 =
)𝑊 𝐻
(𝑘)𝑆−1
(𝑘
)𝑊 𝐻(𝑘)𝑆−1(𝑘)𝑊(𝑘
𝐶 𝑇
𝑘 =
𝑊 𝐻
𝑘 𝑆−1
𝑘 + 𝛽(𝑘)𝑰 −1
)𝑊 𝐻(𝑘) 𝑆−1 𝑘 + 𝛽(𝑘)𝑰 −1 𝑊(𝑘

12. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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Verification (Measurement Setup Procedure)
o The measurements setup for verification was established in a full scale anechoic chamber hall in
well controlled conditions at Daewoo Acoustics Labs, South Korea
o Sound Source
o Three High power omnidirectional dodecahedron
o The positions (in azimuth plane)
o Source-1 = 315o
o Source-2 = 0o
o Source-3 = 45o
o The elevations for all sources are kept constant at 90o
o Capturing system
o Eigenmike
o Data Acquisition and processing
o Matlab and NI-cDAQ9139
o Four analysis were conducted
o Visualization
o DOA and localization
o Directional IRs
o Spatio-temporal analysis

13. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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o PWD-MVDR Localization
Verification (Results) Localization
SOURCE
Expected Location
(𝜃𝑒
𝑜
, 𝜑 𝑒
𝑜
)
Computed Location
(𝜃𝑐
𝑜
, 𝜑𝑐
𝑜
)
Error estimation
∆𝜃0
∆𝜑0
Source-1 315o, 90o 313.7o, 91.3o -1.3o 1.2o
Source-2 0o, 90o 1.4o, 92.1o 1.4o 2.1o
Source-3 45o, 90o 47.0o, 91.5o 2o 1.5o
Source-1 Source-2 Source-3

14. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Auditorium Measurements (Measurement Setup Procedure)
o The measurements were executed in 433-seat Sejong Chamber Hall (SCH) located in
Seoul, South Korea
o Measurements positions R04, R12 and R20
o Results for only R04 position are represented
o Sound Source
o A High power omnidirectional dodecahedron
o The positions of source is on stage at center at 1 meter height
o Capturing system
o Eigenmike
o Four analysis were conducted
o Visualization
o DOA and localization
o Directional IRs
o Spatio-temporal analysis
Reverse-fan shaped and tilted side walls
Saw-tooth-type diffusers (1-D corrugations)
Size of the hall is 17m (width) by 7.6 m (Height) by 19
m (Length) with 3,200 m3 Volume
Mean reverberation time (RT) for this hall is 1.18 sec
Reference coordinate
systems for each
measurement position

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ARCHITECTURAL ACOUSTICS LAB
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Experimental Results (Spatial distribution of sound field)
o PWD-MVDR was employed with spherical harmonics of order six (N=6)
o Measured response of array at 2KHz without time windowing for first 80msec of data
o Spatial distribution of overall sound pressure level of the sound field from all directions
o Most of the sound field is scattered from the right side of the hall, front celling (Stage)
and left side floor of the hall
Sejong Chamber Hall
Measurements positions R04

16. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Experimental Results (Spatio-Temporal analysis of sound field)
o A spatio-temporal analysis was performed
o To localize the direct sound and individual reflection’s arriving directions
o To analyze the influence of the walls scattering elements of the space
o Method
o Approximation of PWD from temporal segmentation
Panoramic View
5 msec window of IRs
1 msec step

17. 1 November 2016
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ARCHITECTURAL ACOUSTICS LAB
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Experimental Results (Spatial distribution of sound/Directional Responses)
o PWD-MVDR was employed with spherical harmonics of order six (N=6)
o Measured response of array at 2KHz without time windowing for first 80msec of data
o Spatial distribution of overall sound pressure level of the sound field from all directions
o Most of the sound field is scattered from the right side of the hall, front celling (Stage)
and left side floor of the hall
o Two directional responses at different azimuth and elevation steering directions

18. 1 November 2016
HANYANG UNIVERSITY
ARCHITECTURAL ACOUSTICS LAB
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Conclusion
o Presented an experimental implementation of algorithms for PWD and MVDR
beamforming using a spherical microphone array
o Spherical harmonics of order (N=6) implemented in Eigenmike
o The direct sound and early reflections were detected
o Showing a prospective for a useful acoustics measurement tool
o The detection and localization of reflections were improved by time windowing to RIRs
o The comparison of results for computed directions of incidence of sound and the
directions known beforehand showed a good agreement with each other
o The directional impulse responses were synthesized based on MVDR beamformer
o MVDR beamformer is used for multiple source localization for difference steering
directions

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ARCHITECTURAL ACOUSTICS LAB
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Potential Contribution
o Analysis (Areal, Underwater and Room Acoustics)
o Distribution of acoustics field in spaces (intensity)
o Spatial and temporal visualization
o Sound source localization
o Sound source tracking
o Sound source recognition
o Various directional acoustic parameters from DIRs can be computed
o Directional reverberation
o Directional Reflections
o Influence of certain boundaries of the spaces (indoor)
o Furthermore
o Audio engineering
o Virtual sound synthesis
o 3D Sound reproduction
o Sound source separation