PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Identification of the Room Characteristics Using a
Spherical Microphone Array
Frederico ARAUJO1; Julio Cesar TORRES2; Fernando Augusto PINTO3
1,2,3

COPPE/UFRJ, Brazil

ABSTRACTThis work proposes the use of a Spherical Microphone Array (SMA) aiming not only to localize soundsources, but also the characteristics of the environment, such as dimensions and baffles positions. This isaccomplished by a spherical microphone array based on dodecahedron geometry. The processing consists inthe spherical harmonics decomposition of the sound field created around the spherical surface by a soundsource inside an enclosure environment. Only the sound source signal must be known, while its location andthe reflections from the surrounding surfaces can be blindly detected by using the Wavelet Transform andBeamforming. The geometry of main room surfaces is obtained by identifying the time of arrival anddirection of the direct sound and first reflections. Results obtained from ray-tracing simulation and in situ
measurements are presented and compared, showing the applicability of the proposed method.
Keywords: Spherical Harmonic Beamforming, Room Identification, Wavelet Transform, Ray-tracing
Simulation

1. INTRODUCTION
Microphone arrays have been used in the last decades to identify sound sources in several
environments. One of the most used techniques is the beamforming, that can be understood as a spatial
filter for selecting sound waves coming from the direction of interest. Nowadays, due to theacquisition hardware and the processing software capacity, it is already to possible apply the
beamforming using higher number of microphones in the array. This condition allows, for example,
the use of a Spherical Microphone Array (SMA) for monitoring all directions in space with highresolution. This is possible because SMA allows to apply the beamforming algorithm in the sphericalharmonics domain.
In this work, it is proposed to extend the application of the Spherical Harmonic Beamforming(SHB) to identify blindly the room geometry where the system is located. This might be an interesting
application to robots and drones, which need to recognize their surrounding environments. Using as
input signals the impulse responses measured by each microphone in the array related with a single
sound source,
The proposed method allows identifying the time and the directions of arrival of the direct soundand the first order reflections of the environment. The method is based on the analysis of the impulse
responses for all array microphones related to a given sound source. Only the emitted signal from thesound source must be known, in order to calculate the impulse responses. The other environment suchas main dimensions or baffles positions, are obtained from the array signal processing.
After a small revision of SHB techniques, it is presented the results using a SMA with 20 equally
spaced microphones in a real classroom with measured signals and signals generated from a
ray-tracing simulation.

2. SPHERICAL HARMONIC BEAMFORMING
Beamforming is a spatial filter technique that uses microphone arrays and signal processing tocontrol computationally the directivity and the sensitivity of the array with respect to the incoming
1

fh.araujo@mecanica.ufrj.coppe.br
julio@poli.ufrj.br
3
fcpinto@ufrj.br
27903

wave. Each sensor in the microphone array is in a different spatial location, thus providing different
time signals according to the relative position between sensor and sound source.
When SMA are used, the SHB appears as an alternative for the conventional algorithm, also known
as Delay-and-Sum algorithm. The SHB is based on the spherical harmonic decomposition of the soundpressure along a spherical surface (1), taking into account the spatial sampling over the sphere, as
shown in (2, 3). The utilization of spherical arrays in acoustics have been em ployed after (4, 5).
In the Delay-and-Sum method, the array response for a given direction is obtained by applying
weights and delays to each sensor signal. The summation of these signals emphasizes the soundcoming from that direction. If there is a single arriving sound wave from the focused direction (unique
sound source), all signals should be in similar phase, with higher amplitude than those coming fromother directions. In the SHB, considering that the sound pressure is known all over the sphericalsurface  , the output B is given by the weighted integral of the sound pressure P in this surface:B(ka, s ,  s )   w(ka, s ,  s , ,  ) P(ka, ,  )d

(1)

where (  ,  ) are, respectively, the elevation and azimuth angle, k is the wave number, a is the radius of
the SMA and the index s represents the direction focused by the algorithm. The weight w will dependon the beampattern intended. The advantage of the spherical arrays is the possibility of having thesame beampattern for all directions in space. The ideal beampattern is a Dirac delta, where signals
coming from the direction of interest are emphasized and from all other attenuated.
Therefore, the weighting for the desired beampattern, according to (6), is given by :Ynm ( s ,  s ) mw(ka,  s ,  s ,  ,  )   Yn ( ,  ) *nn  0 m   n 4i bn ( ka)where bn is the mode strength, i n(2)

 1 and the symbol * denotes the complex conjugated. Ynm is then th degree and mth order spherical harmonic defined as

Ynm ( ,  ) 

2n  1 (n  m)! |m|Ln (cos  )e im
4 (n  m)!

(3)

|m|

where Ln is the associated Legendre polynomial.
and for rigid sphere (5):bn (ka)  j n (ka) 

j ' n (ka)hn (ka)h' n (ka)(4)

where jn and h n are, respectively, Bessel and Hankel sphere functions and j’n and h’n their derivatives.
In practice, the pressure is not known along the entire sphere surface, onlyat discrete points where the microphones are located. For this reason, it is not possible to expand theideal beampattern to infinity orders and the integration over the sphere surface becomes a sum:M

B(ka, s ,  s )    j w(ka, s ,  s , j ,  j ) P(ka, j ,  j )

(5)

j 1

where M is the number of microphones in the array and  j are weights that depends on the
microphones distribution around the sphere. This work uses an equally spaced microphone array, forwhich these weights are constant.
For this reason, the weight w, expressed in Eq. (2), will be truncated in order N. Generally, toensure a truncation of the spherical harmonic decomposition to order N, M microphones are necessary(7), where:(6)M  ( N  1) 2
For greater N, the beampattern tends to the Dirac delta. Figure 1 shows beampattern truncated asfunction of N. The array spatial resolution is given by the angle 0 where the first zero in the
beampattern occurs. Using the Legendre functions, the resolution can be approximate by:7904

20 

2
N(7)

Figure 1 – SHB beampattern truncated to order N
For the truncated expansion of the spherical harmonics decomposition, the following restrictions
must be satisfied (7):bn (ka)  0 | n  0...N , ka  [kamin , kamax ](8)andbn (ka)  0 | n  N , ka  [kamin , kamax ](9)where [kamin , kamax ] is related to the lower and upper frequency of the array. In practice, upper limit
frequency is set for the argument ka when b N+1 (ka) is lower than -10dB.
More details about this procedure can be found in
2.1 Spherical Microphone Array
A spherical array with 100 mm radius and 20 microphones was printed in PLA (Polylactic Acid) for
this application (Figure 2), where the microphones are located at vertices of a dodecahedron.

Figure 2 - SMA with 20 microphones
This array allows a spherical harmonic decomposition up to 3rd order (N = 3), due its geometry andthe microphone distribution. The spatial resolution is about 120°. This means that the algorithm is notcapable to distinguish two simultaneous incoming waves whose relative angle i s smaller than thisresolution angle. The theoretical frequency range for the SHB is between 550 and 1000Hz, according
to Eqs. (9) and (10).

3. Method Description
3.1 Spherical Harmonic Beamforming Combined with Wavelet Transform
The Spherical Harmonic Beamforming is calculated using indirectly measured impulse responses

7905

of an environment for each microphone, by exciting a loudspeaker with a sine sweep with the same
frequency band of the SHB with duration of 10s. A time window was applied in the impulse response
signals in order to select the first 100 ms. This selection intends to reduce the processing time,
focusing only in the early reflections.
After obtaining a signal relative to each direction, these outputs can be analyzed using the Wavelet
Transforms (WT). Multi-resolution discretized maps (time x frequency) are then calculated, allowing
the identification of the time and direction of arrival of the direct sound and the reflection in the room.
The WT allows a time resolution of 0.2 ms.
The Morlet wavelet g(t) family was chosen for the decomposition, due to its exponential decay andfrequency control:g (t )  e



t2
2

e  i 0 t(10)This wavelet family has the advantage that the dilatation and translation parameters, a and b
respectively, can be easily related to time and frequency. The translated and dilated function ar e givenby (8):t b
g a ,b (t )  g 

 a 

(11)

3.2 Environment Surface Identification
Using the arrival time and directional information from the direct sound and the first orderreflections, it is possible to identify the surface responsible for each reflection. Figure 3 shows ageometry sketch of an environment with a surface. Point S represents the sound source location, S’ thesource image related to the surface and O is the observer (receiver) location, in this case, themicrophone array. Using trigonometry the angle β can be determined by knowing the direction andpropagation time of the direct sound (𝑡0 ) and of a given reflection (𝑡𝑅 ). With the time of arrival it ispossible to estimate the distances 𝑐 · 𝑡0 and 𝑐 · 𝑡𝑅 , where 𝑐 is the sound speed. The reflection point
location (R), as well as the surface normal vector n, can also be determined. Therefore, by knowing thedirections of the reflected waves from the spherical beamforming and the time from a temporal energy
analysis of the impulse responses, each plane defined by a given reflection point (R) and a surface
normal n can be determined. Figure 4 shows how a wave is identified, using the direct sound as
example.
3.3 Ray-tracing simulation
In order to evaluate the proposed method, results from simulated and measured scenarios arecompared. The software BRASS (Binaural Room Acoustic Simulator), developed at UFRJ, wasselected to simulate the environment. The software implements a modified version of the raytracing
method proposed by (10) with source and receivers defined after (11). The modified ray-tracing
implements a clustering algorithm applied on the first reflections up to a given order, usually 4th or 5th
reflection order. With such approach, the energy spread by the ray divergence is clustered back into thedirection of the nearest ray to the receiver center. Therefore, the energy can be focused in a specific timeand direction, similar to the image-source method. This software was used in the first moment to create areference list of reflections including the time and direction of arrival when simulating a single point
located in the center of the SMA. Then, it was simulated 20 impulse responses, one for each measurement
point the SMA. These IR’s were used as input in the SHB and the results were compared with the measured
ones.
Figure 5 shows the classroom in UFRJ where the measurements were carried out with a top view andFigure 6 presents the room model used in the simulation.

7906

Figure 3 - Geometry sketch of a surface reflection

Figure 4 - Identification of the direct sound

4. Results
Table 1 shows the time and the direction of arrival of the direct sound and all the first orderreflections for three situations: (a) Ray-Tracing Simulation (RTS) for a single receiver, at the sphericalarray center; (b) the SHB output from measurements and (c) the SHB output from ray-tracing
simulation of 20 receivers at the microphone locations. The beamforming is calculated for anequiangular space for elevation and azimuth, both spacing was set to 2°. The Wavelet translation factor
b was set to 0.2 ms, defining the time resolution.

7907

Figure 5 - Classroom: Top View (left) and Measurement setup (right).

Figure 6 – Simplified room model for the ray-tracing simulation
Table 1 - Incoming reflections

RTS for single receiver
Reflection
TypeTime [ms]SHB from measurements

SHB from simulation

Az [°] El [°] Time [ms] Az [°]El [°]

Time [ms]Az [°]

El [°]

Direct Sound

14.6

351

82

14.6

352

82

14.6

352

84

Floor

16.7

351

119

16.8

352

128

16.8

352

114

Ceiling

18.7

351

51

18.8

352

48

18.8

352

56

Wall 1

23.8

354

85

23.0

356

88

24.1

356

86

Wall 4

26.7

57

86

26.4

62

80

27.0

58

84

Wall 2

27.7

301

86

27.6

308

100

27.6

300

88

Wall 3

34.1

184

86

34.8

184

76

34.2

186

88

Figure 7 shows the room reconstruction from the ray-tracing for a single point and the SHB results,
while Figure 8 and Figure 9 show, respectively, the reconstruction for the measured SHB and thesimulated SHB. As expected, the reconstruction from the single-receiver was very close to aparallelepiped, the real shape from the classroom, while the ones for the SHB have deformed shapes.
However, the calculated dimension, considering the center of the surfaces as reference, were very
close to the real ones, as can be seen in
Table 2.

7908

Figure 7 - Room reconstruction from the single-point ray-tracing simulation: a) plane reconstruction; b) solid
reconstruction

Figure 8 - Room reconstruction from the measured SHB: a) plane reconstruction; b) solid reconstruction

Figure 9 - Room reconstruction from the simulated SHB: a) plane reconstruction; b) solid reconstruction

7909

Table 2 - Calculated room dimensions

Dimension [m]

X

Y

Z

Room

10.00

8.00

3.50

Single-point RTS

9.79

7.85

3.45

Measured SHB

9.79

8.25

3.54

Simulated SHB

8.90

7.81

3.68

5. CONCLUSIONSThis research presented a methodology to identify time and direction of arrival of reflections usinga Spherical Microphone Array with a technique based on the combination of the Spherical Harmonic
Beamforming with the Wavelet Transform. It was applied in a real classroom, where were possible toidentify all the first order reflections, that were compared with a ray-tracing simulation method alsopresented here. With this information, it was possible to measure the dimensions of the room. The
results were very close to the real dimensions, with an error smaller than 3% for the measured data and
11% for the simulated data.
The next steps, it is planned to apply this procedure in rooms with more complex geometry and withmore surfaces to be identified. Also it is intending to include in this procedure an amplitude analysis.
Thus it will be possible to identify some specific characteristics from the surfaces, for instance,
absorption coefficients.

ACKNOWLEDGEMENTS
The authors would like to thank the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado
do Rio de Janeiro (FAPERJ) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES) for the financial support.

REFERENCES
1.

B. Rafaely, Analysis and design of spherical microphone arrays, Speech and Audio Processing, IEEE
Transactions on 13 (1) (2005) 135-143.
2. R. H. DuHamel, Pattern synthesis for antenna arrays on circular, elliptical, and spherical surfaces,
Radio Direction Finding Section Elect. Eng. Res. Lab. Rep., Univ. of Illinois, Urbana, 1952
3. M. Hoffman, Conventions for the analysis of spherical arrays, Antennas and Propagation, IEEE
Transactions on 11 (4) (1963) 390-393
4. T. D. Abhayapala, D. B. Ward, Theory and design of high order sound field microphones using
spherical microphone array, (ICASSP 2002) IEEE International Conference on Signal Processing
5. J. Meyer, G. Elko, A highly scalable spherical microphone array based on an orthonormal
decomposition of the sound field, Acoustics, Speech, and Signal Processing (ICASSP), 2002 IEEE
International Conference on 2.
6. B. Rafaely, Phase-mode versus Delay-and-Sum spherical microphone array processing, Signal
Processing Letters, IEEE 12 (10) (2005) 713-716.
7. T. D. Abhayapala, D. B. Ward, Theory and design of high order sound field microphones using
spherical microphone array, (ICASSP 2002) IEEE International Conference on Signal Processing..
8. M. Vetterli, J. Kovacevic, Wavelets and Subband Coding, Prentice-Hall, Englewood Cli_s, New Jersey,
1995.
9. DE ARAUJO, Frederico Heloui; PINTO, Fernando Augusto de Noronha Castro; TORRES, Julio Cesar
Boscher. Room reflections analysis with the use of spherical beamforming and wavelets. Applied
Acoustics, 2018, 131: 192-202.
10. A. Krokstad, S. Strom, S. Sorsdal, Calculating the acoustical room response by use of a ray tracing
technique, Journal of Sound and Vibration 8 (1) (1986) 118-125.
11. R. A. Tenenbaum, T. S. Camilo, J. C. B. Torres, S. N. Y. Gerges, Hybrid method for numericalsimulation of room acoustics with auralization: part 1 - theoretical and numerical aspects, Journal of theBrazilian Society of Mechanical Sciences and Engineering 29 (2007) 211-221..

7910