High-Resolution MIMO DRIR Measurements in an Opera Hall

Markus Noisternig1, Johannes Klein2, Marco Berzborn2,Arnaud Recher1, Olivier Warusfel1

1 Acoustics and Cognitive Spaces Research Group, UMR IRCAM - CNRS - Sorbonne University UPMC, Paris, France

Email: {noisternig, recher, warusfel}@ircam.fr2 Institute of Technical Acoustics, RWTH Aachen University, 52056 Aachen, Germany

Email: {johannes.klein, marco.berzborn}@akustik.rwth-aachen.de

Introduction

The use of microphone arrays for room acoustic analysishas been widely studied in recent literature. Directionalroom impulse responses (DRIRs) are typically measuredwith spherical microphone arrays (SMA) (see e.g. [1, 2]).In combination with spherical loudspeaker arrays (SLA)also the directivity of the sound source can be controlled(see e.g. [3, 4]). Acoustic energy can be radiated to se-lected directions in space in order to excite individualreflection paths. This improves the separability of reflec-tions in the analysis of a DRIR, compared to the excita-tion with an omni-directional loudspeaker (see e.g. [5]).

Acoustic measurement systems that include both arraytypes have only been recently used for room acousticanalysis (see e.g. [6, 7]). Such joint-systems are typicallyreferred to as acoustic multiple-input multiple-output(MIMO) systems, and according to this, the measuredDRIRs are typically referred to as MIMO DRIRs. MIMOsystems add control over the spatial properties and thushelp to improve the spatial resolution of the room acous-tic analysis.

A theoretical formulation of joint SMA/SLA MIMO sys-tems was recently presented in [8]. In a more recent workby some of the authors a joint-design approach based onthe analysis of spatial-aliasing, spherical-harmonics, andmodel-mismatch errors was presented [9, 10]. In this pa-per the latter approach has been used to design a MIMOsystem for room acoustic analysis [9, 11], which has thenbeen employed to in-situ measurements. MIMO DRIRswere measured for several positions and under differentacoustic conditions in the opera hall (“Großes Festspiel-haus”) of the Salzburg Festival. The following sectionsdescribe the design of the high-resolution MIMO mea-surement system.

Spherical Loudspeaker Array

The SLA has been especially developed to measure direc-tional RIRs. It is employed in a sequential measurementmethod. The array consists of a rigid sound-hard spherewith a radius of r = 20 cm, 28 loudspeakers of threedifferent sizes mounted on the sphere, a turntable forazimuthal rotation, and a mirror-symmetric frame con-struction [5].

The SLA measurement procedure allows for the synthesisof any arbitrary directivity up to the spherical harmonic

order N = 11. The measurement involves the rotationof the sphere to 24 angular positions, which results in672 room impulse response measurements [12]. The totaltime duration of the measurement for a given SMA/SLAposition was about 90 min. To account for the room im-pulse response variations due to temperature fluctuationsthe temperature was measured with multiple calibratedsensors distributed over the auditorium and stage. Therecorded temperature variation was in the range of 0.25degrees Celsius during one measurement period.

Using off-line computed directivity control filters [13],the 672 measurements can be superposed for every SMAchannel to synthesize any desired source directivity in thepost-processing stage. The results for every SMA chan-nel can then be used for further array processing on thereceiver side.

Figure 1: The spherical loudspeaker array (SLA) with themirror-symmetric frame construction mounted on a turntableand the multi-channel amplifier rack.

Figure 1 illustrates the SLA measurement setup usedduring the measurements in the opera hall of theSalzburg Festival. This includes the SLA in its frameconstruction [12] on a stand, the turntable, as well as theamplifiers. The turntable can be remote-controlled usingOSC messages, providing a straightforward interface forthe different software frameworks used during the mea-surements ([14, 15], Fig. 5).

Spherical Microphone Array

The SMA has been designed to match the operating fre-quency range (OFR) of the SLA using the MIMO sys-tem model presented in [9, 11]. The array consists of

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a rigid sound-hard aluminium sphere with a radius ofr = 12.5 cm, 64 Sennheiser KE 4-211-2 back-electretmicrophone capsules, an FPGA-based data acquisitionsystem, and an IP-based multi-channel audio streamingserver [16]. The sampling nodes on the sphere corre-spond to the Sloan-Womersley “hyperinterpolation” (i.e.critical sampling) grid [17]. The SMA captures the 3-Dsound field up to the spherical harmonic expansion orderN = 7.

Figure 2: The spherical microphone array (SMA).

MIMO System

The SLA and SMA performance is limited by severalfactors that bound the OFR:

- Spatial aliasing errors εa,S and εa,R: The use of afinite number of transducers in each array results inspatial-aliasing errors, which typically impose limi-tations at high frequencies.

- Model mismatch errors εm,S and εm,R: Array inac-curacies such as transducer misplacement, gain andphase errors introduce errors at all frequencies. Itcan be shown that these errors become dominantat low frequencies when the spatial resolution is en-hanced using methods such as the plane wave de-composition, which introduce ill-conditioning at lowfrequencies (see e.g. [18]).

- Joint SMA/SLA errors: These errors account for allthe SMA/SLA cross error terms. It can be shownthat these errors are bounded as long as the inde-pendent errors mentioned above are bounded (seee.g. [9]).

In [9] we presented a closed-form MIMO system modelfor the design of a SMA/SLA DRIR measurement systemwith desired specifications (e.g., minimum SNR, maxi-mum dynamic range, etc.), at a desired OFR, given thearray types (e.g., sound-hard rigid sphere) and array ge-ometries.

Figure 3 depicts the independent and total energetic errorbounds for the SMA/SLA-system that has been used forthe MIMO DRIR measurements at the Salzburg Festival.It can be shown that these errors only depend on thearray geometries and that they are independent of thebeamforming algorithms applied [10].

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Figure 3: Independent and total energetic error bounds ofthe applied MIMO system [11] for a spherical harmonic orderof N = 11.

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Figure 4: Independent and total energetic error bounds ofthe applied MIMO system [11] for a spherical harmonic orderof N = 9.

Restricting the spatial resolution of an array can renderan unmatched system feasible. Typically, the spatial res-olution is limited by employing a SH order Ne lower thanthe maximum achievable SH order N . This can be usedto “stabilize” the analysis during the post-processing ofthe data. Figure 4 illustrates this behavior for the dis-cussed MIMO system. In the given example, the spher-ical harmonic order is reduced to N = 9, which resultsin a much broader OFR compared to order N = 11 (seealso Figure 3).

Measurement System Setup

Figure 5 shows the graphic representation of the MIMOmeasurement system and its control structure.

Acknowledgments

This project was supported in part by the French FUI-AAP14 project “Binaural Listening” (BiLi). The authors

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IRCAM-SPAT!Room Acoustics Measurement Toolbox!

ITA TOOLBOX!SLA Control Unit!

Motor Control Functions!

SMA Data Acquisition Unit!

PHY!(Gbit)!

SMA!

SLA!

Step Motor Control!(Nanotec SMCI 35)!

KS 32-ch MADI Amp!

RME!HDSPe!MADI!

PHY!(Gbit)!

FPGA!

WCLK!

RS!232!

ESS Measurement!

Measurement Control!

ADC!

OSC!

Audio over IP!

WCLK!

MADI!

672 x 64 RIR!per!

Measurement Point!

Concert Hall!

Figure 5: Graphic representation of the MIMO measurementsystem and its control structure.

would like to thank the Salzburg Festival for providingaccess to the opera hall for several days, and EdwinPfanzagl-Cordone and his audio engineering team forthe technical support during the measurements. We aregrateful to Hai Morgenstern and Boaz Rafaely for themany fruitful discussions, as well as to Thibaut Carpen-tier and Emmanuel Flety for the help with software andhardware developments.

References

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