# Spatial Analysis and Synthesis Methods:
Subjective and Objective Evaluations Using Various Microphone Arrays in the
Auralization of a Critical Listening Room

Alan Pawlak, Hyunkook Lee, Aki Mäkivirta, and Thomas Lund The research
presented in this paper was funded by Genelec Oy and the University of
Huddersfield.A. Pawlak and H. Lee are with the Applied Psychoacoustics Lab
(APL), University of Huddersfield, HD1 3DH Huddersfield, United Kingdom
(e-mail<EMAIL_ADDRESS>h.lee@hud.ac.uk)A. Mäkivirta and T. Lund are
with Genelec OY, 74100 Iisalmi, Finland (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Parametric sound field synthesis methods, such as the Spatial Decomposition
Method (SDM) and Higher-Order Spatial Impulse Response Rendering (HO-SIRR),
are widely used for the analysis and auralization of sound fields. This paper
studies the performances of various sound field synthesis methods in the
context of the auralization of a critical listening room. The influence on the
perceived spatial and timbral fidelity of the following factors is considered:
the rendering framework, direction of arrival (DOA) estimation method,
microphone array structure, and use of a dedicated center reference microphone
with SDM. Listening tests compare the synthesized sound fields to a reference
binaural rendering condition. Several acoustic parameters are measured to gain
insights into objective differences between methods. A high-quality pressure
microphone improves the SDM framework’s timbral fidelity. Additionally, SDM
and HO-SIRR show similarities in spatial fidelity. Performance variation
between SDM configurations is influenced by the DOA estimation method and
microphone array construction. The binaural SDM (BSDM) presentations display
temporal artifacts impacting sound quality.

###### Index Terms:

Spatial Audio, Binaural Rendering, Spatial Decomposition Method (SDM), Higher-
Order Spatial Impulse Response Rendering (HO-SIRR), Binaural Room Impulse
Responses (BRIR), Auralization, Microphone Arrays, Subjective Audio
Evaluation, MUSHRA, Direction of Arrival (DOA), Time Difference of Arrival
(TDOA), Pseudo Intensity Vectors (PIV)

##  I Introduction

Directional sound field analysis reveals spatial reflection patterns in
enclosed spaces. Its goals include: (i) pinpointing problematic room
reflections [1], (ii) understanding perceptual impacts of room features [1],
(iii) identifying reflections contributing to the desirable perceptual
attributes [2], (iv) assessing the impact of reflection regions on objective
metrics [3], (v) advancing psychoacoustic research [2], and (vi) forming the
foundation for parametric auralisation systems [4, 5].

Over the past two decades, the principles of spatial analysis have driven
significant growth in parametric spatial audio rendering. This trend began
with the introduction of the Spatial Impulse Response Rendering (SIRR) [4],
which utilizes first-order spherical harmonics (SPH) for sound field analysis
and synthesis in the time-frequency domain. A subsequent, more straightforward
approach known as the Spatial Decomposition Method (SDM) was introduced by
Tervo et al. [5]. This method operates in the time domain and interprets each
sample in an impulse response as an image source characterized by both
pressure and direction. The public availability of SDM as a MATLAB toolbox [6]
has made it a popular choice for analyzing enclosed spaces, auralization, and
research [7, 8, 9, 10, 11, 12, 13]. As object-based audio gained prominence,
the Reverberant Spatial Audio Object (RSAO) was developed, parameterizing
spatial room impulse response (SRIR) into a concise set of coefficients. This
was aimed at enabling reverberation synthesis within audio object renderers
[14].

Later, the HO-SIRR, a higher-order adaptation of the SIRR, was introduced
[15], offering enhanced spatial resolution through the use of higher-order
SPH. Concurrently, the Ambisonic SDM (ASDM) was introduced, allowing for the
upscaling of the first-order ambisonics (FOA) to higher-order (HOA).
Subsequent innovations include the binaural versions of SDM (BSDM) [16] and
HO-SIRR[17], an enhanced ASDM known as 4D-ASDM [18], and the Reproduction and
Parameterisation of Array Impulse Responses (REPAIR) [19].

Despite the rapid developments, the SDM and SIRR (and HO-SIRR) remain
predominant. Previous studies, such as [20, 5, 15, 19], have evaluated these
methods primarily through subjective experiments with loudspeakers employing
simulated environments. However, some acoustic simulation methods, like the
Image Source Method (ISM) [21] may favor methods like the SDM due to shared
underlying assumptions. Moreover, inconsistencies arise, such as those between
the SDM and HO-SIRR evaluations, which may stem from different microphone
array configurations or direction-of-arrival (DOA) estimation techniques used.
Previous studies have not comprehensively compared all these methods under
real-life conditions, which this study intends to do.

Additionally, the experimental setups in prior studies appear to be somewhat
limited. While SDM has been used with various microphone arrays, only two
studies have examined how the array affects SDM’s auralization quality [22]
and DOA accuracy [16]. Despite commonly using signals from any omnidirectional
microphone in arrays, no perceptual differences were found between signals
from Ambisonics and a central omni microphone, although the research lacked
methodological detail [23].

In this paper111This paper extends our initial study [24], offering a detailed
analysis with more subjects and source positions, objective metrics, in-lab
experiments (replacing the previous remote setup due to COVID-19), refined
Eigenmike em32 impulse response measurements, and revising evaluated systems.,
we present a comprehensive perceptual evaluation to test the hypothesis that
different synthetic binaural room impulse responses (BRIRs) produced using
various parametric spatial audio rendering techniques—specifically SDM, BSDM,
and HO-SIRR—will differ in spatial and timbral fidelities compared to a
reference BRIR recorded with the KU100 dummy head. Additionally, building on
[5] and [22], we investigate whether a greater number of sensors in an array
leads to improved localization performance. To this end, we employ both an
Eigenmike em32—equipped with 32 omni capsules on a rigid sphere with a 42 mm
radius—and a compact microphone array with six omni microphones for SDM.
Further, we examine the impact of direction of arrival (DOA) estimation
algorithms in SDM, focusing on those based on time difference of arrival
(TDOA) and pseudo intensity vectors (PIVs), and assess the influence of using
a dedicated omnidirectional microphone at the array’s center as a pressure
signal in SDM.

The study is confined to a room that complies with recommendations in ITU-R
1116-3 [25] since our main focus is on the spatial analysis and auralization
of critical listening or sound mixing room. We operate under the assumption
that our findings will be replicable in similar rooms adhering to this widely
recognized standard. Our study utilizes source positions from six
orientations, aligned with industry standards like the ITU-R BS.2051-2 [26]
and Dolby Atmos 7.1.4 configurations. The aim is to ground the discussion in
scientific rigor amidst the rapid expansion of parametric spatial audio
reproduction techniques, delineating current standings, identifying gaps, and
defining a system for optimal spatial data capture and accurate reproduction
in the context of critical listening room.

The paper is structured as follows: Section II introduces the foundational
theories of the direction of arrival estimation, with a focus on time
difference of arrival (TDOA) and Pseudo Intensity Vectors (PIVs) which are
crucial to the SDM and SIRR methods. Section III elaborates on the specifics
of the SDM and SIRR methods. Section IV details our methodology and
experimental design. Section V showcases our perceptual study results, based
on the MUSHRA methodology. Section VI reports on objective metrics. Section
VII synthesizes our key findings. Section VIII concludes the paper.

##  II Direction of Arrival Estimation Methods

Estimating the direction of arrival (DOA) is a fundamental aspect of
parametric sound field synthesis methods, as it determines the wave’s origin
and propagation direction. Various methods have been developed for DOA
estimation, including Time Difference of Arrival (TDOA)-based methods like the
Generalized Cross Correlation (GCC), subspace methods such as ESPRIT or MUSIC,
beamforming approaches, and Pseudo Intensity Vectors (PIVs), with
comprehensive tutorials available in [27]. This section will focus on two
approaches particularly relevant to SDM and SIRR: TDOA and PIVs.

###  II-A Time Difference of Arrival (TDOA)

The time difference of arrival is frequently used to determine the source’s
direction of arrival. It measures the time lag of a signal across multiple
sensors. Knowing the sensors’ relative positions and these time lags allows
estimation of the source’s origin direction. Common TDOA estimation techniques
include cross-correlation with weightings such as GCC-SCOT and GCC-PHAT [28].

While the Spatial Decomposition Method (SDM) can be combined with any
appropriate direction of arrival (DOA) estimation algorithm, the foundational
paper utilized a least squares method for DOA estimation via TDOA using GCC
with no weighting [5]. As this algorithm was incorporated into a popular
toolbox [6], it is often linked with the original SDM. For detailed equations
and further technical specifics, please refer to [5, 29, 28, 30].

###  II-B Pseudo-Intensity-Vectors (PIVs)

Pseudo Intensity Vectors (PIVs) offer a viable alternative to TDOA-based DOA
estimation, building upon historical sound intensity measurement methodologies
[31, 32, 1, 33]. The term ”Pseudo Intensity Vectors” was first introduced by
Jarrett et. al. [34] and refers to the sound intensity vectors computed from
the zeroth and first-order eigenbeams.

The subjective results obtained by McCormack et al.[15] and Ahrens [35]
implied that broadband DOA estimation using PIVs is inferior to other SDM and
SIRR configurations in auralization. However, Zaunschirm et al. showed that
using this method for bandwidth between 200 Hz and just below the microphone
array’s spatial aliasing frequency resulted in SDM rendering nearly identical
to the binaural reference in terms of auditory image width, distance, and
diffuseness [36]. Bassuet stressed minimizing microphone directivity effects
in broadband PIV-based DOA estimation, suggesting a 100 Hz–5 kHz filter range
where the Soundfield first-order Ambisonics microphone exhibits consistent
directivity characteristics [37].

Alternatively, the PIV can be represented in the frequency domain, as done in
SIRR and HO-SIRR [4, 15], the PIV is computed for each frequency bin, averaged
over time windows. This method allows for the calculation of the diffuseness
coefficient $\psi(\omega)$, indicating the balance between the pseudo-
intensity vector magnitude and the energy density (details in [4, 15]).

##  III Parametric Sound Reproduction Methods

###  III-A Spatial Decomposition Method (SDM)

The Spatial Decomposition Method (SDM), introduced in 2013, utilizes the image
source model for parametric spatial encoding, treating impulse response
samples as broadband image sources [5]. The resulting metadata can be utilized
for loudspeaker reproduction or binaural reproduction using Head-Related
Transfer Functions (HRTFs). SDM’s process involves a microphone array for
direction of arrival (DOA) estimation and an omnidirectional microphone for
pressure signal capture. The method comprises two stages: spatial analysis
using DOA estimation algorithms (TDOA or PIVs) and synthesis, which utilizes
DOA data and pressure signals to create directional output signals using
techniques like Vector Base Amplitude Panning (VBAP) [5, 38, 10], K-Nearest
Neighbour (KNN) mapping [38, 8, 35], or Ambisonics [39]. Post-equalization to
mitigate spectral whitening and optimized loudspeaker grids are also utilized
for enhanced sound reproduction [8, 40].

Binaural Spatial Decomposition Method (BSDM), offers improvements for binaural
reproduction [16]. It includes the rotation of the DOA matrix for various head
orientations and post-processing techniques for direct sound enforcement and
DOA quantization. BSDM also features RTMod+AP equalization for better echo
density and decay, building on the previous post-equalization method designed
for loudspeaker reproduction [8]. Later, updates to the publicly available
toolbox have introduced features such as impulse response denoising and band-
limited spatial analysis [41].

SDM’s performance hinges on the microphone array configuration and window
size. Historically, SDM has employed a variety of microphone arrays, from GRAS
50VI probes to custom arrays with varying spacings [5, 7, 42, 8, 22, 23, 9,
43, 16]. Optimal array design, guided by research, focuses on specific
microphone spacings to minimize DOA errors and perceptual discrepancies [5,
22, 16]. PIV-based DOA estimation allows flexibility in microphone array
choice, but it requires an array capable of producing high-quality first-order
spherical harmonics [16]. In this method, windowing aims at smoothing the DOA
while in TDOA-based estimation, the window size is key to performance,
ensuring a balance between temporal and spatial resolution. Larger windows
enhance estimation robustness but increase the risk of multiple reflections,
conflicting with the single-reflection assumption [5]. Historically, window
sizes were chosen arbitrarily [8, 42, 7, 38]. Recent research by Amengual Garí
et al. on optimal window size for DOA estimation in a simulated setup suggests
that for a 100 mm spaced array, 36 or 64 samples at 48 kHz is most effective
[16].

###  III-B Spatial Impulse Response Rendering (SIRR)

Spatial Impulse Response Rendering (SIRR) is the first parametric spatial
encoding method for SRIR, focusing on emulating key perceptual features like
Interaural Time Difference (ITD), Interaural Level Difference (ILD), and
Interaural Coherence (IC) [4]. Distinct from the SDM, SIRR operates in the
time-frequency domain using spherical harmonic input.

The processing in SIRR utilizes the Short Time Fourier Transform (STFT) with a
Hann window, using Pseudo Intensity Vectors (PIVs)—as outlined in Section
II-B—to determine the direction of arrival (DOA) and diffuseness for each
time-frequency bin. In the synthesis stage, the pressure response is divided
into non-diffuse and diffuse parts, guided by the estimated diffuseness
coefficient. The directional part is panned using Vector-Based Amplitude
Panning (VBAP), while the diffuse component is decorrelated and distributed
uniformly among the loudspeakers.

SIRR was extended to Higher-Order Spatial Impulse Response Rendering (HO-SIRR)
[15], which employs higher-order spherical harmonics and beamforming to divide
the sound field into uniform sectors. Each sector undergoes separate analysis,
allowing for a more precise estimation. This is especially valuable in
challenging situations, for instance, when sound events from two distinct
directions reach the array simultaneously. During the synthesis stage, the
directional components from all sectors are panned via VBAP to their
respective channels and then combined. Meanwhile, the diffuse components are
re-encoded into spherical harmonics, decoded to loudspeaker signals, and then
decorrelated.

The binaural variant of HO-SIRR, as detailed by Hold et al. [17], addresses
coloration and HRTF resolution in virtual speaker binauralization. This
approach integrates HRTFs in the synthesis phase of HO-SIRR, rendering
directional components according to arrival directions and diffuse components
by their sector steering directions. Objective analyses have demonstrated a
reduction in coloration compared to the traditional HO-SIRR method.

##  IV Experimental Design

###  IV-A Evaluation Method

The main goal of this study is to determine which synthetic binaural room
impulse response (BRIR) yields an auralization most perceptually similar to
that produced by a BRIR recorded with the KU100 dummy head. To evaluate this
similarity, we adopted the fidelity attribute, as defined by [44]. Zieliński
described it as the ”trueness of reproduction quality to that of the
original”. The experiment had two dependent variables: (i) spatial fidelity
and (ii) timbral fidelity.

The experiment used the MUSHRA methodology [45], in which participants rated
the similarity of test sounds to a reference on a continuous scale from 1.0
(”Extremely different”) to 5.0 (”Same”), with intermediate values of 2.0
(”Very different”), 3.0 (”Different”), and 4.0 (”Slightly different”). This
scale has been used in analogous subjective studies employing the MUSHRA
methodology [46, 5, 47, 23].

The listening experiment took place in the ITU-R BS.1116-compliant listening
room (6.2m x 5.6m x 3.4m) at the University of Huddersfield’s Applied
Psychoacoustics Laboratory (APL). The HULTI-GEN Version 2 software provided
the test interface [48]. The study was structured around a multifactor design,
focusing on two attributes (ATTR): Spatial Fidelity and Timbral Fidelity. The
evaluation for each attribute was divided into six sessions, each dedicated to
a different source position (POSITION). The average session duration was
approximately 15 minutes. Furthermore, within each session, there were three
specific trials (ITEM), each assessing a distinct type of program material.
During each trial, participants rated 10 test conditions (SYSTEM), denoted as
A through J (Table III). Before the experiment, subjects were provided with a
detailed instruction sheet. The purpose of the document was to familiarise
subjects with the procedure and introduce them to the definitions of spatial
and timbral fidelity and methodology.

###  IV-B Measurement of Spatial Room Impulse Responses

Impulse response measurements were conducted in an ITU-R BS.1116-compliant
listening room (6.2m x 5.6m x 3.4m; RT 0.25s; NR 12) at the University of
Huddersfield’s Applied Psychoacoustics Laboratory (APL). The loudspeakers used
for the measurements were Genelec 8040A, offering a free field frequency
response within $\pm$ 2.0 dB across a range from 48 Hz to 20 kHz. The
microphone systems used for the measurements were as follows.

  * •

Neumann KU100 dummy head microphone

  * •

mhAcoustics Eigenmike em32 (referred to as em32 hereon)

  * •

A 6OM1 open microphone array, comprising six omnidirectional Line Audio OM1
microphones. These are arranged in a three-dimensional grid with each
microphone pair spaced 100 mm apart along the X, Y, and Z axes, closely
mimicking the GRAS 50VI intensity probe array as in [5]

Binaural impulse responses acquired using the KU100 were used to create
reference stimuli for the listening tests. Impulse responses with the em32
were used for rendering stimuli for the SDM and HO-SIRR methods. The
particular microphone system was chosen for its high number of capsules (32),
which might enhance the direction of arrival (DOA) estimation [5]. In
contrast, the open mic array was used for SDM and chosen based on studies
suggesting its optimal performance in terms of DOA error and perceptual
quality [16, 22].

For the KU100 and 6OM1, the Merging Horus audio interface served as the AD/DA
converter and microphone preamp. The measurements performed with Eigenmike
em32 involved the use of the Eigenmike Microphone Interface Box (EMIB) as the
recording device and Merging Horus as the playback device. To counter
potential impulse response distortions due to clock mismatch between devices
[49], word clock was used for synchronization, with the Merging Horus device
set as master.

The Exponential Sine Sweep (ESS) was used as an excitation signal as described
in [49], with the following parameters: a sample rate of 48 kHz, frequency
range of 20 Hz to 20 kHz, sweep length of 20 seconds, and fade in/out of 10
ms.

The acoustic centers of the microphone systems were positioned at a height of
127.5 cm from the floor, aligning with the heights of the acoustic axes of the
zero elevation loudspeakers, which form the zero elevation plane of the
system. Although our measurements encompassed a complete Dolby 7.1.4 setup,
conforming to the 4+7+0 loudspeaker layout as per [26], the study primarily
focused on a subset of these configurations, as detailed in Table I. For
azimuth angle measurements, defined as the angle relative to the zero azimuth,
each loudspeaker in the zero elevation level was placed at a distance of 2.00
m ($\pm 0.02\ \text{m}$) from the center of the microphone array. For the
elevation angle measurements, the loudspeakers were placed at a distance of
1.92 m ($\pm 0.1\ \text{m}$) from the center of the microphone array.

TABLE I: Tested Loudspeaker Positions in the ITU-R 4+7+0 Layout Position | Azimuth | Elevation
---|---|---
Front center | $0\degree$ | $0\degree$
Front left | $30\degree$ | $0\degree$
Side left | $90\degree$ | $0\degree$
Back left | $135\degree$ | $0\degree$
Upper front left | $45\degree$ | $45\degree$
Upper back left | $135\degree$ | $45\degree$

###  IV-C Test Conditions and Variables

In this study, SDM conditions were generated using the SDM Toolbox222SDM
Toolbox (version 1.3001, Updated 22 Apr 2018). [6], while PIV-based DOA
estimation algorithm was adapted from Zaunschirm et al.[39]. Given BSDM’s
growing relevance [50, 12, 11, 51, 52], we included two conditions utilizing
the available toolbox333BinauralSDM (version 0.5, commit 965da5c). [41].

HO-SIRR condition was rendered via its MATLAB implementation444HO-SIRR (commit
085f20d). [53]. Both SDM utilizing PIV-based DOA analysis and HO-SIRR
conditions, employed spherical harmonics from the Eigenmike em32, with SDM
additionally using Line Audio OM1 as a pressure signal in one of the
conditions.

Settings for SDM, HO-SIRR, and BSDM adhered to the recommended configurations
in their respective toolboxes [41, 6, 53]. The exception was the window size,
which was standardized at 64 samples across all frameworks, following Amengual
Gari et al.’s recommendations [16]. Additionally, post-equalization [8] was
disabled in the SDM Toolbox.

Both BSDM and PIV-based methods applied band-limited DOA estimation (200
Hz-2400 Hz), aligned with the spatial aliasing frequency of the 6OM1 array.
BSDM’s mixing time was set at 38 ms, based on ISM simulations of our study
room.

We ensured that the anchor demonstrated impairments in both spatial and
timbral fidelity. Specifically, for azimuthal sources at zero elevation
positions, the anchor employed a KU100 BRIR that was offset by an additional
60 to 90 degrees from the source position being evaluated. For sources at
elevated positions, given the limited number of measured positions, a BRIR
corresponding to a diametrically opposite position was chosen, 180 degrees
from the source position being evaluated. To introduce a timbral fidelity
impairment, we applied a 3.5kHz low-pass filter [45].

###  IV-D Synthesis of Binaural Room Impulse Responses

To facilitate a subjective experiment, we employed binaural rendering
techniques for SDM, BSDM, and HO-SIRR to incorporate the KU100 BRIR as a
ground truth reference. Consequently, we employed a dataset of 2702 KU100
head-related impulse responses (HRIRs) sampled on the Lebedev grid [54]. The
synthesis process entailed rendering virtual loudspeaker signals at points on
the Lebedev grid using the evaluated systems. For SDM, this was achieved using
K-nearest neighbor allocation, while HO-SIRR used VBAP. The final stage
involved convolving these virtual loudspeaker signals with corresponding HRTFs
from the SOFA file [55] and summing them to produce the final BRIRs.

###  IV-E Programme Material

Accurate binaural sound-field reproduction requires anechoic audio, free from
original recording environment effects. This is achieved by convolving the
anechoic material with binaural room impulse responses (BRIR), simulating room
acoustics. The anechoic samples employed in our study are as follows: ”Bongo”
(Track 26, 12.780s-–20.330s) and ”Danish Speech” (Track 9, 0.590s-–9.240s)
from Bang & Olufsen’s ”Music for Archimedes” [56, 57], and Handel/Harty’s
”No.6 Water Music Suite” (Track 9, 0.480s-–8.380s) from Denon’s anechoic
orchestral collection [58].

###  IV-F Reproduction Configuration and Calibration

The study employed a reproduction system that included AKG K702 headphones and
a Merging Technologies Horus audio interface. These headphones were fitted
with an inverse filter originally developed for Lee et al.’s research [59],
designed to correct spectral coloration and replicate the response in a KU100
dummy head’s ear. The filter’s creation involved placing AKG K702 headphones
on a KU100 dummy head and conducting five measurements for each ear in both
left/right and right/left positions, then repeating the process with another
pair of headphones, resulting in 40 impulse responses in total. The filter
design followed the high-pass-regularized least-mean-square (LMS) inversion
approach [60], identified as a perceptually sound inversion algorithm [61].

Test stimuli were uniformly normalized to -26 LUFS and the headphone amp gain
was set uniformly throughout the experiment. LAeq loudness for KU100 BRIR at
+30° azimuth, measured via miniDSP EARS, averaged 70.7dB (Bongo), 77.5dB
(Speech), and 73.5dB (Orchestra).

###  IV-G Test Subjects

In total, 14 participants took part in the study. These participants ranged in
age from 20 to 47 years. They were a mixture of staff members, postgraduate
students, and undergraduate researchers affiliated with the Applied
Psychoacoustics Laboratory (APL) at the University of Huddersfield. All
participants claimed to have normal hearing abilities and had previously taken
part in listening experiments. Prior to the formal listening test, the
participants were asked to complete a short 10-minute familiarization phase
for each attribute (ATTR).

###  IV-H Objective Metrics

The present study considered four objective metrics: Interaural Level
Difference ($\mathrm{ILD}$), Interaural Time Difference ($\mathrm{ITD}$),
reverberation time ($\mathrm{T30_{mid}}$), early Interaural Cross-Correlation
Coefficient ($\mathrm{IACC_{E3}}$) and late IACC ($\mathrm{IACC_{L3}}$). To
evaluate accuracy, the Mean Absolute Error (MAE) quantifies the error’s
magnitude, while the Mean Signed Difference (MSD) detects systematic biases,
providing insights into the extent and direction of the system’s performance
deviations.

Each BRIR was energy-normalized to allow fair comparison. This involved
identifying the onset of direct sound, indicated by the earliest sound arrival
in either channel and calculating the Root Mean Square (RMS) value over a 2.5
ms segment starting from this point [62]. This RMS value, representing the
direct sound’s energy, was then used to normalize the entire BRIR, thus
minimizing gain differences and establishing a consistent baseline for
objective analysis.

####  IV-H1 Interaural Level Difference (ILD)

The ILD is a major cue for horizontal sound localization, accentuated by head
shadowing when sources are off-center, with the Just Noticeable Difference
(JND) ranging from 1 to 2 dB [63]. Accounting for the precedence effect, ILD
was derived from the first 2.5 ms of BRIRs over 39 equivalent rectangular
bandwidth (ERB) bands and averaged as follows:

$\mathrm{ILD}_{\text{avg}}=\frac{1}{N}\sum_{f=1}^{N}20\log_{10}\left(\frac{\hat{y}_{L}(f)}{\hat{y}_{R}(f)}\right)$
(1)

where $\mathrm{ILD}_{\text{avg}}$ is the average ILD over $N$ ERB bands, with
$\hat{y}_{L}(f)$ and $\hat{y}_{R}(f)$ as the RMS values for left and right
channels at each frequency band $f$.

####  IV-H2 Interaural Time Difference (ITD)

The ITD is the second of two auditory cues, critical for lateral sound
localization, with JND of about 40 $\mu s$ for frontal sources and
approximately 100 $\mu s$ for lateral sources [64]. The ITD can extend up to
700 $\mu s$ for azimuth angles up to 90 degrees. ITD estimation is based on
the peak time lag of the interaural cross-correlation function:

$\text{ITD}=\arg\max_{-1\ \text{ms}<\tau<1\ \text{ms}}(|\text{IACF}(\tau)|)$
(2)

####  IV-H3 Reverberberation Time ($\text{RT}_{60}$)

The $\text{RT}_{60}$, was calculated in octave bands in accordance with the
standards outlined in [65]. The value presented was derived based on a 30 dB
evaluation range and subsequently averaged across the 500 Hz and 1 kHz octave
bands, resulting in $\text{T30}_{mid}$. The JND for reverberation time is
established at 5% of the $\text{RT}_{60}$ [65]. With a 0.25-second
reverberation time in the auralized room, the JND in the present scenario is
roughly 12.5 ms.

####  IV-H4 Interaural Cross Correlation Coefficient (IACC)

The IACC is a commonly used metric of spatial impression (SI) in concert
halls, with a JND of 0.075 [65]. The Apparent Source Width (ASW) and Listener
Envelopment (LEV) are best estimated by averaging the IACC across 500 Hz, 1
kHz, and 2 kHz octave bands, resulting in $\text{IACC}_{E3}$ and
$\text{IACC}_{L3}$ metrics [66]. In the present study, we calculated
$\text{1-IACC}_{E3}$ and $\text{1-IACC}_{L3}$, which are positively correlated
with ASW and LEV. The IACC is computed as follows:

$\text{IACC}=\max_{-1\ \text{ms}<\tau<1\ \text{ms}}|\text{IACF}(\tau)|$ (3)

##  V Subjective Evaluation Results

TABLE II: Results of the aggregated Friedman test for different factors and attributes ATTR | Factor | Test Statistic ($\chi^{2}$) | DF | p-value | sig.
---|---|---|---|---|---
Spatial | SYSTEM | 101 | 9 |  $<$0.0001 | ****
Spatial | ITEM | 2.43 | 2 | 0.297 | ns
Spatial | POSITION | 21.4 | 5 | 0.0007 | ***
Timbral | SYSTEM | 106 | 9 |  $<$0.0001 | ****
Timbral | ITEM | 0.531 | 2 | 0.767 | ns
Timbral | POSITION | 11.5 | 5 | 0.0417 | *
Figure 1: Subjective evaluation results showing median spatial and timbral
fidelity scores on similarity scale (1-5), for various systems (SYSTEM).
Scores are compiled from multiple source positions (POSITION) and program
materials (ITEM), with 95% non-parametric confidence intervals.

Following ITU guidelines [45], a post-screening process was implemented to
identify and potentially exclude assessors who had rated the hidden reference
below 4.5 (90% of the 5.0 maximum score) for over 15% of test items. This was
done to ensure that only reliable subjects were considered. Ultimately, none
of the assessors met these exclusion criteria.

To verify the normality of the ratings given to each system for each
combination of factors, the data were grouped by SYSTEM, ATTR, ITEM, and
POSITION. Consistently, the ratings assigned to systems ’A’ (Reference) and
’J’ (Anchor) were found not to follow a normal distribution. Excluding these,
non-normal distributions were found in 6.25% of cases for the spatial fidelity
and approximately 6.94% for the timbral fidelity attribute. Considering these
results, we opted for a non-parametric statistical approach in subsequent
analyses.

TABLE III: Systems under test Label |  Test system (SYSTEM)
---|---
A |  Anchor
B |  BSDM 6OM1 Omni
C |  BSDM em32 Omni
D |  SDM em32
E |  SDM em32 Omni
F |  SDM 6OM1 Omni
G |  HO-SIRR diffuse
H |  SDM PIV
I |  SDM PIV Omni
J |  KU100 (Reference)
Figure 2: Subjective evaluation results showing median for spatial and timbral
fidelity scores on similarity scale (1-5), across different systems (SYSTEM)
and source positions (POSITION), aggregated over all program materials (ITEM).
The graph includes 95% non-parametric confidence intervals. Figure 3:
Subjective evaluation results showing median for spatial and timbral fidelity
scores on similarity scale (1-5), across different systems (SYSTEM) and
program materials (ITEM), aggregated over all source positions (POSITION). The
graph includes 95% non-parametric confidence intervals.

Friedman’s tests were conducted to examine the main effects of various
factors—SYSTEM, ITEM, POSITION—on both spatial and timbral fidelity
attributes. The detailed statistical outcomes of these tests, including test
statistics and significance levels, are summarized in Table II.

These results underscore a significant influence of the SYSTEM on both spatial
and timbral attributes, indicating variations in the capability of the
rendering methods to replicate spatial and timbral fidelity. Interestingly,
the specific program material (ITEM) did not have a significant impact on
participant ratings, while the source position (POSITION) demonstrated a
noticeable effect, especially in spatial fidelity.

First, we present the aggregated results across various ITEMs and POSITIONs in
Figure 1, giving an overview of the overall system performance. Given the
significant effect of POSITION and the non-significant effect of ITEM from our
Friedman test findings, we further delved into Position-Based Performance
(Figure 2) and potential subtle influences of Program Material (Figure 3).
Disparities between rendering systems were analyzed using the Wilcoxon signed-
rank test with Holm-Bonferroni correction [67]. Additionally, we calculated
the effect size ($r$) using the method described in [68], which involves
converting the p-value to a z-score and then to $r$, based on the total number
of observations (N).

Figure 1 shows the ratings for spatial and timbral Fidelity of various
systems. Low anchor (A), consistently scored at the lower end of the scale
with a median of 1.0, indicating ’Extremely Different’. In contrast, KU100 (J)
achieved a median score of 5.0 (’Same’) implying that subjects had no problem
in identifying the hidden reference. Systems BSDM 6OM1 Omni (B) to SDM PIV
Omni (I) varied, with spatial fidelity ratings mainly between 3 and 4 and
timbral fidelity also clustering between 3 and 4.2.

Looking more closely at spatial fidelity, SDM em32 Omni (E), HO-SIRR (G), and
SDM PIV Omni (I) displayed comparable performance (medians between 3.9 and 4).
However, SDM PIV (H) with a median of 3.8 was slightly inferior to both SDM
em32 Omni (E) and HO-SIRR (G). SDM 6OM1 Omni (F) trailed behind these three
systems. Additionally, BSDM 6OM1 Omni (B), BSDM em32 Omni (C), and SDM 6OM1
Omni (F) were grouped closely together (medians between 3.7 to 3.8), though
BSDM em32 Omni (C) was outperformed by both HO-SIRR (G) and SDM PIV (H).
Notably, SDM em32 (D) performance was significantly lower than the rest
(median 3.2).

In terms of timbral fidelity, SDM em32 Omni (E) and SDM PIV Omni (I) were
almost indistinguishable (medians between 4.1 and 4.2), with SDM em32 Omni (E)
outperforming HO-SIRR (G) and SDM PIV (H). SDM 6OM1 Omni (F), HO-SIRR (G), and
SDM PIV (H) were on par with each other (medians between 3.9 and 4), whereas
BSDM 6OM1 Omni (B) and BSDM em32 Omni (C), while similar to each other
(medians 3.7), lagged behind the preceding group, and even more so when
compared to SDM em32 Omni (E) and SDM PIV Omni (I). Again, SDM em32 (D) scored
substantially lower than BSDM 6OM1 Omni (B) and BSDM em32 Omni (C).

###  V-A Dedicated center Omnidirectional Microphone

The impact of using a dedicated center omnidirectional microphone can be
analyzed by comparing SDM em32 Omni (E) and SDM em32 (D)—utilizing TDOA-based
DOA, as well as SDM PIV Omni (I) and SDM PIV (H)—utilizing PIV-based DOA.
These conditions used SRIR from em32 (and obtained SPH), with and without
center omnidirectional microphone.

The dedicated omnidirectional microphone (SDM em32 Omni, E) notably enhanced
the em32 array’s performance in the context of SDM’s TDOA-based DOA variant
(SDM em32, D), with significant improvements in overall results for both
spatial and timbral fidelity, exhibiting a large effect size ($p<0.001$,
$r>0.7$). The same trend was also observed for individual positions and
stimuli, however, for certain positions with medium effect size, for instance,
+45°, +45° (Spatial) and +135°, +45° (Timbral) with $p<0.005$ and $r=0.4$.

Improvements were also noticeable with a dedicated center microphone in SDM’s
PIV-based DOA estimation variant, but they were less pronounced. SDM PIV (H)
used a zeroth-order eigenbeam, and SDM PIV Omni (I), which utilized a
dedicated omni microphone, showed significant enhancement in spatial and
timbral fidelity, albeit with a small effect size ($p<0.009$, $r<0.3$).
Interestingly, for the +135° source position, the improvement was significant
with a large effect size ($p<0.001$, $r=0.61$). Across most source positions,
the improvement for both attributes was observed with a small effect size
($p<0.04$, $r<0.26$), except for Bongo and Speech in spatial fidelity.

###  V-B Microphone Array and DOA Estimation Method

This research evaluated TDOA and PIV-based DOA estimation methods in SDM for
spatial data capture and auralization. It focused on TDOA-based DOA using em32
and 6OM1 arrays, represented by SDM em32 Omni (E) and SDM 6OM1 Omni (F), and
PIV-based DOA with first-order SPH, denoted as SDM PIV Omni (I), all utilizing
a central pressure signal from the array.

As depicted in Figure 1, our results indicate that SDM em32 Omni (E), which
relies on TDOA-based DOA estimation, exhibited performance on par with SDM PIV
Omni (I)—utilizing a PIV-based DOA estimation—when the identical
omnidirectional pressure signals were used. The comparison revealed no
substantial differences in either spatial or timbral fidelity. Conversely, SDM
6OM1 Omni (F)—also based on TDOA but incorporating an array of only six
microphones, was found to perform significantly worse than SDM em32 Omni (E)
with a small effect size ($p<0.001$, $r<0.26$) and SDM PIV Omni (I) with
medium effect size ($p<0.001$, $0.3<r<0.36$) for both spatial and timbral
fidelity.

Upon examining the specific source positions (Figure 2), we observed a similar
pattern. SDM 6OM1 Omni (F) generally underperformed compared to SDM em32 Omni
(E) and SDM PIV Omni (I). This was particularly pronounced for source
positions at +30° and +90°, where SDM 6OM1 Omni (F) demonstrated significant
deviation from SDM em32 Omni (E) ($p<0.007$, medium and large effect size:
$0.41<r<0.61$) and SDM PIV Omni (I) ($p<0.001$, large effect: $0.66<r<0.69$)
concerning spatial fidelity. On the other hand, it was observed that SDM PIV
Omni (I) outperformed SDM em32 Omni (E) at +30° and +45°, +45° source
positions with medium effect size ($p<0.013$, $0.38<r<0.46$) in terms of
spatial fidelity. Regarding timbral fidelity, SDM em32 Omni (E) and SDM PIV
Omni (I) notably outperformed SDM 6OM1 Omni (F) at the +135° position
($p<0.001$, large effect: $0.5<r<0.54$), with SDM PIV Omni (I) also showing
superior performance at the +30° and +90° source positions with medium effect
size ($p=0.011$, r = 0.39).

An analysis of stimulus-dependent performance revealed that there were no
significant differences between SDM em32 Omni (E) and SDM PIV Omni (I), except
in two specific scenarios. SDM PIV Omni (I) exhibited superior spatial
fidelity over SDM em32 Omni (E) for Orchestra stimuli, with a small effect
size ($p<0.045$, $r=0.22$). For Speech stimuli, SDM PIV Omni (I) also showed
greater timbral fidelity than SDM em32 Omni (E), again with a small effect
size ($p<0.028$, $r=0.24$). In contrast, SDM 6OM1 Omni (F) underperformed in
both spatial and timbral fidelity for Speech compared to SDM em32 Omni (E) and
SDM PIV Omni (I), with a medium effect size ($p<0.005$, $0.3<r<0.36$).
However, the exception was the comparison of timbral fidelity between SDM PIV
Omni (I) and SDM 6OM1 Omni (F), where SDM PIV Omni (I) demonstrated a large
effect size ($p<0.001$, $r=0.57$). Additionally, for Orchestra stimuli, SDM
PIV Omni (I) outperformed SDM 6OM1 Omni (F) in both spatial and timbral
fidelity with medium ($p<0.001$, $r=0.36$) and small ($p<0.022$, $r=0.24$)
effect sizes, respectively.

###  V-C Spatial Encoding Systems

This section analyzes the impact of different rendering systems on spatial
encoding efficacy, comparing SDM’s performance in SDM em32 (D), SDM em32 Omni
(E), SDM 6OM1 Omni (F), SDM PIV (H), and SDM PIV Omni (I), with HO-SIRR (G),
and BSDM’s optimizations in BSDM 6OM1 Omni (B) and BSDM em32 Omni (C).

It is noteworthy that no enhancement in spatial fidelity was observed between
SDM 6OM1 Omni (F) and BSDM 6OM1 Omni (B). Intriguingly, SDM 6OM1 Omni (F)
generally outperformed BSDM 6OM1 Omni (B) in terms of timbral fidelity, albeit
with a modest effect size ($p=0.001$, $r=0.2$), considering the overall
results. A similar trend was evident for BSDM em32 Omni (C) and SDM em32 Omni
(E), indicating that the optimizations employed by BSDM frequently led to
degradation of these attributes, exhibiting small ($p<0.001$, $r=0.25$) and
medium ($p<0.001$, $r=0.49$) effect sizes for spatial and timbral fidelity,
respectively.

Looking at how performance varies with position, BSDM 6OM1 Omni (B) generally
matched the performance of SDM 6OM1 Omni (F) in terms of spatial and timbral
fidelity, with the exception of the +30° position. At this position, SDM 6OM1
Omni (F) outperformed BSDM 6OM1 Omni (B) with a large effect size ($p<0.001$,
$r=0.54$) in terms of timbral fidelity. Similarly, at +30° BSDM 6OM1 Omni (B)
underperformed compared to systems SDM em32 Omni (E) to SDM PIV Omni (I) with
a large effect size ($p<0.001$, $r>0.52$) in terms of timbral fidelity. In
terms of spatial fidelity at +30°, BSDM 6OM1 Omni (B) did not show a
significant difference when compared to SDM 6OM1 Omni (F), yet HO-SIRR (G),
SDM PIV (H), and SDM PIV Omni (I) outperformed BSDM 6OM1 Omni (B) with a large
effect at +90° ($p<0.001$, $r>0.5$). Additionally, at the +135°, +45°
position, BSDM 6OM1 Omni (B) underperformed with a medium effect size
($p<0.016$, $r=0.37$) in terms of both spatial and timbral fidelity compared
to SDM 6OM1 Omni (F).

(a) Spatial Fidelity

(b) Timbral Fidelity

Figure 4:  Principal Component Analysis (PCA) of spatial and timbral fidelity
scores for evaluated systems (SYSTEM), considering the median spatial and
timbral fidelity scores across different program materials (ITEM) and source
positions (SYSTEM). Systems are clustered in a two-dimensional space by the
first two principal components, highlighting the similarities in their
fidelity scores.

Similar observations were made for BSDM em32 Omni (C) and SDM em32 Omni (E).
Both systems performed similarly for most positions, except at the +90° and
+135°, +45° source positions in terms of both spatial and timbral fidelity. At
these positions, SDM em32 Omni (E) outperformed BSDM em32 Omni (C) with large
($p<0.001$, $0.51<r<0.65$) and medium ($p<0.002$, $0.44<r<0.48$) effect sizes
in terms of spatial fidelity. However, in terms of timbral fidelity, the
differences were less pronounced, with the main differences observed at the
+135°, +45° source position. Moreover, BSDM em32 Omni (C) underperformed for
spatial fidelity when compared with systems SDM em32 Omni (E) to SDM PIV Omni
(I) at +135°, +45° and +90° with large ($p<0.001$, $r>0.5$) and medium effect
sizes ($p<0.02$, $0.35<r<0.45$).

Examining the results for individual stimuli reveals an interesting pattern
regarding spatial fidelity. BSDM 6OM1 Omni (B) and BSDM em32 Omni (C)
performed comparably to systems utilizing SDM (E, F, H, and I) and HO-SIRR (G)
for Orchestra and Speech stimuli in terms of spatial fidelity. However, their
performance significantly deteriorated for the Bongo stimulus, with a large
effect size ($p<0.001$, $r>0.5$). A similar trend was observed for timbral
fidelity, though BSDM 6OM1 Omni (B) and BSDM em32 Omni (C) occasionally
underperformed compared to systems SDM em32 Omni (E), SDM 6OM1 Omni (F), SDM
PIV (H), and SDM PIV Omni (I) for Orchestra and Speech stimuli with small to
large effect sizes.

While we previously concluded that systems utilizing SDM–SDM em32 Omni (E) and
SDM PIV Omni (I) tend to perform better than SDM 6OM1 Omni (F), this
observation suggests the impact of the microphone array used. When examining
the performance differences between SDM and HO-SIRR (G) in terms of spatial
fidelity, we observe no significant difference between HO-SIRR (G), SDM em32
Omni (E), SDM PIV (H), and SDM PIV Omni (I). However, HO-SIRR (G) shows
significantly better performance compared to SDM 6OM1 Omni (F) with a small
effect size ($p<0.009$, $r=0.16$). On the other hand, it performed worse than
SDM em32 Omni (E) and SDM PIV Omni (I) in terms of timbral fidelity, but with
a small effect size ($p<0.018$, $0.15<r<0.27$). Interestingly, HO-SIRR (G) and
H (SDM PIV) did not demonstrate a significant difference in terms of spatial
and timbral fidelity, which may imply that the use of the zeroth-order
eigenbeam as the pressure signal in SDM PIV (H) and HO-SIRR (G) is a
contributing factor.

The results for individual source positions implied that HO-SIRR (G) performed
similarly to SDM em32 Omni (E) and SDM PIV Omni (I) in most of the evaluated
source positions, with the occasional exceptions when it underperformed, for
instance at +135° source position with large effect size ($p=0.001$, $r>0.5$).
Conversely, at +45°, +45° source position, HO-SIRR (G) outperformed SDM em32
Omni (E) with a medium effect size for spatial fidelity ($p=0.024$, $r>0.34$).
Interestingly, the performance of HO-SIRR (G) mirrored that of SDM PIV (H) in
spatial and timbral fidelity for individual stimuli, with only occasional
differences. For instance, regarding timbral fidelity, HO-SIRR (G) was
outperformed by SDM em32 Omni (E) and SDM PIV Omni (I) for the Orchestra
stimulus with a medium effect size ($p<0.004$, $r>0.31$).

###  V-D Principal Component Analysis

In the spatial analysis and auralization of a critical listening room, SDM and
HO-SIRR systems exhibited similar performance, particularly in terms of
spatial fidelity. Systems such as SDM em32 Omni (E), HO-SIRR (G), SDM PIV Omni
(I), and SDM PIV (H) demonstrated comparable results, though with some
variations. With respect to timbral fidelity, SDM em32 Omni (E) and SDM PIV
Omni (I), which utilize TDOA-based analysis with Eigenmike em32 and PIV-based
analysis with a dedicated pressure signal, closely aligned with the reference.

This alignment is supported by Principal Component Analysis (PCA), as shown in
Figure 4. The PCA clusters these systems together based on their median
spatial and timbral fidelity scores across all positions and stimuli. The
analysis revealed that the first two principal components accounted for about
77% of the variance in spatial fidelity and 80% in timbral fidelity.

###  V-E Correlation between Spatial and Timbral fidelity

Figure 5: Correlation between median scores of spatial and timbral fidelity
across all source positions and stimuli.

To explore the link between spatial and timbral fidelity, we calculated
Spearman’s correlation based on median scores across all positions and
stimuli, as depicted in Figure 5.

The weakest correlations between spatial and timbral fidelity were observed in
SDM em32 Omni (E, $\rho=0.41$), SDM em32 (D), and SDM 6OM1 Omni (F,
$\rho=0.45$), followed by SDM PIV Omni (I, $\rho=0.52$). A significant
increase in correlation was noted for HO-SIRR (G, $\rho=0.59$) and SDM PIV (H,
$\rho=0.6$), with BSDM em32 Omni (C, $\rho=0.72$) and BSDM 6OM1 Omni (B,
$\rho=0.77$) exhibiting the strongest positive correlations.

The strong correlation in BSDM-rendered conditions (B and C) indicates a
uniform impact of artifacts on both spatial and timbral fidelity, possibly due
to reverb equalization effects. Conversely, the pronounced correlation between
spatial and timbral fidelity in HO-SIRR (G) and SDM PIV (H) implies an effect
resulting from the use of a zeroth-order spherical harmonic as a pressure
signal within these systems.

##  VI Objective Evaluation Results

(a) ILD computed from BRIRs across 39 ERB bands, averaged above and below 1.5
kHz as detailed in [69].

(b) Interaural cross-correlation coefficients: Early ($\text{1-IACC}_{E3}$)
and Late ($\text{1-IACC}_{L3}$).

(c) ITD calculated using maximum interaural cross-correlation (MaxIACCr)
method.

(d) Mid-frequency reverberation time $\text{T30}_{mid}$ as defined in [65].

Figure 6: Objective metrics presented using mean absolute error (MAE) and mean
signed difference (MSD) using the reference KU100 (J) as the ground truth.

###  VI-A Interaural Level Difference (ILD)

Figure 6a illustrates the mean absolute error (MAE) and mean signed difference
(MSD) for ILD across systems (B through I), categorized by the ERB bands above
and below 1500 Hz used for averaging. At higher frequencies, SDM em32 (D), SDM
em32 Omni (E), and SDM 6OM1 Omni (F) showed notable deviation with high MAEs
and negative MSDs, underscoring a tendency to underestimate ILDs beyond the
established JND [63]. HO-SIRR (G) also tended to underestimate ILD but to a
lesser extent. In contrast, lower frequencies exhibited reduced MAEs for most
systems, except HO-SIRR (G), and MSDs near zero, indicating minimal bias
except for the consistent underestimation by SDM em32 (D), SDM em32 Omni (E),
and SDM 6OM1 Omni (F). Overall, all systems faced more difficulty with higher
frequency ILDs, implying challenges in capturing spatial cues accurately.
However, performance improved at frequencies below 1500 Hz, with SDM em32 (D)
being the exception.

###  VI-B Interaural Time Difference (ITD)

Figure 6c demonstrates ITD accuracy with MAE and MSD values, indicating that
BSDM 6OM1 Omni (B) and BSDM em32 Omni (C) consistently underestimate ITD,
whereas SDM em32 (D), SDM em32 Omni (E), and SDM 6OM1 Omni (F) overestimate,
particularly SDM 6OM1 Omni (F) with the highest MAE of 34.7 $\mu s$. HO-SIRR
(G) has minor overestimations, while SDM PIV (H) and SDM PIV Omni (I) maintain
the highest accuracy with slight underestimation tendencies. Given the JND for
ITD ranges from 40 $\mu s$ frontally to 100 $\mu s$ laterally [64], most
systems’ deviations fall within perceptually insignificant limits. Notably,
there is an inconsistency in MSD and MAE magnitudes and a suggested ILD-ITD
trade-off in systems SDM em32 (D) through HO-SIRR (G).

###  VI-C Reverberberation Time

Figure 6d shows that all systems tend to overestimate reverberation time, as
indicated by positive MSD values. Most systems’ errors exceed the JND of 12.5
ms, which may affect perception, except for BSDM 6OM1 Omni (B) and BSDM em32
Omni (C) which maintain minimal perceptible errors with MAEs of 12.4 and 14.7
ms. These results align with Amengual et al.’s findings, confirming that RTMod
maintains synthesized BRIR’s reverberation time within the JND [16]. On the
other hand, HO-SIRR (G), with an MAE of 108 ms, significantly overshoots the
JND, hinting at a noticeable impact on spatial fidelity.

###  VI-D Interaural Cross Correlation Coefficient (IACC)

Figure 6b presents MAE and MSD for systems using $\text{1-IACC}_{E3}$ and
$\text{1-IACC}_{L3}$. Evaluated systems vary in accuracy, with
$\text{1-IACC}_{E3}$ MAE ranging from 0.0427 to 0.0836 and
$\text{1-IACC}_{L3}$ MAE from 0.0637 to 0.134. Errors for $\text{1-IACC}_{E3}$
mostly fall within the JND of 0.075, implying that the errors are unlikely to
be perceptible. Low MSDs suggest non-systematic errors, except for SDM em32
(D) and SDM PIV Omni (I), which show a bias in $\text{1-IACC}_{E3}$ estimates,
potentially affecting ASW.

In contrast, MAEs for $\text{1-IACC}_{L3}$ surpass the JND of 0.075 for all
but HO-SIRR (G) and SDM PIV Omni (I), with several systems showing negative
MSDs, hinting at consistent underestimation and possible LEV impact. HO-SIRR
(G) and SDM PIV Omni (I), however, remain within JND bounds for both MAE and
MSD, suggesting minimal LEV alteration.

##  VII Discussion

McCormack et al. [15] found that the post-equalized Spatial Decomposition
Method (SDM) using pseudo-intensity vectors (PIVs) underperforms compared to
spatial impulse response rendering (SIRR) in simulated environments. Improved
performance of SDM is observed when PIV-based direction of arrival (DOA)
estimation incorporates band-limitation [36, 39]. More recently, McCormack et
al. [19] found that SDM, utilizing time difference of arrival (TDOA) based DOA
estimation, shows comparable performance to Higher-Order SIRR (HO-SIRR) for
stationary stimuli in a small simulated room, but exhibits reduced performance
for transient stimuli.

Our study finds similar spatial fidelity for HO-SIRR, and SDM employing TDOA
and PIVs for DOA estimation. Although objective measurements showed HO-SIRR to
overestimate reverberation time by more than 100 ms, potentially impacting
spatial fidelity for non-stationary stimuli, subjective evaluations did not
reflect this. The present study stands out by using real-life measurements,
contrasting with previous studies’ simulated conditions. This offers a more
realistic context, directly relevant to practical room acoustics applications.

The performance of SDM with optimizations for binaural rendering (BSDM)
depends on the stimulus type. The Bongo stimulus adversely impacted spatial
and timbral fidelity, suggesting that BSDM’s equalization quality might be
compromised by suboptimal reverberation time estimation in low-reverb
environments [50]. While objective measurements confirm RTmod’s efficacy,
showing the reverberation time’s mean absolute error (MAE) within the just
noticeable difference (JND) range, the observed poor performance may be linked
to artifacts related to RTmod, appearing in transient sounds [16].

BSDM significantly underestimated $\text{1-IACC}_{L3}$, a key metric for
listener envelopment [66]. This underestimation surpasses the established JND
[65], suggesting a potential reduction in listener envelopment relative to the
reference.

Amengual et al. observed that BSDM’s perceived plausibility was rated
similarly to that of real loudspeakers [16]. However, in an ITU-R
BS.1116-3-compliant listening room, BSDM shows lower consistency and
robustness compared to the standard, unoptimized SDM. This finding, alongside
insights from our pilot study—which focused exclusively on DOA enforcement for
direct sound and band-limited DOA estimation—suggests that more fundamental
optimizations from BSDM could lead to a more robust SDM framework, especially
when compared to the full BSDM including RTmod+AP optimization.

Both TDOA and PIVs can be equally effective DOA estimators in SDM when a
sufficient number of microphones is utilized for TDOA estimation. In band-
limited PIV-based DOA estimation, the condition utilizing an omnidirectional
pressure signal demonstrates superior performance compared to the TDOA-based
algorithm with a six-microphone array. McCormack et al. [15] and Ahrens [22]
conducted studies that did not incorporate band limitation in the DOA
estimation with the PIV method. In their findings, Ahrens demonstrated that
the SDM variant utilizing the PIV method, without band limitation, tended to
cause a larger perceived difference in the presented auralizations when
compared to most other array geometries, with the dummy head reference serving
as the baseline for comparison. Similarly, McCormack et al. observed that the
SDM utilizing PIV-based DOA estimation without band limitation, significantly
underperformed in comparison to any variant of the SIRR. Zaunschirm et al.
[36] found that applying band limitation to PIV-based DOA estimation
significantly enhances SDM performance. Their effective frequency range, from
200 Hz to just below the spatial aliasing frequency of the microphone array,
led to SDM results closely mirroring the binaural reference in terms of image
width, distance, and diffuseness. These findings align with our study,
reinforcing the critical role of band limitation in PIV-based DOA estimation
for optimal spatial analysis and synthesis.

We did not expect SDM em32 Omni (E) to match in performance with SDM PIV Omni
(I) given the complexity of the time difference of arrival estimation using
spherical microphone arrays and the rigid sphere design of em32 [27]. Although
the larger number of microphones in em32 suggests a potential for improved
TDOA estimation, objective measurements indicate higher errors in ILD, ITD,
and reverberation time, aligning em32 more with SDM 6OM1 Omni (E) rather than
SDM PIV Omni (I). Previous applications of SDM employed small microphone
separations with the smallest inter-mic distance of 17.7 mm [8]. The 26.5 mm
inter-mic distance in em32 may suit well for TDOA estimation. Optimizing the
TDOA model for microphones on rigid spheres [70] could improve estimation
accuracy in em32.

SDM em32 Omni (E) with 32 sensors outperforms the SDM 6OM1 Omni (F) with six
sensors. In contrast, Ahrens’ study using different array configurations,
including a 12-microphone array, found that a six-microphone array, especially
with radii of 50 mm and 100 mm, produced the smallest perceptual differences
to the dummy head reference [22]. The superior performance of the em32 in our
study might be attributed to the larger number of microphones in em32 aiding
in localization [5], as well as a higher spatial aliasing frequency which
could positively impact the TDOA estimation [71].

Using the em32 array with a dedicated pressure signal—obtained from a separate
high-quality omnidirectional microphone—seems to give substantial benefits for
SDM. Amengual Gari et al.’s [23] find the benefit of an omnidirectional
microphone over an Ambisonic microphone being small, suggesting the influence
of equipment and setup on the auralization quality to be more significant.

The spatial and timbral fidelity similarities between HO-SIRR (G) and SDM PIV
(H) methods, along with the improvements observed between SDM PIV (H) and SDM
PIV Omni (I), suggest that adding a dedicated pressure microphone may improve
SIRR methods, as noted in [4].

##  VIII Conclusion

The study evaluated spatial analysis and synthesis methods, specifically SDM,
BSDM, and HO-SIRR, along with their variations, in creating synthetic binaural
room impulse responses (BRIRs) of an ITU-R BS.1116 compliant listening room.
The objective was to achieve auralization perceptually similar to the KU100
dummy head in terms of spatial fidelity and timbral fidelity, using
Zieliński’s fidelity attribute [44]. Certain SDM configurations exhibited
spatial fidelity levels comparable to those of HO-SIRR, while BSDM suffered
from artifacts in the temporal structure of stimuli. A larger number of
microphone capsules enhanced the performance of SDM methods, and a separate
pressure signal improved timbre. The results are expected to more generally
describe the performance of synthetic binaural room impulse responses in small
rooms, such as critical listening rooms and audio mixing rooms. Future work
can include the study of other rooms, additional subjective dimensions and new
systems like 4D-ASDM [18] or REPAIR [19].

## Acknowledgments

The research presented in this paper was funded by Genelec Oy and the
University of Huddersfield. The authors would like to thank everyone who took
part in the listening test.

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