# A binaural implementation of the Hearing Aid Speech Perception Index (HASPI)

James M Kates, Mathieu Lavandier, Kathryn H Arehart, Emily M.H.

Lundberg, Ramesh Kumar Muralimanohar

► To cite this version:

James M Kates, Mathieu Lavandier, Kathryn H Arehart, Emily M.H. Lundberg, Ramesh Kumar Muralimanohar. A binaural implementation of the Hearing Aid Speech Perception Index (HASPI). Acta Acustica, 2025, 9, pp.74. 10.1051/aacus/2025054. hal-05388034

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https://hal.science/hal-05388034v1

Submitted on 28 Nov 2025

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# A binaural implementation of the Hearing Aid Speech Perception Index (HASPI)

James M. Kates<fnref n="1" />*, Mathieu Lavandier<fnref n="2" />, Kathryn H. Arehart<fnref n="1" />, Emily M.H. Lundberg<fnref n="1" />, and Ramesh Kumar Muralimanohar<fnref n="3" />

Received 21 February 2025, Accepted 14 October 2025

**Abstract** – *Introduction:* The Hearing Aid Speech Perception Index version 2 (HASPI v2) is an intrusive speech intelligibility metric fitted to the intelligibility of sentence stimuli presented monaurally over headphones. It compares the time-frequency envelope modulation of a degraded signal, processed through a peripheral model matched to the subject's audiogram, to the envelope modulation of an unprocessed noise-free signal processed through a normal-hearing (NH) peripheral model. This paper presents a binaural extension of HASPI v2. *Methods:* The binaural modifications are increasing the indicated hearing loss and providing a model of binaural interaction. The binaural HASPI was fit to binaural sentence-level intelligibility scores for NH and hearing-impaired (HI) subjects. The experimental conditions comprised combinations of room acoustics, spatial source configuration, noise, and simulated hearing-aid processing.

*Results:* The Pearson correlation coefficients between the binaural HASPI predictions and the observed binaural intelligibility scores were 0.982 for the NH group, 0.981 for the HI group, and 0.983 for the combined groups. The corresponding RMS errors for intelligibility scores on a 0 to 1 scale were 0.050, 0.049, and 0.049. *Discussion and Conclusions:* The accuracy of the binaural HASPI is similar for HI and NH subjects. The accuracy compares favorably to that of existing binaural metrics.

**Keywords.** Speech intelligibility, Binaural hearing, Binaural intelligibility, Intelligibility prediction models, Hearing aids

## 1 Introduction

The Hearing Aid Speech Perception Index (HASPI) [1–3] is an intrusive intelligibility metric in which the time-frequency envelope modulation of a degraded sentence is compared to that for a noise- and distortion-free reference sentence. The current implementation is HASPI version 2 (HASPI v2) [2, 3]. HASPI v2 is designed to deal with a wide range of speech degradations such as additive noise, reverberation, nonlinear distortion, and hearing-aid (HA) processing. The basic structure of HASPI v2 is a model of the auditory periphery followed by time-frequency envelope modulation analysis and an ensemble of neural networks that transform the envelope modulation correlations between degraded and reference signals into subject sentence-level intelligibility scores. The

peripheral model is not meant to be a complete representation of auditory physiology; rather, it is meant to reproduce a salient subset of physiological and perceptual behaviors that can be used by the curve-fitting back end of the system to fit the subject data. The peripheral model can be adjusted based on the subject's audiogram, making HASPI v2 appropriate for both normal-hearing (NH) and hearing-impaired (HI) subjects. For NH subjects both the degraded and reference signals are passed through models of the normal auditory periphery, while for HI subjects the amplified degraded signal is passed through a model of the impaired periphery while the reference signal is passed through a model of the normal periphery.

HASPI v2 was fitted to intelligibility scores for sentence stimuli presented monaurally over headphones. The monaural headphone presentation is a potential limitation of the metric since it bypasses the cues used for

<footnote n="1">¹Department of Speech, Language, and Hearing Sciences, University of Colorado, Boulder, Colorado, USA</footnote>

<footnote n="2">²ENPTE, Ecole Centrale de Lyon, CNRS, LTDS, UMR5513, 69518 Vaulx-en-Velin, France</footnote>

<footnote n="3">³Department of Communication Sciences and Disorders, University of Northern Colorado, Greeley, Colorado, USA</footnote>

<footnote>*Corresponding author: james.kates@colorado.edu</footnote>
spatial unmasking of speech [4, 5]. For binaural listening, spatial separation of the speech and noise sources provides interaural level differences (ILD) and interaural time differences (ITD) between the two ears. The ILD can lead to different signal-to-noise ratios (SNRs) at the left and right ears, an effect exploited by better-ear listening wherein intelligibility is determined by the ear having the higher SNR in each auditory frequency band. The ITD can introduce interaural phase differences that can lead to binaural unmasking of the target speech [6] and which can be modeled using the equalization-cancellation (EC) theory [7, 8] or via interaural cross-correlation [9].

The objective of this paper is to develop a binaural version of HASPI v2 by combining the HASPI v2 peripheral model and envelope modulation analysis with a model of binaural interaction. The general approach of combining a monaural intelligibility metric with a binaural model has been adopted in most binaural intelligibility models. The most common approach is to use an EC front end combined with the speech intelligibility index (SII) [10] to predict intelligibility [11–14]. The EC front end has also been modified and combined with other monaural speech intelligibility predictors including the Short-Time Objective Intelligibility metric (STOI) [15] to produce the Deterministic Binaural STOI (DBSTOI) [16] and the Modified Binaural STOI (MBSTOI) [17], and also combined with the envelope power SNR [18, 19]. Several of these models (e.g. [17–19]) combine simplified interaural processing related to an EC front end with better-ear SNR estimates, and the results presented in [20] suggest that better-ear glimpsing may also make an important contribution to binaural intelligibility.

An interaural cross-correlation front end has also been effectively combined with the speech transmission index (STI) [21] to yield binaural intelligibility predictions relevant to room acoustics [22]. Other approaches include using the HASPI peripheral model at each ear followed by a deep neural network (DNN) to estimate the binaural interaction [23, 24] or directly estimating the binaural masking level difference (BMLD) from the left and right ear signals [6, 25, 26]. Most of these papers only deal with NH subjects, although some also consider HI subjects [12, 23, 24, 27]. The general success of these combined models suggests that modifying HASPI v2 by adding a model of binaural interaction should also lead to accurate binaural intelligibility predictions.

The EC theory assumes that the auditory system adjusts the interaural amplitude and phase of the noisy speech in each frequency band to minimize the residual noise power when the left and right ear signals are delayed, weighted, and subtracted [7, 8, 13]. While several of the studies cited above indicate that the EC approach may be appropriate for noisy speech, this approach may not be valid for HA processed speech where the processing introduces nonlinear distortion that can be highly correlated with the speech signals [28]. An alternative approach to modeling binaural interaction is an auditory filterbank followed by dynamic-range compression and envelope extraction at each ear [9]; the compressed

left- and right-ear envelopes are then cross-correlated to give the perceptual decision variable. This envelope cross-correlation approach is consistent with the structure of HASPI v2 and is therefore an attractive candidate to use in developing the binaural implementation.

The remainder of this paper presents the design and evaluation of the binaural HASPI. The binaural intelligibility data are presented in the next section; sentence-level intelligibility scores were obtained for NH and HI subjects for a variety of noise, acoustic, and HA processing conditions. The structure of the binaural HASPI is then described and contrasted with the monaural HASPI v2. The predictions for the binaural intelligibility data are then presented, including the adjustment to the peripheral hearing loss for modeling binaural intelligibility and comparisons between the better-ear values for the monaural HASPI v2 and the binaural HASPI and between NH and HI subjects. The paper concludes with a discussion of the model results and their accuracy and a final summary.

## 2 Intelligibility data

The binaural HASPI metric was fitted to a binaural intelligibility dataset scored for sentences correct [29]. An extensive description of the dataset is provided in [29], so only a summary is provided here. Data were acquired from 15 younger adult NH (mean age 22 years, age range 19–28 years) and 15 older adult HI (mean age 78 years, age range 57–84 years) subjects having symmetric bilateral mild to moderately-severe sensorineural hearing losses; audiograms averaged across the two ears are provided in Figure 1. The experiment used dummy-head head-related impulse response (HRIR) recordings and binaural headphone stimulus presentation. A total of 54 processing conditions were implemented, comprising all possible combinations of two simulated acoustic spaces, three spatial configurations of the speech and noise sources, three SNRs, and three simulated hearing-aid processing settings.

The two simulated acoustic spaces were an anechoic room and a concert hall. The simulations used recordings from a horizontal loudspeaker array located in a semi-anechoic chamber that also contained electronics associated with audio-visual signal presentation and recording. The loudspeakers were located at 10-degree increments in a full circle around the periphery of the chamber, and a virtual-image “shoebox” room simulation [30] system controlled the inputs to the loudspeakers to create the acoustic environments that included the propagation delays and power-law attenuation for each virtual image. Atmospheric sound absorption was added using the procedure of [31], which reduced the metallic artifacts that can occur in simulated reverberation. The resultant simulated concert hall had a reverberation time (RT) of 2.4 s and a direct-to-reverberant ratio (DRR) of 4.3 dB when measured for the center front speech source 1.9 m in front of the dummy head. The virtual image matrix used for
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Audiograms in dB HL for the HI subjects averaged across the two ears. The individual audiograms are indicated by the dashed lines and the group average by the solid black line (from Kates et al. [29]).</figcaption></figure>

the room simulation incorporated all reflections out to 2.6 s.

A sentence embedded in continuous discourse may be masked by the reverberant tail of a preceding sentence. This energetic masking was simulated by concatenating a time-reversed version of the sentence in front of the normal-time version, processing the sentence pair through the simulated reverberation, and then removing the time-reversed sentence, thus leaving the reverberant tail overlaying the beginning of the normal-time sentence. The time reversal preserves the sentence envelope statistics and long-term spectrum while minimizing intelligibility. After reverberation was applied to both the speech and the noise, the preceding sentence with its associated noise was pruned, leaving the noisy target sentence with its onset masked by the reverberant tail from the time-reversed noisy sentence. The input signals for the HA processing were recorded using commercial HA microphones located in behind-the-ear (BTE) shells mounted behind the ears of the KEMAR manikin [32], and ear-canal signals were recorded simultaneously from the manikin ears. The left and right front HA microphones provided the input signals for the simulated HA processing. Ear-canal responses were also recorded simultaneously from both ears of KEMAR. The recorded microphone signals thus included the simulated room reverberation (if present) and the KEMAR HRIR associated with each loudspeaker location.

The HA simulation combined the KEMAR microphone recordings with the HA processing, with the processing operating independently in the two ears [33]. The processing simulated a six-channel hearing aid. The

inputs to the left and right hearing aids were the speech and noise stimuli convolved with the reverberation and the KEMAR HA microphone and ear canal responses. Frequency analysis was implemented using a six-channel linear-phase finite impulse response (FIR) filterbank having band center frequencies at (250, 500, 1000, 2000, 4000, and 6000) Hz. The HA processing within each frequency band used a series configuration, with noise suppression first followed by WDRC and then frequency compression.

Noise suppression for both the NH and HI subjects was implemented with an adaptive Wiener filter [34] where the gain in each frequency band depended on the ratio of the short-time speech power to the noise power averaged over the entire stimulus; more information is provided in [29, 34]. Compensation for the hearing impairment was provided by either NAL-R linear amplification [35] or NAL-NL2 wide dynamic-range compression (WDRC) [36] having a 5 ms attack time and a 50 ms release time. High frequencies for the HI subjects were shifted lower to fit into their impaired auditory bandwidths using frequency compression based on sinusoidal modeling [37]. A flat receiver frequency response was used and the system simulated earmold venting with a radius of 0.6 cm [38]; the venting was simulated by a complementary pair of 2nd order highpass and lowpass filters having cutoff frequencies of 350 Hz, with the ambient ear canal signal passed through the lowpass filter without modification and the HA output passed through the highpass filter.

Three HA processing settings were used for the NH subjects: (1) a flat 0 dB gain, (2) noise suppression with a maximum attenuation of 6 dB, and (3) noise suppression with a maximum attenuation of 12 dB. For the HI subjects, the three processing settings were (1) linear NAL-R amplification, (2) WDRC plus noise suppression limited to 6 dB, and (3) WDRC plus noise suppression limited to 12 dB and frequency compression matched to the audiogram. The frequency compression was applied above the specified cutoff frequency and bypassed below; the cutoff frequencies ranged from 4.7 to 2.0 kHz and the associated compression ratios ranged from 2.9 to 1.5 as the loss went from mild to severe [39].

Intelligibility was scored as the proportion completely correct IEEE sentences [40] for stimuli presented at 65 dB SPL. The sentences were spoken by 15 male and 18 female talkers [41]. The combination of talker, IEEE list, and sentence within the list was chosen at random for each processed sentence presented to each subject. The speech was mixed with two six-talker babble sources [42] at SNRs of 3, 8, and 20 dB [43] for three spatial configurations: (1) speech and both noise sources collocated at 0 deg (directly in front of the subject), (2) speech at 0 deg and noise at ±60 deg, and (3) speech at 60 deg and noise at 0 and -60 deg; a positive angle is towards the subject's right. The SNRs were computed as the ratio of the power in the speech signal averaged across the left and right HA microphones in the selected room simulation (anechoic or concert hall) to the power in the composite noise signal averaged across the two HA microphones for the same
room simulation. The experiment comprised 54 processing conditions: 2 simulated rooms × 3 SNRs × 3 spatial configurations × 3 HA settings, with 10 randomized repetitions of each condition for each subject.

For the stimulus presentation, each subject was seated in a sound isolation booth. Stimuli were presented through Sennheiser HD-25 headphones, and the subjects repeated back the sentences that they heard. Compensation for the headphone response was not provided, but the dummy head headphone response is flat within ±3 dB from approximately 40 to 4000 Hz. A short unscored training session comprising ten sentences was provided for acclimation, after which the test sentences were played out and scored; two sessions of approximately 1.5–2 h each were needed for the complete experiment.

# 3 Intelligibility metric

The binaural HASPI is an extension of HASPI v2 [3]. It uses the same basic model of the auditory periphery [44] for the left and right ears, but the peripheral model parameters are adjusted for binaural hearing and are followed by a model of binaural interaction; explanations of these modifications are provided in Section 3.2. The output of the binaural interaction model is in turn evaluated using an envelope modulation analysis that is the same as used for HASPI v2. An ensemble of neural networks is then used to transform the time-frequency envelope modulation measurements to the binaural subject intelligibility scores, with the neural networks designed using the same procedure as for HASPI v2. Each of these processing steps is described below.

## 3.1 Peripheral model

The overall block diagram for the peripheral model is shown in Figure 2. The reference signal is the average of the left and right ear-canal signals for the test sentence reproduced in an anechoic environment; the averaging smooths out the slight differences between the KEMAR left and right ears. The left and right ear degraded signals can include compensation for hearing loss (for HI subjects) as well as the room, noise, and processing effects. The signal sampling rates are all converted to 24 kHz, followed by broadband temporal alignment of the left and right ear signals to the reference signal. A second temporal alignment stage is later provided within each frequency band. For both NH and HI subjects the reference signal is passed through a model of the NH periphery. The left and right ear degraded signals for the NH subjects are also passed through a model of the NH periphery, while the degraded signals for the HI subjects are passed through a model of the HI periphery.

A more detailed block diagram for the peripheral model used for both NH and HI ears is presented in Figure 3. After sampling-rate conversion, the signal is passed through a middle ear filter [45], followed by an

auditory frequency analysis and a separate control filter-bank. Both filterbanks use a 4th-order gammatone filter-bank [46, 47]; 32 filters span the frequency range from 80 to 8000 Hz. The auditory filter bandwidths are determined by the RMS level measured over the duration of the sentence when passed through the control filterbank and are held constant over the sentence duration. The control filter bandwidths for both NH and HI subjects are set to the widest values used in the model and correspond to the auditory filters adjusted for the greatest hearing loss and/or highest signal intensity. The maximum relative bandwidth of the control filters increases with increasing frequency and is 4 times normal at 8 kHz. The auditory filter bandwidths for HI subjects [48] are wider than those for NH subjects [49], and the filter bandwidths for both NH and HI subjects within each band increase with increasing signal intensity above 50 dB SPL [44, 50, 51].

The control filterbank outputs also control the dynamic-range compression mediated by the outer hair cells (OHC) [52]. The envelopes of the control filter output signals in each band are passed through an 800 Hz lowpass filter [53] to provide a small time delay. The amplitudes of the filtered envelopes control the gains applied to the auditory filter outputs in each band. Linear amplification is applied to inputs below 30 or above 100 dB SPL while amplitude compression is applied to signals lying between 30 and 100 dB SPL. The compression ratio for NH listeners ranges from 1.25:1 at 80 Hz to 3.5:1 at 8 kHz. The OHC damage associated with hearing loss shifts the auditory threshold upwards and reduces the compression ratio. For the maximum allowed hearing loss of 100 dB, the system reverts to linear amplification with the output for an input at 100 dB SPL matched to the NH output for the same signal intensity.

Following compression, the envelope in each auditory band is converted to dB re auditory threshold with sound levels below threshold set to a lower limit of 0 dB SL plus a 0.1 dB dither. Inner hair cell (IHC) damage is modeled as additional envelope attenuation, and IHC adaptation is applied to the envelope dB output using a rapid time constant of 2 ms and a short-term time constant of 60 ms [54]. A final in-band time alignment is applied to align the left and right ear envelope signals with the reference signals, followed by compensation for the delays associated with the auditory filters [55].

## 3.2 Binaural modifications

In addition to adjusting the peripheral model parameters for separate audiograms at the two ears, the left and right ear models are further adjusted for binaural hearing. The auditory filters for binaural hearing, when measured using a notched-noise paradigm, are wider than the filters measured monaurally in both NH and HI subjects [56, 57]. An auditory model incorporating contralateral inhibition between the left- and right-ear frequency bands has been proposed to account for this apparent difference [58]. However, broader auditory filters can also
<figure><img src="image_3.png" /><figcaption>Figure 2. Binaural HASPI block diagram showing the comparison of the left and right ear signals with the reference signal.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3. Binaural HASPI block diagram of the auditory model used to extract the signal envelopes in each frequency band.</figcaption></figure>

be induced in the HASPI v2 peripheral model by adjusting the audiogram passed to the model. This simpler approach is based on multiplying the measured hearing loss by an audiogram scale factor greater than 1, which will increase the auditory filter bandwidth implemented in the HASPI peripheral model for the HI subjects with a side effect of modifying the auditory threshold.

The resultant audiogram scale factor applied to the hearing loss is a free parameter in developing the binaural HASPI. As indicated in the paragraph above, in addition to broadening the auditory filters the audiogram scale factor has the side effect of shifting the auditory threshold since the auditory filter gain is reduced in the peripheral model with increasing hearing loss. The impact of this additional threshold shift is expected to be small as long as the amplified stimulus spectrum lies above the impaired auditory thresholds [59]. The audiogram scale

factor has no effect on the audiogram of a NH subject, but increases the apparent loss for HI subjects. For example, if the scale factor is set to 1.5, a hearing loss of 0 dB remains at 0 dB but a loss of 30 dB at a given audiometric frequency would become an indicated loss of 45 dB in the audiogram input to the HI peripheral model.

A second modification is the inclusion of a binaural interaction model. The interaction in each band comprises the two steps of (1) temporal alignment of the left and right ear signals with the reference and (2) the band gain adjustment blocks shown in Figure 2. The temporal alignment step maximizes the cross-covariance between the envelope of the left ear signal and the reference envelope and the cross-covariance between the envelope of the right ear signal and the reference envelope, thus by default aligning the left and right ear envelopes with each other. The envelope is extracted from the gammatone auditory filter outputs via complex demodulation down to baseband, followed by a raised-cosine lowpass FIR filter having a cutoff frequency of 320 Hz.

The gain adjustment weights the aligned left and right ear envelopes to maximize the correlation of the weighted left+right sum with the reference subject to a constant power constraint (constant power cross-fader) on the left- and right-ear weights used to form the weighted sum. The weighted sum is given by:

$$z(n, k) = \cos \left[ 0.5 \left( \varphi(k) + \frac{\pi}{2} \right) \right] y_L(n, k) + \cos \left[ 0.5 \left( \varphi(k) - \frac{\pi}{2} \right) \right] y_R(n, k), \quad (1)$$

where $z(n, k)$ is the weighted summed output envelope for sample $n$ in frequency band $k$, $y_L(n, k)$ is the left ear envelope after temporal alignment, $y_R(n, k)$ is the right ear envelope after temporal alignment, and the angle $\varphi(k)$ maximizes the cross-correlation of $z(n, k)$ with the reference envelope in band $k$, with $-\frac{\pi}{2} \le \varphi(k) \le \frac{\pi}{2}$.
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Binaural HASPI block diagram showing the time-frequency envelope analysis incorporating the model of binaural interaction. The model includes the amplitude adjustment of the left and right ear signal envelopes to maximize the cross-correlation of the weighted sum with the reference signal envelope.</figcaption></figure>

The power constraint preserves the approximate signal loudness [60, 61] and the signal levels relative to the auditory thresholds built into the HASPI peripheral model. Loudness preservation is important because the HASPI v2 peripheral model is nonlinear. Intelligibility depends on the absolute intensity of the speech relative to the auditory threshold and the compression ratio for signals above the normal or impaired threshold, as well as on the auditory filter bandwidth. Maximizing the cross-correlations at the output of the peripheral model is consistent with binaural detection models that are based on maximizing the interaural envelope cross-correlation [9] rather than cancelling the noise corrupting the desired signal as proposed in the EC theory [7, 8, 13].

### 3.3 Envelope modulation analysis

The envelope modulation analysis is shown in the block diagram of Figure 4. The dB SL envelope in each frequency band is lowpass filtered at 320 Hz using a linear-phase filter having a raised-cosine impulse response. The raised-cosine filter response was chosen to ensure that no negative envelope values were produced by the lowpass filtering operation. The lowpass-filtered envelopes for the left and right ears, still at the 24 kHz sampling rate, are then weighted and summed so that the cross-correlation of the resultant summed envelope with the reference envelope is maximized; the left- and right-ear weights satisfy the constant-power constraint given by equation (1). The filtered reference and monaural sum envelopes are subsequently subsampled at 2560 Hz, which is 8 times the lowpass filter cutoff frequency.

<table><caption>**Table 1.** Characteristics of the ten filters implemented in the modulation filterbank.</caption><thead><tr><th>Filter No.</th><th>Center frequency, Hz</th><th>Lower edge, Hz</th><th>Upper edge, Hz</th></tr></thead><tbody><tr><td>1</td><td>2</td><td>0.0</td><td>4.0</td></tr><tr><td>2</td><td>6</td><td>4.0</td><td>8.0</td></tr><tr><td>3</td><td>10</td><td>8.0</td><td>12.5</td></tr><tr><td>4</td><td>16</td><td>12.5</td><td>20.5</td></tr><tr><td>5</td><td>25</td><td>20.5</td><td>30.5</td></tr><tr><td>6</td><td>40</td><td>30.5</td><td>52.4</td></tr><tr><td>7</td><td>64</td><td>52.4</td><td>78.1</td></tr><tr><td>8</td><td>100</td><td>78.1</td><td>128.0</td></tr><tr><td>9</td><td>160</td><td>128.0</td><td>200.0</td></tr><tr><td>10</td><td>256</td><td>200.0</td><td>328.0</td></tr></tbody></table>

The remaining steps in the modulation analysis are identical with those used for HASPI v2, and the reader is referred to [2] for a complete description. At each time sample at the 2560 Hz sampling rate, the dB envelope values in the 32 frequency bands give the log spectrum on an auditory frequency scale [49]. These auditory spectra are fitted with a set of five basis functions ranging from 1/2 cycle per spectrum to 21/2 cycles per spectrum; these basis functions correspond to mel-frequency cepstral coefficients [62] and also to the principal components of speech short-time spectra [63]. The basis function sequences are then pruned to remove pauses in the speech. Each of the five pruned sequences of cepstral coefficients is passed through a modulation filterbank. There are ten filters in the filterbank; the filter characteristics are shown in Table 1. The filters have Q values of 1.5, which are
consistent with the *Q* values between 1 and 2 that have been fitted to amplitude modulation discrimination data [64, 65].

The envelope modulation filter analysis produces a total of 50 output envelope sequences: five cepstral coefficient sequences each filtered through the ten modulation filters. Cross-covariance is used to compare each of these 50 filtered sequences for the left+right sum to the corresponding sequences for the reference. The basis function cross-correlations are similar to one another [66], so the cross-covariance functions are averaged over the five basis functions to produce an output vector comprising the averaged cross-covariances for each of the ten envelope modulation filters.

## 3.4 Neural network ensemble

The final processing stage for the binaural HASPI is an ensemble of ten neural networks that map the averaged modulation filter outputs to the subject sentence intelligibility scores. The configuration and design procedure used for the binaural HASPI ensemble of neural networks is identical to that used for the monaural HASPI v2 [2], but the networks here are fitted to the binaural intelligibility data. Each neural network in the ensemble has 10 inputs (the modulation filter outputs), a hidden layer comprising 4 neurons, and an output layer comprising a single neuron. A sigmoid activation function is used for all layers. The ten networks were each initialized to a different independent set of random weights, and network training used backpropagation with a mean-squared error loss function [67]. A total of 16200 training vectors were available to train the neural networks, with each vector comprising the subject sentence correct score (0 or 1) and the set of averaged modulation filter outputs for the ten modulation filter bands computed for the 540 sentences heard by each of the 15 NH and 15 HI subjects.

Ensemble averaging was implemented to reduce the possibility of overfitting the data. Bootstrap aggregation [68] was used to combine the outputs from the neural networks. Each neural network was trained using a subset of the 16200 possible training vectors, with each subset comprising $(1 - 1/e) \approx 0.632$ of the available data, selected with replacement. Each neural network was trained on 1000 iterations of its randomly selected binaural data subset. An ensemble comprising ten networks was chosen since a group that size provides the main benefits of bootstrap aggregation in reducing overfitting [68, 69].

# 4 Results

## 4.1 Audiogram scale factor

The binaural HASPI metric includes the audiogram scale factor described in the Binaural Modifications

section above. The audiogram scale factor, although not needed for monaural stimulus presentation, is expected to be relevant for modeling binaural intelligibility for any system using the HASPI or a similar peripheral model. To investigate this hypothesis, the audiogram scale factor was applied to three binaural intelligibility prediction models based on the HASPI peripheral framework.

The simplest modeling approach is to add the audiogram scale factor to the existing HASPI v2, thus increasing the bandwidth of the HI monaural auditory filters while making no other changes to the HASPI v2 intelligibility calculation. This monaural metric was converted into a better ear value by first computing HASPI v2 separately for the left and right ears for all stimulus presentations. The higher of the left-ear and right-ear HASPI values were then selected across the presentations to give the better-ear values. These better-ear HASPI v2 values were then averaged over subject and repetition for each processing condition, producing 54 averaged stimulus condition intelligibility predictions. The RMS error and Pearson correlation coefficient between the averaged better-ear HASPI predictions and the subject intelligibility scores were then computed over the 54 conditions. This procedure was repeated for each of the audiogram scale factors. This modeling approach is denoted as "v2 Better Ear".

The second model starts with the left and right ear monaural HASPI v2 envelope modulation features calculated using the broadened HI auditory filters as described in the paragraph above. However, separate ensembles of neural networks were computed for the sets of left-ear and right-ear modulation features and each ensemble was fitted to the binaural intelligibility scores. The higher of the computed left and right ear values for each stimulus presentation were then selected and averaged over repetition and subject. This modeling approach is denoted as "Bin Data Better Ear".

The final approach applies the audiogram scale factor to the peripheral models, but this time followed by the binaural interaction processing stage. The binaural interaction adjusts the time delays and amplitudes between the left and right ear envelopes to maximize the cross-correlation between each ear and the reference and then sums the adjusted left and right ear signals. The envelope modulation correlations obtained using this combined signal are then fitted to the binaural intelligibility scores using an ensemble of neural networks. This third approach is the procedure proposed for the binaural HASPI metric, and is denoted by "Binaural Sum".

The results plotted in Figure 5 show the RMS error (a) and Pearson correlation coefficient (b) for predicted binaural intelligibility compared to the subject responses for the three models as the audiogram scaling factor was increased from 1 (audiogram used without modification) to 2 (hearing loss doubled in dB at all audiometric frequencies). HASPI v2 fitted to the monaural data (v2 Better Ear) gives the greatest RMS error for audiogram
<figure><img src="image_6.png" /><figcaption>**Figure 5.** RMS binaural intelligibility prediction error (a) and Pearson correlation coefficient (b) for the better-ear monaural HASPI v2 with the neural networks fitted to the monaural intelligibility scores (v2 Better Ear), the better-ear monaural HASPI v2 with the neural networks fitted to the binaural intelligibility scores (Bin Fit Better Ear), and the binaural interaction model fitted to the binaural intelligibility scores (Binaural Sum). The model accuracy is indicated for the combined NH plus HI subjects; each point represents data averaged over processing conditions, subjects, and repetitions.</figcaption></figure>

scale factors below 1.50, while fitting the same envelope modulation features to the binaural intelligibility scores (Bin Data Better Ear) greatly reduces the RMS error for audiogram scale factors over this range. The HASPI v2 better-ear (v2 Better Ear) and the better-ear fit to the binaural data (Bin Data Better Ear) show a decrease in RMS error over the audiogram scale factor range of 1–1.67, while the binaural sum model (Binaural Sum) shows decreasing RMS error as the audiogram scale factor increases from 1 to 1.50. The Binaural Sum model shows lower RMS error than either of the models lacking the binaural interaction stage for all audiogram scale factors except for the extremum of 2. The minimum binaural sum RMS error of 0.0493 occurs for an audiogram scale factor of 1.50; this audiogram scale factor was therefore chosen for the implementation of the binaural HASPI. The other two models also show minima in the RMS error, but occurring at audiogram scale factors of 1.67 or 2.00.

The correlation coefficients tend to inversely mirror the RMS error. For all three models the correlation increases monotonically as the audiogram scale factor increases from 1 to 1.67; the binaural interaction model has the highest correlations over this range while the v2 better ear has the lowest. All three models have a maximum correlation peak at the audiogram scale factor of 1.67, although the difference for the binaural sum curve between 1.50 and 1.67 is quite small. Note that the correlation coefficients measure the degree to which the intelligibility scores are linear transformations of the model predictions; the correlations are immune to shifts or biases in the predictions or to differences in the slopes. The RMS error includes both factors and for this reason is our preferred criterion for selecting the audiogram scale factor for the binaural interaction system.

In summary, increasing the audiogram scale factor tends to reduce the RMS error and increase the correlation for all three modeling approaches considered in

this section. Furthermore, the binaural interaction model proposed in this paper further reduces the RMS error and increases the correlation coefficient beyond the reduction provided just by increasing the audiogram scale factor, so the benefits of applying both the audiogram scale factor and the binaural interaction model appear to be additive.

## 4.2 Monaural HASPI v2 and binaural HASPI for binaural data

This section provides an analysis of the improvement in prediction accuracy offered by the proposed binaural HASPI as contrasted with the existing HASPI v2. The HASPI v2 procedure is the same better-ear calculation as used for evaluating the audiogram scale factor in the section above, with the audiogram scale factor set to 1 to give the conventional HASPI v2 peripheral model and with the neural networks fitted to the monaural data. The binaural HASPI values were computed using the optimal audiogram scale factor of 1.5 determined above and with the binaural interaction procedure described in the intelligibility Metric section, and the neural networks were fitted to the binaural data.

The scatterplot for the better-ear monaural HASPI v2 values plotted against the subject binaural sentence intelligibility scores is presented in Figure 6a, and the binaural HASPI scatterplot for the binaural data is presented in Figure 6b. The NH subject group is identified by open circles, while the HI group is identified by filled squares. The diagonal lines in the two figures represent perfect performance; a point below the line indicates that the predicted intelligibility is higher than the observed score, while a point above the diagonal indicates that the predicted intelligibility is lower than observed. Points close to the diagonal line indicate a low error, while points arrayed along a line, even if not congruent with the diagonal, indicate a high Pearson correlation coefficient. The
RMS error and correlations (Pearson, Spearman rank order, and Kendall's tau based on pairwise comparisons) corresponding to the data in Figure 6 are presented in Table 2.

Significant differences between the two subject groups for a given intelligibility model and between models for a given subject group were determined using bootstrapping [68–70]. Group or model differences for 20 000 replications with resampling of the selected comparison (RMS error or correlation criterion) were used to provide confidence limits from which the statistical significance was estimated. Bonferroni adjustments were applied for multiplicity.

In Figure 6a, the HI data lie below but roughly parallel to the NH data. The NH to HI comparisons do not show significant differences for Pearson, Spearman, or Kendall's tau correlations. However, the RMS error is significantly larger ($p < 0.001$) for the HI subjects than for the NH subjects. The results for the binaural model are presented in Figure 6b. The HI and NH data now overlap. No significant differences are found for any of the three correlation calculations or for the RMS error, so the binaural model, with its audiogram scale factor, binaural interaction, and fitting to the binaural data, has successfully reduced the RMS error.

The intelligibility models can also be compared for each of the two subject groups. For the NH group, the binaural model has significantly higher Pearson correlation ($p = 0.012$) than the better-ear model and significantly lower RMS error ($p < 0.001$). For the HI group, no significant differences were found for any of the three correlation procedures, but, as illustrated in Figure 6b, the binaural model yields significantly lower RMS error ($p < 0.001$).

# 5 Discussion

## 5.1 Comparison to other modeling approaches

Processing, stimuli, and Pearson correlation coefficient results for several existing binaural intelligibility models are summarized in Table 3. Note that it is difficult to compare different binaural intelligibility metrics since not all tested HI subjects and the target speech, noise and interference, HA processing, acoustic environments, and intelligibility criteria varied across studies. Furthermore, most of the models were fitted to the specific data cited in the respective papers and may not be as accurate for different datasets. Despite these caveats, the accuracy of the binaural HASPI, with Pearson correlation coefficients of 0.982, 0.981, and 0.983 for the NH, HI, and combined NH + HI subjects, respectively, compares quite favorably with these previously published results. Even the better-ear HASPI v2, which was trained on monaural headphone data, produces respectable correlation values of 0.961, 0.972, and 0.887 for NH, HI, and NH+HI subjects, respectively. The largest difference in accuracy occurs for the binaural HASPI compared to the models

of [23, 24]. However, both these studies evaluated their intelligibility models with the CPC1 dataset; there was no averaging over stimulus repetitions for a given subject or over subject responses for the same stimulus across subjects. The difference in the correlation coefficients could thus be primarily due to greater individual and stimulus variability in the unaveraged responses.

The high accuracy for the binaural HASPI indicates that the EC model of binaural interaction is not a requirement for building an accurate binaural metric. The first six models in Table 3 all use EC followed by a monaural metric, but the HASPI approach of independent left- and right-ear peripheral models followed by a cross-correlation model of binaural interaction appears to work just as well.

## 5.2 HI bias

The significantly higher RMS error shown in Figure 6a, combined with no significant differences in correlations, indicated a substantial bias for the better-ear HASPI v2 approach: The HI subject sentence intelligibility was consistently predicted to be too high. Existing binaural intelligibility models have shown similar biases. For example, the study reported in [11] used the same model for NH and HI subjects; hearing loss was modeled as an additive internal noise in the EC model and in the SII calculation. Their speech reception threshold (SRT) predictions were underestimated (intelligibility over-estimated) for HI subjects, with errors as large as –5 dB in the SRT predicted for an anechoic room. The study reported in [12] extended the previous model [11] for modulated noises. In the revised model, they found an SRT bias for both NH and HI subjects. The overall bias across hearing groups was –3.4 dB, and the magnitude of the bias for the HI group was equal to or greater than that for the NH group for all rooms, speech and noise azimuths, and noise types. The RMS error in the SRT was 1.3 dB for the NH subjects and was 1.9 dB for the HI subjects. In the study reported in [71], using the Beutelmann and Brand model [12], the authors found that audiograms alone were insufficient to accurately predict individual SRTs. Prediction accuracy was improved when the individual audiogram was combined with SII calibration using the measured individual SRT for a baseline test condition. The calibration was likened to the use of a proficiency factor in the calculation of the SII [72, 73] that reduces the calculated SII values based on individual intelligibility data.

The HI bias can be reduced when separate models are derived for the NH and HI groups; the separate models may indirectly compensate for changes in binaural processing in the impaired as opposed to the normal periphery. The model proposed in [74] represents hearing loss as an internal noise spectrally shaped to correspond with the individual audiogram which is then adjusted in amplitude using different gains for the NH and HI groups. This procedure for calibrating the SRTs effectively eliminates the HI bias but
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Scatterplots comparing (a) better-ear HASPI v2 predictions to the binaural subject intelligibility scores using an audiogram scale factor of 1, and (b) binaural HASPI predictions to the binaural subject intelligibility scores using an audiogram scale factor of 1.5. Each point represents the data for a single processing condition averaged over repetitions and either NH or HI subjects for that condition. Data for the NH subjects are plotted using open circles and data for the HI subjects are plotted using filled squares.</figcaption></figure>

<table><caption>**Table 2.** RMS error and correlations between the model predictions and the subject responses for the better-ear monaural HASPI v2 model with its audiogram scale factor set to 1 and the binaural sum HASPI model with its audiogram scale factor set to 1.5. The data are averaged over subjects and repetitions for each hearing group.</caption><thead><tr><th>Model</th><th>Subj. Group</th><th>RMS Error</th><th>Pearson</th><th>Spearman</th><th>Kendall</th></tr></thead><tbody><tr><td rowspan="3">Better-Ear HASPI v2</td><td>NH</td><td>0.078</td><td>0.963</td><td>0.964</td><td>0.836</td></tr><tr><td>HI</td><td>0.252</td><td>0.963</td><td>0.948</td><td>0.796</td></tr><tr><td>NH+HI</td><td>0.186</td><td>0.881</td><td>0.874</td><td>0.686</td></tr><tr><td rowspan="3">Binaural Sum HASPI</td><td>NH</td><td>0.050</td><td>0.982</td><td>0.973</td><td>0.858</td></tr><tr><td>HI</td><td>0.049</td><td>0.981</td><td>0.967</td><td>0.851</td></tr><tr><td>NH+HI</td><td>0.049</td><td>0.983</td><td>0.979</td><td>0.878</td></tr></tbody></table>

yields two separate models, one for NH and one for HI subjects. The study of [26] improved upon this model by using an internal noise that separates the estimated influences of inner and outer hair cell losses and which is dependent on the level of the external stimuli. These changes allowed predictions of NH and HI SRTs with a single model without any prediction bias. The model in [75] further refined this approach to predict individual differences among HI SRTs for a given test condition.

The HI bias present in the better-ear HASPI v2 was greatly reduced in the binaural HASPI by multiplying the audiogram in dB by an audiogram scale factor of 1.5, adding the model of binaural interaction, and fitting the model to the binaural data. The remainder of the underlying left and right ear peripheral models are the same as used for the monaural HASPI v2. Scaling the audiogram broadened the auditory filters and shifted the auditory threshold for the HI subjects. It is possible that these changes in the peripheral behavior represent aspects of the auditory efferents and binaural interaction that are not directly included in the binaural HASPI model. The effective auditory bandwidth, for example, is influenced by auditory cross-correlation [76, 77] and interaural modulation processing [78], and auditory gain is reduced by preceding signals activating the efferent system [79, 80]. Modeling the auditory efferents to produce a more accu-

rate model of binaural interaction could potentially lead to a more physiologically valid binaural intelligibility metric. However, the results presented in this paper suggest that modifying the auditory periphery to provide more hearing loss than indicated by the audiogram may be a simple but effective way to improve the accuracy of binaural intelligibility models.

## 5.3 Limitations

The presentation level used for the speech stimuli was 65 dB SPL for the NH subjects and 65 dB SPL plus compensation for the hearing loss for the HI subjects. However, the gains and auditory filter bandwidths in the HASPI peripheral model depend on the signal intensity, and this level dependence could interact with the proposed audiogram scaling for the hearing loss. For speech at levels greater than the 65 dB SPL used in this paper, the peripheral model will increase the signal levels in each frequency band relative to auditory threshold, with the amount of increase depending on the OHC compression ratio, and will also increase the auditory filter bandwidths. The increased signal level could improve audibility for the HI subjects since more of the speech will fall above the impaired threshold, which
<table><caption>**Table 3.** Representative binaural speech intelligibility model results. Abbreviations introduced in this table: Intel- ligibility (Intel.), Speech-shaped noise (SSN), Ideal Binaural Mask (IBM), International Speech Test Signal (ISTS), Reverberation Time (RT), Clarity Prediction Challenge 1 (CPC1).</caption><thead><tr><th>Paper</th><th>Binaural model</th><th>Intel. metric</th><th>Subj.</th><th>Noise, interference, and processing</th><th>Room</th><th>Correlation coefficient</th></tr></thead><tbody><tr><td>Beutelmann et al. (2006) [11]</td><td>EC</td><td>SII</td><td>NH, HI</td><td>SSN (single source)</td><td>Anechoic, Office, Cafeteria</td><td>SRT: NH &amp; HI 0.90-0.97</td></tr><tr><td>Beutelmann et al. (2010) [12]</td><td>EC</td><td>SII</td><td>NH, HI</td><td>Modulated SSN</td><td>Anechoic, Room, Classroom, Church</td><td>SRT: NH 0.80-0.93 HI 0.59-0.80</td></tr><tr><td>Hauth et al. (2020) [14]</td><td>EC</td><td>SII</td><td>NH</td><td>SSN (single source)</td><td>Anechoic, Office, Cafeteria</td><td>SRT 0.98</td></tr><tr><td>Andersen et al. (2016) [16]</td><td>EC</td><td>DBSTOI</td><td>NH</td><td>SSN, Café, Factory, Car IBM Proc., Beamform.</td><td>Anechoic</td><td>SRT and Intel 0.950-0.988</td></tr><tr><td>Andersen et al. (2018) [17]</td><td>EC</td><td>MBSTOI</td><td>NH</td><td>SSN, ISTS, Beamform, Wiener Filter</td><td>Anechoic</td><td>Intel Range 0.973-0.987</td></tr><tr><td>Chabot-Leclerc et al. (2016) [18]</td><td>EC</td><td>Env Power SNR</td><td>NH</td><td>SSN</td><td>Anechoic, Room, Classroom, Church</td><td>SRT 0.91</td></tr><tr><td>Biberger and Ewert (2022) [19]</td><td>Better Ear plus Binaural Matrix Feature Decoder</td><td>Env Power SNR</td><td>NH</td><td>SSN, Modulated SSN, ISTS, Single talker</td><td>Anechoic headphone (dichotic stimuli)</td><td>SRT: 0.985-0.990</td></tr><tr><td>Lavandier and Culling (2010) [6]</td><td>BMLD Formula</td><td>Effective SNR</td><td>NH</td><td>SSN</td><td>Anechoic, Various Rooms. RT = 0.22 s, 1.30 s</td><td>SRT 0.95-0.97</td></tr><tr><td>Lavandier et al. (2012) [25]</td><td>BMLD Formula</td><td>Effective SNR</td><td>NH</td><td>SSN for single and multiple sources</td><td>Two meeting rooms, lecture hall</td><td>SRT 0.95-0.99</td></tr><tr><td>Vicente et al. (2020) [27]</td><td>BMLD Formula</td><td>Effective SNR</td><td>NH, HI</td><td>SSN, Noise Vocoder</td><td>Anechoic, Anechoic + ILD, ITD</td><td>SRT 0.93-0.98</td></tr><tr><td>Titalim et al. (2022) [23]</td><td>DNN</td><td>DNN</td><td>HI</td><td>CPC1 Dataset: Various scenes</td><td>CPC1 Dataset: Various scenes</td><td>Intel 0.74 (Closed set)</td></tr><tr><td>Mawalim et al. (2022) [24]</td><td>DNN</td><td>DNN</td><td>HI</td><td>CPC1 Dataset: Various scenes</td><td>CPC1 Dataset: Various scenes</td><td>Intel 0.77 (Closed set)</td></tr></tbody></table>

would be expected to improve speech intelligibility. However, the broader auditory filter bandwidths will provide greater spectral smoothing that can reduce the cepstral correlation values used to compute the HASPI speech features. The increased signal level thus produces audibility and auditory filter effects that work in opposition. For speech intensities below 65 dB SPL the audibility and auditory filter bandwidth effects are reversed, causing lower audibility combined with improved short-time spectral contrast. It is possible that the magnitude of these stimulus intensity effects could be affected by the audiogram scaling proposed for binaural HASPI, and further investigation of the impact of stimulus intensity is warranted.

## 6 Conclusions

The goal of this paper was to develop a new version of HASPI that is accurate for binaural speech intelligibility.

The starting point for the binaural HASPI was HASPI v2, which was derived for monaural headphone presentation. That model was fitted to a wide range of speech stimuli including additive noise, reverberation, nonlinear distortion, and hearing-aid processing. HASPI v2 incorporates a peripheral model that can be adjusted in response to the subject's audiogram, making HASPI v2 appropriate for both NH and HI subjects.

The binaural HASPI uses the HASPI v2 peripheral models for the left and right ears. Three modifications were made for predicting binaural intelligibility data. It was found that using the peripheral models as originally developed led to overestimation of the HI speech intelligibility for better-ear monaural predictions; this estimation bias was greatly reduced by multiplying the subject's audiogram in dB by an audiogram scale factor of 1.5 while keeping the rest of the peripheral model as originally designed. The second modification was the addition of the binaural interaction stage where the left and right ear envelopes are temporally aligned with the center-
front anechoic reference and the gains of the aligned left and right ear signals are adjusted to maximize the cross-correlation of the weighted sum with the reference. The final stages of the binaural HASPI then follow the same procedure as used for HASPI v2; the time-frequency envelope modulation extracted from the degraded stimulus summed across the two ears is compared to that of the reference and the sentence intelligibility is estimated using an ensemble of neural networks. The third modification was generating a new ensemble of neural networks based on fitting the binaural HASPI model to the binaural intelligibility data considered in this paper. The binaural HASPI results show that its RMS error and correlation with measured data are comparable to those for previously developed binaural metrics, and that the accuracy for HI subjects is similar to that for NH subjects.

## Funding

The authors were supported by a research grant to the University of Colorado from GN ReSound.

## Conflicts of interest

The authors declare that they have no conflicts of interest.

## Data availability statement

The MATLAB code for the binaural HASPI is available on request from the authors. The stimulus sound files and the subject responses used for this paper are available in the Open Science Framework (OSF) public-domain repository, under the reference https://osf.io/nf23j (NH data) and https://osf.io/yz64u (HI data).

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**Cite this article as:** Kates J.M. Lavandier M. Arehart K.H. Lundberg E.M.H. & Muralimanohar R.K. 2025. A binaural implementation of the Hearing Aid Speech Perception Index (HASPI). Acta Acustica, **9**, 74. https://doi.org/10.1051/aacus/2025054.