The study was approved by the Swedish Ethical Review Authority (2020-01235). All participants provided written informed consent prior to participation and were informed of their right to withdraw from the study at any time without consequence. All procedures adhered to clinical standards and were conducted in accordance with relevant ethical guidelines and regulatory requirements.

The inclusion criteria required participants to have normal hearing, defined as AC thresholds of 20 dB HL or better at frequencies from 125 Hz to 8 kHz, and to have Swedish as their first language. Exclusion criteria included ongoing or past ear surgery and any known pathology that could affect skull anatomy.

Twenty-one volunteers were initially recruited. One volunteer had elevated high-frequency hearing thresholds (>20 dB HL) and was excluded. The final sample thus comprised 20 participants, of whom 4 were male, with a mean age of 24.3 years (SD = 6.7).

To enable controlled manipulation of BC cross-head transmission, all experimental testing was performed using AC stimulation. Perceived BC hearing was simulated by applying an estimated cross-head transmission function. To avoid lengthy recording of individual cross-head transfer functions, an average cross-head transmission model was derived. Although several studies report perceptual estimates of cross-head transmission magnitude (Stenfelt, 2012; Reinfeldt et al., 2013; Nolan and Lyon, 1981), relatively few provide both magnitude and phase across a broad frequency range (Surendran and Stenfelt, 2023; Barnsley and Culling, 2025; Mcleod and Culling, 2019). In the present study, cross-head transmission was simulated for mastoid placement of the BC transducers, using the average data reported in Surendran and Stenfelt (2023). These data were available at one-third-octave center frequencies from 250 Hz to 4 kHz. Because the magnitude values in Surendran and Stenfelt (2023) were slightly higher than those reported in other perceptual studies (e.g., Stenfelt, 2012; Stenfelt and Zeitooni, 2013; Mcleod and Culling, 2017) the magnitude response was reduced by 3 dB to better align with those findings. The phase response reported in Surendran and Stenfelt (2023) was converted to the time domain to obtain the corresponding interaural time delay. The original magnitude and delay functions are shown in red in Figure 1.

To minimize spectral artifacts in the simulated cross-head transmission, both the magnitude and time-delay functions were smoothed and extended to cover the frequency range 100 Hz to 10 kHz (blue curves in Figure 1). These extended frequency-domain functions were transformed to the time domain using an inverse Fourier transform, yielding an impulse response used to construct a finite impulse response (FIR) cross-head filter. The filter comprised 512 coefficients and was implemented at a sampling frequency of 44,100 Hz. BC cross-head transmission was simulated by adding the left-ear input to the right-ear input after filtering through the cross-head filter, and vice versa (Figure 2). Thus, the cross-head transmission was assumed to be symmetric in the simulation.

Stimulation from different horizontal positions was simulated using head-related transfer functions (HRTFs) obtained from the MIT database (Gardner and Martin, 1994). These HRTFs were measured on the KEMAR manikin (Burkhard and Sachs, 1975); therefore, individualized HRTFs were not used. To simulate a specific source position, the left and right ear signals were convolved with the corresponding HRTF impulse responses (Figure 2). Two source positions were used: 0° (front) and 45° to the left. For the 0° condition, the 0° HRTF was presented identically to both ears. For the 45° condition, the 45° HRTF was applied to the left ear and the −45° HRTF to the right ear.

Pure-tone hearing thresholds were measured using an Interacoustics AC40 audiometer equipped with Radioear DD45 earphones. All speech-in-noise stimuli were computer generated and delivered via an external sound card (Focusrite Scarlett 2i2) to Sennheiser HDA 200 audiometric headphones at a sampling frequency of 44,100 Hz.

Participants were seated comfortably in a sound-attenuated booth. Pure-tone hearing thresholds were measured first to verify that each participant met the inclusion criteria. Hearing-in-noise testing was then initiated.

Speech-in-noise performance was assessed using the Swedish Matrix Test (Hagerman sentences) (Hagerman, 1982). The test material consists of five-word sentences spoken by a female talker and presented in 10% modulated, speech-shaped noise. Although syntactically correct, the sentences have low semantic predictability. After each presentation, participants verbally repeated the words they perceived. The objective was to determine the speech-to-noise ratio (SNR) corresponding to 50% correct word recognition. Intelligibility data were fitted with a logistic regression model to generate a psychometric function, from which the 50%-correct SNR threshold was extracted (Jalalkamali et al., 2026).

SRM was calculated as the difference in SNR thresholds between conditions in which speech and noise were co-located vs. spatially separated. In the present study, co-location was achieved by presenting both speech and noise from the front (S₀N₀), whereas spatial separation was created by presenting speech from the front and noise 45° to the left (S₀N₄₅).

Each participant completed eight speech-in-noise tests, representing four stimulation conditions at two spatial configurations (S₀N₀ and S₀N₄₅). The stimulation conditions included one AC condition (no cross-head transmission) and three simulated BC conditions, each implementing a different magnitude of cross-head transmission:

Thus, the three BC simulations shared identical temporal characteristics but varied in transmission magnitude.

Test order was counterbalanced across participants as far as possible, and participants were blinded to the specific condition being tested. Total testing time, including pure-tone audiometry and brief breaks between speech-in-noise runs, was approximately 1 h.

Descriptive statistics were calculated as means and standard deviations for each condition, as well as for the computed SRM. Differences among conditions were evaluated using repeated-measures ANOVA, with Sidak-adjusted post-hoc comparisons. All statistical analyses were performed using IBM SPSS Statistics, version 29.

The results presented in Figure 3 demonstrate that cross-head transmission inherent to BC stimulation disrupts binaural processing and reduces the ability to suppress noise when speech and noise were spatially separated. As expected, when speech and noise were co-located, performance was highly similar across conditions. The slightly poorer performance observed for simulated BC without attenuation (BC_0dB) in the S₀N₀ configuration likely reflects altered spectral characteristics introduced by the unattenuated cross-head signal, which may degrade speech fidelity. This effect appears to be largely mitigated by even a modest 5-dB attenuation of the cross-head component.

SRM increased substantially, and significantly, following a 5-dB reduction in cross-head transmission. The observed improvement of 2.25 dB accounts for more than half of the total difference between the simulated BC and AC conditions (3.95 dB). This finding is encouraging, as it suggests that relatively small reductions in cross-head transmission can yield meaningful improvements in speech-in-noise performance with BC stimulation. Importantly, commonly proposed strategies for reducing cross-head transmission rely on cancellation techniques that are highly sensitive to small variations in magnitude and phase (Surendran and Stenfelt, 2023; Barnsley and Culling, 2025; Mcleod and Culling, 2019; Stenfelt, 2007). Given that cross-head transmission properties vary with exact transducer placement and other uncontrollable factors (Barnsley and Culling, 2025; Wang et al., 2022; Dobrev et al., 2016), our results indicate that a less precise but more robust attenuation-based approach may still offer substantial benefit in bilateral BC applications.

Although the additional improvement observed with 10 dB attenuation relative to 5 dB attenuation was 1 dB and did not reach statistical significance, inspection of individual SRM values (Figure 3B) shows a consistent performance advantage for the 10 dB attenuation condition. Thus, the difference may still be clinically meaningful, and the lack of statistical significance could be attributable to limited sample size given the small effect size and the number of conditions tested. Notably, SRM performance with 5 dB attenuation remained significantly poorer than with AC stimulation, whereas the 10 dB attenuation condition did not differ significantly from AC. These findings suggest that a 10 dB reduction in cross-head transmission offers additional benefit beyond that achieved with a 5 dB reduction.

A small (0.6 dB) difference remained between the SRM obtained with 10 dB attenuation and that obtained with AC stimulation, although this difference was not statistically significant. Examination of individual data nevertheless indicates that simulated BC with 10 dB attenuation still does not fully match AC performance. We therefore interpret these findings to mean that while a 10 dB attenuation yields performance that is statistically indistinguishable from AC, it does not completely eliminate the disadvantage associated with BC stimulation. Small but potentially relevant improvements may still be achievable beyond the 10 dB attenuation level.

A limitation of the present study is that BC stimulation was simulated using AC earphones combined with an averaged cross-head transmission function. This approach may not fully capture the perceptual characteristics of true BC hearing. However, when comparing our findings with studies that used a similar methodology but employed actual BC stimulation at the mastoids (Stenfelt and Zeitooni, 2013; Stenfelt et al., 2024; Zeitooni et al., 2016), the present results show good general agreement. For example, studies using the same Matrix test and computing SRM as the SNR difference between S₀N₀ and S₀N₄₅ reported AC S₀N₀ thresholds of approximately −8.0 dB, comparable to those observed here (Stenfelt and Zeitooni, 2013; Stenfelt et al., 2024). Their S₀N₄₅ thresholds and resulting SRM values under AC stimulation were 1–2 dB better than the current results, a difference likely attributable to the distinct HRTFs used. Specifically, the current study employed KEMAR-based HRTFs, whereas the earlier studies used a simplified analytical model that represented the head as a rigid sphere. We therefore suggest that differences in HRTF accuracy and anatomical realism may explain the slightly reduced spatial benefit observed in our results compared with Stenfelt and Zeitooni (2013); Stenfelt et al. (2024).

The BC cross-head transmission used in the present simulations was derived from a smoothed, averaged version of the perceptual cross-head function reported in Surendran and Stenfelt (2023). Although estimates of BC interaural magnitude and phase have been obtained using cochlear promontory vibration (Stenfelt and Goode, 2005b; Eeg-Olofsson et al., 2011), intracochlear pressure measurements (Mattingly et al., 2020; Farrell et al., 2017), and ear-canal sound pressure recordings (Irwansyah and Nakagawa, 2022), none of these measures are definitively known to replicate perceived BC sound. While intracochlear differential pressure is believed to drive basilar membrane motion for both AC and BC stimuli (Stenfelt et al., 2003), and cochlear promontory vibration correlates with perceived BC sound (Eeg-Olofsson et al., 2013), these metrics remain indirect. The perceptual estimates used here were based on cancellation parameters for ipsilateral and contralateral BC tones at discrete frequencies (Surendran and Stenfelt, 2023; Barnsley and Culling, 2025; Mcleod and Culling, 2019). Limitations in frequency resolution, as well as averaging across individuals, introduce additional uncertainty and may reduce the accuracy of the simulated BC experience for participants in the current study.

Relative to the SNR thresholds reported in Stenfelt and Zeitooni (2013) and Stenfelt et al. (2024), our simulated BC condition without cross-head attenuation showed approximately 1 dB poorer performance for both spatial configurations (S₀N₀ and S₀N₄₅), as well as lower SRM values. These discrepancies are consistent with the combined effects of using non-individualized cross-head transmission functions and differing HRTFs, as discussed above. Despite these limitations, the overall similarity between the current simulated BC results and those obtained using real BC stimulation (Stenfelt and Zeitooni, 2013; Stenfelt et al., 2024), suggests that the applied cross-head transmission model captured the essential features of BC binaural processing and provides a reasonable approximation for investigating BC-related binaural phenomena.

The present study examined only one aspect of binaural BC hearing, SRM, and only for stimulation delivered at the mastoid. Most previous investigations of binaural BC processing have focused on bilateral BCHAs (Caspers et al., 2022; Priwin et al., 2004; Brassington et al., 2023; den Besten et al., 2020), and only a subset of these have employed mastoid stimulation, such as studies using transcutaneous (Chen et al., 2022) or skin-driven BCHAs (Liu et al., 2023). Importantly, the HRTFs associated with BCHAs differ from those measured with the KEMAR used in the current study, as BCHA microphones are typically positioned behind and above the ear (Stenfelt, 2005). Other research has assessed binaural BC perception in normal-hearing individuals using mastoid stimulation to evaluate speech intelligibility (Stenfelt and Zeitooni, 2013; Wang et al., 2023a), localization (Wang et al., 2023b, 2026b), and externalization (Wang et al., 2025). Collectively, these studies demonstrate benefits of bilateral BC stimulation, though these benefits are generally smaller than those observed, or expected, with AC stimulation (Heath et al., 2022; Janssen et al., 2012), consistent with the pattern observed in the present work.

The position of BC stimulation strongly influences interaural differences and thus the potential for binaural benefit. The present study evaluated BC sound transmitted predominantly via the skull bone, with inner-ear excitation driven mainly by the direct BC pathway (Stenfelt, 2015, 2016). When stimulation is applied closer to the ear canal opening or to the pinna cartilage, the resulting ear-canal sound pressure dominates perception in normal-hearing listeners (Surendran et al., 2023; Nishimura et al., 2015). In such cases, the interaural cues are less degraded than with mastoid stimulation, resulting in binaural performance that more closely resembles that obtained with AC stimulation.

Previous investigations into cancellation of BC cross-head transmission have demonstrated that such approaches can yield improvements in tone detection in noise, speech perception in noise, and sound localization, although the reported benefits have generally been modest and have not reached the level of binaural advantage observed with AC stimulation (Wang et al., 2023b; Barnsley and Culling, 2025; Mcleod and Culling, 2019; Irwansyah and Nakagawa, 2022). The present findings extend this body of work by showing that complete cancellation is not a prerequisite for meaningful binaural benefit. While ideal cancellation would require equal amplitudes and perfectly opposing phases, conditions that are practically unattainable, the current results indicate that partial attenuation is sufficient to substantially improve performance. Specifically, a 5 dB reduction in cross-head transmission produced a clear benefit in speech perception, whereas a 10 dB reduction yielded outcomes approaching those obtained with bilateral AC stimulation.

From a practical perspective, these attenuation levels correspond to relatively tolerant requirements in the estimation of the cross-head transmission function. A 10 dB cancellation can be achieved despite magnitude mismatches of approximately 3 dB or phase mismatches of up to 47°, and a 5 dB cancellation allows for even larger deviations. Although combined magnitude and phase errors reduce the maximum tolerable mismatch, the results suggest that estimating the cross-head transmission within approximately 3 dB and 47°, and applying this estimate to attenuation, would reliably yield at least a 6 dB reduction. According to the present data, such a reduction is sufficient to provide a significant improvement in binaural hearing. These findings imply that cancellation algorithms need not focus on exact point cancellation, but rather on achieving a robust and stable reduction of cross-head transmission under realistic conditions.

The present study implemented a broadband attenuation of cross-head transmission across frequencies. It may be argued that attenuation is primarily critical at frequencies above 1 kHz, where head-shadow effects provide important binaural cues (Barnsley and Culling, 2025). However, cancellation at higher frequencies is inherently more sensitive to small timing errors, as minor delays translate into large phase shifts, making stable attenuation difficult to maintain. In contrast, lower-frequency cancellation is more robust and easier to implement, although the contribution of low-frequency attenuation to binaural BC hearing remains unclear. Determining the relative importance of frequency-specific attenuation, particularly at low frequencies, represents an important direction for future research and may further inform the development of effective bilateral BC systems.