Concave Curvilinear WDRC: Optimizing the Shape of Compression

Cochlear sensorineural hearing loss manifests itself by a shift of hearing threshold and by a reduction of the ear’s dynamic range known as recruitment. Most advanced hearing instruments use wide dynamic range compression (WDRC) to compensate for recruitment. Concave curvilinear compression is designed to provide enhancements in WDRC processing, with the aim of improving the normalization of loudness perception.

Normal “Linear” WDRC Processing
he basic compensation for hearing threshold shift is the provision of amplification. In principle, it is possible to fully compensate the shift in hearing threshold by providing amplification equal to the amount of the shift. However, at very loud levels, the amplification must be reduced in order not to exceed the Uncomfortable Loudness Level (UCL). WDRC is designed to vary the amplification as a function of the input sound level. By using WDRC, it is possible to provide optimal gain at each input level. It is also possible, in principle, to restore the loudness perception of the hearing-impaired individual to the same perception as that of a normal-hearing person.

Fig. 1. Example of a standard “linear” WDRC input-output curve. The output, gain and compression ratio are shown as a function of input level. The broken light line is the zero gain line. The WDRC compressor is set at a kneepoint of 40 dB SPL and compression ratio of 2.7:1.

WDRC can be visualized by an input-output curve as shown in Fig. 1. This figure shows the amplified output as a function of the input sound level. In this example, the maximum gain is 35 dB at soft sounds below 40 dB SPL. Above an adjustable kneepoint (shown at 40 dB SPL), the gain will gradually decrease. The rate of change of the output level is given by the compression ratio (CR= dx/dy) which, in this example, is equal to a factor of 2.7:1. The corresponding gain and compression characteristics are also shown in Fig. 1.

In general, a compressor is called WDRC when the compressor kneepoint can be set as low as the average level of soft speech: 45 dB SPL or less. Additionally, it must be possible to set the compression ratio at several ratios between 1:1 and 4:1 in order to be able to compensate for different levels of recruitment.

Upon examination of the cochlea’s own “compressor,” it can be seen that compression ratios above 4:1 are not generally needed (this will be discussed later). Within the control range of WDRC, the compression ratio is a constant. WDRC with a constant compression ratio can be termed “linear” WDRC. Most WDRC systems provide “linear” compression, which means that the input/output (I/O) curve is a straight line with a constant compression ratio that will not change by level in the normal operating range from soft to loud sounds. Note that normal “linear” WDRC is still a type of non-linear signal processing.

Curvilinear Compression and Loudness Perception
The standard linear WDRC input-output curve is a first approximation of the “optimum” compression shape. This shape can be derived by looking at the effects of recruitment on loudness perception and by looking at the physiological mechanisms of the natural cochlear compressor.

Loudness scaling is a procedure that gives insight into the perception of loudness of individuals with hearing loss. By comparing results from the hearing-impaired person with data for normal-hearing persons, any loudness perception problems will be identified, not only at threshold and UCL, but throughout the range of hearing levels.

Extensive study on loudness perception has been done since the early years of psychoacoustics, including landmark work in the 1930s by Fletcher & Munson.¹ These studies have been the basis for the loudness unit named “sone” as defined in 1971. Each doubling of loudness corresponds to a doubling of the number of sones. One sone refers to the loudness of 40 dB SPL at 1 kHz for normal-hearing persons.

In most cases, an abnormal loudness perception due to sensorineural hearing impairment is caused by a loss of inner and outer hair cells in the cochlea. The ratio between inner and outer hair cell loss determines the shape of the impaired loudness curve. Normal and abnormal loudness function can be calculated by using a model for loudness perception as developed by Moore & Glasberg.² This model has been derived from a cochlear model and has been validated by experimental loudness data.

Fig. 2. Loudness as a function of input level for the normal ear (dark line) and the impaired ear (thin line), having 80% hearing loss attributed to outer hair cell loss. The arrows show the required amplification.

Fig. 2 shows the loudness function at 1KHz for a person with normal hearing compared to that for a person with a typical cochlear hearing loss. This hearing loss corresponds to a loss of 40 dB where 80% is caused by the loss of outer hair cells and 20% by the loss of inner hair cells.

Fig. 3. Amplification characteristics corresponding to the hearing loss shown in Fig. 2. The solid line represents the “optimal” curvilinear amplification as given by the arrows in Fig. 2. Also shown is linear compression (broken line), as well as the output, gain and compression ratio as a function of input level.

The difference between the impaired and normal loudness curve is the amplification required for restoring normal loudness perception. The corresponding “optimal” amplification curve is shown in Fig. 3. Note that this input-output curve is not a straight line, but has a curved shape. The type of curvature is concave or “hollow” as opposed to a convex shape. Accordingly, the required compression can be called concave curvilinear compression.

The corresponding gain and compression ratio are also shown in Fig. 3. Like the I/O curve, the gain curve also shows the concave shape. From the compression curve, it is seen that compression varies from a ratio of 3:1 at soft sounds to a ratio of near unity (CR=1:1) at loud sounds. This reduction from high to low compression ratio is characteristic for the concave shape of curvilinear compression. Notice also that no compression is needed at high sound levels, as has been reported in many patient cases. This has also been applied in the past in several circuits, such as the K-AMP.³

Cochlear Compression
The shape of the cochlear compressor also lends support to selecting concave curvilinear as the optimal compressor shape. Cochlear compression is the natural mechanism to increase the sensitivity of hearing. This natural compressor originates from the activity of the outer hair cells.

It is generally accepted that the inner hair cells convert the sound/vibrations of the basilar membrane into a sensorineural signal, which is then transferred to the brain. However the inner hair cells alone are not sensitive to sound vibrations below 50-60 dB SPL. In order to increase the sensitivity to soft sounds, the outer hair cells come to the assistance of inner hair cells by performing an active amplification process. By this manner, the vibrations of the basilar membrane itself are boosted, such that very soft levels near the normal threshold of hearing (approaching as low as 0 dB SPL) can be perceived. This mechanism is depicted in Fig. 4, giving the input-output diagram of the cochlear compressor as based on a model by Moore & Oxenham.⁴

Fig. 4. Response of basilar membrane as a function of input level, according to a model by Moore & Oxenham.4 The light straight line corresponds to a cochlea having inner hair cells only; the curved heavy line corresponds to the intact cochlea having outer and inner hair cells. At medium sound levels the compression reaches a maximum of about 4:1 (light dashed line). The arrows indicate the required gain to compensate for a hearing loss of outer hair cells.

In Fig. 4, the light straight line represents the activity of the cochlea when only the inner hair cells are present. It shows that only input levels above 55 dB will be above threshold and can be mapped on the audibility range of the sensorineural system. The thick curved line shows the activity for a cochlea having both inner and outer hair cells. It is seen that, near 0 dB input, the vibrational and neural activity are amplified, such to bring it above hearing threshold. This is represented as a curved line which has a maximum compression ratio of 4:1 at medium level sounds, changes to a ratio of near 1:1 for very loud sounds, then to a ratio of 1.6:1 for very soft sounds. In the case of cochlear sensorineural hearing impairment, the actual curve will be determined by the individual combination of inner and outer hair cell loss.

Fig. 5. Amplification characteristics corresponding to the hearing loss of Fig. 4 and based on the cochlear compression model. The thick curved line represents the ideal curvilinear amplification, as indicated by the arrows of Fig. 4. Also shown is linear compression (straight thin line).

According to this premise, a hearing impairment can be compensated for by providing a level-dependent amplification as denoted by the arrows. The derived input-output curve shows a concave shape, as shown in Fig. 5. The compression ratio is about 2:1 for soft sounds, increasing to a maximum of 4:1 at medium levels, and decreasing to 1:1 at very loud sounds. Accordingly, the input-output curve is not a straight line as for “linear” WDRC, but indeed has a concave curvilinear shape, much the same as seen in Fig. 3 based on the loudness model data.

Completing the Curvilinear Compression System
Figs. 3 and 5 provide two examples of curvilinear compression, having the appropriate concave shape for the specified type of hearing loss. This shape is of importance to optimally control loudness of the daily life soft-to-loud sounds. However, when dealing with very soft and very loud sounds, additional effects must be taken into account.

• MPO compression: MPO compression is a basic and widely known compression mechanism used to protect the ear from loud sounds that would otherwise exceed the UCL. WDRC compressors work in reference to input signals and are intended to restore loudness perception. MPO compression works in addition to WDRC compression and is intended to protect the ear from excessive output sound levels.

The need for MPO compression can be demonstrated physiologically. The natural stapedius reflex compression system normally operates at sound levels that exceed 80-90 dB HL. By contraction of the stapedius muscle, the stapedial vibration mode is changed (into a stapedius tilt movement instead of a piston-like movement), thereby reducing the energy flow into the cochlear system. However, due to hearing impairment, the threshold of the reflex will also shift to higher levels. This may cause a potential danger to the cochlear system, since it may aggravate the hearing impairment not only in magnitude but also by spreading the hearing loss to undamaged areas of the cochlea. Thus, for a safe compensation of hearing loss, it may be advisable to include a separate MPO compressor that compensates for the shifted activation level of the stapedius reflex.

Fig. 6. Example of MPO compression and “expansion function”: Curvilinear compression with MPO compression at 105 dB SPL output level and noise silencer (expansion) below 30 dB SPL input level. The broken line is standard WDRC with a kneepoint of 35 dB SPL without MPO compression and without expansion.

Fig. 6 shows an example of the implementation of a practical combination of the concave curvilinear WDRC system, with a separate MPO compressor for the very loud sounds and an expansion system (see next section) for the very soft sounds. The MPO compressor system consists of a separate output compressor (AGC-O) with a kneepoint that can be adjusted to the required output level. This level should correspond closely to the individual UCL. By providing a very fast attack time (1-10 ms), it is designed to react to rapidly changing signals. In some ways, this might even be seen as an improvement over the normal stapedius reflex which needs up to 100 ms to react. By applying this fast reaction, the MPO compression is designed to add extra listening comfort with respect to sudden loud sounds like slamming doors or impulse-type sounds like that of clanking kitchenware.

The MPO compressor is always positioned at the output stage of a hearing instrument. In this way, it works independently of a possible slow-acting WDRC compressor, noise suppression circuit(s) and manual volume control changes. The MPO compressor can operate in a wideband mode, but variants of two or more bands are also possible. A multiband MPO system can be adjusted more precisely to varying UCL levels with frequency. Additionally, a multiband MPO compressor system can react independently to band-limited loud sounds, without suppressing gain in the other frequency band(s).

• Noise silencers (Expansion): It is known that WDRC low-kneepoint compressor systems can be perceived as being noisy in quiet environments. This is due to the large amount of amplification provided at low levels, even when the gain is limited by using a compressor kneepoint below which the amplification is linear.

This large gain may exaggerate the perception of soft sounds. To compensate for this, the gain can be reduced for as long as the soft sounds (and only the soft sounds) are present. This is an extension of the WDRC compressor concept also known variously as “expander”, “expansion”, “noise silencer” or “soft noise suppression” functions. It is realized by applying an expansion circuit in which the gain is reduced by, for instance, 10 dB at low input levels, and growing (expanding) to the nominal compressor gain at (adjustable) input levels between 35-50 dB SPL. This expansion action is shown in Fig. 6. Below the expansion kneepoint, the compression ratio is less than unity (e.g., CR=0.5:1). An additional benefit is that internal microphone noise is suppressed and (sub-oscillatory) feedback due to large loop gains is reduced. This type of noise suppression is designed to add substantially to the listener’s comfort.

• Convex curvilinearity: The general definition of curvilinear compression says that the input-output compression shape is not a straight line (linear). Instead, it has a shape that may have any curvature, which means that the compression ratio is not a constant but varies (usually gradually) with input level. The resulting shape can be concave, as advocated in this article, but in principle the curve can be reversed to give a convex shape. A convex type of compression is best applied when the MPO compression must be integrated with the WDRC input-compressor. In this way a separate MPO compressor can be omitted. An example of such a convex curvilinear compressor (in contrast to the concave shape in Fig. 6) is shown in Fig. 7.

Fig. 7. Curvilinearity and MPO. Shown are concave curvilinearity with expansion and MPO compression in comparison with convex curvilinearity. The convex curve limits the output by the convex compression shape which gradually increases the compression ratio. The concave curve reduces compression with increasing input levels, as does the natural cochlear compressor. At high output levels, an independent MPO compressor, utilizing a high compression ratio, is used to protect the ear.

With a convex curvilinear shape, the compression ratio increases with growing input level. As a result it provides protection at very loud input levels. However, such an input-related convex curvilinear system with integrated UCL protection has a number of drawbacks:

• With a convex shape, the compression ratio will increase with input level. Loudness restoration and cochlear compression require a concave shape that reduces compression with input. A high compression ratio is required only at very high output levels for protection against loud sounds.
• The UCL protection of a convex shape is reacting on the input signal level, without any guarantee that it will limit the actual output near UCL. Therefore, it may not be suitable for a hearing instrument with a manual volume control.
• The protection near UCL of the convex shape is linked to the relative slow timing of WDRC input compression, instead of fast-acting compression as is required for protection against potentially dangerous impulse-like sound levels.

Note in Fig. 7 that the concave curvilinear system closely corresponds to the required curve of Figs. 3 or 5, whereas the convex curvilinear curve largely deviates from the required compression that can be derived from the loudness and cochlear compressor arguments.

Practical Considerations
In principle, the concave curvilinear shape can be optimized for each individual hearing impairment. However, we lack the availability of accurate clinical diagnostic methods that can determine the ratio of inner or outer hair cell loss or that can accurately measure the individual loudness characteristics. Therefore, in practice, a standard set of concave curvilinear curves is used. With a set of standard curves, the amount of curvilinearity is based on an average ratio of inner and outer hair cell loss, common for most types of sensorineural hearing losses, depending on the hearing thresholds. For some special types of losses, a different shape can be more appropriate. Future studies will be required to diagnose and to determine the optimal shape for these types of hearing losses.

At present the new NAL non-linear fitting rationale (NAL-NL)⁵ also displays a compression characteristic having a curvilinear shape. The amount of concave curvilinearity is roughly comparable to the degree shown in Fig. 3.

Categorical Loudness Scaling
The individual loudness growth curve can also be measured clinically by categorical loudness scaling methods like VIOLA, LGOB, the European “Würzburger Hörfeld Skalierung” method and others. In these methods, the vertical scale is denoted by categorical phrases like “very loud,” “comfortable” and “very soft.” The required gain curve, in principle, can be calculated as the difference between the responses of normal-hearing and hearing-impaired listeners. A concave curvilinear input-output curve will be obtained similar to that of Fig. 3 or 5. It should be noted, however, that an individual loudness-scaling test will have insufficient accuracy to demonstrate the curvilinear shape. This is due to the relatively large scaling errors, adaptation and bias effects which vary greatly per individual. (Author’s Note: Loudness scaling data for large groups of normal-hearing and hearing-impaired people have been the basis for validating the models referred to in this article. Of course, the limited accuracy of the individual loudness tests should not necessarily exclude the use of individual loudness measurements for diagnostic and research purposes.)

While the above-described concave curvilinear compression system, including a separate MPO compression and expansion system, pertain to the Beltone Digital hearing instrument series and the Philips SpaceLine Multi-Mode-Compression hearing instrument system⁶, several other digital hearing instruments also offer the option to choose a curvilinear compressor shape in concave and/or convex variants, as well as other features similar to those described in this article.

This article was submitted by Marcel Vlaming, PhD, director of the Audiological Competence Centre at Beltone Netherlands, BV, Eindhoven, The Netherlands. Correspondence can be addressed to HR or Marcel Vlaming, Beltone Netherlands BV, Hurksetraat 42, 5652 AL Eindhoven, The Netherlands; email: [email protected].

References
1. Fletcher H & Munson W: Loudness, its definition, measurement, and calculation. J Acoust Soc Amer 1933; 5: 82-108.
2. Moore B & Glasberg B: A model of loudness perception applied to cochlear hearing loss, Auditory Neuroscience 1997; 3: 289-311.
3. Killion M: The K-Amp hearing aid, Amer Jour Aud 1993; 2 (2): 52-74.
4. Moore B & Oxenham A: Psychoacoustic consequences of compression in the peripheral auditory system. Psychological Review 1998; 105 (1): 108-124.
5. Dillon H: NAL-NL1: A new procedure for fitting non-linear hearing aids. Hear Jour 1999; 52(4): 10-16.
6. Vlaming M & Garcia H: SpaceLine in depth. Philips technical brochure, Eindhoven, The Netherlands: Beltone BV, 1999.