Sound Cues and Horizontal Plane Localization
There are different sound cues we naturally learn to be able to localize sound sources.
These cues may be related to the sound energy (amplitude) and to the time or frequency domains.
One that quickly comes to mind is the interaural time difference (ITD), which "is the difference in arrival time of a sound between two ears".
Also, there is its amplitude counterpart, interaural level difference (ILD), but they won't serve us well in the proposed scenario of single-sided deafness (SSD).
However, they are usually accompanied with another cue, which is filtering, due to sound diffraction around the head.
In classical physics, diffraction is explained by the Huygens-Fresnel principle1.
Put in a practical way, since wavelengths that are relative large compared to the size of head will be able to "go around it", the spectral content of low frequencies will be better preserved between ears, while high frequency content will be attenuated.
Also, important filtering happens around the pinna.
On this way, without ITD and ILD because of the single-sided deafness, the high frequency sounds are easier to localize than the low frequency ones, as pointed in the paper by Agterberg et al. brought by @Noil.
Median Plane Localization
ITD, ILD and the filtering resulted from diffraction around the head are useful for horizontal plane localization; if the sound source is horizontally centered in relation to the receiver, i.e. it is on the median plane, the sound arrives at both ears, ideally, at the same time, with same levels and filtering.
The diffraction from the pinna is then important to the sound localization at the median plane and single-sided deafness (SSD) is less of a hindrance.
However, it is important to keep in mind the Blauert's "determining frequency bands" effect, which is commented, for example, in Psychoacoustics2 (a main reference in the field).
The effect states that some frequency bands, regarding the median plane, will always be perceived as coming from a specific orientation.
There are more recent studies referring to Blauert's original paper that confirmed the effect for some of the frequencies.
Distance
The Wikipedia page on sound localization seems relatively complete on the whole matter.
Regarding the list of sound distance cues, only the last two (ILD and moving sound sources, depending on the scenario) appear to be affected by SSD (this is more of a personal thought/analysis, though).
There Are Many Variables Involved
As from the Wikipedia page on the sound distance cues, let's take the direct/reflection cues.
If in a room, there may be a close speaker and a resulting clear speech, as also a distant speaker and less intelligible speech due to reflections.
Also, voice timber changes if the speaker is speaking either quietly or loudly.
These, accompanied with the arriving sound level and ambient noise, help determine if the speaker is close or far away (apparently independently of SSD).
It is relatively easy to imagine some of these scenarios, but speech is something we're very familiar with.
So knowing the sound already, having an expectation or experience, may influence our perception.
Also, we move and turn our heads when trying to localize the sound source.
In summary, depending on the matter, I think it's important to think on real life scenarios and that there may be a lot of variables involved.
Headphones
If in a virtual reality environment, there seems to be no need for extra speakers as is usual to convolute the original/dry signal with an appropriate HRIR3 (head related impulse response), which applies the sound cues we talked about depending on source-receiver orientation.
Also, technology that understands head movements and changes the HRIR accordingly would be of great benefit.
It is important to keep in mind, though, that different people have different personal HRIRs and things like how the headphones couple on someone's head may interfere in the final perception.
Auditory System
@Noil already talked about how the sound that gets into the inner ear is a single signal (independently if there are multiple sound sources and from different directions).
However, I'd like to point out that yes, there are multiple receptors in a latter stage.
The basilar membrane, inside the cochlea, vibrates differently depending on frequency, causing differences on the excitation of the multiple hair cells that send electrical signals to the brain.
Not Hyperlinked References and Notes
- Wikipedia page on diffraction.
- Fastl, H.; Zwicker, E. Psychoacoustics: Facts and Models. 3 ed. Springer. 2007. p. 310.
- HRTF is the frequency domain dual of the HRIR and is where Wikipedia redirects to.