# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 3 Coding of Stereo Signals
### Generalization to Coding of Multi-Channel Audio  
The next evolutionary steps after coding of two-channel stereo signals are coding of _multi-channel (surround) audio_ (e.g., 5.1 or 7.1) [48] and coding of _3D audio_ (e.g., 5.1 + 2 height (H), 7.1 + 4 H or 22.2) [49; 50]. While the number of loudspeakers grows tremendously along this path, the relevant psychoacoustic considerations still remain the same, since human auditory perception is based on reception of two ear signals, where the ears are positioned on the left and right side of the head. For these reasons, the perception of surround and 3D sound is based on a set of cues with different dominance:  
* Left/right perception: The most important (and thus most sensitive) aspect of spatial sound relates to the perception of the left/right distribution of auditory events relative to the listener's head, since this is directly represented by inter-aural (binaural) cues, i.e., ILD, ITD, and ICC, as they originate from the HAS's differential analysis of the two ear signals. Thus, in order to deliver excellent audio quality, these aspects of surround and 3D sound have to be represented most carefully by audio codecs. * Front/back perception: Compared to left/right perception, front/back perception is much less dominant, since it cannot rely on inter-aural difference cues but has to exclusively evaluate spectral colorization in the ear signals, as described in [PERSON]'s concept of _directional bands_[51]. The effect of directional filtering of the incoming signals (i.e., spectral coloration according to the angle of coincidence) is a comparably weak auditory cue as compared to inter-aural difference based cues, and consequently psychoacoustic studies indicate a high tendency for front/back confusion in 2D and 3D localization experiments. More generally, locations with identical left/right cues form so-called _cones of confusion_[51], within which differentiation between candidate locations on the same cone of confusion has to rely solely on the (weak) directional filtering cues. Thus, for audio coding this means that front/back localization aspects of surround and 3D signals have to be preserved less accurately than left/right aspects, since distortions are less likely to be perceivable. * Elevation perception: Very much like front/back perception, elevation perception on the same cone of confusion is exclusively based on (weak) directional filtering cues, and thus the related signal aspects have to be handled less accurately than left/right aspects. Considering this psychoacoustic background, a number of approaches for joint coding of surround and 3D sound have been proposed. The simplest strategy is to apply traditional M/S stereo coding to multiple left/right pairs of the audio input. As an example, for coding of 5.1 audio, the left and right front channel form an M/S channel pair and the corresponding surround channels form a second one. For coding of 5.1 + 4H, the corresponding height channels form pairs as well. The center channel is not included into any joint stereo processing. This approach is implemented in multichannel AAC [17; 31] and later generations of multichannel-enabled MPEG-4 audio codecs. It addresses the above-mentioned aspects of left/right perception and successfully prevents ICC distortions (and thus BMLD-type artifacts) in the spatial sound image. Other strategies for coding of surround and 3D sound employ generalizations of intensity stereo coding, which are addressed in the section on parametric audio coding. In the context of 3D audio coding, a hybrid approach between M/S channel pairs and parametric coding of associated height channels can be found in previous studies [19; 52] under the name Quad-Channel-Element (QCE). A further extension of the M/S coding approach conceived for use in 3D audio coding is called the Multichannel Coding Tool (MCT) [53].