Color-Shift Keying—How Its Largest Obtainable “Minimum Distance” Depends on Its Preset Operating Chromaticity and Constellation Size

Color-shift keying (CSK) is a type of visible light wireless communication, where a visible color is preset and is to appear constant during the human vision's “critical flicker fusion threshold” and “critical color fusion threshold.” This paper is first in the open literature to systematically investigate how CSK's largest achievable “minimum distance” (d
_min
) would vary with the preset chromaticity and with the constellation size (M). This paper discovers this elegant approximation: The best d
_min
≈ 1.921 M
^-0.5985
- 2.736M
^-0.645
(x̃
²
+ ỹ
²
)
^0.7802
(log
₂
M)
^-0.436
, where (x̃, ỹ) refers to the preset chromaticity's displacement (in a two-dimensional space) from the case of all LEDs emitting with an equal intensity.