Symbol error rate analysis for colour-shift keying modulation in visible light communication system with RGB light-emitting diodes

The symbol error rate (SER) is investigated for colour-shift keying (CSK) modulation in visible light communication system with red/green/blue LEDs. A new concept of pseudo signal-to-noise ratio is proposed to illustrate the relationship between the signal power and the noise power since the traditional electrical signal-to-noise ratio fails to capture the properties of CSK signals. The authors map the three-dimensional (3D) signal space of CSK signals to a 2D plane because the decision region of constellations in 2D space is easy to analyse and is proved to be equivalent to that of 3D signal space. The symbol error probability for a certain constellation is calculated as the summation of the probabilities of the received signals lying outside the decision region. As the SER is formulated as the weighted sum of error probabilities for all constellations, an analytical expression for SER is derived for certain constellation distribution. Moreover, a general formula for 22n -CSK modulation is derived by exploiting the distribution regularity of 4CSK and 16CSK. The SER expression for CSK modulation is evaluated approximately using the numerical Gaussian formula. Simulation results show that the analytical expression can predict SER performance accurately.