  This paper analyses the statistics of the clipping noise in orthogonal
frequency-division-multiplex (OFDM) based visible light Communication systems.
The clipped signal is generally modelled as the summation of the scaled
original signal and clipping noise, which is treated by the linear equalizer in
the receiver. Generally, it is assumed that the clipped and original signal
share the same statistics. Although valid in some cases, we show that such
assumption is invalid when the transmitter is tightly constrained. We derive
closed-form probability distribution function (pdf) for the clipping noise and
use the pdf for statistical hypothesis testing in an optimum receiver
