*2.1. Water Turbidity Measurement*

For water turbidity measurement, assume that **y***t* is the sampled version of the received signal *y*(*t*) at a sampling rate of *ft* and window size of *Nt*-point. The root mean square (RMS) value of **y***t* can be computed as

$$\mathbf{y}\_{\text{RMS}} = \sqrt{\frac{\mathbf{y}\_t \mathbf{y}\_t^T}{N\_t}} \tag{3}$$

Assume that *y*0 is the reference RMS value of transparent water. The di fference between *yRMS* and *y*0 can then be calculated as

$$
\Delta\_{RMS} = \mathcal{Y}\_0 - \mathcal{Y}\_{RMS} \tag{4}
$$

Notably, Equation (4) is the attenuated power energy caused by the attenuated light path through the turbid water. The proposed system applies Δ*RMS* to measure water turbidity.
