**VLC SYSTEM MODEL SISO**

- SISO: Single Input Single Output

In this section, we describe the Single Input Single Output VLC system and discuss the parameter of the VLC link. First, we consider the LOS link between the single transmitter and the receiver. The link configuration is shown in (fig1) [1].

Where θ is the angle of incidence with respect to the axis of the receiver surface. Ҩ is receiver’s FOV. At transmitter side viewing angle (Irradiance) with respect to transmitter surface is Ø and transmitter FOV is ɸ. Lambertian emission defined as m [11].

Optical concentrator gain of the receiver [2] defined as.

VLC channel gain for LOS link determined by HLOS is,

Where 𝑅0(Ҩ) is [11],

𝑅0(Ҩ)=(𝑚+1)/(2∗𝜋)*𝑐𝑜𝑠2(∅) [4]

Where 𝐴𝑝𝑑 the collection area of the receiver is, 𝑑2is the distance from the transmitter to the receiver. θ is the angle of incidence on the receiver and Ҩ is the receiver’s FOV. For SISO system we have to consider only one LOS link so at receiver side only one channel gain calculated. A received signal is given by [2]

𝑅𝑥 = R∗𝑃𝑡∗HLOS + √σ2 [5]

Where R is the photodiode responsively. Pt is transmitted optical power and σ2 is the mean square noise current of a receiver. Transmitted power is defined as [11]

𝑃𝑡=𝑃𝐿𝐸𝐷∗𝑅0(Ҩ) [6]

Where PLED is, the power emitted by LED. Received data is recovered using the inverse of HLOS as [2]

𝑅𝑟𝑒𝑐𝑜𝑣𝑒𝑟𝑒𝑑=𝑅𝑥∗𝐻𝑇 [7]

Received power 𝑃𝑟 depends upon the filter transmission 𝑇𝑠(𝜃) and concentrator gain. Ideally, concentrator gain and transmission filter are considered as 1 [2].

𝑃𝑟= 𝑃𝑡∗𝐻𝐿𝑂𝑆∗g(𝜃)∗𝑇𝑠(𝜃), 0≤θ≤Ҩ [8]

SNR depend upon the photodetector responsivity R, received optical power and noise variance. SNR is [2]

SNR = (𝑅𝑃𝑡)2/𝜎𝑠ℎ𝑜𝑡2+𝜎𝑡ℎ𝑒𝑟𝑚𝑎𝑙2 [9]

Shot noise is photon generated noise in the detector by received signal and calculated as [1]

𝜎𝑠ℎ𝑜𝑡2=2𝑞𝑅𝑃𝑟𝐵 [10]

Thermal noise is given by [1],

𝜎𝑡ℎ𝑒𝑟𝑚𝑎𝑙2= 4𝐾𝑇𝐵𝐹𝑅𝑡 [11]

BER depends on the modulation scheme and SNR of the system. Where Q is a function that depends upon the modulation scheme which used.

BER = Q√𝑆𝑁𝑅 [12]