Smart traffic information system transmits information from light source to detector. The most important ability of smart traffic information system is to detect signals including given information with background noise [10, 11]. Traffic light can be used for signal transmission based on vehicle infrastructure system. The network of smart traffic information includes left turn assistant, lane change warning, and precash sensing [3, 12, 13], as shown in Fig. 1.
The SNR is related to the acquired light power, which means that smart traffic information system perform high signal transmission mass with low signal loss. The noise sources of smart traffic information system are critical factors of signal distortion performance.
The LED should be used as signal transmission and lighting application. The illuminance, heatsink temperature and driver parameters of LED systems are highly related to each other. Modelling of the photometric, electric, thermal and colorimetric aspects of white LED devices is proposed [14]. The photoelectrothermal (PET) theory has provided a series studying for the white LED system. There are given technical specifications for LED systems based on Energy Star Program and IEC standards [15, 16]. The proposed new PCLED model considered several factors, such as energystorage and dynamic properties of the phosphor coating. This new model can accurately predict dynamic optical and energy loss in PC LED device [17, 18].
Normally, the illuminance is dependent on the heatsink temperature, voltage amplitude, and bias voltage. The relationship is reflected on the heatsink temperature and illuminance of LED with the constant voltage amplitude and bias voltage as shown in Fig. 2. LED sample is mounted on a temperaturecontrollable heatsink. The illuminance as a function of the heatsink temperature for constant LED voltage amplitude and bias voltage operation is fairly linear. Therefore, the illuminance of LED as a function of the heatsink temperature T_{hs} for constant LED voltage amplitude V_{a,0} and bias voltage V_{b,0} operation can be approximated as a linear relationship.
$$E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)={a}_1{T}_{\mathrm{hs}}+{a}_2$$
(1)
Where α_{1} is a constant representing the slop and α_{2} is another constant. Both α_{1} and α_{2} can be obtained from the measurement in Fig. 2.
Using the Everfine LFA3000 light flicker analyzer system, the practical measurements of the illuminance as a function of the LED voltage amplitude under “constant heatsink temperature and constant bias voltage” operation are obtained and shown in Fig. 3. Therefore, it is can be given as
$$E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)={\beta}_1{V_a}^2+{\beta}_2{V}_a+{\beta}_3$$
(2)
Where β_{1}, β_{2}, and β_{3} are coefficients that can be extracted from Fig 3 with constant heatsink temperature and bias voltage.
Based on the above analysis, E can be obtained as heatsink temperature T_{hs} and voltage amplitude V_{a} with constant bias voltage using a twodimensional mathematical function. Similar modeling method based on the 2D linear behavior has been proposed to [14]. Therefore, the illuminance E can be constructed as in the following
$$E\left({V}_a,{T}_{\mathrm{hs}},{V}_{b,0}\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)}{c_1}$$
(3)
Where c_{1} is intersection values of (1) and (2). It should be pointed out that the model can predict the illuminance of the LED at any heatsink temperature and voltage amplitude with constant bias voltage. Equation (3) links the illuminance to heatsink temperature and voltage amplitude together under constant bias voltage operation.
The illuminance of the LED device is highly related to the bias voltage. To establish the dependence on illuminance E on the bias voltage, the LED device is operated in the bias voltage 1 to 5 V under constant heatsink temperature T_{hs,0} and constant voltage amplitude V_{a,0} operation. Generally, illuminance E obviously increases with bias voltage, as shown in Fig. 4. The theoretical model of the illuminance behavior as quadratic function of the bias voltage is indicated in Fig. 4, as shown in the following.
$$E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)={\chi}_1{V_b}^2+{\chi}_2{V}_b+{\chi}_3$$
(4)
Where χ_{1}, χ_{2}, and χ_{3} are coefficients that can be extracted from the experimental results in Fig. 4.
Combined with (3) and (4), the behavior of the illuminance of the LED is given by 3D nonlinear function, as shown in (5), where c_{2} is the intersection value of function of (3) and (4). It is a model that combines the heatsink temperature T_{hs}, amplitude voltage V_{a} and bias voltage V_{b} aspects of an LED source.
$$E\left({V}_a,{T}_{\mathrm{hs}},{V}_b\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}$$
(5)
The experimental results of the illuminance behavior of the LED are related to bias voltage with constant amplification factors and frequency. It can be seen that illuminance curve is similar with Fig. 4. In practice, the illuminance E is approximately nonlinearly proportional to the bias voltage V_{b} at constant amplification factors A_{f,0} and constant frequency f_{0}, so it can be given as
$$E\left({V}_b,{A}_{\mathrm{f},0},{f}_0\right)={\delta}_1{V_b}^2+{\delta}_2{V}_b+{\delta}_3$$
(6)
Where δ_{1}, δ_{2}, and δ_{3} are coefficients that can be extracted from experimental results of the illuminance as a function of the LED bias voltage with constant amplification factors and frequency.
Figure 5 shows the practical measurements of the illuminance E as a function of the LED amplification factors A_{f,} with constant bias voltage V_{b,0} and constant frequency f_{0}. Therefore, the illuminance can be expressed as
$$E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)={\varepsilon}_1{A}_{\mathrm{f}}+{\varepsilon}_2$$
(7)
Where ε_{1} and ε_{2} are coefficients that can be extracted from Fig. 5.
Based on the above analysis, E can be related to amplification A_{f} and bias voltage V_{b} using a twodimensional function. Combined (6) and (7), illuminance of the LED device with bias voltage and amplification factors with constant frequency can be given as
$$E\left({A}_{\mathrm{f}},{V}_b,{f}_0\right)=\frac{E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_3}$$
(8)
Where c_{3} is intersection values of (6) and (7). It should be pointed out that this model can estimate the illuminance variation of the LED at any bias voltage and amplification factors with constant frequency. Equation (8) links the illuminance to bias voltage and amplification factors together.
Figure 6 shows the practical measurements of the illuminance E as a function of the LED frequency f with constant bias voltage V_{b,0} and constant amplification factors A_{f,0}. Therefore, the illuminance can be expressed as
$$E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)={\mu}_1{f}^2+{\mu}_2f+{\mu}_3$$
(9)
Where μ_{1}, μ_{2}, and μ_{3} are coefficients that can be extracted from the practical measurements of the illuminance as a function of the frequency with constant amplification factors and bias voltage, as shown in Fig. 6.
Combined with (8) and (9), illuminance of the LED device with bias voltage, amplification factors and frequency can be given as
$$E\left({A}_{\mathrm{f}},{V}_b,f\right)=\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}$$
(10)
Where c_{4} is intersection values of function of (8) and (9). It should be pointed out that this equation can estimate the illuminance of the LED at any bias voltage, amplification factors and frequency. Equation (10) links the illuminance to bias voltage, amplification factors and frequency together.
Combined with (5) and (10), the illuminance as function of the LED device with fivedimensional parameters can be determined as
$${\displaystyle \begin{array}{l}E\left({V}_a,{T}_{\mathrm{hs}},{V}_b,{A}_f,f\right)=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}\right]}{c_5}\\ {}=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a}},{V}_{\mathrm{b}}\right)}{c_2}\frac{E\left({A}_{\mathrm{f}},{V}_b,f\right)}{c_4}\right]}{c_5}\end{array}}$$
(11)
Therefore, the overall illuminance of a mixed white LED device E_{t}(V_{a,t},T_{hs,t},V_{b,t},A_{f,t}, f_{t}) with a cool white LED and a warm white LED is shown as Eq. (12)
$${\displaystyle \begin{array}{l}{E}_t\left({V}_{a,t},{T}_{\mathrm{hs},\mathrm{t}},{V}_{b,t},{A}_{f,t},{f}_t\right)={E}_c\left({V}_{a,c},{T}_{\mathrm{hs},\mathrm{c}},{V}_{b,c},{A}_{f,c},{f}_c\right)+{E}_w\left({V}_{a,w},{T}_{\mathrm{hs},\mathrm{w}},{V}_{b,w},{A}_{f,w},{f}_w\right)\\ {}=\frac{\left[\frac{E_c\left({T}_{\mathrm{hs},\mathrm{c}},{V}_{\mathrm{a},\mathrm{c}},{V}_{\mathrm{b},\mathrm{c}}\right)}{c_{2,\mathrm{c}}}\frac{E\left({A}_{\mathrm{f},\mathrm{c}},{V}_{b,c},{f}_c\right)}{c_{4,\mathrm{c}}}\right]}{c_{5,c}}+\frac{\left[\frac{E_w\left({T}_{\mathrm{hs},\mathrm{w}},{V}_{\mathrm{a},\mathrm{w}},{V}_{\mathrm{b},\mathrm{w}}\right)}{c_{2,\mathrm{w}}}\frac{E\left({A}_{\mathrm{f},\mathrm{w}},{V}_{b,w},{f}_w\right)}{c_{4,\mathrm{w}}}\right]}{c_{5,w}}\end{array}}$$
(12)
Where Φ_{c}(V_{a,c},T_{hs,c},V_{b,c},A_{f,c},f_{c}) is individual illuminance of the cool white LED and Φ_{w}(V_{a,w},T_{hs,w},V_{b,w},A_{f,w}, f_{w}) is individual illuminance of the warm white LED.
Several important observations should be pointed out from Eq. (12):

(1)
Equation (12) relates the illuminance to the heatsink temperature T_{hs}, frequency f, amplitude voltage V_{a}, bias voltage V_{b} and amplification factors V_{f} altogether. It is an equation that integrates the heatsink temperature and driver parameters of the LED device altogether.

(2)
LED device manufactures can use heatsink temperature T_{hs}, frequency f, amplitude voltage V_{a}, bias voltage V_{b} and amplification factors V_{f} in Eq. (12) to quantify the overall illuminance of a mixed white LED device. This new equation quantitatively sums up the relationship of illuminance, heatsink temperature T_{hs}, frequency f, amplitude voltage V_{a}, bias voltage V_{b} and amplification factors V_{f.}

(3)
The required parameters of the proposed model are calibrated from a series of measurement as shown in Figs. 2, 3, 4, 5, and 6.