Fundamental Channel Characteristic Comparison of Distinct LED Beams-Based Outdoor Free Space Optical Communications for 6G Wireless Networks

Abstract

In upcoming 6G era, free space optical wireless communications (FSOC) are viewed as promising enabling techniques for backhaul and access of next-generation wireless networks. Channel modeling and characterization is the essential composition to predict FSOC system performance and feature, especially for outdoor application. Objectively, light emitting diodes (LED) are the popular and cost-efficient optical sources for short- and middle-range outdoor FSOC links. Up to know, the concerned LED beams are assumed to follow the well-known Lambertian radiation patterns for outdoor FSOC domain, which actually ignore the diversity and effect of the non-Lambertian radiation patterns of the commercially customized LEDs. For addressing the above issue, typical LUXEON Rebel non-Lambertian optical beam is adopted to configure the distinct LED beams-based outdoor FSOC links. Numerical results illustrate that more dispersive horizontal coverage characteristic could be derived from the LUXEON Rebel non-Lambertian FSOC links.

1. Introduction

Thanks to the impressive advantages in ultra-high capacity, abundant optical spectrum resource, low latency, electromagnetic interference free and reliable security, free-space optical wireless communications (FSOC) are considered and investigated as one promising enabling technique for the upcoming 6G wireless networks [1, 2, 3, 4, 5]. Specifically, the FSOC has been consistently explored in various outdoor application scenarios including wireless backhauls, drone communications, vehicle communications, satellite communications, and emergency communications. Due to the harsh optical signal propagation condition, the actual performance of FSOC is significantly affected by the outdoor optical channel characteristics in distinct application scenarios. Up to know, most works are limited to the investigation of outdoor long range, even ultra-long range FSOC channel characterization and performance optimization, which to a large extent ignore the research and exploration of middle- or short-range FSOC, especially the promising Internet of Things (IoT) scenarios [6, 7, 8, 9, 10].

Unlike the popularity of laser diode (LD) in the long-range FSOC domain, the light-emitting diodes (LED) are more frequently adopted in the middle- or short-range FSOC, thanks to its low cost, safety, and ubiquity [11, 12, 13, 14, 15, 16]. At the same time, it must be noted that the current LED-based FSOC works are still restricted to the Lambertian optical beam configuration, which obviously could not touch or present the link performance of FSOC using distinct non-Lambertian LED source [11, 12]. For addressing this fundamental challenge, to the best of our knowledge, for the first time, the LUXEON Rebel non- Lambertian LED source beam is proposed to configure the outdoor FSOC links, as shown in Figure 1. Moreover, the key performance metrics are comparatively analyzed for the channel characteristics of envisioned non-Lambertian outdoor FSOC and the baseline outdoor Lambertian FSOC.

Figure 1.

Typical outdoor FSOC link horizontal configuration.

2. Channel modeling of outdoor FSO communications

In this part, the typical non-Lambertian FSOC links is explored in typical outdoor scenario, as shown in Figure 1 for the first time.

2.1 Case 1 of benchmark Lambertian FSO communications

As the benchmark outdoor link configuration of FSOC, the Lambertian LED source is utilized at the optical transmitter. For the purpose of clarity, the respective Lambertian optical beam could be profiled by the angle-dependent radiation intensity as [1, 12]:

$$I_{\mathrm{L}}\left(\theta \right)=\frac{m_{\mathrm{L}}+1}{2\pi }{cos}^{m_{\mathrm{L}}}\left(\theta \right)$$E1

where mL is related to the order of Lambertian with half power at φ1/2, and θ is the angle of irradiance with respect to the axis normal to the transmitter surface, while the typical 3D spatial radiation pattern of Lambertian optical beam for horizontal FSOC link is shown in Figure 2a. Accordingly, the optical intensity channel gain H(S^Lam, R) between the Lambertian source S^Lam and the optical receiver R can be expressed by [12, 14, 15, 16]:

Figure 2.

3D spatial radiation patterns of (a) Lambertian optical beam and (b) typical non-Lambertian optical beam for outdoor horizontal FSOC links.

$$H\left(S^{\mathrm{Lam}},R\right)=\left\{\begin{array}{l}\frac{A_R}{d_0^2}{I}_{\mathrm{L}}\left(\theta \right)cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},0\le \psi \le \mathit{FOV}\\ 0,\psi >\mathit{FOV}\end{array}\right.$$E2

where AR is the physical area of the photodiode at the receiver, d0 is the line of sight distance from source S^Lam and the optical receiver R, and ψ is the angle of incidence with respect to the axis normal to the receiver surface. FOV is the field of view (FOV) of the optical receiver. Moreover, Cof represents the optical filter gain of the receiver, Coc represents the optical concentrator gain of the receiver, and μ denotes the atmospheric attenuation coefficient, which is wavelength dependent and could be given by [14, 15, 16]:

$$\begin{array}{c}\mu =\frac{3.91}{V}{\left(\frac{\lambda }{550}\right)}^{-q},\end{array}$$E3

where V is the atmospheric visibility, λ is the optical signal wavelength, and q is the parameter related to the visibility, expressed as [14, 15, 16]:

$$q=\left\{\begin{array}{ll}0.585{\mathrm{V}}^{1/3},& \mathrm{V}<6\mathrm{km}\\ 1.3,& 6\mathrm{km}<\mathrm{V}<50\mathrm{km}\end{array}\right.$$E4

In addition, replacing Eq. (1) in Eq. (2), we obtain the renewed optical intensity channel gain as:

$$H\left(S^{\mathrm{Lam}},R\right)=\left\{\begin{array}{ll}\frac{\left(m_{\mathrm{L}}+1\right)A_R}{2\pi d_0^2}{cos}^{m_{\mathrm{L}}}\left(\theta \right)cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},& 0\le \psi \le \mathit{FOV}\\ 0,& \psi >\mathit{FOV}\end{array}\right.$$E5

In this situation, the received optical power at the receiver could be expressed as:

$$P_{\mathrm{r}}\left(S^{\mathrm{Lam}},R\right)=\left\{\begin{array}{l}\frac{P_{\mathrm{t}}\left(m_{\mathrm{L}}+1\right)A_R}{2\pi d_0^2}{cos}^{m_{\mathrm{L}}}\left(\theta \right)cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},0\le \psi \le \mathit{FOV}\\ 0,\psi >\mathit{FOV}\end{array}\right.$$E6

where Pt is the emitted optical power at the LED transmitter and the distance between the source S^Lam and the optical receiver R can be calculated as follows:

$$\begin{array}{c}{d}_0=\sqrt{{\left(X_S-X_R\right)}^2+{\left(Y_S-Y_R\right)}^2+{\left(Z_S-Z_R\right)}^2}\end{array}$$E7

where (XS, YS, ZS) denotes the coordinated position of the LED transmitter and (XR, YR, ZR) denotes the coordinated position of the optical receiver.

2.2 Case 2 of typical non-Lambertian FSO communications

Without loss of generality, the typical non-Lambertian radiation pattern from the commercially available LUXEON Rebel LED is adopted to configure the outdoor FSOC link for the envisioned case 2. Following the work of Refs. [11, 12], the radiant intensity of this rotational symmetric non-Lambertian type could be given as:

$$I_{\mathit{NL}}\left(\theta \right)=\sum _{i=1}^2{g}_{1i}exp\left[-ln2{\left(\frac{\left|\mathrm{\theta }\right|-g_{2i}}{g_{3i}}\right)}^2\right]$$E8

where the involved equation coefficients are set as g11 = 0.76, g21 = 0°, g31 = 29°, g12 = 1.10, g22 = 45°, g32 = 21°successively. The respective 3D spatial radiation pattern of this non-Lambertian optical beam for outdoor horizontal FSOC link is illustrated in Figure 2b. Apparently, like the mentioned Lambertian case, the intensity is independent of the azimuthal angle Φ which fundamentally induces the radiation pattern symmetry in the far field. Therefore, similar to the Lambertian case, the line of sight optical channel gain for this novel non-Lambertian case could be presented as:

$$H\left(S^{\mathit{NL}},R\right)=\left\{\begin{array}{l}\frac{A_R}{d_0^2}{I}_{\mathit{NL}}\left(\theta \right)cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},0\le \psi \le \mathit{FOV}\\ 0,\psi >\mathit{FOV}\end{array}\right.$$E9

Moreover, replacing Eq. (8) in Eq. (9), the renewed optical intensity channel could be given as:

$$H\left(S^{\mathit{NL}},R\right)=\left\{\begin{array}{l}\frac{{\sum }_{i=1}^2{g}_{1i}exp\left[-ln2{\left(\frac{\left|\theta \right|-g_{2i}}{g_{3i}}\right)}^2\right]}{d_0^2}{A}_{R}cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},0\le \psi \le \mathit{FOV}\\ 0,\psi >\mathit{FOV}\end{array}\right.$$E10

Such that, for the concerned non-Lambertian configuration, the angle dependent received optical power at the receiver could be expressed as:

$$P_{\mathrm{r}}\left(S^{\mathit{NL}},R\right)=\left\{\begin{array}{l}\frac{P_t{\sum }_{i=1}^2{g}_{1i}exp\left[-ln2{\left(\frac{\left|\theta \right|-g_{2i}}{g_{3i}}\right)}^2\right]}{d_0^2}{A}_{R}cos\left(\psi \right)G_{\text{of}}{G}_{\mathrm{oc}}{e}^{-\mu d_0},0\le \psi \le \mathit{FOV}\\ 0,\psi >\mathit{FOV}\end{array}\right.$$E11

For convenience of analysis, the multipath non-line of sight components are ignored in this work, which is solid and acceptable for the most outdoor FSOC application scenarios.

3. Numerical studies

For fair comparison, the whole emitted optical power of the LUXEON Rebel LED emission patterns is normalized to 1 W. The main parameters for the following comparative simulation are included in the Table 1. In this Lambertian optical beam configuration case, the outdoor FSO received optical power spatial distribution experiences up to 39.88 dB intensity variation, specifically ranging from −30.40 to 9.48 dBm, as shown in Figure 3a.

Parameters	Value
Wavelength	570 [nm]
Visibility	20 [km]
Link length	50 [m]
Emitted optical power	30 [W]
Lambertian index	1
Detection area of receiver	0.01 m^2
Field of view	90°
Optical filter gain	1
Optical concentrator gain	1

Table 1.

Parameters for outdoor FSOC channel characteristics simulation.

Figure 3.

Received optical power spatial distribution within horizontal plane coverage of outdoor FSOC for 6G wireless networks in the case of (a) Lambertian optical beam configuration, (b) LUXEON Rebel non-Lambertian optical beam configuration.

Due to the intrinsic wider and more dispersive spatial emission characteristics of the concerned LUXEON Rebel non-Lambertian optical beam configuration, the received optical power spatial distribution ranges from −32.86 to 13.23 dBm with variation reduced to 46.09 dB. Accordingly, the horizontal coverage performance difference brought by the pattern replacement could been observed by the cumulative distribution function (CDF) in Figure 4 as well.

Figure 4.

CDF curve comparison of received optical power within horizontal plane coverage for two distinct optical beam configurations.

For up to 80% outdoor FSO receiver positions under Lambertian optical beam configuration, the received optical power is more than −28.63 dBm, while the counterpart of the LUXEON Rebel non-Lambertian optical beam configuration is changed to –32.71 dBm, accordingly. Therefore, the discussed LUXEON Rebel non-Lambertian optical beam configuration is capable of providing more dispersive horizontal coverage at the price of 4.08 dB maximum intensity loss for 80% receiver positions. As also shown in Figure 4, the similar tendency and statistical characteristics difference could be identified when the emitted optical power is increased to 60 W and 90 W for the concerned Lambertian optical beam configuration and LUXEON Rebel non-Lambertian optical beam configuration.

4. Conclusion

The ultra-high capacity, abundant optical spectrum resource, low latency, electromagnetic interference free, and reliable security of FSOC are quite competitive and attractive to developing 6G wireless networks. For overcoming the limitation of current LED-based outdoor FSOC technology in optical beam configuration, in this work, the relevant channel characteristics induced by the non-Lambertian LED beam are investigated in typical outdoor FSOC scenario. The respective results illustrate that more dispersive for outdoor FSOC could be introduced by the LUXEON Rebel non-Lambertian optical beam configuration, compared with the baseline Lambertian FSOC case.

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grants No. 62061043), Natural Science Foundation of the Xinjiang Uygur Autonomous Region (Grants No. 2019D01C020), and Tianshan Cedar Project of Xinjiang Uygur Autonomous Region (Grants No. 202101528).

Conflict of interest

The authors declare no conflict of interest.