**1. Introduction**

With population aging is emphasized around the world, more attention is paid to the development of the healthcare application with new paradigm. Nevertheless, most of the current health application is based on conventional radio frequency (RF) techniques, such as WiFi (Wireless Fidelity) or UWB (Ultra-Wide Band), and the annoying interference issue frequently degrades the user experience. On the other side, the emerging solid source based optical wireless (OW) technology is consistently investigated to complement the wireless capacity for various healthcare application in EM (electromagnetic) sensitive scenarios [1–5]. Specifically, the validity is examined to achieve the diffuse OW communication between the on-body nodes [6–10].

Up to now, the works of OW healthcare system are still limited to the wellknown Lambertian emission pattern which is quite consistent with the conventional solid state sources e.g. LED (Light Emitting Diodes) [11–15]. Nevertheless, there are a number of variations following non-Lambertian emission pattern is still waiting for discussion. In this paper, the typical non-Lambertian OW links is explored in typical healthcare scenario, as shown in **Figure 1** for the first time. And the healthcare OW channel gains comparison are made between the Lambertian & the non-Lambertian configuration.

*Moving Broadband Mobile Communications Forward - Intelligent Technologies for 5G…*

### **2. Indoor optical wireless application for healthcare scenario**

In this part, the typical non-Lambertian OW links is explored in typical healthcare scenario, as shown in **Figure 1** for the first time. And the healthcare OW channel gains comparison are made between the Lambertian & the non-Lambertian configuration.

#### **2.1 Lambertian & non-Lambertian emission pattern**

To the best of our knowledge, in the indoor medical related system shown in the radiation intensity of the transmitter is modeled by the generalized Lambertian pattern as [1, 2]:

$$I\_L(\theta) = \frac{m\_L + 1}{2\pi} \cos^{m\_L}(\theta),\tag{1}$$

**2.2 Optical wireless link characteristics comparison**

8 < : ð Þ *m*<sup>L</sup> þ 1 *AR* 2*πd*<sup>2</sup> 0

*3D spatial emission patterns in (a) Lambertian type and (b) typical non-Lambertian type.*

*Healthcare Application-Oriented Non-Lambertian Optical Wireless Communications…*

described non-Lambertian emission pattern could be derived as:

*<sup>g</sup>*1*<sup>i</sup>* exp � ln 2 j j *<sup>θ</sup>* � *<sup>g</sup>*2*<sup>i</sup>*

ð Þ *m*<sup>L</sup> þ 1 *AR* 2*πd*<sup>2</sup> 0

*HL* ¼

*DOI: http://dx.doi.org/10.5772/intechopen.98275*

*AR d*2 0 X 2

Lambertian case could be rewritten as:

could been simplified as well:

*HNL* ¼

**129**

*HL* ¼

*AR d*2 0 X 2

8 ><

>:

*i*¼1

8 < :

8 ><

>:

*i*¼1

expressed as [1, 2]:

**Figure 2.**

*HNL* ¼

In typical indoor healthcare scenario, the OW channel gain form the optical transmitter on the patient to the optical receiver on the ceiling center could be

where *AR* is the effective receiver area, *d0* is the direct distance from source to optical receiver, and *ψ* is the angle of incidence on the receiver location. *FOV* is the field of view of the optical receiver. At the same time, the OW channel gain of the

*g*3*i*

For simplifying analysis, the orientation of the optical transmitter is set upward vertically. And the orientation of the optical receiver is set downward vertically. In such situation, emission angle of line of sight (LOS) optical signal equals to the incidence angle at the receiver, i.e. *θ* = *ψ*. Such that the optical channel gain of the

cos *<sup>m</sup>*Lþ<sup>1</sup>

On the other side, the expression of the non-Lambertian pattern channel gain

*<sup>g</sup>*1*<sup>i</sup>* exp � ln 2 j j *<sup>θ</sup>* � *<sup>g</sup>*2*<sup>i</sup>*

cos *<sup>m</sup>*<sup>L</sup> ð Þ*<sup>θ</sup>* cos *ψ ψ* <sup>&</sup>lt;*FOV*

(3)

(4)

(5)

(6)

0 *ψ* ≥*FOV*

� �<sup>2</sup> " # cos *ψ ψ* <sup>&</sup>lt;*FOV*

0 *ψ* ≥*FOV*

ð Þ*θ θ* < *FOV*

0 *θ* ≥ *FOV*

� �<sup>2</sup> " # cos *θ θ* <sup>&</sup>lt;*FOV*

0 *θ* ≥*FOV*

*g*3*i*

where *m*<sup>L</sup> is the Lambertian index and *θ* is the elevation angle, as shown in **Figure 2a**. At the same time, due to the distinct manufacture process of the solid sources, there are many optical sources could not be characterized by the mentioned Lambertian emission pattern. Typically, one non-Lambertian pattern of the commercially available product i.e. LUXEON® Rebel from Lumileds Philips is presented in **Figure 2b** for comparison.

Following the work of [3, 4], the radiant intensity of this non-Lambertian type could be expressed as:

$$I\_{\rm NL}(\theta) = \sum\_{i=1}^{2} \mathbf{g}\_{\rm 1i} \exp\left[-\ln \left(\frac{|\theta| - \mathbf{g}\_{2i}}{\mathbf{g}\_{3i}}\right)^{2}\right] \tag{2}$$

where g11 = 0.76, g21 = 0°, g31 = 29°, g12 = 1.10, g22 = 45°, g32 = 21°. Obviously, like the Lambertian case, the intensity is independent of the azimuthal angle *Φ* which basically dominates its symmetry in the far field.

*Healthcare Application-Oriented Non-Lambertian Optical Wireless Communications… DOI: http://dx.doi.org/10.5772/intechopen.98275*

**Figure 2.**

**2. Indoor optical wireless application for healthcare scenario**

*Moving Broadband Mobile Communications Forward - Intelligent Technologies for 5G…*

*IL*ð Þ¼ *<sup>θ</sup> mL* <sup>þ</sup> <sup>1</sup>

where *m*<sup>L</sup> is the Lambertian index and *θ* is the elevation angle, as shown in **Figure 2a**. At the same time, due to the distinct manufacture process of the solid sources, there are many optical sources could not be characterized by the mentioned Lambertian emission pattern. Typically, one non-Lambertian pattern of the commercially available product i.e. LUXEON® Rebel from Lumileds Philips is

Following the work of [3, 4], the radiant intensity of this non-Lambertian type

where g11 = 0.76, g21 = 0°, g31 = 29°, g12 = 1.10, g22 = 45°, g32 = 21°. Obviously, like the Lambertian case, the intensity is independent of the azimuthal angle *Φ* which

*<sup>g</sup>*1*<sup>i</sup>* exp � ln 2 j j *<sup>θ</sup>* � *<sup>g</sup>*2*<sup>i</sup>*

*g*3*i*

(2)

� �<sup>2</sup> " #

**2.1 Lambertian & non-Lambertian emission pattern**

presented in **Figure 2b** for comparison.

*INL*ð Þ¼ *<sup>θ</sup>* <sup>X</sup>

basically dominates its symmetry in the far field.

2

*i*¼1

configuration.

**Figure 1.**

*Typical indoor mobile healthcare scenario.*

pattern as [1, 2]:

could be expressed as:

**128**

In this part, the typical non-Lambertian OW links is explored in typical healthcare scenario, as shown in **Figure 1** for the first time. And the healthcare OW channel gains comparison are made between the Lambertian & the non-Lambertian

To the best of our knowledge, in the indoor medical related system shown in the radiation intensity of the transmitter is modeled by the generalized Lambertian

<sup>2</sup>*<sup>π</sup>* cos *mL* ð Þ*<sup>θ</sup>* , (1)

*3D spatial emission patterns in (a) Lambertian type and (b) typical non-Lambertian type.*

#### **2.2 Optical wireless link characteristics comparison**

In typical indoor healthcare scenario, the OW channel gain form the optical transmitter on the patient to the optical receiver on the ceiling center could be expressed as [1, 2]:

$$H\_L = \begin{cases} \frac{(m\_L + 1)A\_R}{2\pi d\_0^2} \cos^{m\_L}(\theta)\cos\psi & \text{ $\mu < FOV} \\ & \mathbf{0} & \text{$ \mu \ge FOV} \end{cases} \tag{3}$$

where *AR* is the effective receiver area, *d0* is the direct distance from source to optical receiver, and *ψ* is the angle of incidence on the receiver location. *FOV* is the field of view of the optical receiver. At the same time, the OW channel gain of the described non-Lambertian emission pattern could be derived as:

$$H\_{\rm NL} = \begin{cases} A\_R \sum\_{i=1}^2 \mathbf{g}\_{i\bar{i}} \exp\left[-\ln 2 \left(\frac{|\theta| - \mathbf{g}\_{2\bar{i}}}{\mathbf{g}\_{3\bar{i}}}\right)^2\right] \cos \psi & \text{ $\psi < FOV} \\ \mathbf{0} & \text{$ \psi \ge FOV} \end{cases} \tag{4}$$

For simplifying analysis, the orientation of the optical transmitter is set upward vertically. And the orientation of the optical receiver is set downward vertically. In such situation, emission angle of line of sight (LOS) optical signal equals to the incidence angle at the receiver, i.e. *θ* = *ψ*. Such that the optical channel gain of the Lambertian case could be rewritten as:

$$H\_L = \begin{cases} \frac{(m\_L + 1)A\_R}{2\pi d\_0^2} \cos^{m\_L + 1}(\theta) & \theta < \text{FOV} \\ & 0 \\ \end{cases} \tag{5}$$

On the other side, the expression of the non-Lambertian pattern channel gain could been simplified as well:

$$H\_{\rm NL} = \begin{cases} A\_R \sum\_{i=1}^2 \mathbf{g}\_{1i} \exp\left[-\ln \left(\frac{|\theta| - \mathbf{g}\_{2i}}{\mathbf{g}\_{3i}}\right)^2\right] \cos\theta & \theta < \text{FOV} \\ 0 & \theta \ge \text{FOV} \end{cases} \tag{6}$$

For fair comparison, the whole emitted optical power of the both emission patterns are normalized to 1 W. The main parameters for the following simulation are included in the **Table 1**. In this Lambertian pattern case, the mobile patient experiences up to 5.77 dB channel gain variation, specifically ranging from 58.71 to 52.94 dB, as shown in **Figure 3a**. Thanks to the intrinsic spatial emission characteristics of the concerned non-Lambertian pattern, the channel gain ranges from 57.79 to 55.26 dB with variation reduced to 2.53 dB. Accordingly, the performance uniformity brought by the pattern replacement could been observed by the probability distribution function (PDF) in **Figure 3b** as well.

**3. Conclusion**

*DOI: http://dx.doi.org/10.5772/intechopen.98275*

power.

202101528).

**Conflict of interest**

**Author details**

Jupeng Ding1

**131**

The authors declare no conflict of interest.

\*, I. Chih-Lin<sup>2</sup> and Jiong Zheng<sup>1</sup>

University, Urumqi, Xinjiang, China

provided the original work is properly cited.

2 China Mobile Research Institute, Beijing, China

\*Address all correspondence to: jupeng7778@163.com

1 Key Laboratory of Signal Detection and Processing in Xinjiang Uygur

Autonomous Region, School of Information Science and Engineering, Xinjiang

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Acknowledgements**

The high bandwidth, abundant spectrum resources and high confidentiality of wireless optical communication are suitable for 5G and B5G communication systems. With the rapid development of OWC technology, discussions on different beam characteristics and active research will be unprecedentedly released. In this study, the potential channel gain induced by the non-Lambertian beam is investigated in typical healthcare scenario. The results show that the channel gain fluctuation could be reduced up to about 3.24 dB, with constant transmitted optical

*Healthcare Application-Oriented Non-Lambertian Optical Wireless Communications…*

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), High-level Talents Introduction Project in Xinjiang Uygur Autonomous Region (Grants No. 042419004), Tianchi Doctor Program of the Xinjiang Uygur Autonomous Region (Grants No. 04231200728), Natural Science Foundation of Xinjiang University (Grants No. 62031224624), National Natural Science Foundation of China (Grants No. 61401420), and Tianshan Cedar Project of Xinjiang Uygur Autonomous Region (Grants No.


**Table 1.** *Parameters for simulation.*

**Figure 3.** *Optical channel gain comparison in (a) spatial distribution and (b) PDF statistics.*

*Healthcare Application-Oriented Non-Lambertian Optical Wireless Communications… DOI: http://dx.doi.org/10.5772/intechopen.98275*
