**Multi-User Visible Light Communications**

Oswaldo González, Marcos F. Guerra Medina and Inocencio R. Martín

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59053

## **1. Introduction**

Communication Conference and Exposition and the National Fiber Optic Engineers

[35] Roberts P.J., Couny F., Sabert H., Mangan B.J., Williams D.P., Farr L., Mason M.W., Tomlinson A., T. Birks A., Knight J.C., and Russell P. St.J. Ultimate low loss of hol‐

[36] Bobrovs, V., Spolitis, S., and Ivanovs, G. Comparison of chromatic dispersion com‐ pensation techniques for WDM-PON solution. In: Proc. of 2nd Baltic Congress on Fu‐

[37] Bobrovs V., Spolitis S., Ivanovs G. and Gavars P. Performance Improvement of High Speed Spectrum-Sliced Dense WDM-PON System. In: Proc. of IX International Sym‐

[38] ITU-T Recommendation G.655. Characteristics of a non-zero dispersion-shifted sin‐

Conference (OFC/NFOEC), 2013, pp.1,3, 17-21 March, 2013.

ture Internet Communications, pp.64,67, 25-27 April 2012.

posium on Telecommunications, pp.1-6, 25-27 October, 2012.

[39] Chomycz B. Planning Fiber Optic Networks. – McGraw-Hill, 401 pp, 2009.

[40] OFS. Technical specification of TrueWave RS Low Water Peak (LWP) Fiber, 2013.

[41] ITU-T Recommendation G.653. Characteristics of a dispersion-shifted, single-mode

[42] Fredrik S., Bengt J., and David M. FBG dispersion compensation improves amplifica‐ tion designs and strategies", Lightwave Magazine, August 1, 2008.www.lightwa‐

[43] Agrawal G. Fiber – Optic Communication Systems. Third Edition. – USA: John Wiley

[44] Bobrovs, V., Ivanovs G. Investigation of Mixed Data Rate and Format Transmission in WDM Networks, Electronics and Electrical Engineering. Vol. 4(84), pp. 63-66,

[45] Al-Qazwini Z., Kim H. Ultranarrow Spectrum-Sliced Incoherent Light Source for 10- Gb/s WDM PON. In: IEEE Journal of Lightwave Technology, vol.30, issue 19, pp.

veonline.com/articles/print/volume-25/issue-8/applications/fbg-dispersioncompensation-improves-amplification-designs-and-strategies-54888677.html

gle-mode optical fibre and cable, 2009.

optical fibre and cable, 2010.

and Sons, 561 pp, 2002.

3157-3163, Oct. 2012.

2008.

34 Advances in Optical Communication

low-core photonic crystal fibres. In: Opt. Express 13, 236-244, 2005.

Nowadays, the demand for high capacity wireless connectivity is endless. Radiofrequency networks try to meet this demand but strict regulations and the increasing number of users mean service providers have to look for new alternatives to radio communications. Wireless optical communications could be a practical solution.

Among optical communication systems, visible light communications (VLC), first proposed by researchers at Keio University in Tokyo [1][2], have prompted great interest in the scientific community in the last few years [3][4][5]. There have also been regulatory efforts made in this technology that have led to the appearance of a standard [6]. These new VLC systems, based on the use of sustainable, energy-efficient, visible LED (light-emitting diode) lamps [7] to simultaneously transmit information together with their normal use as illumination devices, share the same advantages as their infrared counterparts [8]. They are also eye-safe (visible light is not harmful to the human eye), which enables the use of higher transmission powers. However, the main drawback is the limited transmission bandwidth of current LED devices, typically several MHz, and whose enhancement has been one of the main issues addressed by researchers [9][10][11][12].

Zeng *et al.* [13] have proposed the use of multiple-input multiple-output (MIMO) schemes based on imaging receivers to obtain high capacity VLC networks. Additionally, the orthog‐ onal frequency division multiplexing (OFDM) technique has proved to be a feasible candidate to obtain these high-speed networks [14], demonstrating impressive experimental data rates for short-range communications [15][16][17][18]. In [19], it was forecast that combining OFDM technique and imaging reception could be a potential research field for the future, which was rapidly demonstrated experimentally by Azhar *et al.* [20]. Alternatively, Burton *et al.* have

© 2014 The Author(s). Licensee InTech. 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 eproduction in any medium, provided the original work is properly cited.

proposed the use of non-imaging receivers for MIMO-OFDM-based VLC, also demonstrating very interesting results [21].

This chapter describes the characteristics of MIMO-OFDM schemes applied to multi-user visible light communications, comparing the capacity of both non-imaging and imaging reception to separate the information corresponding to each individual user.

#### **2. The indoor wireless visible-light optical channel**

The indoor wireless visible-light optical channel is basically composed of three elements: the emitting sources (the visible-light LED lamps), the room where lamp emissions are enclosed and the optical receiver. In this section, the different components of the communication channel are described thoroughly, highlighting their impact on the effective channel band‐ width.

#### **2.1. Emitting sources**

Visible-light LED lamps are commonly made up of a significant number of single chips, each presenting a generalized Lambertian radiation pattern, typically of *mode number n=*1 or *radiation semiangle* (at half power) *ϕ*1/2*=*arccos 1 / 2 *<sup>n</sup>* =60° (see Fig. 9(a)). The Lambertian radiation pattern, having uniaxial symmetry, is given by [22]:

$$R\_E\left(\phi\right) = P\_E \frac{n+1}{2\pi} \cos^n \phi\_\prime - \frac{\pi}{2} \le \phi \le \frac{\pi}{2} \tag{1}$$

where *PE* is the total power emitted by the single LED chip. There are two major types of visiblelight (white) LEDs: those consisting of a blue LED chip with a phosphor wavelength conver‐ sion, which enables re-emission at longer wavelengths thus leading to a combined broadband optical spectrum in the visible region, and those devices composed of three independent LED chips emitting at blue (B), green (G) and red (R) wavelengths, whose joint radiation is perceived as white light [23][24]. The first group of devices, after suppressing the slow phosphorescent component by means of a blue filter (see Fig. 1), experience a modulation bandwidth enhance‐ ment from ~2 MHz to ~20 MHz [4], whereas tri-chip RGB LEDs present a modulation band‐ width of ~25 MHz [24]. In this chapter, phosphor-based white LED will be mostly considered, although bearing in mind the results are directly transferable to the case when RGB LEDs are used.

Fig. 1 shows the *power spectral density* (PSD), which describes the radiant power per unit wavelength, of a typical phosphor-based white LED (WLED) [25] and the *eyesensitivity function* under daylight (well-lit) conditions [23], denoted as *p(λ*) and *V(λ*), respectively. The WLED optical power [W] (*radiant* fl*ux*) is given by

proposed the use of non-imaging receivers for MIMO-OFDM-based VLC, also demonstrating

This chapter describes the characteristics of MIMO-OFDM schemes applied to multi-user visible light communications, comparing the capacity of both non-imaging and imaging

The indoor wireless visible-light optical channel is basically composed of three elements: the emitting sources (the visible-light LED lamps), the room where lamp emissions are enclosed and the optical receiver. In this section, the different components of the communication channel are described thoroughly, highlighting their impact on the effective channel band‐

Visible-light LED lamps are commonly made up of a significant number of single chips, each presenting a generalized Lambertian radiation pattern, typically of *mode number n=*1 or *radiation semiangle* (at half power) *ϕ*1/2*=*arccos 1 / 2 *<sup>n</sup>* =60° (see Fig. 9(a)). The Lambertian radiation pattern,

> cos , 2 22 *n*

 ff

where *PE* is the total power emitted by the single LED chip. There are two major types of visiblelight (white) LEDs: those consisting of a blue LED chip with a phosphor wavelength conver‐ sion, which enables re-emission at longer wavelengths thus leading to a combined broadband optical spectrum in the visible region, and those devices composed of three independent LED chips emitting at blue (B), green (G) and red (R) wavelengths, whose joint radiation is perceived as white light [23][24]. The first group of devices, after suppressing the slow phosphorescent component by means of a blue filter (see Fig. 1), experience a modulation bandwidth enhance‐ ment from ~2 MHz to ~20 MHz [4], whereas tri-chip RGB LEDs present a modulation band‐ width of ~25 MHz [24]. In this chapter, phosphor-based white LED will be mostly considered, although bearing in mind the results are directly transferable to the case when RGB LEDs are

Fig. 1 shows the *power spectral density* (PSD), which describes the radiant power per unit wavelength, of a typical phosphor-based white LED (WLED) [25] and the *eyesensitivity function* under daylight (well-lit) conditions [23], denoted as *p(λ*) and *V(λ*), respectively. The WLED

p

 p

<sup>+</sup> <sup>=</sup> - ££ (1)

reception to separate the information corresponding to each individual user.

**2. The indoor wireless visible-light optical channel**

( ) <sup>1</sup>

p

*E E <sup>n</sup> R P*

f

fl

*ux*) is given by

very interesting results [21].

36 Advances in Optical Communication

width.

used.

optical power [W] (*radiant*

**2.1. Emitting sources**

having uniaxial symmetry, is given by [22]:

**Figure 1.** Normalized power spectral density (PSD) of a typical phosphor-based white LED (WLED) and eye sensitivi‐ ty function under daylight (well-lit) conditions versus wavelength.

$$P\_{\mathbb{E}} = \int\_{\mathbb{A}\_{\text{min}}(380\,\text{nm})}^{\mathbb{A}\_{\text{max}}(380\,\text{nm})} p(\mathcal{A})d\mathcal{A} \tag{2}$$

In the PSD of a WLED, the blue component comprises approximately 50% of the power emitted by the device [4]. In most communication applications, this component will solely be detected by filtering the phosphorescent one to attain high data rates.

In visible-light communications, it is important to remember the relationship between photometric and radiometric quantities [23], as LED lamps are used as illumination devices too. The *luminous flux* [lm] can be obtained from the radiometric light power by [23]

$$\mathfrak{O}\_{\text{luw}} = 683 \frac{\text{lm}}{\text{W}} \int\_{\lambda\_{\text{min}}}^{\lambda\_{\text{max}}} V\left(\mathcal{A}\right) p\left(\mathcal{A}\right) d\mathcal{A} \tag{3}$$

The normalization factor 683 lm/W denotes that a monochromatic 1-W optical source emitting at 555 nm, where photopic eye sensitivity is maximal (see *V*(*λ*) in Fig. 1), has a luminous flux of 683 lumens. The *luminous efficacy* is then given by

$$\eta\_{\rm lum} = \frac{\boldsymbol{\Phi}\_{\rm lum}}{P\_{\rm E}} = \left[ 683 \frac{\rm lm}{\rm W} \int\_{\lambda\_{\rm min}}^{\lambda\_{\rm max}} V\left(\boldsymbol{\lambda}\right) p\left(\boldsymbol{\lambda}\right) d\boldsymbol{\lambda} \right] \Big/ \int\_{\lambda\_{\rm min}}^{\lambda\_{\rm max}} p\left(\boldsymbol{\lambda}\right) d\boldsymbol{\lambda} \tag{4}$$

This describes the conversion efficiency from the LED power to luminosity. The *illuminance* [lx=lm/m<sup>2</sup> ] is the incident luminous flux per unit area. The horizontal illuminance at a point (*x*,*y*) can be obtained as [2]

$$E\_{\rm hor} = I \left(\phi\right) \cos\left.\phi\right| \,d^2 = I\_0 \cos^\nu\phi \cos\left.\phi\right| \,d^2\tag{5}$$

where *d* is the distance between the optical source (LED) and the illuminated surface, *ϕ* is the angle of irradiance, *φ* is the angle of incidence on the surface (see Fig. 9(a)), and *I0* is the center *luminous intensity* of the LED [4]

$$I\_{\phi} = I\left(\phi = 0\right) = \frac{n+1}{2\pi} \Phi\_{luv} \tag{6}$$

and *n* being the Lambert index of the optical source, which typically equals unity in WLEDs.

Fig. 2 depicts the direct illuminance at the working plane (0.75-m height) of a room with two large windows (see parameters for characterization study in Table 1), due to the line-of-sight (LOS) component, i.e. the one generated by the LED lamps in their direct paths to the illumi‐ nated point. When considering the reflection of light on walls and windows (see Fig. 3), the values of illuminance are significantly enhanced and this becomes more uniform at the working plane. In this last case, we can verify that standard levels for workplaces (> 400 lx) are clearly achieved [26].

4 Optical Communication

2 ̅ *=* 460 lx). **Figure 2.** Direct (line-of-sight) illuminance at the receiver plane (*Emin*=185 lx; *Emax*=640 lx; *<sup>E</sup>*¯*<sup>=</sup>*460 lx).

1 **Fig. 2.** Direct (line-of-sight) illuminance at the receiver plane (*Emin* = 185 lx; *Emax* = 640 lx;

#### **2.2. Reflective surfaces**

5 **2.2. Reflective surfaces**

11 where *PI* is the incident optical power,

*,* and 

9 number *n* = 1:

12 on the wavelength

Rough reflective surfaces commonly present a purely diffuse reflection pattern, as shown in Fig. 4(a), i.e. they do not favor any particular direction after reflection regardless of the incidence angle. Moreover, this reflection pattern follows Lambert's model with mode number *n=*1:

(a) 3D illustration (b) Contours map

3 **Fig. 3.** Illuminance at the receiver plane, considering contributions of reflections on walls

6 Rough reflective surfaces commonly present a purely diffuse reflection pattern, as shown in 7 Fig. 4(a), i.e. they do not favor any particular direction after reflection regardless of the 8 incidence angle. Moreover, this reflection pattern follows Lambert"s model with mode

( ) ( )

(

<sup>10</sup> (7)

13 glass, additionally exhibit a strong specular component, which is dependent upon the 14 incidence angle of the incoming ray, as illustrated in Fig. 4(b), therefore they are more

4 and windows (*Emin* = 445 lx; *Emax* = 845 lx; ̅ *=* 690 lx).

$$R\_{\mathbb{S}}\left(\theta,\mathcal{X}\right) = \rho\left(\mathcal{X}\right)P\_{l}\frac{1}{\pi}\cos\theta\tag{7}$$

) the surface reflection coefficient, which depends

is the observation angle. However, some smooth surfaces, e.g.

4 Optical Communication

( ) 2 2 <sup>0</sup> cos / cos cos / *<sup>n</sup> hor E I dI d* = =

where *d* is the distance between the optical source (LED) and the illuminated surface, *ϕ* is the angle of irradiance, *φ* is the angle of incidence on the surface (see Fig. 9(a)), and *I0* is the center

 fj

2 *lum*

<sup>+</sup> = = = F (6)

p

and *n* being the Lambert index of the optical source, which typically equals unity in WLEDs.

Fig. 2 depicts the direct illuminance at the working plane (0.75-m height) of a room with two large windows (see parameters for characterization study in Table 1), due to the line-of-sight (LOS) component, i.e. the one generated by the LED lamps in their direct paths to the illumi‐ nated point. When considering the reflection of light on walls and windows (see Fig. 3), the values of illuminance are significantly enhanced and this becomes more uniform at the working plane. In this last case, we can verify that standard levels for workplaces (> 400 lx) are

4 Optical Communication

(a) 3D illustration (b) Contours map

Rough reflective surfaces commonly present a purely diffuse reflection pattern, as shown in Fig. 4(a), i.e. they do not favor any particular direction after reflection regardless of the incidence angle. Moreover, this reflection pattern follows Lambert's model with mode number

(a) 3D illustration (b) Contours map

p

 q

) the surface reflection coefficient, which depends

<sup>=</sup> (7)

is the observation angle. However, some smooth surfaces, e.g.

3 **Fig. 3.** Illuminance at the receiver plane, considering contributions of reflections on walls

( ) ( ) <sup>1</sup> , cos *R P S I*

 rl

ql

6 Rough reflective surfaces commonly present a purely diffuse reflection pattern, as shown in 7 Fig. 4(a), i.e. they do not favor any particular direction after reflection regardless of the 8 incidence angle. Moreover, this reflection pattern follows Lambert"s model with mode

( ) ( )

(

<sup>10</sup> (7)

13 glass, additionally exhibit a strong specular component, which is dependent upon the 14 incidence angle of the incoming ray, as illustrated in Fig. 4(b), therefore they are more

4 and windows (*Emin* = 445 lx; *Emax* = 845 lx; ̅ *=* 690 lx).

5 **2.2. Reflective surfaces**

11 where *PI* is the incident optical power,

*,* and 

9 number *n* = 1:

12 on the wavelength

1 **Fig. 2.** Direct (line-of-sight) illuminance at the receiver plane (*Emin* = 185 lx; *Emax* = 640 lx;

**Figure 2.** Direct (line-of-sight) illuminance at the receiver plane (*Emin*=185 lx; *Emax*=640 lx; *<sup>E</sup>*¯*<sup>=</sup>*460 lx).

(5)

f

*luminous intensity* of the LED [4]

38 Advances in Optical Communication

clearly achieved [26].

2 ̅ *=* 460 lx).

*n=*1:

**2.2. Reflective surfaces**

 j

<sup>0</sup> ( ) <sup>1</sup> <sup>0</sup>

*<sup>n</sup> I I* f

4 and windows (*Emin* = 445 lx; *Emax* = 845 lx; ̅ *=* 690 lx). **Figure 3.** Illuminance at the receiver plane, considering contributions of reflections on walls and windows (*Emin*=445 lx; *Emax*=845 lx; *<sup>E</sup>*¯=690 lx).

3 **Fig. 3.** Illuminance at the receiver plane, considering contributions of reflections on walls

where *PI* is the incident optical power, *ρ*(*λ*) the surface reflection coefficient, which depends on the wavelength *λ,* and *θ* is the observation angle. However, some smooth surfaces, e.g. glass, additionally exhibit a strong specular component, which is dependent upon the incidence angle of the incoming ray, as illustrated in Fig. 4(b), therefore they are more properly modeled by Phong's model, where the reflection pattern behaves as the sum of both diffuse and specular components [27] Multi-user visible light communication 5 5 **2.2. Reflective surfaces** 6 Rough reflective surfaces commonly present a purely diffuse reflection pattern, as shown in 7 Fig. 4(a), i.e. they do not favor any particular direction after reflection regardless of the 8 incidence angle. Moreover, this reflection pattern follows Lambert"s model with mode 9 number *n* = 1: ( ) ( ) <sup>10</sup> (7)

1 properly modeled by Phong"s model, where the reflection pattern behaves as the sum of

(

( ) ( ) \*

11 where *PI* is the incident optical power,

2 ̅ *=* 460 lx).

$$R\_{\rm s} \left( \theta, \theta', \lambda \right) = \rho(\lambda) P\_{\parallel} \left[ r\_d \frac{1}{\pi} \cos \theta + \left( 1 - r\_d \right) \frac{m+1}{2\pi} \cos^n \left( \theta - \theta' \right) \right] \tag{8}$$

) the surface reflection coefficient, which depends

Here, *rd* is the fraction (0 ≤ *rd* ≤ 1) of the incident signal that is reflected diffusely, *m* denotes the directivity of the specular reflection component (mode number), *θ'* is the incidence angle with respect to the normal of the reflective surface, and the remaining parameters maintain the same meaning as those of eqn. (7). 4 Here, *rd* is the fraction (0 ≤ *rd* ≤ 1) of the incident signal that is reflected diffusely, *m* denotes 5 the directivity of the specular reflection component (mode number), is the incidence angle 6 with respect to the normal of the reflective surface, and the remaining parameters maintain 7 the same meaning as those of eqn. (7).

9 reflections. **Figure 4.** Purely diffuse (Lambert's model) and combined diffuse-specular (Phong's model) reflections.

Number of LED arrays (lamps): 6 (3 × 2) Number of LEDs per array: 900 (30 × 30) Dimensions of each LED array: 0.6 m × 0.6 m

Power of a single LED (*PE*): 20 mW LED Lambertian mode number (*n*): 1

LED transmission bandwidth: ∼ 15 MHz Receiver plane height: 0.75 m

Windows dimensions (width × height): 2.5 m × 1.5 m

Surface materials parameters: ( ) ̅̅̅̅̅̅ *rd m* Ceiling 0.35 1 - Floor 0.55 1 - Walls (plaster) 0.69 1 - Windows (glass) 0.04 0 280

Positions of LED arrays (central point)

(*x*, *y*, *z*):

10 **Table 1.** Parameters for environment characterization.

8 **Fig. 4.** Purely diffuse (Lambert"s model) and combined diffuse-specular (Phong"s model)

Room size (length × width × height): 7.5 m × 5.5 m × 3.5 m

array 1: (1.50, 1.50, 3.50) array 2: (3.75, 1.50, 3.50) array 3: (6.00, 1.50, 3.50) array 4: (1.50, 4.00, 3.50) array 5: (3.75, 4.00, 3.50) array 6: (6.00, 4.00, 3.50)


**Table 1.** Parameters for environment characterization.

#### **2.3. Optical receivers**

In this section, two kinds of angle-diversity receivers will be considered [28]: *imaging diversi‐ ty receivers*, which use a lens for projecting an image of the optical sources (lamps) onto a pixelated detecting surface, and *non-imaging diversity receivers*, which consist of several detecting branches, each with its own optical detector, oriented in different directions which provides angle-diversity reception.

#### *2.3.1. Imaging receiver*

In a VLC scenario based on an imaging receiver, the lamps' images are projected on an array of photodetectors (PD) by means of a lens, as depicted in Fig. 5. This projection can illuminate several detecting pixels. However, when the photodetecting surface is divided into a signifi‐

cant number of pixels, the lamps impressions will be spread out over different detecting areas, therefore being able to separate the information relative to each individual lamp. In this study, we will consider a paraxial optics approach, as in [13]. 7 **2.3.1. Imaging receiver** 8 In a VLC scenario based on an imaging receiver, the lamps" images are projected on an array 9 of photodetectors (PD) by means of a lens, as depicted in Fig. 5. This projection can 10 illuminate several detecting pixels. However, when the photodetecting surface is divided

11 into a significant number of pixels, the lamps impressions will be spread out over different 12 detecting areas, therefore being able to separate the information relative to each individual

13 lamp. In this study, we will consider a paraxial optics approach, as in [13].

6 Optical Communication

2 In this section, two kinds of angle-diversity receivers will be considered [28]: *imaging*  3 *diversity receivers*, which use a lens for projecting an image of the optical sources (lamps) 4 onto a pixelated detecting surface, and *non-imaging diversity receivers*, which consist of

15 In a lens of *diameter D* and *f-number f#*, its *focal length L* is given by *L = D· f#*. Then, the 16 *magnification* of the system, when the lens is located at a vertical distance *hL* from the ceiling **Figure 5.** Imaging-receiver-based visible-light communication scenario.

14 **Fig. 5.** Imaging-receiver-based visible-light communication scenario.

6 directions which provides angle-diversity reception.

1 **2.3. Optical receivers**

Room size (length × width × height): 7.5 m × 5.5 m × 3.5 m

array 1: (1.50, 1.50, 3.50) array 2: (3.75, 1.50, 3.50) array 3: (6.00, 1.50, 3.50) array 4: (1.50, 4.00, 3.50) array 5: (3.75, 4.00, 3.50) array 6: (6.00, 4.00, 3.50)

(*λ*) *rd m*

¯

Number of LED arrays (lamps): 6 (3 × 2)

Power of a single LED (*PE*): 20 mW

LED transmission bandwidth: ∼ 15 MHz

Windows dimensions (width × height): 2.5 m × 1.5 m

**Table 1.** Parameters for environment characterization.

provides angle-diversity reception.

**2.3. Optical receivers**

*2.3.1. Imaging receiver*

Ceiling 0.35 1 -

Floor 0.55 1 -

Walls (plaster) 0.69 1 -

Windows (glass) 0.04 0 280

In this section, two kinds of angle-diversity receivers will be considered [28]: *imaging diversi‐ ty receivers*, which use a lens for projecting an image of the optical sources (lamps) onto a pixelated detecting surface, and *non-imaging diversity receivers*, which consist of several detecting branches, each with its own optical detector, oriented in different directions which

In a VLC scenario based on an imaging receiver, the lamps' images are projected on an array of photodetectors (PD) by means of a lens, as depicted in Fig. 5. This projection can illuminate several detecting pixels. However, when the photodetecting surface is divided into a signifi‐

Receiver plane height: 0.75 m

LED Lambertian mode number (*n*): 1

Surface materials parameters: *ρ*

Positions of LED arrays (central point)(*x*, *y*, *z*):

40 Advances in Optical Communication

Number of LEDs per array: 900 (30 × 30)

Dimensions of each LED array: 0.6 m × 0.6 m

17 (see Fig. 5(b)), is *M* = *hL*/*L*, i.e. any dimension *do* of the original object in the ceiling creates a 18 replica (image) on the PD surface of size *di* = *do*/*M*. For example, for the width of the lamp, 19 we have AD = *M*· A"D". Geometrically, we can determine the image that is drawn on the PD 20 surface by projecting every environment point along its path towards the imaging receiver 21 through the lens center, similar to that shown in Fig. 5(b) for points A, B, C and D of the LED lamp. Therefore, a square *N*×*N* photodetector array of width *wr* (area *A* = *wr* <sup>2</sup> 22 ) will only 23 be able to observe any point inside of its square-shape equivalent *field of view* (FOV), as 24 shown in Fig. 6 for a 4×4-pixel imaging receiver. The total equivalent FOV, *observation semi-*25 *angle*, varies between *FOV*min = arctg(*wr*/2*L*), in the center of a PD side, and *FOV*max = 26 arctg(*wr*/√ *L*), in a PD corner. For example, for the 4×4-pixel imaging receiver whose 27 characteristics are specified in Table 2, we have 56.3º ≤ *FOV* ≤ 64.8º. However, this total 28 equivalent FOV is shared by the *N*×*N* detector elements. For example, for an inner single 29 detector element, this FOV reduces to *FOV*min = arctg(*wr*/*NL*)/2 = 18.4º and *FOV*max = In a lens of *diameter D* and *f-number f#*, its *focal length L* is given by *L=D f#*. Then, the *magnification* of the system, when the lens is located at a vertical distance *hL* from the ceiling (see Fig. 5(b)), is *M*=*hL*/*L*, i.e. any dimension *do* of the original object in the ceiling creates a replica (image) on the PD surface of size *di* =*do*/*M*. For example, for the width of the lamp, we have AD=*M* A'D'. Geometrically, we can determine the image that is drawn on the PD surface by projecting every environment point along its path towards the imaging receiv‐ er through the lens center, similar to that shown in Fig. 5(b) for points A, B, C and D of the LED lamp. Therefore, a square *N*×*N* photodetector array of width *wr* (area *A=wr* 2 ) will only be able to observe any point inside of its square-shape equivalent *field of view* (FOV), as shown in Fig. 6 for a 4×4-pixel imaging receiver. The total equivalent FOV, *observation semi-angle*, varies between *FOV*min*=*arctg(*wr*/2*L*), in the center of a PD side, and *FOV*max=arctg(*wr*/ 2*L*), in a PD corner. For example, for the 4×4-pixel imaging receiver whose characteristics are specified in Table 2, we have 56.3° ≤ *FOV* ≤ 64.8°. However, this total equivalent FOV is shared by the *N*×*N* detector elements. For example, for an inner single detector element, this FOV reduces to *FOV*min*=*arctg(*wr*/*NL*)/2=18.4° and *FOV*max=arctg( 2*wr*/ *NL*)/2=23.3°. Therefore, this kind of receiver is very directed, where every pixel only observes a small portion of its tridimensional environment. Owing to the dimensions of the receiver structure with respect to the room size, a single LED is seen as a point by the receiver too, i.e. it will only illuminate a specific pixel of the PD array. The line-of-sight contribution of a single LED to the received optical power is given by

12 *p'*(

Multi-user visible light communication

14 contribute to the total received optical power.

$$P\_R = R\_\varepsilon(\phi) \int\_{\mathbb{A}} p'(\lambda) T(\rho, \lambda) A\_{\text{eff}}(\rho) d\lambda / \, d^2 = P\_\varepsilon \frac{n+1}{2\pi d^2} \cos^n \phi A\_r \cos \rho \delta\_{\downarrow \downarrow} p'(\lambda) T(\rho, \lambda) d\lambda \tag{9}$$

7

where *RE*(*ϕ*) is the LED radiation pattern in the outgoing angle *ϕ* defined in (1) and illustrated in Fig. 9(a), *A*eff=*Ar*cos *φ* is the *effective area* of the photodetecting element (pixel), whose physical area is *Ar=A*/*N*<sup>2</sup> , for an observation angle *φ* and *d* is the distance from the LED to the PD. Moreover, *T*(*φ*,*λ*) is the signal transmission of the filter, if this is incorporated (e.g. a blue filter to enhance the modulation bandwidth as described in section 2.1), and *p'*(*λ*)=*p*(*λ*)/*PE* is the normalized PSD of the WLED. When no filter is attached, *T*(*φ,λ*)=1 and *∫ <sup>λ</sup> p'*(*λ*)*T* (*φ*, *λ*)*dλ* =1. As we will describe in section 2.4, the light reflected on walls can also contribute to the total received optical power. 5 of-sight contribution of a single LED to the received optical power is given by ( ) ∫ ( ) ( ) ( ) ∫ ( ) ( ) <sup>6</sup> (9) 7 where *RE*() is the LED radiation pattern in the outgoing angle defined in (1) and 8 illustrated in Fig. 9(a), *A*eff = *Ar*cos is the *effective area* of the photodetecting element (pixel), whose physical area is *Ar* = *A*/*N*<sup>2</sup> 9 , for an observation angle and *d* is the distance from the 10 LED to the PD. Moreover, *T*(,) is the signal transmission of the filter, if this is incorporated 11 (e.g. a blue filter to enhance the modulation bandwidth as described in section 2.1), and )=*p*()/*PE* is the normalized PSD of the WLED. When no filter is attached, *T*(*,*) = 1 and

∫ ( ) ( ) <sup>13</sup> As we will describe in section 2.4, the light reflected on walls can also

16 Fig. 7 depicts the received light intensity images projected, through the lens, onto the 17 photodetector surface for three different positions of the imaging receiver in the room, as **Figure 6.** Equivalent field of view (FOV) of the 4×4-pixel imaging receiver.

15 **Fig. 6.** Equivalent field of view (FOV) of the 4×4-pixel imaging receiver.

18 specified in Fig. 7(a). Here, not only LOS image is considered but also the reflections of light 19 on the room"s surfaces. In Fig. 7(d), we can clearly recognize the reflections of lamps 5 and 6 20 on one of the windows, whereas for positions 1 and 2, the windows are out of the field of 21 view of the receiver. 22 Actually, each photodetecting element (pixel) integrates the total light arriving to it; 23 therefore, there will eventually be a 4×4 image. However, this figure is interesting to 24 illustrate which lamps directly illuminate a certain pixel and to see how two lamps never Fig. 7 depicts the received light intensity images projected, through the lens, onto the photo‐ detector surface for three different positions of the imaging receiver in the room, as specified in Fig. 7(a). Here, not only LOS image is considered but also the reflections of light on the room's surfaces. In Fig. 7(d), we can clearly recognize the reflections of lamps 5 and 6 on one of the windows, whereas for positions 1 and 2, the windows are out of the field of view of the receiver.

25 illuminate a single pixel without at least one of these lamps also illuminating another pixel. 26 As we will see, this characteristic of imaging receivers is what makes them very appropriate 27 for visible light communications. Actually, each photodetecting element (pixel) integrates the total light arriving to it; therefore, there will eventually be a 4×4 image. However, this figure is interesting to illustrate which lamps directly illuminate a certain pixel and to see how two lamps never illuminate a single pixel without at least one of these lamps also illuminating another pixel. As we will see, this characteristic of imaging receivers is what makes them very appropriate for visible light communications.

( ) ( ) ( ) ( ) ( ) ( ) <sup>2</sup> eff 2

*<sup>n</sup> PR p T A dd P A p T d <sup>d</sup>*

 arctg(√ *wr*/*NL*)/2 = 23.3º. Therefore, this kind of receiver is very directed, where every pixel only observes a small portion of its tridimensional environment. Owing to the dimensions of the receiver structure with respect to the room size, a single LED is seen as a point by the receiver too, i.e. it will only illuminate a specific pixel of the PD array. The line-

∫ ( ) ( ) <sup>6</sup> (9)

11 (e.g. a blue filter to enhance the modulation bandwidth as described in section 2.1), and

∫ ( ) ( ) <sup>13</sup> As we will describe in section 2.4, the light reflected on walls can also

 Fig. 7 depicts the received light intensity images projected, through the lens, onto the photodetector surface for three different positions of the imaging receiver in the room, as specified in Fig. 7(a). Here, not only LOS image is considered but also the reflections of light on the room"s surfaces. In Fig. 7(d), we can clearly recognize the reflections of lamps 5 and 6 on one of the windows, whereas for positions 1 and 2, the windows are out of the field of

 Actually, each photodetecting element (pixel) integrates the total light arriving to it; therefore, there will eventually be a 4×4 image. However, this figure is interesting to illustrate which lamps directly illuminate a certain pixel and to see how two lamps never illuminate a single pixel without at least one of these lamps also illuminating another pixel. As we will see, this characteristic of imaging receivers is what makes them very appropriate

)/*PE* is the normalized PSD of the WLED. When no filter is attached, *T*(

*R E E r*

5 of-sight contribution of a single LED to the received optical power is given by

 j l

normalized PSD of the WLED. When no filter is attached, *T*(*φ,λ*)=1 and *∫*

) is the LED radiation pattern in the outgoing angle

l

Multi-user visible light communication

 l jl

( ) ∫ ( ) ( ) ( )

whose physical area is *Ar* = *A*/*N*<sup>2</sup> 9 , for an observation angle

,

15 **Fig. 6.** Equivalent field of view (FOV) of the 4×4-pixel imaging receiver.

**Figure 6.** Equivalent field of view (FOV) of the 4×4-pixel imaging receiver.

f

42 Advances in Optical Communication

received optical power.

14 contribute to the total received optical power.

8 illustrated in Fig. 9(a), *A*eff = *Ar*cos

area is *Ar=A*/*N*<sup>2</sup>

10 LED to the PD. Moreover, *T*(

7 where *RE*(

)=*p*(

21 view of the receiver.

receiver.

27 for visible light communications.

communications.

12 *p'*(

<sup>1</sup> ' , / cos cos ' , <sup>2</sup>

where *RE*(*ϕ*) is the LED radiation pattern in the outgoing angle *ϕ* defined in (1) and illustrated in Fig. 9(a), *A*eff=*Ar*cos *φ* is the *effective area* of the photodetecting element (pixel), whose physical

Moreover, *T*(*φ*,*λ*) is the signal transmission of the filter, if this is incorporated (e.g. a blue filter to enhance the modulation bandwidth as described in section 2.1), and *p'*(*λ*)=*p*(*λ*)/*PE* is the

As we will describe in section 2.4, the light reflected on walls can also contribute to the total

(a) Lateral view of FOV (b) Top view of FOV

Fig. 7 depicts the received light intensity images projected, through the lens, onto the photo‐ detector surface for three different positions of the imaging receiver in the room, as specified in Fig. 7(a). Here, not only LOS image is considered but also the reflections of light on the room's surfaces. In Fig. 7(d), we can clearly recognize the reflections of lamps 5 and 6 on one of the windows, whereas for positions 1 and 2, the windows are out of the field of view of the

Actually, each photodetecting element (pixel) integrates the total light arriving to it; therefore, there will eventually be a 4×4 image. However, this figure is interesting to illustrate which lamps directly illuminate a certain pixel and to see how two lamps never illuminate a single pixel without at least one of these lamps also illuminating another pixel. As we will see, this characteristic of imaging receivers is what makes them very appropriate for visible light

p

<sup>+</sup> = = ò ò (9)

*n*

, for an observation angle *φ* and *d* is the distance from the LED to the PD.

is the *effective area* of the photodetecting element (pixel),

) is the signal transmission of the filter, if this is incorporated

f

l

 l jl l

*<sup>λ</sup> p'*(*λ*)*T* (*φ*, *λ*)*dλ* =1.

) = 1 and

defined in (1) and

*,*

and *d* is the distance from the

7

 j

(c) Image at receiver for location 2 (d) Image at receiver for location 3

(a) Top view of receiver locations (b) Image at receiver for location 1

**Figure 7.** Images impressed on photodetector surface for three different receiver locations.

1 **Fig. 7.** Images impressed on photodetector surface for three different receiver locations.

#### 3 An angle-diversity receiver makes use of multiple receiving elements (branches), oriented in *2.3.2. Angle-diversity non-imaging receiver*

12 angle,

2 **2.3.2. Angle-diversity non-imaging receiver**

5 has a different view of its environment, this diversified received signal can be used to 6 separate the information relative to several users by using an appropriate multi-user 7 detection scheme. Moreover, each receiving branch can be equipped with a *concentrator*, 8 increasing the gathering of received optical power. In this case, for a specific branch, the 9 *effective signal-collection area* becomes [8] ( ) { ( ) 10 (10) 11 where *Ar* is the physical area of the photodetector placed in that branch, the observation An angle-diversity receiver makes use of multiple receiving elements (branches), oriented in different directions, to collect the power emitted from optical sources. Since each element has a different view of its environment, this diversified received signal can be used to separate the information relative to several users by using an appropriate multi-user detection scheme. Moreover, each receiving branch can be equipped with a *concentrator*, increasing the gathering of received optical power. In this case, for a specific branch, the *effective signal-collection area* becomes [8]

4 different directions, to collect the power emitted from optical sources. Since each element

8 Optical Communication

$$A\_{\rm eff}(\boldsymbol{\varphi}) = \begin{cases} A\_{\rm r} \mathbf{g}(\boldsymbol{\varphi}) \cos \boldsymbol{\varphi}, & 0 \le \boldsymbol{\varphi} \le \boldsymbol{\varphi}\_{\boldsymbol{\varepsilon}} \\ 0 & \boldsymbol{\varphi} > \boldsymbol{\varphi}\_{\boldsymbol{\varepsilon}} \end{cases} \tag{10}$$

where *Ar* is the physical area of the photodetector placed in that branch, *φ* the observation angle, *φc* the concentrator FOV, and *g*(*φ*) its gain, which, for an idealized non-imaging concentrator with internal refractive index *n*, is given by [8]

$$g\left(\boldsymbol{\rho}\right) = \begin{cases} n^2 \;/\,\sin^2\boldsymbol{\rho}\_c & 0 \le \boldsymbol{\rho} \le \boldsymbol{\rho}\_c \\ 0 & \boldsymbol{\rho} > \boldsymbol{\rho}\_c \end{cases} \tag{11}$$

9

Fig. 8 depicts the equivalent FOV of a 7-branch non-imaging receiver with each branch having an individual FOV of 25° (the remaining parameters of the receiver are summarized in Table 2). Compared to the imaging receiver of section 2.3.1, its total equivalent FOV is 75°, and considering the individual single-element FOVs, the non-imaging receiver becomes very directed too. However, this structure, which requires a separate optical concentrator for each photodetector, is bulky and more costly than the imaging receiver, and, additionally, it does not provide so much diversity as the latter. ( ) { 1 (11) 2 **Fig. 8** depicts the equivalent FOV of a 7-branch non-imaging receiver with each branch 3 having an individual FOV of 25º (the remaining parameters of the receiver are summarized 4 in Table 2). Compared to the imaging receiver of section 2.3.1, its total equivalent FOV is 75º, 5 and considering the individual single-element FOVs, the non-imaging receiver becomes 6 very directed too. However, this structure, which requires a separate optical concentrator for 7 each photodetector, is bulky and more costly than the imaging receiver, and, additionally, it


**Table 2.** Parameters of imaging and non-imaging receivers. 9 **Table 2.** Parameters of imaging and non-imaging receivers.

8 does not provide so much diversity as the latter.

**Figure 8.** Equivalent field of view (FOV) of the 7-branch non-imaging receiver.

10 **Fig. 8.** Equivalent field of view (FOV) of the 7-branch non-imaging receiver.

#### **2.4. Simulation algorithm**

where *Ar* is the physical area of the photodetector placed in that branch, *φ* the observation angle, *φc* the concentrator FOV, and *g*(*φ*) its gain, which, for an idealized non-imaging

j

Fig. 8 depicts the equivalent FOV of a 7-branch non-imaging receiver with each branch having an individual FOV of 25° (the remaining parameters of the receiver are summarized in Table 2). Compared to the imaging receiver of section 2.3.1, its total equivalent FOV is 75°, and considering the individual single-element FOVs, the non-imaging receiver becomes very directed too. However, this structure, which requires a separate optical concentrator for each photodetector, is bulky and more costly than the imaging receiver, and, additionally, it does

 1 (11)

 **Fig. 8** depicts the equivalent FOV of a 7-branch non-imaging receiver with each branch having an individual FOV of 25º (the remaining parameters of the receiver are summarized in Table 2). Compared to the imaging receiver of section 2.3.1, its total equivalent FOV is 75º, and considering the individual single-element FOVs, the non-imaging receiver becomes very directed too. However, this structure, which requires a separate optical concentrator for each photodetector, is bulky and more costly than the imaging receiver, and, additionally, it

ìï £ £ <sup>=</sup> <sup>í</sup> ï > î

**Imaging receiver Non-imaging receiver**

Lens f-number (*f*#): 1 Concentrator refractive index (*n*): 1.5

**Imaging receiver Non-imaging receiver** Detector physical area (*A*): 36 cm2 Physical area of each PD (*Ar*): 2.25 cm2 Number of pixels (*P*): 16 (4×4) Number of branches (*P*): 7

(elevation, azimuth):

(a) Lateral view of FOV (b) Top view of FOV

ches (elevation, azimuth):

Detector physical area (*A*): 36 cm2 Physical area of each PD (*Ar*): 2.25 cm2 Number of pixels (*P*): 16 (4×4) Number of branches (*P*): 7 Pixel physical area (*Ar*): 2.25 cm2 Concentrator FOV (*φc*): 25° Lens f-number (*f* #): 1 Concentrator refractive index (*n*): 1.5

Lens diameter (*D*): 2 cm Orientation of detector branches

Lens diameter (*D*): 2 cm Orientation of detector bran-

10 **Fig. 8.** Equivalent field of view (FOV) of the 7-branch non-imaging receiver.

**Figure 8.** Equivalent field of view (FOV) of the 7-branch non-imaging receiver.

Pixel physical area (*Ar*): 2.25 cm2 Concentrator FOV (

*c c*

j j

 jj

*c*

(11)

9

(0°,0°), (50°,0°), (50°,60°), (50°,120°), (50°,180°), (50°,

(0º,0º), (50º,0º), (50º,60º), (50º,120º), (50º,180º), (50º,240º), (50º,300º)

240°), (50°,300°)

*<sup>c</sup>*): 25º

( ) 2 2 / sin 0 0

*n*

( ) {

concentrator with internal refractive index *n*, is given by [8]

*g*

not provide so much diversity as the latter.

8 does not provide so much diversity as the latter.

Multi-user visible light communication

44 Advances in Optical Communication

**Table 2.** Parameters of imaging and non-imaging receivers.

9 **Table 2.** Parameters of imaging and non-imaging receivers.

j

In wireless optical communications, the optical link is typically established by means of *intensity modulation* (IM), in which the desired waveform is modulated onto the instantaneous power of the carrier, in conjunction with *direct detection* (DD) as a down-conversion technique at the receiver end. Therefore, the transmitted waveform *x*(*t*) is the instantaneous optical power of the emitter, and the received waveform *y*(*t*) is the instantaneous current in the receiving photodetector. In this way, the optical channel with IM/DD can be modeled as a baseband linear system with impulse response *h*(*t*) or, alternatively, it can be described in terms of the frequency response

$$H(f) = \int\_{-\infty}^{\infty} h(t)e^{-j2\pi ft}dt\tag{12}$$

which is the Fourier transform of *h*(*t*). This channel model *h*(*t*) is practically stationary because it only varies when emitter, receiver or objects in the room are moved by tens of centimeters. In many applications, optical links are operated in the presence of intense infrared and visible background light. The received background light adds *shot noise*, which is usually the limiting noise source in a well-designed receiver. Due to its high intensity, this shot noise can be modeled as white, Gaussian, and independent of *x*(*t*). When little or no ambient light is present, the dominant noise source is receiver preamplifier noise, which is also signal-independent and Gaussian (though often nonwhite) [8]. Thus, the noise *n*(*t*) is usually modeled as Gaussian and signal-independent, and the instantaneous output current at the receiver can be represented as

$$y(t) = R\,\mathbf{x}(t) \otimes h(t) + n(t) \tag{13}$$

where the "⊗" symbol denotes convolution and *R* is the detector *responsivity* (A/W). According to (13), the optical link can be completely characterized by means of the impulse response *h*(*t*) and noise sources *n*(*t*). Knowing *h*(*t*) allows us to determine the multipath penalty, which limits the maximum baud rate. The second term is related to the *signal-to-noise ratio* (SNR), which determines the performance of the digital link.

In order to evaluate the impulse response on indoor wireless optical channels, several deterministic methods were first proposed [22]. However, these methods can only be imple‐ mented to determine the impulse response up to the third reflection due to their computational complexity. Later on, modified Monte Carlo-based ray-tracing algorithms were introduced, which present a lower computational cost and no limit to the number of reflections that can be considered [29][30].

In these algorithms, ray directions are randomly generated according to the radiation pattern from the emitter. The contribution of each ray from the source or after a bounce to the receiver is computed deterministically. Consequently, the discretization error is due to the number of random rays. The line-of-sight (LOS) and multiple-bounce impulse responses are considered when calculating the total impulse response.

2 as described in (10) an (11).

1()

19 for the observation angle

The LOS contribution to the received optical power at a certain detector, illustrated in Fig. 9(a), can be directly determined by using (9). In the case of non-imaging receivers, when they are equipped with a concentrator, their effective area *A*eff(*φ*) is also affected by its gain as described in (10) an (11). Multi-user visible light communication 11 1 they are equipped with a concentrator, their effective area *A*eff() is also affected by its gain

4 contribution after reflection off a wall. **Figure 9.** Line-of-sight (LOS) contribution of a single LED chip to received power and its power contribution after re‐ flection off a wall.

3 **Fig. 9.** Line-of-sight (LOS) contribution of a single LED chip to received power and its power

5 Additionally, when the communication is established in a room with reflectors, the

6 radiation from the emitter can reach the receiver after any number of reflections, as depicted 7 in Fig. 9(b) for the first-order reflection. In a ray-tracing algorithm, many rays are generated 8 at the emitter position with a probability distribution equal to its normalized radiation 9 pattern *RE*(,*n*)/*PE* (see eqn. (1)). The power of each generated ray is initially *PE*/*N*, where *N* 10 is the number of rays used to discretize the source. When a ray impinges on a surface, the 11 reflection point is converted into a new optical source, thus, a new ray is generated with a 12 probability distribution provided by the normalized reflection pattern of that surface, 13 *RS'*(,") = *RS*(,",)/*PI*(), described by Phong"s model according to (8). The process 14 continues throughout the simulation time *t*max. After each reflection, the reflected power 15 reaching the receiver is computed by ( ) ( ) ( ) ∫ ( ) ( ) ( ) ( ) ( ) (14) Additionally, when the communication is established in a room with reflectors, the radiation from the emitter can reach the receiver after any number of reflections, as depicted in Fig. 9(b) for the first-order reflection. In a ray-tracing algorithm, many rays are generated at the emitter position with a probability distribution equal to its normalized radiation pattern *RE*(*ϕ*,*n*)/*PE* (see eqn. (1)). The power of each generated ray is initially *PE*/*N*, where *N* is the number of rays used to discretize the source. When a ray impinges on a surface, the reflection point is converted into a new optical source, thus, a new ray is generated with a probability distribution provided by the normalized reflection pattern of that surface, *RS'*(*θ*,*θ*')=*RS*(*θ*,*θ*',*λ*)/ *PI ρ*(*λ*), described by Phong's model according to (8). The process continues throughout the simulation time *t*max. After each reflection, the reflected power reaching the receiver is com‐ puted by

$$P\_{\mathbb{R}}^{(l)} = \mathbb{R}\_{\mathbb{S}}^{\cdot}(\boldsymbol{\theta}, \boldsymbol{\theta}^{\cdot}) A\_{\text{eff}}\left(\boldsymbol{\varphi}\right) \frac{\mathsf{P}\_{\mathbb{E}}}{N} \int\_{\mathbb{X}} \rho\_{1}(\boldsymbol{\lambda}) \rho\_{2}(\boldsymbol{\lambda}) ... \rho\_{\boldsymbol{\lambda}}(\boldsymbol{\lambda}) p^{\prime}(\boldsymbol{\lambda}) \mathrm{T}\left(\boldsymbol{\varphi}, \boldsymbol{\lambda}\right) d\boldsymbol{\lambda} \,\mathrm{\/}\mathrm{d}^{2} \tag{14}$$

. The remaining parameters were previously described for eqn.

20 (8)-(11). 21 In the VLC multi-user application, each lamp is composed of a significant number *M* of 22 single emitters (LEDs) and we require an angle-diversity, imaging or non-imaging, receiver, composed of multiple receiving elements. By using (14), the contribution of the *i*th 23 ray emitted by the *m*th LED (of the *l*th lamp) to the received power reaching each *j* 24 th branch of the where (*k*) denotes *k*th reflection of the ray since it originated from an emitter, *ρ*1(*λ*)*ρ*2(*λ*)…*ρk*(*λ*) are the reflection coefficients of the surfaces against which the ray collided, *d* is the distance between the last reflection point and receiver and *A*eff(*φ*) the effective area for the observation angle *φ*. The remaining parameters were previously described for eqn. (8)-(11).

In the VLC multi-user application, each lamp is composed of a significant number *M* of single emitters (LEDs) and we require an angle-diversity, imaging or non-imaging, receiver, com‐ posed of multiple receiving elements. By using (14), the contribution of the *i* th ray emitted by the *m*th LED (of the *l* th lamp) to the received power reaching each *j* th branch of the receiver during a certain time interval (*pi*, *<sup>j</sup>*,*<sup>k</sup>* (*l*,*m*) , *k*th time interval) can be computed. The total received power due to the *l* th LED lamp at the *j* th branch of the optical detector in the *k*th time interval (width Δt) is computed as the sum of the power of the *N <sup>j</sup>*,*<sup>k</sup>* (*l*) =∑ *m N <sup>j</sup>*,*<sup>k</sup>* (*l*,*m*) rays that contribute in

that interval

The LOS contribution to the received optical power at a certain detector, illustrated in Fig. 9(a), can be directly determined by using (9). In the case of non-imaging receivers, when they are equipped with a concentrator, their effective area *A*eff(*φ*) is also affected by its gain as

(a) LOS contribution (b) Power contribution after a reflection

,*n*)/*PE* (see eqn. (1)). The power of each generated ray is initially *PE*/*N*, where *N*

) are the reflection coefficients of the surfaces against which the ray collided,

), described by Phong"s model according to (8). The process

. The remaining parameters were previously described for eqn.

ò (14)

3 **Fig. 9.** Line-of-sight (LOS) contribution of a single LED chip to received power and its power

**Figure 9.** Line-of-sight (LOS) contribution of a single LED chip to received power and its power contribution after re‐

Additionally, when the communication is established in a room with reflectors, the radiation from the emitter can reach the receiver after any number of reflections, as depicted in Fig. 9(b) for the first-order reflection. In a ray-tracing algorithm, many rays are generated at the emitter position with a probability distribution equal to its normalized radiation pattern *RE*(*ϕ*,*n*)/*PE* (see eqn. (1)). The power of each generated ray is initially *PE*/*N*, where *N* is the number of rays used to discretize the source. When a ray impinges on a surface, the reflection point is converted into a new optical source, thus, a new ray is generated with a probability distribution provided by the normalized reflection pattern of that surface, *RS'*(*θ*,*θ*')=*RS*(*θ*,*θ*',*λ*)/

 Additionally, when the communication is established in a room with reflectors, the radiation from the emitter can reach the receiver after any number of reflections, as depicted in Fig. 9(b) for the first-order reflection. In a ray-tracing algorithm, many rays are generated at the emitter position with a probability distribution equal to its normalized radiation

10 is the number of rays used to discretize the source. When a ray impinges on a surface, the 11 reflection point is converted into a new optical source, thus, a new ray is generated with a 12 probability distribution provided by the normalized reflection pattern of that surface,

14 continues throughout the simulation time *t*max. After each reflection, the reflected power

where (*k*) denotes *k*th 16 reflection of the ray since it originated from an emitter,

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) <sup>2</sup> eff 1 2 ' ,' ' ,/ *<sup>k</sup> <sup>E</sup>*

*<sup>P</sup> PR A p T dd <sup>N</sup>*

21 In the VLC multi-user application, each lamp is composed of a significant number *M* of 22 single emitters (LEDs) and we require an angle-diversity, imaging or non-imaging, receiver, composed of multiple receiving elements. By using (14), the contribution of the *i*th 23 ray emitted by the *m*th LED (of the *l*th lamp) to the received power reaching each *j* 24 th branch of the

angle *φ*. The remaining parameters were previously described for eqn. (8)-(11).

where (*k*) denotes *k*th reflection of the ray since it originated from an emitter, *ρ*1(*λ*)*ρ*2(*λ*)…*ρk*(*λ*) are the reflection coefficients of the surfaces against which the ray collided, *d* is the distance between the last reflection point and receiver and *A*eff(*φ*) the effective area for the observation

In the VLC multi-user application, each lamp is composed of a significant number *M* of single emitters (LEDs) and we require an angle-diversity, imaging or non-imaging, receiver, com‐

∫ ( ) ( ) ( ) ( ) ( )

*ρ*(*λ*), described by Phong's model according to (8). The process continues throughout the simulation time *t*max. After each reflection, the reflected power reaching the receiver is com‐

11

) is also affected by its gain

(14)

the effective area

described in (10) an (11).

46 Advances in Optical Communication

2 as described in (10) an (11).

Multi-user visible light communication

4 contribution after reflection off a wall.

15 reaching the receiver is computed by

( ) ( ) ( )

qq

 j 18 *d* is the distance between the last reflection point and receiver and *A*eff(

l= ¼

 r l r l r l l jl l

*R S k*

9 pattern *RE*(

flection off a wall.

,") = *RS*(,",)/*PI*(

)…*k*(

19 for the observation angle

13 *RS'*(

*PI*

1()17 (

puted by

20 (8)-(11).

1 they are equipped with a concentrator, their effective area *A*eff(

$$p\_{l,k}^{(l)} = \sum\_{m=1}^{M} \sum\_{i=1}^{N\_{l,k}^{(l,m)}} p\_{l,j,k}^{(l,m)} \tag{15}$$

At the receiver end, the impulse responses *hj* (*l*) (*t*) at all branches (*j*=1,..., *P*) due to the *l* th lamp (*l*=1,..., *L*) are given by

$$h\_{\rangle}^{(l)}\left(t\right) = \sum\_{k=0}^{K-1} p\_{\rangle,k}^{(l)} \mathcal{S}\left(t - k\Delta t\right) \tag{16}$$

where *K*=*t*max/Δ*t*, and where we have assumed as the time origin the instant when the rays are generated from the emitter (lamp). This process must be repeated in order to obtain the different impulse responses between each emitter and each receiving branch in the multi-user scenario.

Fig. 10 shows the power balance at the receiver plane for the imaging receiver (see parameters for the study by referring to Table 1 and Table 2) when a blue filter is incorporated to enhance modulation bandwidth. Fig. 11 presents the same study results when, in its place, a nonimaging receiver is used (see Table 2 for parameters of this receiver). In both results, five reflections of light on walls have been considered, which ensures that at worst we are only neglecting less than 1% of received power if a greater number of reflections were considered. We can observe that the changes in power level when moving around the room are smoother for an imaging-receiver, but, more importantly, a non-imaging receiver offers a power gain of about 12 dB due to the use of the concentrator.

Fig. 12 and Fig. 13 show the impulse responses for imaging and non-imaging receivers, respectively, when these are located at position 1, as indicated in Fig. 7(a). In the case of the imaging receiver, we can observe a clear connection between image of Fig. 7(b) and the obtained impulse responses. We can also verify that they are responses with a substantial LOS component (more than 80% of the received power, in the blue region, is due to this factor), in contrast with those at the non-imaging receiver, where multiple-bounce components, after the first large impulse, are more noteworthy (in this second case, the LOS components represent approximately 66% of the total received power). In spite of these components corresponding to reflections on walls, we can observe in Fig. 13 that users 3 and 6 are overshadowed by users 2 and 5, respectively, i.e. the first ones are practically delayed replicas of smaller intensity of the latter ones, which, as we will see, will limit maximum achievable joint data rates. This is something that does not occur in the imaging receiver case.

**Figure 10.** Power balance at the receiver plane for the imaging receiver (*Pmin*=-10.4 dBm; *Pmax*=-6.2 dBm; *<sup>P</sup>*¯=*-*7.4 dBm).

**Figure 11.** Power balance at the receiver plane for the non-imaging receiver (*Pmin*=2.2 dBm; *Pmax*=5.8 dBm; *<sup>P</sup>*¯=4.5 dBm).

**Figure 12.** Impulse responses between transmitting users (lamps) and each receiving branch (pixel) for imaging receiv‐ er at position 1 (see Fig. 7(a)).

**Figure 10.** Power balance at the receiver plane for the imaging receiver (*Pmin*=-10.4 dBm; *Pmax*=-6.2 dBm; *<sup>P</sup>*¯=*-*7.4 dBm).

48 Advances in Optical Communication

**Figure 11.** Power balance at the receiver plane for the non-imaging receiver (*Pmin*=2.2 dBm; *Pmax*=5.8 dBm; *<sup>P</sup>*¯=4.5 dBm).

**Figure 13.** Impulse responses between transmitting users (lamps) and each receiving branch for non-imaging receiver at position 1 (see Fig. 7(a)).

Finally, we have determined the available signal-to-noise ratio (SNR) throughout the room at the receiver plane. For that, we have considered the windows as planar Lambertian ambient light (noise) sources with spectral radiant emittance *Sw*=0.2 W/(nm m2 ), as in [31]. The SNR is expressed as [8]

$$\text{SNR} = \frac{(\rho\_s \rho\_s)^2}{\sigma\_{\text{total}}^2} \tag{17}$$

where *R* is the detector responsivity, *Ps* is the average received signal power and *σ*total is the total noise variance, which is the sum of the contributions of shot and thermal noises

$$
\sigma\_{\text{total}}^2 = \sigma\_{\text{shot}}^2 + \sigma\_{\text{thermal}}^2 \tag{18}
$$

In a well-designed receiver, and in the presence of intense background light, the shot noise is the dominant term in (18), and is given by [8] Multi-user visible light communication 15

$$
\sigma\_{\text{total}}^2 \approx \sigma\_{\text{shot}}^2 = 2qR\{P\_s + P\_n\}B \tag{19}
$$

where *q* is the electron charge, *R* the detector responsivity, *Ps* and *Pn* the average received optical power corresponding to the desired signal and the ambient light, respectively, and *B* is the channel bandwidth (20 MHz). ( ) (19) 3 where *q* is the electron charge, *R* the detector responsivity, *Ps* and *Pn* the average received 4 optical power corresponding to the desired signal and the ambient light, respectively, and *B*

Fig. 14 shows the available SNR throughout the room at the receiver plane for imaging and non-imaging receivers. The SNR values descend when approaching the windows, as expected, but they are considerably above 50 dB throughout the room for both types of receivers, with a not insignificant SNR gain in the case of non-imaging receivers. 5 is the channel bandwidth (20 MHz). 6 Fig. 14 shows the available SNR throughout the room at the receiver plane for imaging and 7 non-imaging receivers. The SNR values descend when approaching the windows, as 8 expected, but they are considerably above 50 dB throughout the room for both types of 9 receivers, with a not insignificant SNR gain in the case of non-imaging receivers.

**Figure 14.** Signal-to-noise ratio (SNR) throughout the room at the receiver plane.

11 **3. The MIMO-OFDM system**

 ( )

10 **Fig. 14.** Signal-to-noise ratio (SNR) throughout the room at the receiver plane.

12 Fig. 15 shows the block diagram of the MIMO-OFDM system for multi-user 13 communications over an indoor wireless optical channel. As we can see in the transmitter structure, *pbp*(*l*) data bits are generated by *l* 14 th user and modulated by using an appropriate


**Figure 15.** Multi-user MIMO-OFDM system for optical wireless communications.

#### **3. The MIMO-OFDM system**

Finally, we have determined the available signal-to-noise ratio (SNR) throughout the room at the receiver plane. For that, we have considered the windows as planar Lambertian ambient

> RPs)2 σtotal

where *R* is the detector responsivity, *Ps* is the average received signal power and *σ*total is the

In a well-designed receiver, and in the presence of intense background light, the shot noise is

qR(Ps + Pn)B

1 In a well-designed receiver, and in the presence of intense background light, the shot noise

3 where *q* is the electron charge, *R* the detector responsivity, *Ps* and *Pn* the average received 4 optical power corresponding to the desired signal and the ambient light, respectively, and *B*

6 Fig. 14 shows the available SNR throughout the room at the receiver plane for imaging and 7 non-imaging receivers. The SNR values descend when approaching the windows, as 8 expected, but they are considerably above 50 dB throughout the room for both types of

where *q* is the electron charge, *R* the detector responsivity, *Ps* and *Pn* the average received optical power corresponding to the desired signal and the ambient light, respectively, and *B*

Fig. 14 shows the available SNR throughout the room at the receiver plane for imaging and non-imaging receivers. The SNR values descend when approaching the windows, as expected, but they are considerably above 50 dB throughout the room for both types of receivers, with

(a) SNR for imaging receiver (b) SNR for non-imaging receiver

12 Fig. 15 shows the block diagram of the MIMO-OFDM system for multi-user 13 communications over an indoor wireless optical channel. As we can see in the transmitter structure, *pbp*(*l*) data bits are generated by *l* 14 th user and modulated by using an appropriate


), as in [31]. The SNR is

15

<sup>2</sup> (17)

<sup>2</sup> (18)

( ) (19)

(19)

light (noise) sources with spectral radiant emittance *Sw*=0.2 W/(nm m2

σtotal <sup>2</sup> =σshot <sup>2</sup> <sup>+</sup> σthermal

σtotal <sup>2</sup> ≈σshot <sup>2</sup> =2

a not insignificant SNR gain in the case of non-imaging receivers.

9 receivers, with a not insignificant SNR gain in the case of non-imaging receivers.

10 **Fig. 14.** Signal-to-noise ratio (SNR) throughout the room at the receiver plane.

**Figure 14.** Signal-to-noise ratio (SNR) throughout the room at the receiver plane.

the dominant term in (18), and is given by [8]

Multi-user visible light communication

2 is the dominant term in (18), and is given by [8]

 

is the channel bandwidth (20 MHz).

5 is the channel bandwidth (20 MHz).

11 **3. The MIMO-OFDM system**

 ( ) SNR= (

total noise variance, which is the sum of the contributions of shot and thermal noises

expressed as [8]

50 Advances in Optical Communication

Fig. 15 shows the block diagram of the MIMO-OFDM system for multi-user communications over an indoor wireless optical channel. As we can see in the transmitter structure, Σ*pbp* (*l*) data

bits are generated by *l* th user and modulated by using an appropriate 2 *bp* (*l*) -QAM (*quadrature amplitude modulation*) modulator, *bp* (*l*) being the number of bits conveyed by the *p*th subcarrier (1 ≤ *p* ≤ *SI* ), according to a rate adaptive algorithm [32][33]. Then, *N – SI* zeros are padded to this set of *SI* symbols generated by the modulators, the first zero being added before, corre‐ sponding to the direct-current (DC) value, and the remaining ones after. Finally, the complex conjugate of the mirror of the word of *N* symbols is added before computing the IFFT. The outgoing IFFT symbol is a real sequence of 2*N* points, which can be made non-negative by adding an appropriate DC level. Moreover, a cyclic prefix (*Ne*-sample extension) is inserted to combat inter-symbol interference (ISI), leading to a transmitted signal with a total of *NS*=2*N* +*Ne* samples and duration *TS*. This positive and real signal can modulate the intensity of light emitted by the optical source. Note that the cyclic extension prefix will be ISI-corrupted due to the low-pass channel response and will be discarded at receiver. Next, the FFT of the remaining 2*N* points will be computed at each receiving branch, and only the first *SI* points (after the DC value) will be considered by the multi-user (MU) detector.

As we have *L* transmitters and the receiver possesses *P* receiving branches, the optical channel constitutes a MIMO system, whose individual impulse responses are given by (16). We can consider that, after the FFT processing carried out by each branch of a new received OFDM symbol, the *P*-branch detector array provides the MU detector with a vector of complex symbols*xp* at *p*th subcarrier. This is the superposition of the independently distorted signals associated with the *L* users sharing the same space-frequency resource and also corrupted by noise at the detector array elements

$$\mathbf{x}\_p = \mathbf{H}\_p \mathbf{s}\_p + \mathbf{n}\_p \tag{20}$$

where the vector *x<sup>p</sup>* ∈ ℂ*P*×1 of received signals at the *p*th subcarrier, the vector *s<sup>p</sup>* ∈ ℂ*<sup>L</sup>* ×1 of transmitted signals and the array noise *np* ∈ ℂ*P*×1 , respectively, are given by

$$\begin{aligned} \mathbf{x}\_p &= \left(\mathbf{x}\_{1p}, \mathbf{x}\_{2p}, \dots, \mathbf{x}\_{Np}\right)^T\\ \mathbf{s}\_p &= \left(\mathbf{s}\_p^{(1)}, \mathbf{s}\_p^{(2)}, \dots, \mathbf{s}\_p^{(L)}\right)^T\\ \mathbf{n}\_p &= \left(\mathbf{n}\_{1p}, \mathbf{n}\_{2p}, \dots, \mathbf{n}\_{Np}\right)^T \end{aligned} \tag{21}$$

where ()*<sup>T</sup>* means the transpose of (), thus *xp*, *sp* and *np* are all column vectors. The frequency domain channel transfer function factor matrix *Hp* ∈ ℂ*P*×*<sup>L</sup>* is composed of the set of channel transfer vectors *H<sup>p</sup>* (*l*) ∈ ℂ*P*×1 , *l*=1,..., *L* of the *L* users

$$\mathbf{H}\_p = \left( \mathbf{H}\_p^{(1)}, \mathbf{H}\_p^{(2)}, \dots, \mathbf{H}\_p^{(L)} \right) \tag{22}$$

each of which hosts the frequency domain channel transfer factor between the single emitter source associated with a particular user *l* and the receiving branches *j*=1,..., *P* at the *p*th subcarrier band

$$\mathbf{H}\_p^{(l)} = \left( H\_{1p}^{(l)}, H\_{2p}^{(l)}, \dots, H\_{pp}^{(l)} \right)^T \tag{23}$$

with *l*=1,..., *L*. Note that the frequency domain channel transfer factors *Hjp* (*l*) , ∀*p* between the *l* th emitter and the *j* th receiving branch are obtained by computing the Fourier transform (12) at the subcarrier frequency *f=pf*<sup>0</sup> over the corresponding impulse response (16), where *f*0=1/*T*. Here, *T* is the time duration of the part of the OFDM symbol which actually conveys infor‐ mation, i.e. the OFDM symbol duration excluding the cyclic prefix extension, *T*=2*NTS*/ *NS*=2*NTS*/(2*N*+*Ne*).

#### **3.1. Least squares error detector**

As we have *L* transmitters and the receiver possesses *P* receiving branches, the optical channel constitutes a MIMO system, whose individual impulse responses are given by (16). We can consider that, after the FFT processing carried out by each branch of a new received OFDM symbol, the *P*-branch detector array provides the MU detector with a vector of complex symbols*xp* at *p*th subcarrier. This is the superposition of the independently distorted signals associated with the *L* users sharing the same space-frequency resource and also corrupted by

( )

*T*

*T*

*<sup>T</sup> <sup>L</sup>*

, ,,

*xx x*

1 2

*x*

*s*

*n*

= ¼

*p p p Pp*

1 2

, *l*=1,..., *L* of the *L* users

= ¼

*p p p Pp*

*p pp p*

= ¼

( )

, ,,

*ss s*

(1) (2) ( )

( )

where ()*<sup>T</sup>* means the transpose of (), thus *xp*, *sp* and *np* are all column vectors. The frequency domain channel transfer function factor matrix *Hp* ∈ ℂ*P*×*<sup>L</sup>* is composed of the set of channel

( ) (1) (2) ( ) , ,, *<sup>L</sup>*

each of which hosts the frequency domain channel transfer factor between the single emitter source associated with a particular user *l* and the receiving branches *j*=1,..., *P* at the *p*th subcarrier

at the subcarrier frequency *f=pf*<sup>0</sup> over the corresponding impulse response (16), where *f*0=1/*T*. Here, *T* is the time duration of the part of the OFDM symbol which actually conveys infor‐ mation, i.e. the OFDM symbol duration excluding the cyclic prefix extension, *T*=2*NTS*/

( ) () () () () 1 2 , ,, *<sup>T</sup> l ll l*

with *l*=1,..., *L*. Note that the frequency domain channel transfer factors *Hjp*

, ,,

*nn n*

*p pp p x Hs n* = + (20)

of received signals at the *p*th subcarrier, the vector *s<sup>p</sup>* ∈ ℂ*<sup>L</sup>* ×1 of

, respectively, are given by

*p pp p H HH H* = ¼ (22)

*<sup>p</sup> HH H p p Pp H* = ¼ (23)

th receiving branch are obtained by computing the Fourier transform (12)

(*l*)

, ∀*p* between the

(21)

noise at the detector array elements

transmitted signals and the array noise *np* ∈ ℂ*P*×1

where the vector *x<sup>p</sup>* ∈ ℂ*P*×1

52 Advances in Optical Communication

transfer vectors *H<sup>p</sup>*

th emitter and the *j*

*NS*=2*NTS*/(2*N*+*Ne*).

band

*l*

(*l*) ∈ ℂ*P*×1 Using a linear detector, an estimate *ŝ<sup>p</sup>* ∈ ℂ*<sup>L</sup>* ×1 at the *p*th subcarrier band of the vector of transmitted signals *sp* of *L* simultaneous users is generated by linearly combining the signals received by *P* different receiving branches with the aid of a weight matrix *Hp* ∈ ℂ*P*×*<sup>L</sup>*

$$
\hat{\mathbf{s}}\_p = \mathbf{W}\_p^H \mathbf{x}\_p \tag{24}
$$

where *W<sup>p</sup> <sup>H</sup>* denotes the complex conjugate matrix of matrix *Wp*. When least-squares (LS) error detector is considered, also called zero-forcing (ZF) combiner, the weight matrix *W<sup>p</sup>*,LS ∈ ℂ*P*×*<sup>L</sup>* is given by [34]

$$\mathbf{W}\_{p, \text{LS}} = \mathbf{H}\_p (\mathbf{H}\_p^H \mathbf{H}\_p)^{-1} \tag{25}$$

By substituting the received signal's model of (20) and the LS estimation based weight matrix (25) into (24), we obtain

$$
\hat{\mathbf{s}}\_{p, \text{LS}} = \mathbf{s}\_p + \mathbf{W}\_{p, \text{LS}}^H \mathbf{n}\_p \tag{26}
$$

which indicates that the LS-estimate *ŝp,*LS of the transmitted signal vector *sp* of *L* simultaneous users is an unbiased noise-contaminated version of *sp*, so that *E*{ *ŝp,*LS }=*sp*. When using the LS combiner, the *l* th user's associated vector component of estimate (24) of the vector of transmitted signals at the *p*th subcarrier can be expressed as

$$
\hat{\mathbf{s}}\_{p,\rm LS}^{(l)} = \mathbf{W}\_{p,\rm LS}^{(l)H} \mathbf{x}\_p \tag{27}
$$

where the *l* th user's associated weight vector W*<sup>p</sup>*,LS (*l*)*<sup>H</sup>* ∈ ℂ*P*×1 coincides with the *l* th column vector of the matrix *Wp*,LS. The complex symbol that is most likely to have been transmitted by the *l* th user can be determined by minimizing the Euclidean distance between estimate (27) of the transmitted signal obtained at the *l* th user's combiner output and all the constellation points associated with the specific modulation scheme employed. This only requires *M=*2 *bp* (*l*) evalua‐ tions compared to the *ML* ones of the optimum *maximum likelihood* (ML) detector [34], and the performance degradation is not significant [19].

#### **3.2. Frequency-domain channel transfer factor matrix estimation**

From (25) and (27), we can observe that the LS detector requires knowledge of the transfer factor matrix *Hp*. The method described in [35], where TS known training sequences are used to estimate the channel transfer function between a single user and the receiver, can be used to estimate matrix *Hp*, assuming that only one user is transmitting in a specific instant during the training periods. If a certain known training sequence *Xp* is transmitted by the *l* th user over the slowly time-varying wireless optical channel, the channel response of each sub-band *Hjp* (*l*) for this user at the *j* th receiving branch can be estimated from the *SI* received symbols (*Yjp* (*l*) ) as follows

$$
\hat{H}^{(j)}\_{\;\;\!\!\!p} = Y^{(j)}\_{\;\!\!\!p} \mid X\_p \tag{28}
$$

Note that *Ĥjp* (*l*) values are distorted by noise and therefore several training sequences should be transmitted, and then the mean values of the estimates can be used to obtain a better channel characterization. In fact, by using ten training sequences, the channel response estimation given by (28) is very close to the actual channel response, and we will obtain a system performance very similar to that of the ideal case when a perfect knowledge of the channel response is available [35].

#### **3.3. Rate adaptive algorithm**

In this chapter, we will apply the rate adaptive algorithm described in [32]. Here, we will only describe it briefly. Effective demodulation SNR can be computed at receiver as follows (Fig. 16): after each OFDM symbol demodulation, the retrieved data bits are modulated again and the average SNR of received QAM symbols is computed, using outgoing QAM modulators symbols as reference (we are assuming error-free transmission). The calculation of the *l* th user's effective demodulation SNR is given by

$$\overline{\text{SNR}}\_{\text{eff}}^{(l)} = \left| \overline{\mathbf{s}\_p^{(l)}} \right|^2 / \left| \overline{r\_p^{(l)} - \mathbf{s}\_p^{(l)}} \right|^2 \tag{29}$$

where *sp* (*l*) and *rp* (*l*) are the *l* th user's transmitted and received (before demodulation) data symbols, respectively. From (29), it can be deduced that the effective SNR is an average of all constituent data symbols (*p*=1,..., *SI* ) of each received OFDM frame. The channel response estimation and the mean effective demodulator SNR of each received OFDM symbol can be used to determine the SNR at the *p*th subcarrier band as follows [32]

$$\text{SNR}\_p^{(l)} = \frac{\overline{\left[\left(\boldsymbol{H}\_p^H \boldsymbol{H}\_p\right)^{-1}\right]}\_{\text{[l,l]}}}{\overline{\left[\left(\boldsymbol{H}\_p^H \boldsymbol{H}\_p\right)^{-1}\right]}\_{\text{[l,l]}}} \overline{\text{SNR}\_{\text{off}}^{(l)}}\tag{30}$$

The sub-band SNR value can be compared with switching levels for picking out the modulation mode (including 'no transmission', i.e. *bp* (*l*) =0) that ensures the instantaneous bit error rate (BER) always remains below a certain threshold [35]. In addition, disabled subcarriers, owing to their low SNR values, must carry on sending dummy data so as to compute their current sub-band SNR by means of (30). These dummy symbols should be known *a priori* by receiver in order to avoid an erroneous calculation of the effective demodulation SNR.

A further improvement can be made if subcarriers with higher SNR values between two switching levels are prompted to use the next modulation mode, whenever the average error probability does not exceed the imposed threshold [32]. Let *bp* (*l*) be the number of bits conveyed by the *p*th subcarrier, and *Pp* (*l*) the bit error probability of the subcarrier when the modulation mode 2 *bp* (*l*) -QAM is used by the *l* th user, thus the average error probability is given by

$$P\_{\text{avg}}^{\text{(j)}} = \frac{1}{\mathcal{B}^{\text{(J)}}} \sum\_{p=1}^{S\_l} b\_p^{\text{(j)}} P\_p^{\text{(j)}} \{ b\_p^{\text{(j)}}, \text{SNR}\_p^{\text{(j)}} \} \tag{31}$$

where *B*(*l*) is the total throughput of the *l* th user's adaptive system: *B*(*l*) =Σ*pbp* (*l*) . The bit error probability *Pp* (*l*) (*bp* (*l*) ,SNR*<sup>p</sup>* (*l*) ) can be determined from the estimated signal-to-noise ratio of each sub-band (SNR*<sup>p</sup>* (*l*) ) given by (30) and the BER curves against SNR obtained over AWGN channel [34][35]. Initially, the modulation modes of subcarriers are set to those that exceed the switching levels for a certain target BER, and then the modulation modes are successively increased for the 'best subcarriers' trying to enhance *B*(*l*) , while ensuring that *P*avg (*l*) does not exceed the imposed BER threshold value [32].

**Figure 16.** Multi-user adaptive detector.

to estimate matrix *Hp*, assuming that only one user is transmitting in a specific instant during

the slowly time-varying wireless optical channel, the channel response of each sub-band *Hjp*

th user over

(*l*) ) as

th user's

(30)

received symbols (*Yjp*

(28)

*p pp* = - *s rs* (29)

) of each received OFDM frame. The channel response

=0) that ensures the instantaneous bit error rate (BER)

th user's transmitted and received (before demodulation) data

(*l*)

the training periods. If a certain known training sequence *Xp* is transmitted by the *l*

H

(l) =Y jp

^ jp

th receiving branch can be estimated from the *SI*

(l) / X p

be transmitted, and then the mean values of the estimates can be used to obtain a better channel characterization. In fact, by using ten training sequences, the channel response estimation given by (28) is very close to the actual channel response, and we will obtain a system performance very similar to that of the ideal case when a perfect knowledge of the channel

In this chapter, we will apply the rate adaptive algorithm described in [32]. Here, we will only describe it briefly. Effective demodulation SNR can be computed at receiver as follows (Fig. 16): after each OFDM symbol demodulation, the retrieved data bits are modulated again and the average SNR of received QAM symbols is computed, using outgoing QAM modulators

symbols as reference (we are assuming error-free transmission). The calculation of the *l*

2 2 ( ) () () () SNR / eff *<sup>l</sup> l ll*

symbols, respectively. From (29), it can be deduced that the effective SNR is an average of all

estimation and the mean effective demodulator SNR of each received OFDM symbol can be

1


[ ]

*l, l*

*l, l*

( ) [ ] ( ) eff' <sup>1</sup>


The sub-band SNR value can be compared with switching levels for picking out the modulation

always remains below a certain threshold [35]. In addition, disabled subcarriers, owing to their low SNR values, must carry on sending dummy data so as to compute their current sub-band

( )

*H H*

é ù ê ú ë û <sup>=</sup> é ù ê ú ë û

SNR SNR *H p p <sup>l</sup> <sup>l</sup>*

( )

*H H*

(*l*)

*p p*

*<sup>p</sup> <sup>H</sup>*

(*l*) values are distorted by noise and therefore several training sequences should

for this user at the *j*

54 Advances in Optical Communication

follows

Note that *Ĥjp*

where *sp*

(*l*) and *rp* (*l*)

response is available [35].

**3.3. Rate adaptive algorithm**

effective demodulation SNR is given by

constituent data symbols (*p*=1,..., *SI*

mode (including 'no transmission', i.e. *bp*

are the *l*

used to determine the SNR at the *p*th subcarrier band as follows [32]

#### **4. Results and discussion**

In this section, we will consider two communication scenarios. The first is concerned with jointly demodulating the information of all the users, which we will denote as *joint detection*, and a second scenario in which, despite having a multi-user environment (several lamps transmitting information simultaneously), the receiver is only concerned, at a specific receiver point, with the data corresponding to a particular user lamp, which we will refer to as *singleuser detection*.

#### **4.1. Joint detection**

In this section, we show the results obtained with an adaptive MIMO-OFDM system based on LS detection, which can select the most appropriate modulation mode for each subcarrier from the 5-ary group ('no transmission', BPSK, QPSK, 16-QAM, 64-QAM). The main parameters of this adaptive MIMO-OFDM system are summarized in Table 3. In all the results presented below, the number of subcarriers is *N*=64 (128-point FFT), but only *SI* =48 convey data (QAM modulated). A cyclic prefix extension of *Ne*=8 samples was used and the transmission symbol rate was 250 ksymbol/s, which leads to a maximum total system throughput of (*B*max × *SI* × *L)*/ *TS* bit/s (e.g. 432 Mbit/s for *L=*6 users –lamps– when every subcarrier is 64-QAM modulated). This OFDM symbol extension (*TS Ne*/(2*N*+*Ne*) ≈ 235 ns) is large enough to compensate for ISI in most of the non-LOS diffuse-link scenarios. The separation between subcarriers is Δ*f*=*f*<sup>0</sup> ≈ 266 kHz, leading to a transmission bandwidth of approximately *BT*=*SI* Δ*f*=12.75 MHz plus a convenient out-of-band guard [35], which is extremely practical for typical optical WLED devices. Finally, we used twenty training sequences to estimate (using the method described in section 3.2) the frequency-domain channel transfer function factors of matrix *Hp* required by LS detector to obtain the weight matrix (25).


**Table 3.** Parameters of adaptive MIMO-OFDM system.

Fig. 17 and Fig. 18 show the system performance for imaging and non-imaging receivers, respectively; when the information from each user (lamp) is jointly demodulated at a particular position of the receiver. Fig. 17(a) presents the achievable average throughput (BPS, *bits per symbol*) at every information subcarrier as a function of the average SNR at the receiving branches (pixels), when three different target bit error rates (*Pe*) are sought and for the receiver located at position 1 inside the room (see Fig. 7(a)). We can see how the BER is maintained nearly constant around the specified target BER in all the cases until maximum achievable throughput (6 BPS in all the subcarriers) is reached. From that point on, BER decreases rapidly

21

Multi-user visible light communication

point, with the data corresponding to a particular user lamp, which we will refer to as *single-*

In this section, we show the results obtained with an adaptive MIMO-OFDM system based on LS detection, which can select the most appropriate modulation mode for each subcarrier from the 5-ary group ('no transmission', BPSK, QPSK, 16-QAM, 64-QAM). The main parameters of this adaptive MIMO-OFDM system are summarized in Table 3. In all the results presented

modulated). A cyclic prefix extension of *Ne*=8 samples was used and the transmission symbol rate was 250 ksymbol/s, which leads to a maximum total system throughput of (*B*max × *SI*

*TS* bit/s (e.g. 432 Mbit/s for *L=*6 users –lamps– when every subcarrier is 64-QAM modulated). This OFDM symbol extension (*TS Ne*/(2*N*+*Ne*) ≈ 235 ns) is large enough to compensate for ISI in most of the non-LOS diffuse-link scenarios. The separation between subcarriers is Δ*f*=*f*<sup>0</sup> ≈

convenient out-of-band guard [35], which is extremely practical for typical optical WLED devices. Finally, we used twenty training sequences to estimate (using the method described in section 3.2) the frequency-domain channel transfer function factors of matrix *Hp* required

): 48 Available modulation modes: ('no transmission', BPSK,QPSK, 16-QAM,

Fig. 17 and Fig. 18 show the system performance for imaging and non-imaging receivers, respectively; when the information from each user (lamp) is jointly demodulated at a particular position of the receiver. Fig. 17(a) presents the achievable average throughput (BPS, *bits per symbol*) at every information subcarrier as a function of the average SNR at the receiving branches (pixels), when three different target bit error rates (*Pe*) are sought and for the receiver located at position 1 inside the room (see Fig. 7(a)). We can see how the BER is maintained nearly constant around the specified target BER in all the cases until maximum achievable throughput (6 BPS in all the subcarriers) is reached. From that point on, BER decreases rapidly

64-QAM)

=48 convey data (QAM

Δ*f*=12.75 MHz plus a

× *L)*/

below, the number of subcarriers is *N*=64 (128-point FFT), but only *SI*

266 kHz, leading to a transmission bandwidth of approximately *BT*=*SI*

by LS detector to obtain the weight matrix (25).

Number of information subcarriers (*SI*

Total number of subcarriers (*N*): 64

Maximum number of bits per subcarrier (*B* max): 6 (64-QAM)

Maximum aggregate throughput: 432 Mbit/s

OFDM symbol period (*TS*): 4 μs Cyclic prefix extension (*Ne*): 8

Number of training sequences (TS): 20

**Table 3.** Parameters of adaptive MIMO-OFDM system.

*user detection*.

**4.1. Joint detection**

56 Advances in Optical Communication

(a) Performance for several target *Pe* (pos. 1) (b) Performance at different positions (*Pe*=10-3)

1 **Fig. 17.** Performance (aggregate throughput, bits per symbol (BPS)) of MIMO-OFDM system

3 Fig. 17(b) compares the system performance at the three receiver locations specified in

2 with imaging receiver at several positions versus average SNR at receiving branches (pixels). **Figure 17.** Performance (aggregate throughput, bits per symbol (BPS)) of MIMO-OFDM system with imaging receiver at several positions versus average SNR at receiving branches (pixels).

as SNR grows. Equally, demanding a lower target BER requires greater SNR values to attain a specific average throughput, as expected. (a) Performance for several target *Pe* (pos. 1) (b) Performance at different positions (*Pe*=10-3) 4 Fig. 7(a). Once again, we observe a near-constant BER around the imposed threshold (*Pe* = 10-3 5 for these simulations), while the maximum achievable throughput is not reached. The

Fig. 17(b) compares the system performance at the three receiver locations specified in Fig. 7(a). Once again, we observe a near-constant BER around the imposed threshold (*Pe*=10-3 for these simulations), while the maximum achievable throughput is not reached. The BER drops dramatically when maximum throughput is attained and SNR continues increasing. Addi‐ tionally, we can see an improved system performance at position 2 (center of the room) compared to positions 1 and 3. This is due to the better signal quality received at that location (from Fig. 7, for positions 1 and 3, there seems to be a clear degradation of the signals coming from farther emitting lamps; these lamps appear less illuminated in Fig. 7(b) and Fig. 7(d), which eventually deteriorates the achievable aggregate throughput). 1 **Fig. 17.** Performance (aggregate throughput, bits per symbol (BPS)) of MIMO-OFDM system 2 with imaging receiver at several positions versus average SNR at receiving branches (pixels). 3 Fig. 17(b) compares the system performance at the three receiver locations specified in 4 Fig. 7(a). Once again, we observe a near-constant BER around the imposed threshold (*Pe* = 10-3 5 for these simulations), while the maximum achievable throughput is not reached. The 6 BER drops dramatically when maximum throughput is attained and SNR continues 7 increasing. Additionally, we can see an improved system performance at position 2 (center 8 of the room) compared to positions 1 and 3. This is due to the better signal quality received 9 at that location (from Fig. 7, for positions 1 and 3, there seems to be a clear degradation of 10 the signals coming from farther emitting lamps; these lamps appear less illuminated in 6 BER drops dramatically when maximum throughput is attained and SNR continues 7 increasing. Additionally, we can see an improved system performance at position 2 (center 8 of the room) compared to positions 1 and 3. This is due to the better signal quality received 9 at that location (from Fig. 7, for positions 1 and 3, there seems to be a clear degradation of 10 the signals coming from farther emitting lamps; these lamps appear less illuminated in 11 Fig. 7(b) and Fig. 7(d), which eventually deteriorates the achievable aggregate throughput).

11 Fig. 7(b) and Fig. 7(d), which eventually deteriorates the achievable aggregate throughput).

(a) Performance for several target *Pe* (pos. 1) (b) Performance at different positions (*Pe*=10-3) 16 (about 20 dB in performance degradation) to attain an identical objective. As before, we

12 **Fig. 18.** Performance (aggregate throughput, bits per symbol (BPS)) of MIMO-OFDM system

17 observe how receiver position affects system performance (see Fig. 18(b)). However, the

 Fig. 18 presents the same results as Fig. 17, but for a non-imaging receiver. In general, we can see similar system performance behavior, although requiring much larger SNR values (about 20 dB in performance degradation) to attain an identical objective. As before, we observe how receiver position affects system performance (see Fig. 18(b)). However, the larger field of view of a non-imaging receiver means position 2 (center of the room) is not so

19 advantageous compared to locating the receiver closer to the room corners.

13 with non-imaging receiver at several positions versus average SNR at receiving branches. **Figure 18.** Performance (aggregate throughput, bits per symbol (BPS)) of MIMO-OFDM system with non-imaging re‐ ceiver at several positions versus average SNR at receiving branches. 18 larger field of view of a non-imaging receiver means position 2 (center of the room) is not so 19 advantageous compared to locating the receiver closer to the room corners.

Fig. 18 presents the same results as Fig. 17, but for a non-imaging receiver. In general, we can see similar system performance behavior, although requiring much larger SNR values (about 20 dB in performance degradation) to attain an identical objective. As before, we observe how receiver position affects system performance (see Fig. 18(b)). However, the larger field of view of a non-imaging receiver means position 2 (center of the room) is not so advantageous compared to locating the receiver closer to the room corners.

#### **4.2. Single-user detection** 22 Optical Communication

In many applications, we are not concerned with jointly demodulating the information coming from all the lamps, but only with decoding the data corresponding to one lamp which has been assigned to a specific receiver. Fig. 19 presents the performance of the adaptive MIMO-OFDM system in this second situation (single-user detection) as compared with the joint detection case described in the previous section. In the simulations, the receiver is located in positions 1, 2 or 3, as defined in Fig. 7(a), and only demodulates the data coming from its nearest lamp (for position 2, in the center of the room, lamps 2 and 5 are symmetrically equivalent, thus either of them can indistinctly be considered, both delivering identical results). Moreover, detection complexity reduction described in section 4.3 of [19] was applied to optimize and accelerate single-user detection. 1 **4.2. Single-user detection** 2 In many applications, we are not concerned with jointly demodulating the information 3 coming from all the lamps, but only with decoding the data corresponding to one lamp 4 which has been assigned to a specific receiver. Fig. 19 presents the performance of the 5 adaptive MIMO-OFDM system in this second situation (single-user detection) as compared 6 with the joint detection case described in the previous section. In the simulations, the 7 receiver is located in positions 1, 2 or 3, as defined in Fig. 7(a), and only demodulates the 8 data coming from its nearest lamp (for position 2, in the center of the room, lamps 2 and 5 9 are symmetrically equivalent, thus either of them can indistinctly be considered, both 10 delivering identical results). Moreover, detection complexity reduction described in section

For all cases, except for the non-imaging receiver at position 2, single-user detection requires much lower SNR values to obtain a certain average throughput per subcarrier concerning the data corresponding to that lamp. This is logical because the receiver is positioned very close to the emitting lamp, thus receiving very directive and intense optical signals from its associ‐ ated emitter. Therefore, each individual receiving user, if located appropriately close to its assigned lamp, would benefit from a high-quality signal level while sharing the room with other simultaneous users. 11 4.3 of [19] was applied to optimize and accelerate single-user detection. 12 For all cases, except for the non-imaging receiver at position 2, single-user detection requires 13 much lower SNR values to obtain a certain average throughput per subcarrier concerning 14 the data corresponding to that lamp. This is logical because the receiver is positioned very 15 close to the emitting lamp, thus receiving very directive and intense optical signals from its 16 associated emitter. Therefore, each individual receiving user, if located appropriately close 17 to its assigned lamp, would benefit from a high-quality signal level while sharing the room 18 with other simultaneous users.

(a) Performance for imaging receiver (b) Performance for non-imaging receiver

detection at several positions versus average SNR at receiving branches when *Pe* = 10-3 20 . **Figure 19.** Performance comparison of MIMO-OFDM system for single-user detection and joint detection at several po‐ sitions versus average SNR at receiving branches when *Pe*=10-3.

19 **Fig. 19.** Performance comparison of MIMO-OFDM system for single-user detection and joint

 Additionally, the system performance degradation of a non-imaging receiver compared to an imaging one is not so significant, except when the former is positioned in the center of the room. This is because a non-imaging receiver does not provide as much diversity as an imaging-based type. This is more noticeable at the center of the room where emissions from lamps 2 and 5 can scarcely be distinguished, leading to the observed important SNR losses experienced by a non-imaging detector at position 2. Fig. 19(b) also shows the single-user performance in the center of the room when lamp 5 is "disabled" (the result shown by a pink line), i.e. this lamp, although maintaining its functionality as an illumination device, stops sending data information. In this situation, the single-user performance is enhanced greatly, which demonstrates the problems of the non-imaging receiver to separate the information

Additionally, the system performance degradation of a non-imaging receiver compared to an imaging one is not so significant, except when the former is positioned in the center of the room. This is because a non-imaging receiver does not provide as much diversity as an imaging-based type. This is more noticeable at the center of the room where emissions from lamps 2 and 5 can scarcely be distinguished, leading to the observed important SNR losses experienced by a non-imaging detector at position 2. Fig. 19(b) also shows the single-user performance in the center of the room when lamp 5 is 'disabled' (the result shown by a pink line), i.e. this lamp, although maintaining its functionality as an illumination device, stops sending data information. In this situation, the single-user performance is enhanced greatly, which demonstrates the problems of the non-imaging receiver to separate the information coming simultaneously from lamps 2 and 5. However, the cost of this performance improvement is the new maximum achievable aggregate throughput, since, with only five active lamps, it falls to 360 Mbit/s (5 users × 6 bits/subcarrier symbol × 48 subcarriers/OFDM symbol × 250 ⋅ 103 OFDM symbols/second) as compared with the maximum throughput of 430 Mbit/s when all six lamps were active. Therefore, it seems evident that positioning the non-imaging receiver in the center of the room must be avoided to prevent an excessive system performance penalty.

#### **5. Conclusions**

Fig. 18 presents the same results as Fig. 17, but for a non-imaging receiver. In general, we can see similar system performance behavior, although requiring much larger SNR values (about 20 dB in performance degradation) to attain an identical objective. As before, we observe how receiver position affects system performance (see Fig. 18(b)). However, the larger field of view of a non-imaging receiver means position 2 (center of the room) is not so advantageous

In many applications, we are not concerned with jointly demodulating the information coming from all the lamps, but only with decoding the data corresponding to one lamp which has been assigned to a specific receiver. Fig. 19 presents the performance of the adaptive MIMO-OFDM system in this second situation (single-user detection) as compared with the joint detection case described in the previous section. In the simulations, the receiver is located in positions 1, 2 or 3, as defined in Fig. 7(a), and only demodulates the data coming from its nearest lamp (for position 2, in the center of the room, lamps 2 and 5 are symmetrically equivalent, thus either of them can indistinctly be considered, both delivering identical results). Moreover, detection complexity reduction described in section 4.3 of [19] was applied to optimize and

 In many applications, we are not concerned with jointly demodulating the information coming from all the lamps, but only with decoding the data corresponding to one lamp which has been assigned to a specific receiver. Fig. 19 presents the performance of the adaptive MIMO-OFDM system in this second situation (single-user detection) as compared with the joint detection case described in the previous section. In the simulations, the receiver is located in positions 1, 2 or 3, as defined in Fig. 7(a), and only demodulates the data coming from its nearest lamp (for position 2, in the center of the room, lamps 2 and 5 are symmetrically equivalent, thus either of them can indistinctly be considered, both delivering identical results). Moreover, detection complexity reduction described in section

22 Optical Communication

For all cases, except for the non-imaging receiver at position 2, single-user detection requires much lower SNR values to obtain a certain average throughput per subcarrier concerning the data corresponding to that lamp. This is logical because the receiver is positioned very close to the emitting lamp, thus receiving very directive and intense optical signals from its associ‐ ated emitter. Therefore, each individual receiving user, if located appropriately close to its assigned lamp, would benefit from a high-quality signal level while sharing the room with

(a) Performance for imaging receiver (b) Performance for non-imaging receiver

**Figure 19.** Performance comparison of MIMO-OFDM system for single-user detection and joint detection at several po‐

19 **Fig. 19.** Performance comparison of MIMO-OFDM system for single-user detection and joint detection at several positions versus average SNR at receiving branches when *Pe* = 10-3 20 .

 Additionally, the system performance degradation of a non-imaging receiver compared to an imaging one is not so significant, except when the former is positioned in the center of the room. This is because a non-imaging receiver does not provide as much diversity as an imaging-based type. This is more noticeable at the center of the room where emissions from lamps 2 and 5 can scarcely be distinguished, leading to the observed important SNR losses experienced by a non-imaging detector at position 2. Fig. 19(b) also shows the single-user performance in the center of the room when lamp 5 is "disabled" (the result shown by a pink line), i.e. this lamp, although maintaining its functionality as an illumination device, stops sending data information. In this situation, the single-user performance is enhanced greatly, which demonstrates the problems of the non-imaging receiver to separate the information

sitions versus average SNR at receiving branches when *Pe*=10-3.

 For all cases, except for the non-imaging receiver at position 2, single-user detection requires much lower SNR values to obtain a certain average throughput per subcarrier concerning the data corresponding to that lamp. This is logical because the receiver is positioned very close to the emitting lamp, thus receiving very directive and intense optical signals from its associated emitter. Therefore, each individual receiving user, if located appropriately close to its assigned lamp, would benefit from a high-quality signal level while sharing the room

compared to locating the receiver closer to the room corners.

11 4.3 of [19] was applied to optimize and accelerate single-user detection.

**4.2. Single-user detection**

58 Advances in Optical Communication

1 **4.2. Single-user detection**

accelerate single-user detection.

other simultaneous users.

18 with other simultaneous users.

In this chapter, the use of multi-user LS detection in conjunction with angle-diversity imaging and non-imaging receivers and adaptive OFDM modulation technique for visible light communications has been evaluated. The indoor wireless visible-light channel model, which can be determined by a Monte Carlo-based ray-tracing algorithm, has been described thor‐ oughly, detailing the main features associated with the different elements constituting this kind of optical channel: white light-emitting diodes, reflective room surfaces and optical receivers. This algorithm allows us to determine very accurately the impulse responses between the WLEDs of the lamps and the optical angle-diversity detector, while considering LOS and also not insignificant multiple-bounce reflection contributions to the received optical power at the photodetector. This algorithm accuracy is essential to enable a more reliable analysis of the proposed MIMO-OFDM performance.

A rate adaptive MIMO-OFDM scheme, based on a linear combination of the incoming signals at its receiving branches and dynamic throughput adaptation to channel occupa‐ tion (number of users) and signal quality (SNR at each subcarrier for a specific user), has been proposed for multi-user visible-light communications. The system performance for imaging and non-imaging reception, and considering joint and single-user detection scenarios, has been assessed. The results have shown that imaging receivers provide an improved performance with SNR gains of about 20 dB with respect to non-imaging ones when evaluating joint detection scenario, i.e. the former offer greater diversity in a VLC environment. Additionally, for single-user detection only demodulating data coming from a specific lamp, we find that although not so evident at positions closer to the room walls, non-imaging receivers present considerable performance degradation when moving into the room's central area. Therefore, it can be concluded from the previous results that, in general terms, imaging receivers provide the best solution as an angle-diversity detection method for multi-user visible light communications.

#### **Acknowledgements**

This work has been funded by Spanish Government (MINECO) and the European Regional Development Fund (ERDF) programme under projects TEC2013-47682-C2-2-P, MAT2013-46649-C4-4-P, MAT2010-21270-C04-02 and Malta Consolider Ingenio 2010 (CSD2007-0045).

## **Author details**

Oswaldo González1\*, Marcos F. Guerra Medina1 and Inocencio R. Martín2

\*Address all correspondence to: oghdez@ull.es

1 Department of Industrial Engineering, University of La Laguna, Spain

2 Department of Physics, University of La Laguna, Spain

### **References**


[5] Elgala H., Mesleh R., Haas H. Indoor optical wireless communication: potential and state-of-the-art. IEEE Communications Magazine 2011;49(9) 56–62.

non-imaging receivers present considerable performance degradation when moving into the room's central area. Therefore, it can be concluded from the previous results that, in general terms, imaging receivers provide the best solution as an angle-diversity detection

This work has been funded by Spanish Government (MINECO) and the European Regional Development Fund (ERDF) programme under projects TEC2013-47682-C2-2-P, MAT2013-46649-C4-4-P, MAT2010-21270-C04-02 and Malta Consolider Ingenio 2010

[1] Komine T., Nakagawa, M. Integrated system of white LED visible-light communica‐ tion and power-line communication. IEEE Transactions on Consumer Electronics

[2] Komine T., Nakagawa M. Fundamental analysis for visible-light communication sys‐ tem using LED lights. IEEE Transactions on Consumer Electronics 2004;50(1): 100–

[3] O'Brien D.C., Zeng L., Minh H.L., Faulkner G.E., Walewski J.W., Randel S. Visible light communications: challenges and possibilities. In: PIMRC 2008: proceedings of the IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Com‐

[4] Grubor J., Randel S., Langer K.-D., Walewski J.W. Broadband information broadcast‐ ing using LED-based interior lighting. Journal of Lightwave Technology 2008;26(24):

and Inocencio R. Martín2

method for multi-user visible light communications.

Oswaldo González1\*, Marcos F. Guerra Medina1

\*Address all correspondence to: oghdez@ull.es

2 Department of Physics, University of La Laguna, Spain

1 Department of Industrial Engineering, University of La Laguna, Spain

munications, 15-18 September 2008, Cannes, France.

**Acknowledgements**

60 Advances in Optical Communication

(CSD2007-0045).

**Author details**

**References**

107.

3883–3892.

2003;49(1): 71–79.


[29] López-Hernández F.J., Pérez-Jiménez R., Santamaría A. Modified Monte Carlo scheme for high-efficiency simulation of the impulse response on diffuse IR wireless indoor channels. Electronics Letters 1998;34(19) 1819-1820.

[17] Cossu G., Khalid A.M., Choudhury P., Corsini R., Ciaramella E. 3.4 Gbit/s visible op‐ tical wireless transmission based on RGB LED. Optics Express 2012;20(26) B501–

[18] Tsonev D., Chun H., Rajbhandari S., McKendry J.J.D., Videv S., Gu E., Haji M., Wat‐ son S., Kelly A.E., Faulkner G., Dawson M.D., Haas H., O'Brien D. A 3-Gb/s single-LED OFDM-based wireless VLC link using a Gallium Nitride μLED. IEEE Photonics

[19] González O. Multiple-input multiple-output (MIMO) optical wireless communica‐ tions. In: Das N. (ed.) Optical Communication. Rijeka: InTech; 2012. p393–414. Avail‐ able from http://www.intechopen.com/books/optical-communication/multiple-inputmultiple-output-mimo-optical-wireless-communications (accessed 3 October 2012).

[20] Azhar A.H., Tran T.-A., O'Brien D. A gigabit/s indoor wireless transmission using MIMO-OFDM visible-light communications. IEEE Photonics Technology Letters

[21] Burton A., Minh H.L., Ghassemlooy Z., Bentley E., Botella C. Experimental demon‐ stration of 50-Mb/s visible light communications using 4×4 MIMO. IEEE Photonics

[22] Barry J.R., Kahn J.M., Krause W.J., Lee E.A., Messerschmitt D.G. Simulation of multi‐ path impulse response for wireless optical channels. IEEE Journal on Selected Areas

[23] Schubert E.F. Light-emitting diodes. Cambridge: Cambridge University Press; 2006. [24] Cui K., Chen G., He Q., Xu Z. Indoor optical wireless communication by ultraviolet and visible light. In: Majumdar A.K., Davis C.C. (eds.) Proc. SPIE 7464: Free-Space Laser Communications IX: proceedings of the International Society for Optics and

[25] Lee K., Park H., Barry J.R. Indoor channel characteristics for visible light communica‐

[26] European Standard EN 12464-1. Lighting of indoor work places. European Commit‐

[27] Lomba C.R., Valadas R.T., de Oliveira Duarte A.M. Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces. IEE Proceed‐

[28] Kahn J.M., You R., Djahani P., Weisbin A.G., Teik B.K., Tang A. Imaging diversity re‐ ceivers for high-speed infrared wireless communication. IEEE Communications

B506.

62 Advances in Optical Communication

2013;25(2) 171–174.

Technology Letters 2014;26(7) 637–640.

Technology Letters 2014;26(9) 945–948.

in Communications 1993;11(3) 367-379.

tee for Standardization (CEN) 2002.

Magazine 1998;36(12) 88-94.

ings-Optoelectronics 1998;145(3) 191–197.

Photonics (SPIE), 2-3 August 2009, San Diego, USA.

tions. IEEE Communications Letters 2011;15(2) 217-219.


**High-Speed Optical Communication: Optical Devices**
