Channel Simulation of Non-imaging Optical MIMO Communication

doi:10.4236/opj.2013.32B050

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Optics and Photonics Journal, 2013, 3, 212-216

doi:10.4236/opj.2013.32B050 Published Online June 2013 (http://www.scirp.org/journal/opj)

Channel Simulation of Non-imaging Optical MIMO

Communication

Jiao Feng, Liwei Ding, Yongjin Wang

Institute of Communication Technology, Nanjing University of Posts and Telecommunications, Jiangsu, China

Email: [email protected]

Received 2013

ABSTRACT

This paper reports a channel simulation of an indoor optical wireless multiple-input-multiple-output (MIMO) system

with non-imaging receivers. The system consists of a 2×2 array of white light-emitting diodes (LEDs) and 2×2 array

of PDs. An overview of the model specifications, channel impulse response and channel capacity are demonstrated in

this paper. The distribution of the first reflection is analyzed. The effect of SNR and the location of receivers on

non-imaging optical MIMO communications are investigated. In addition, by moving the receivers, the optimal location

of the communication is found.

Keywords: MIMO; LEDs; Non-imaging; Channel Impulse Response; Channel Capacity

1. Introduction

Energy-saving is gradually becoming the key focus all

over the world. LED devices have been widely applied to

home and industry because of this trend. In addition to

the function of illumination, the white LEDs can also be

used for communication [1]. The main challenge of

LEDs communications is the limited modulation band-

width of sources, just several MHZ [2,3]. Many solutions

are proposed in the past several years such as high effi-

cient modulation schemes, RGB multi chip LED mod-

ules and so on. Recently, researchers pay more attention

to the multiple-input-multiple-output (MIMO) technol-

ogy which could provide parallel data transmission for

the sake of achieving high data rates[4-8]. Many works

are also done to explore the channel capacity. [9] inves-

tigates the MIMO channel capacity in correlated chan-

nels and [10] shows the channel capacity of the imaging

receivers system. In this paper, an entirely possible

non-imaging optical MIMO communications model is

established to explore the design specifications, channel

impulse response and distribution of the channel capac-

ity.The rest of this paper is organized as follows, section

2 describes the specifications of the system we setup.

Section 3 gives the channel impulse response. Section 4

shows the capacity of the model. Section 5 concludes the

work before and analyses the future of the visible light

communication.

2. System Setup

The MIMO system in this paper is implemented through

intensity modulation and direct detection (IM/DD). The

system consists of four transmitter units (LEDs). The

arrangement of the LEDs in the room is shown in Figure

1. The room size is 5 m * 5 m * 2.5 m. The LEDs are

arranged in four corners of room. Table 1 shows the pa-

rameters of the system.

Figure 1. The distribution of the LEDs in the room.

Table 1. Parameters of MIMO model.

Parameters values

Room size (W × L × H) 5 m × 5 m × 2.5 m

power of single LED 5 w

FOV at a receiver(half-angle) 60°

Detector physical are a of a PD 0.15 * 0.15

Center luminous intensity 50 cd

Number of LEDs 25 (5 * 5)

LED interval 0.02 m

Semi-angle at half power 70°

J. FENG ET AL. 213

2.1. Illuminance of LED Lighting

The illuminance expresses the brightness of an illumi-

nated surface [1]. A horizontal illuminance at a

point (x, y) is given by horE

(0)cos ()

cos( )

hor I





 (1)

where I(0) is the center luminous intensity of an LED,



is the angle of irradiance,



is the angle of incidence,

and R is the distance between an LED and a detector’s

surface. It is assumed that an LED has a Lambertian ra-

diation pattern according to [1]. Thus, the radiant inten-

sity depends on the angle of irradiance



. n is the order

of Lambertian emission and is expressed as the function

of semi -a ng le at half po wer given b elow.

ln 2

ln(cos )



 (2)

Standard illuminance of lights for common office

room is defined by the International Organization for

Standardization (ISO). Illuminance of 300 to 1500 lx is

required according to this standard. Figure 2 shows that

sufficient illuminance can be obtained all over the room.

As the minimum illuminance is 344.3 lx and the maxi-

mum is 456.0 lx. Therefore, the result verifies that LED

lighting devices can meet the lighting demands for in-

door environment.

3. Channel Model

In an empty room, the light emitted from the LEDs will

be reflected several times between the walls before ar-

riving at the receiver (PD). So the calculation of the

overall response which consists of direct and reflection

response is more complicated. [5] presents a recursive

method for calculating the impulse response containing

multiple reflections. Room surfaces acting as Lambertian

reflectors reflect an incident signal in all directions [5].



Figure 2. The distribution of the received illuminance of the

floor. Min.344.3 lx, Max.456.0 lx, Ave.424.0 lx.

In an optical link, the channel DC gain is given as

1cos ()cos()

(0) 2

FOV

hRothers

 















(3)

where

is the physical area of the detector in a PD. R

is the distance between a transmitter and a receiver,



is the angle of irradiance,



is the angle of incidence, n

is the mode number of Lambertian radiation. The re-

ceived optical power

P is derived by the transmitted

optical power , as follows

(0)

SPh P



 (4)

In the Figure 3, we show the distribution of received

power on the floor. The average power received is 21.5

dbm. From the formula (4), we can learn

P has the

same distribution trend as the channel matrix (H).

We simplified the channel model and only considered

the first reflection of the light emitting from the LEDs.

The more times of reflections occur, the lower received

power we get. Proportion of response for each reflection

compared to the total response is described in [3]. The

first reflection response is given as follows [3]

1cos()cos()

'(0) 2

(1) 2

nhA

others





















(5)

where



is the angle of irradiance,



is the angle of

incidence in the first reflection, N is the total number of

elements. i



is the reflectivity at the i the element.

is the response of the reflection area to the floor.

'(0)h



is the element’s area.



is given by [5]

/tA c (6)

where c is the light speed.

Figure 3. The distribution of r ece ive d powe r. Min. 20.4 dbm,

Max.22.0 dbm, Ave.21.5 dbm.

J. FENG ET AL.

214

Figure 4 shows the distribution of impulse response

with first reflection on the floor. the first reflection

makes more contribution to the four boundaries on ac-

count of the limitation of FOV. The average response

3.9372e-006 is an order of magnitude lower than that of

the LOS impulse response(1.1e-003). The each corner

has the maximum impulse response which is 6.1279e-

005. It means that the reflection has little influence on the

optical MIMO communication performance in this

model.

The distribution of the to tal impulse response and LOS

impulse response are showed separately in Figure 5 and

Figure 6. There are four peaks just under the four LEDs

arrays. It can be found that the LOS impulse response

and the response including first reflection is same with

the value and distribution of LOS impulse response. The

maximum is 0.0013 and the average is 0.0011.

4. Channel Capacity

Channel capacity expresses the maximum data rate that

can be obtained by a given channel, The Shannon capac-

ity of the MIMO system is followed by [9]

2log det()//CIH Hbitss Hz





 (7)

where m is the number of transmission/receivers,



the average signal-to-noise ratio (SNR), I is mm



iden-

tity matrix, H is the normalized channel matrix, and “+”

means transpose conjugate.

Table 2: Parameters for the first reflection.

Parameters values

WESTEASTSOUTHNORTH



 0.8

Mode of Lambertian radiation (walls) 1

t 0.2ns

Figure 4. The distribution of impulse response with first

reflection Min.8.5715e-008, Max.6.1279e-005, Ave.3.9372e-

006.

Figure 5. The distribution of total impulse response contain-

ing direct and first reflection. Min. 9.2952e-004, Max.0.0013,

Ave.0.0011.

Figure 6. The distribution of LOS impulse response. Min.

8.7831e-004, Max.0.0013, Ave.0.0011.

According to the equation 7, it can be found that the

channel capacity of the MIMO system depends on the

channel matrix H (total impulse response) when average

SNR



is constant. The channel matrix H is deter-

mined by the configuration of the transceiver elements.

Then the relationship between SNR, channel matrix H

and capacity C are analyzed .

The four PDs lie in (0.75,0.75,0), (4.25,0.75,0), (4.25,

4.25,0), (0.75,4.25,0) separately in the room showed in

Figure 7. Figure 8 is the relationship between the aver-

age SNR



and the MIMO channel capacity, where the

receivers are the four PDs. The simulation curve shows

that the MIMO channel capacity beco mes larger with the

increase of



, So the high



of the LED can result to

the large capacity of the optical MIMO communication.

Figure 9 is the distribution of th e capacity of one cor-

ner. Th e av erag e SN R is 50 db. The capacity ranges from

2.6 bit/s/HZ to 0.8 bit/s/HZ. It is assumed in the simula-

J. FENG ET AL. 215

tion that the four receivers are placed symmetrically in

the room. So we just display the distribution of one cor-

ner. The maximum capacity shown in Figure 9 is

achieved at the point just under the transmitter. In the

MIMO model, the optimal location is just under each

transmitter. We can achieve the maximum data rate in

this location.

Figure 7. The distribution of four LED array s and four PDs

in the room.

Figure 8. The MIMO channel capacity vs. average SNR.

The receiver’s location is (0.75,0.75,0), (4.25,0.75,0), (4.25,

4.25,0), (0.75,4.25,0).

Figure 9. The distribution of the capacity of corner of the

floor. The average SNR = 50db. Min.0.8 (bit/s/HZ), Max.2.6

(bit/s/HZ), Ave.1.6 (bit/s/HZ).

5. Conclusions

The MIMO model discussed in this paper can provide the

functions including lighting and communication. We

carried out the fundamental analysis for optical MIMO

system which can provide theoretical basis for con-

structing the optimal visible light communication system.

In this paper, the feasibility of visible light MIMO com-

munication is verified by simulating the illuminance and

capacity received. The effect of the parameters on the

channel capacity of the MIMO system needs to be further

studied in the future such as the properties of the trans-

mitter receiver. Higher efficiency LED developed re-

cently could largely promote the progress of visible light

communications.

6. Acknowledgements

This work is jointly supported by NSFC (11104147),

Jiangsu 973 project (BK2011027) and research project

(NY211001, BJ211026) .

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