Multi-user THSS system for visible light links

S. Rodríguez, B.R. Mendoza, O. González, A. Ayala Dept. of Fund. and Exp. Physics, Electronics and Systems

University of La Laguna La Laguna (Tenerife), Spain

J.A. Rabadán, R. Pérez-Jiménez Dept. of Signals and Communications

University of Las Palmas de Gran Canaria Las Palmas de Gran Canaria, Spain

Abstract—In this paper, a system based on time-hopping spread spectrum techniques for indoor visible light communications is studied via simulation. A 2-PPM modulation scheme is selected because it yields good results in wireless optical communications. Furthermore, the system allows for selecting the number of pulses per symbol to be transmitted and makes use of an optimum maximum-likelihood receiver for AWGN channels with the ability to choose between hard- or soft-decision decoding. The system designed allows for comparing the performance based on the computation of the bit error rate as a function of the pulse energy to noise power spectral density ratio, for different configurations in single-user and multi-user environments.

Keywords—VLC channel; THSS techniques; PPM modulation, simulation, bit error rate (BER)

I. INTRODUCTION Recently, there has been a growing interest in visible light

communications (VLC) in some indoor application scenarios, video/audio transmission for in-home applications, secure network access or sensor networking [1-3]. Furthermore, wireless optical communications present certain advantages over radiofrequency (RF) transmission that make them suitable in certain specific scenarios.

In this paper, a system based on time-hopping spread-spectrum (THSS) techniques for indoor VLC is studied via simulation. Time-Hopping codification is based on splitting the symbol period into several short slots. In order to specify which slots are used to transmit and which are not, the use of maximum length sequences (MLS) is considered. The remaining time slots can be used by other users so as to provide the system with multiple access capabilities. In this paper, a 2-PPM modulation scheme is selected because it yields good results in wireless optical communications. Furthermore, the THSS system provides for physical level redundancy, i.e., it allows for selecting the number of pulses per symbol to be transmitted. The system makes use of an optimum maximum-likelihood receiver for AWGN channels, and hard or soft decision decoding can be selected. Finally, the system allows for comparing the performance based on the computation of the bit error rate (BER) as a function of the pulse energy to noise power spectral density ratio (Ep/N0), for different configurations in single-user and multi-user environments.

II. PROPAGATION MODEL In general, for diffuse links, the indoor VLC system

consists of an emitter, a receiver and reflection surfaces. The

propagation model is composed by the simulation algorithm and mathematical models used to describe the features of the elements of the optical link. To evaluate the impulse response of the VLC channel, a Monte Carlo ray-tracing algorithm has been employed [4,5]. In general, the multi-wavelength impulse response for an arbitrary position of emitter E and receiver R can be expressed as an infinite sum of the form:

∑∞

=+=

1

)()0( ),,;(),,;(),,;(k

k REthREthREth λλλ (1)

where h(0)(t;E,R,λ) represents the line-of-sight (LOS) impulse response, h(k) (t;E,R,λ) is the impulse response of the light undergoing k reflections, i.e., the multiple-bounce impulse responses, λ is the wavelength, and t is the time.

Given an emitter E and a receiver R in an environment free of reflectors with a large distance d0,R between both, the LOS impulse response is approximately

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −=c

dtAnR

dREth R

effER

,02

,0

)0( )(),,(1),,;( δψλφλ (2)

where RE(φ,n,λ) represents the generalized Lambertian model used to approximate the radiation pattern of the emitter [6], c is the speed of light and Aeff(ψ) is the effective signal-collection area of the receiver [6].

Fig. 1. Emitter and receiver geometry with reflectors. The dashed lines represent the ray paths and the solid ones the power contributions

Consider an emitter and a receiver in an environment with reflectors (see Fig. 1). Radiation from the emitter can reach the receiver after any number of reflections. In order to calculate the multiple-bounce impulse responses using the Monte Carlo ray-tracing algorithm, many rays are generated at the emitter position with a probability distribution equal to RE(φ,n,λ). The power of each ray generated is initially PE(λ)/N(λ), where N = N(λ) is the number of rays used to discretize the source for each wavelength. Integrating PE(λ) over the emitter wavelength interval yields the nominal power

This study was funded in part by the Government of the Canary Islands (ProID20100117).

978-1-4799-0768-7/13/$31.00 c©2013 IEEE

PE emitted by the emitter. 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 reflection pattern of that surface. The process continues throughout the maximum simulation time, tmax. After each reflection, the power of the ray is reduced by the reflection coefficient of the surface ρ(λ) and the reflected power reaching the receiver is computed.

For each wavelength, the power contribution of the ith ray generated by emitter (1 ≤ i ≤ N) after k reflections can be expressed by

( ) ( )

cd

cd

t

ARd

REP

Rkk

j

jjki

RkeffRkSRk

ki

,

1

,1,

,,2,

, ),',(1),,(

+⎟⎟⎠

⎞⎜⎜⎝

⎛=

=

∑=

−

ψλθθλ (3)

where ti,k represents the time instant in which the power is detected by the receiver and RS(θk,R ,θ’,λ) is the model used to describe the reflection pattern. In this paper, Phong’s model has been used [7,8]. The surfaces in Phong’s model are defined by three parameters for each wavelength: the reflection coefficient ρ(λ), the percentage of incident signal that is reflected diffusely rd(λ), and the directivity of the specular component of the reflection m(λ). The parameters rd(λ) and m(λ) can be considered as constant for each wavelength. Finally, θk,R and θ’ are the observation angle and the incidence angle, respectively.

Summing Pi,k in (3) for the total number N of rays, each undergoing a maximum of K reflections, yields the multiple-bounce response, which is described by

( )∑∑∑= =

∞

=

−=N

i

K

kkiki

k

k ttREPREth1 1

,,1

)( ),,(),,;( δλλ (4)

Substituting equations (2) and (4) in (1), the total impulse response as a function of wavelength can be obtained. Defining M = tmax/Δt, and assuming as the time origin the arrival of the LOS component, we can express the impulse response histogram as

( ) ( )

( )∑∑∑−

= = =

Δ−+

=

1

1 1 1,

2,0

),,(

)(),,(1),,;(

M

n

N

i

K

kki

effER

n n

tntREP

tAnRd

REth

δλ

δψλφλ (5)

where n symbolizes the nth interval time (width Δt) or bin of the power histogram. Furthermore, Kn and Nn are the number of reflections of the ith ray and the number of rays that contribute in the nth time interval, respectively.

Fig. 2. Block diagram of the proposed system model

Fig. 3. Transmitter block diagram

III. WIRELESS OPTICAL THSS SYSTEM Fig. 2 shows the block diagram for the multi-user THSS

system designed, which consists of the following components: the data source, the 2-PPM-THSS transmitter, the VLC channel with AWGN noise and the receiver system. The data sources generate the binary data sequences with equal probability.

A. The 2-PPM-THSS transmitter The transmitter block is charged with generating the

2-PPM-THSS signal based on the binary data sequence supplied by the data source. The signal generated is characterized by a series of pulses distributed pseudo-randomly in time. When redundancy is assumed to be non-existent, a single PPM pulse is transmitted for every data bit in one of the temporary slots available per frame. Fig. 3 shows the block diagram for one of the 2-PPM-THSS transmitters. The sequence to be transmitted, b = (..., b0 , b1, ..., bk, bk+1, ...), generated at a rate Rb = 1/Tb bps, is input to the first block, called a code repetition coder, whose function is to repeat each bit Ns times, resulting in the generation of the binary sequence (..., b0, b0, ..., b0, b1, b1, ..., b1, bk, bk, ..., bk, bk+1, bk+1, ..., bk+1, ...) = (..., a0 , a1, ..., aj, aj+1, ...) = a at a rate of Rcb = Ns /Tb = 1/Ts bps. Notice how this block lets us introduce redundancy in the binary sequence to be transmitted by letting Ns>1. The second block, called a transmission coder, applies an entire code c = (..., c0 , c1, ..., cj, cj+1, ...) to the binary sequence a = (..., a0 , a1, ..., aj, aj+1, ...), generating a new sequence d, a generic element of which can be expressed by:

εjcjj aTcd += (6)where Tc is known as the chip time. Tc and ε are constant terms that satisfy the condition cjTc + ε < Ts, for all cj , and, in general, ε < Tc . Note that d is a real sequence, unlike sequence a, which is binary, and sequence c, which is whole.

At this point we select the most common option, which consists of assuming that c is a pseudorandom code in which 0 ≤ cj ≤ Nh – 1 holds for a whole element cj.. Code c could be periodic, in which case its periodicity is given by Np. Two cases in particular merit discussion. The most commonly adopted corresponds to Np = Ns, i.e., the periodicity of the code matches its repetition length. This second block may be regarded as acting like a CDMA coder and as a spectrum shaper for the signal transmitted.

Sequence d is the input to the third block, the PPM modulator, whose function is to generate a sequence of unit impulses, or Dirac deltas, at a rate of Rp = Ns /Tb = 1/Ts pulses/s. These pulses are located at time instants jTs + dj, and are thus shifted in time from their nominal positions jTs by a displacement factor indicated by dj. The impulses generated will therefore be located at instants (jTs + cjTc + ajε). Code c introduces a time shift or hop (TH) in the generated signal, which is why code c is known as a TH code. In this paper we use the MLS sequences for the TH code. The last block is the

pulse shaping filter, which is a linear system whose impulse response is equal to the shape of the pulse chosen in the transmission.

B. The receptor system In this paper, we have used a receiver system with optimal

performance in terms of error probability for an AWGN channel in the absence of ISI and MUI when the decision criterion used is that of maximum likelihood (ML). The optimal receiver basically consists of two components: the correlator and the decider. The role of the correlator is to convert the signal received into a value, from among a possible range of values, which allows the decider to determine the waveform or the symbol transmitted. Besides the threshold detection, the simulation model developed provides for two detection methods: hard- and soft-decision detection.

Fig. 4. Parameters and simulation environment.

IV. RESULTS The results reported in this section were obtained assuming

a VLC channel consisting of an emitter and a receiver inside the simulation environment shown in Fig. 4. The remaining parameters used in the simulations are reported in the table that is included in Fig. 4. The impulse response of the VLC channel was obtained by the weighted sum of the impulse responses for RGB wavelengths, based on the responsivity that the receiver presents for each wavelength (0.41, 0.3 and 0.2 for λRed = 635 nm, λGreen = 525 nm and λBlue = 455 nm, respectively).

Fig. 5 shows the BER as a function of the Ep/N0 for a 2-PPM-THSS system with redundancy equal to 3, operating at 10 Mbps in a single-user environment. As we can see, the use of hard- or soft-decision detection yields better results than the use of threshold detection, the soft-decision detection method which exhibits the best BER. Fig. 6 displays the results obtained for a 2-PPM-THSS system without redundancy, operating at 1 Mbps in a multi-user environment. The channel is shared by four systems or users. In this case, the use of hard- or soft-decision detection provides the same BER because the system is operating without redundancy.

V. CONCLUSIONS In this paper, a system based on 2-PPM-THSS techniques

for indoor VLC has been studied. The system allows selecting the number of pulses per symbol to be transmitted (redundancy). It makes use of an optimum maximum-likelihood receiver for AWGN channels in the absence of ISI and MUI, and hard- or soft-decision decoding can be selected.

Finally, the results obtained can be used to compare the performance based on the computation of the BER as a function of Ep/N0, for different configurations in single-user and multi-user environments.

-10 -5 0 5 10 15 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Ep/No(dB)

BER

threshold detection

hard-decision detection.soft-decision detection

Fig. 5. BER for 2-PPM-THSS systems at 10 Mbps versus Ep/N0 in a single-user environment.

-10 -5 0 5 10 15 2010

-4

10-3

10-2

10-1

100

Ep/No(dB)

BER

threshold detection

hard-decision detectionsoft-decision detection

Fig. 6. BER for 2-PPM-THSS systems at 1 Mbps versus Ep/N0 in a multi-user environment.

REFERENCES [1] K.D. Langer, J. Vucic, C. Kottke, L.F. del Rosal, S. Nerreter, J.

Walewski, “Advances and prospects in high-speed information broadcast using phosphorescent white-light LEDs”, Proc. 11th Int. Conf. Transparent Optical Networks, Azores, 2009. pp. 1-6.

[2] T. Komine, M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights”, IEEE Trans. Consumer Electron., vol. 50, no. 1, pp. 100-107, February 2004.

[3] K. Lee, H. Park, J.R. Barry, “Indoor channel characteristics for visible light communications”, IEEE Commun. Lett., vol. 15, pp. 217-219, February 2011.

[4] F.J. López-Hernandez, R. Pérez-Jiménez, A. Santamaría, “Ray-Tracing algorithms for fast calculation of the channel impulse response on diffuse IR-wireless indoor channels”, Opt. Eng., vol. 39, no. 10, pp. 2775-2780, October 2000.

[5] S. Rodríguez, B.R. Mendoza, R. Pérez-Jiménez, F.J. López-Hernádez, A. Ayala, “Simulation of impulse response for indoor visible light communications using 3D CAD models“, EURASIP J. Wirel. Commun. Netw. 2013, vol. 2013, no. 7, January 2013.

[6] J.R. Barry, J.M. Kahn, E.A. Lee, D.G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels”, IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367-379, April 1993.

[7] C.R. Lomba, R.T. Valadas, A.M. Oliveira Duarte, “Experimental characterisation and modelling of the reflection of infrared signals on indoor surfaces”, IEE Proc. Optoelectron., vol. 145, no. 3, pp. 191-197, June 1998.

[8] S. Rodríguez, R. Pérez-Jiménez, F.J. López-Hernádez, O. González, A. Ayala, “Reflection model for calculation of the impulse response on IR-wireless indoor channels using ray-tracing algorithm”, Microw. Opt. Techn. Lett., vol. 32, no. 4, pp. 296-300, January 2002.