Next-generation LED lighting is more advantageous than existing fluorescent and incandescent lighting in terms of long life expectancy, high tolerance to humidity, low power consumption, and minimal heat generation [1]. In addition, LEDs are used not only for illumination but also for many products such as monitors, cell phones, cars, and others. Recently, there have been many attempts to converge LED with IT technology [2,3]. Among them, Visible Light Communication (VLC), which is the convergence of illumination and communication, has emerged [4-6]. A corresponding VLC standardization was recently published by the IEEE Standards Association [7,8]. Generally, VLC uses the Intensity Modulation with a Direct Detection (IM/DD) scheme, which uses the amplitude (or intensity) of light to transmit data. Human eyes perceive only the average intensity when light changes faster than the Maximum Flickering Time Period (MFTP), which is defined as 5 ms [8]. Therefore, both lighting and communication can be simultaneously implemented. By considering both terms together, many modulation methods have been proposed, such as inverted pulse position modulation (I-PPM), subcarrier inverted pulse position modulation (SC-I-PPM) [9], pulse width modulation (PWM) [10], and variable PPM (VPPM) [8]. Among them, VPPM is the modulation scheme proposed by the IEEE 802.15 standard group. To support illumination with dimming control and communication simultaneously, it uses binary PPM for communication and PWM for dimming control. However, the main drawback of the VPPM scheme is that the data rate is limited to the bandwidth of an LED since it uses only binary PPM modulation.

In this paper, we propose a new VLC modulation scheme called multi-coded variable pulse position modulation (MCVPPM). Two groups of signals (PWM and PPM group) are multi-coded by orthogonal codes for transmitting data simultaneously. Then, each multi-level value of the multicoded signal is converted to pulse width and position, which results in not only an improved data rate, but improved processing gain in reception as well. In addition, we introduce average duty ratio and cyclic shift concepts in PWM. To this effect, it is possible to support dimming control for light illumination without any degradation in communication performance. Through simulations, we compare BER and the achievable data rate of MC-VPPM and conventional VPPM schemes in a visible light optical channel environment. When comparing BER to VPPM, much greater achievable data rate is shown in BER. The rest of the paper is organized as follows. Section II describes the proposed MC-VPPM scheme. Simulation results and conclusions are given in Sections III and IV, respectively.

Fig. 1 shows the block diagram of the proposed multi-coded VPPM scheme for VLC. As shown in the Figure, the transmitting data block is divided into two separate parts. b_pwm = [b₁, _pwm…b_L1, _pwm]^T is the PWM data block that contains the L₁ antipodal signaled data. b_ppm = [b₁, _ppm…b_L2, _ppm]^Tis the PPM data block that contains the L₂ antipodal signaled data. Then, PWM and PPM data blocks are each encoded by using L₁ and L₂ binary orthogonal multi-codes of length N_s. Then two multi-coded signal vectors of length N_s are obtained as follows:

where

C_pwm, C_ppm are N_s × L₁ and N_s × L₂ binary orthogonal

code matrices. C_l,pwm [ c_1,l,pwm … c_Ns,_l,pwm ]^T where C _n,l,pwm ∈ { + 1, ？1 } denotes the l-th N_s + 1 orthogonal codes of the PWM and PPM data group, respectively. Then, each element of d_pwm and d_ppm have L₁ + 1 and L₂ + 1 symmetric possible multi-level values, i.e., d_n,pwm∈ {？ L₁, ？ L₁ + 2,… ,L₁？2,L₁}, d_n,ppm∈ {？ L₂, ？ L₂ + 2,… ,L₂？2,L₂}

In this paper, we propose a new concept called average duty ratio of pulse X(%), which determines the average intensity of the light source. Dimming control can be supported by varying the average duty ratio. In the proposed scheme the following values are chosen as initial system parameters: the average duty ratio of pulse X(%) for dimming support; the pulse width variation interval K (%) for PWM; the pulse width margin M (%) for limiting maximum and minimum pulse width; and the number of pulse positions N for PPM. Based on these basic system parameters, the possible amount of PWM and PPM data (L₁, L₂) and the orthogonal codes of length N_s are determined as follows:

To transmit the signal, each element of a multi-coded signal vector for PWM is converted to a pulse width vector as shown below:

where

and the corresponding pulse width W_n is given as

Here, T_f is the duration of a frame, where T_f= (L₂+1)δ, and denotes the pulse spacing for PPM. Table 1 shows the PWM mapping rule according to eq. (7) and (8).

In the case of PPM, each element of a multi-coded signal vector for PPM is converted to a pulse position vector as follows:

where

Table 2 shows the PPM mapping rule according to eq. (10).

Based on the pulse width and pulse position vector, the transmitted multi-coded VPPM signal has the form

where P _mw,_wn represents the transmitting pulse of width W_n, position m_n , and energy

The transmitted signal that contains L₁ + L₂ data occupies a total of N_s frames of duration T_f, and requires a time duration of T_s= N_sT_f. Because we set the average duty ratio of a pulse at X (%) for dimming support, the average pulse energy

satisfies the following constraint:

The signaling example of the proposed multi-coded VPPM is shown in Fig. 2.

In order to produce the corresponding signals b_pwm = [b_1,pwm…b_L1pwm]^T= [1,1, - 1 ]^T and b_ppm = [b_1,ppm…b_L2ppm]^T= [1,1, - 1 ]^T; and the orthogonal code matrices; C_pwm and C_ppm are generated based on Walsh-Hardamard (WH) orthogonal codes of length 4 as follows:

From the Figure, we can see that there are pulses that exceed their own frame durations (T_f) and introduce Inter- Frame Interferences (IFI). This is because we use PWM and PPM mapping simultaneously. Because IFI makes it difficult to detect and demodulate the transmitted MCVPPM signal on the receiver side, we introduce a Cyclic Shift scheme, which can remove IFI. By considering the energy constraints in Eq. (12) and (13) and providing Cyclic Shift, the shape of the transmitting pulse can be designed as follows:

where

The graphical representation of the Cyclic Shift scheme by using the example given in Fig. 2 is shown as below:

Finally, an LED is driven by the current signal controlled by the MC-VPPM signal s(t). The LED emits the light signal X(t) ≥ 0, which has the average optical power P_t given as follows:

After passing through the VLC optical channel h(t), X(t) is received by a photodiode (PD). The received signal r(t) is given as [4,5,11]:

Here, R is the detector responsibility [A/W], n(t) is Additive White Gaussian Noise (AWGN), and * indicates the convolution operator.

The average received optical power becomes P_r=H(0)

P_t, where H(0)

represents the channel DC gain. If we consider a LOS case with no reflections, the channel DC gain is:

where m is the order related to Φ_1/2, the transmitter semiangle (at half power), given by

For example, Φ_1/2 = 60° (Lambertian transmitter) corresponds to m = 1. A is the physical detection area of the PD, d is the distance between the LED and the PD, ？ is the angle of irradiance, and ψ is the angle of incidence. T_s(ψ) is the signal transmittance of the optical filter, g(ψ) is the concentrator gain, and ψc is the concentrator field of view (FOV).

We assume that the Gaussian noise n(t) has a total variance N that consists of shot noise, thermal noise, and inter frame interference P_rIFI by an optical path difference.

If the duration of the signal is long enough, the ISI is negligible. Therefore, the main noise sources become shot and thermal noises. A shot noise variance is given by [4]

where q is the electronic charge, P_rSingnal is the received signal power, B is the equivalent noise bandwidth, and I_bg is the background current. We define the noise bandwidth factor I_bg=0.562. The thermal noise variance is also given as [4]:

where the first two terms represent feedback-resistor noise and RET channel noise, respectively. K is Boltzmann’s constant, T_k is absolute temperature, G is the open-loop voltage gain, η is the fixed capacitance of a photo detector per unit area, ？ is the FET channel noise factor, g_m is the FET transconductance, and I₃=0.0868.

Here, we assume that the detector responsibility is ideal (R =1) and the receiver is exactly synchronized with the transmitter. Upon reception of r(t) , the receiver performs demodulation at the ith signal interval and pulse width, and produces the correlation metric r of length (L₁+1) ？ (L₂+ 1) ？ N_sas follows:

where

Here, q_a,b(t) = P_a,b (t)*h(t) denotes the template pulse, which is the transmitted pulse dispersed by the VLC optical channel.

Based on the maximum-likelihood (ML) decision rule, we detect the position and pulse width

of the transmitted pulses and regenerate the multi-coded signal vector as shown below:

where

Then, the two multi-coded signal vectors received,

are given as follows:

where

Finally, L₁ and L₂ data contained in

are decoded by orthogonal codes used at the transmitter with hard decision as follows:

Until now, we have discussed the overall description of the proposed MC-VPPM scheme. Now, we present the simulated result to validate the proposed scheme. The initial system parameters of MC-VPPM for simulation are shown in Table 3.

We used the VLC channel environment [12] and parameters for determining noise variances in [4] and [12]. For performance comparison, we include the conventional VPPM scheme [8], which is coded with an orthogonal code of length 4 to obtain the same processing gain as the proposed MC-VPPM scheme. Note that we are focusing on evaluating the BER performance of the proposed MC-VPPM modulation scheme. Therefore, we consider an uncoded system.

Fig. 4 shows the comparison of BERs for the proposed MC-VPPM and VPPM scheme according to the received E_b/N₀ (E_b/N₀)_rx) by changing the dimming levels. BER plots were widely used to express the data transmission performance of the proposed scheme in regard to communication, including optical communication. We perform a Monte-Carlo simulation that repeats data transmission 10⁹ times for obtaining a 10^-8 BER curve. In order to investigate the performance in the operating (E_b/N₀)_rx range of interest, we change 1) the dimming ratio and 2) the distance between the LED and PD. Fig. 5 illustrates the relationship between MC-VPPM’s (E_b/N₀)_rx performance according to the dimming ratio under the VLC scenario in [12] and the distance between LED and PD. Because VLC performance based on MC-VPPM affects the design of LED illumination infrastructure, it will be meaningful to express communi

cation performance based on distance and dimming ratio under the given VLC scenario.

From the above result, it is observed that MC-VPPM shows better BER performance as the dimming level decreases. This is because the interference caused by increased dimming levels in determining correlation metrics results in performance degradation, even though more energy is allocated to the transmitted signal thanks to higher dimming level increases in (E_b/N₀)_rx. Compared with the conventional VPPM scheme, the BER of MC-VPPM in 30% dimming levels always shows better BER performance than VPPM. In regard to BERs of the proposed MC-VPPM with 50% and 70% dimming, the proposed MC-VPPM still shows better performance in the low (E_b/N₀)_rx region even though the BERs of the proposed scheme with 50% and 70% dimming in higher (E_b/N₀)_rx regions are a little bit less than that of VPPM. However, as one can see in Fig. 6, the achievable data rate of the proposed MC-VPPM scheme is much higher than that of the VPPM scheme (by a factor of 2 in our simulation). This means that it is possible to compensate for the degraded BER performance of the proposed MC-VPPM scheme in high (E_b/N₀)_rx conditions by utilizing more power channel coding schemes with the benefit of a higher data rate. For example, MCVPPM can use 1/2 channel coding schemes under the same data rate condition while VPPM cannot use any kind of channel coding scheme. Therefore, the proposed MC-VPPM scheme shows reasonably robust BER performance compared with the conventional VPPM scheme.

As mentioned before, we compared the achievable data rate (ADR) between the proposed MC-VPPM and VPPM schemes. ADR represents how much data can be transmitted without error per unit time. Therefore, ADR can be expressed as a function of the maximum data rate and the bit error rate (BER):

where P_b and R _max denote BER and the maximum transmission rate per unit time (bits/sec), respectively. Here, the maximum transmission rate R _max is calculated as shown below:

Finally, we can obtain the achievable data rate (ADR) of the proposed MC-VPPM given as

Fig. 6 shows the comparison of achievable data rate between two schemes when the optical rate of the LED is 400kHz. As expected, the achievable data rate of MCVPPM is much greater than that of the VPPM scheme.

We have proposed a new VLC scheme based on multi-coded variable PPM (MC-VPPM) for VLC. By converting multi-level values of the multi-coded signals to pulse positions and pulse width, the proposed MC-VPPM gives both improved data rate and robust BER. For light illumination, dimming can be also supported without any degradation in communication performance by introducing average duty ratio and cyclic shift concepts in to the PWM. Through simulations based on VLC scenarios, we confirmed the robust BER curves and much-greater achievable data rates of the proposed MC-VPPM in comparison with conventional VPPM schemes.