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Comparison of Hybrid Optical Modulation Schemes for Visible Light Communication Volume 9, Number 3, JUNE 2017 Yaqi Sun Fang Yang, Senior Member, IEEE Junnan Gao

DOI: 10.1109/JPHOT.2017.2705040 1943-0655 © 2017 IEEE

IEEE Photonics Journal

Comparison of Hybrid Optical Modulation Schemes for VLC

Comparison of Hybrid Optical Modulation Schemes for Visible Light Communication Yaqi Sun, Fang Yang, Senior Member, IEEE, and Junnan Gao Research Institute of Information Technology, Tsinghua National Laboratory for Information Science and Technology and Department of Electronic Engineering, Tsinghua University, Beijing 100084, China DOI:10.1109/JPHOT.2017.2705040 C 2017 IEEE. Translations and content mining are permitted for academic research only. 1943-0655 Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received April 2, 2017; revised May 6, 2017; accepted May 12, 2017. Date of publication May 17, 2017; date of current version May 25, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61401248, in part by the New Generation Broadband Wireless Mobile Communication Network of the National Science and Technology Major Projects under Grant 2015ZX03002008, in part by the Tsinghua University Initiative Scientific Research Program under Grant 2014Z06098, and in part by the Young Elite Scientist Sponsorship Program by CAST. Corresponding author: F. Yang (e-mail: [email protected]).

Abstract: In this paper, three hybrid modulation schemes for visible light communication based on orthogonal frequency division multiplexing (OFDM) are compared, which are asymmetrically clipped dc-biased optical OFDM, hybrid asymmetrically clipped optical OFDM, and layered asymmetrically clipped optical OFDM (LACO-OFDM). The following aspects are analyzed and compared, such as the probability distribution functions, the peakto-average power ratio, and the bit error ratio performance in terms of optical bit energy to noise power under different conditions. Furthermore, the optimal proportion of the optical power on different layers for LACO-OFDM is also investigated. Simulation results show that LACO-OFDM has better performance than other hybrid schemes in high signal-to-noise ratio (SNR) scenario, and the improvement is slight when more than four layers signals are utilized, while in low SNR condition, LACO-OFDM with two layers performs better than that with more layers. Index Terms: Visible light communication (VLC), orthogonal frequency division multiplexing (OFDM), asymmetrically clipped DC biased optical OFDM (ADO-OFDM), hybrid asymmetrically clipped optical OFDM (HACO-OFDM), layered asymmetrically clipped optical OFDM (LACO-OFDM).

1. Introduction Motivated by the rapid development of light emitting diodes (LEDs), visible light communication (VLC) has been considered as a promising technology due to its features such as broad license-free bandwidth, low cost, no harm to health, and privacy protection [1]–[3]. Single-subcarrier schemes are simple for application with low complexity, such as on-off-keying (OOK) and pulse position modulation (PPM) [4]–[6]. Recently, orthogonal frequency division multiplexing (OFDM) technique has been widely used in VLC with its advantages of resistance to inter symbol interference (ISI), and it is more optical power efficient than single-subcarrier schemes [7], [8]. VLC systems use intensity modulation and direct detection (IM/DD), where the transmitted signal is modulated onto the intensity of light [9]. Therefore, the OFDM signal designed for VLC has to be real and non-negative. In order to obtain the real signal, the input signal in the frequency domain usually satisfies the Hermitian symmetry property. After inverse fast Fourier transform

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(IFFT), the signal should be ensured to be unipolar, which could be achieved by adding a DC bias in DC biased optical OFDM (DCO-OFDM) [10], or by clipping the negative part of the output signal directly based on its anti-symmetric features in asymmetrically clipped optical OFDM (ACOOFDM) [11] and pulse-amplitude-modulated discrete multitone (PAM-DMT) [12]. However, there are disadvantages in these conventional schemes. For example, DCO-OFDM is not efficient in terms of optical power [13], while only half of the subcarriers and signal dimensions are utilized in ACO-OFDM and PAM-DMT, respectively, which leads to a spectral efficiency loss. Several strategies have been proposed to improve the conventional schemes. In [14], asymmetrically clipped DC biased optical OFDM (ADO-OFDM) is developed, where the ACO-OFDM is transmitted on the odd subcarriers and the DCO-OFDM is transmitted on the even subcarriers. A hybrid ACO-OFDM (HACO-OFDM) is also described by modulating ACO-OFDM only on odd subcarriers and utilizing PAM-DMT only on the imaginary part of the even subcarriers in [15]. More recently, a new technique, layered ACO-OFDM (LACO-OFDM) or enhanced ACO-OFDM (eACOOFDM) is proposed in [16]–[18] by combining different layers of ACO-OFDM signals, which can improve the spectral efficiency by up to 2 times with the increment of the computational complexity and has been experimentally demonstrated over a fiber link in [19]. Similarly, an enhanced unipolar OFDM (eU-OFDM) is proposed in [20], which combines multiple unipolar data streams in order to improve the spectral efficiency of U-OFDM. At different depth, each U-OFDM frame is repeated different times without any interference in demodulation process for lower depth. Moreover, some optical multiple input multiple output (MIMO) solutions are proposed to improve the whole system spectrum efficiency, such as non-DC-biased OFDM (NDC-OFDM) in [21] and generalized LED index modulation optical OFDM (GLIM-OFDM) in [22]. Conventional ACO-OFDM and DCO-OFDM are compared in [13]. In [23], comparisons of ACOOFDM, DCO-OFDM, and ADO-OFDM are presented in terms of probability density function (PDF) and optical power efficiency. In [24], LACO-OFDM with 3 layers, ACO-OFDM, PAM-DMT, DCOOFDM, ADO-OFDM, and eU-OFDM are compared with equal optical powers. In this paper, the comparisons of hybrid ACO-OFDM-based modulation schemes are the main concerns. The comparisons are made on the assumption that the proportions of the out-of-limit signals are all the same, considering the restrictions of the whole dynamic range [25]. On the one hand, peak-to-average power ratio (PAPR) is taken into consideration for the comparisons, since high PAPR results in signal distortion, which is the major flaw of OFDM. On the other hand, the bit error rate (BER) performance of LACO-OFDM depends on the optical power allocation of different layers, which is investigated by theoretical analysis and computer simulations in this paper. Since the performance of LACO-OFDM would vary with the layer number, the optimal amount of layer is also analyzed and could be achieved by simulations of LACO-OFDM with different layers. The rest of this paper is organized as follows. In Section II, the conventional optical modulation schemes, i.e., ACO-OFDM, PAM-DMT, and DCO-OFDM, are briefly introduced, while the hybrid ACO-OFDM-based modulation methods, such as HACO-OFDM, ADO-OFDM, and LACO-OFDM, are also presented. The comparisons in terms of PDF of the hybrid modulation methods as well as a detailed analysis of LACO-OFDM are provided in Section III. In Section IV, simulation results of optimal power allocation for LACO-OFDM and comparisons of the hybrid modulation schemes in terms of PDF, PAPR, and BER performance are presented. The paper concludes in Section V.

2. Optical Modulation Schemes In this section, conventional ACO-OFDM, PAM-DMT, and DCO-OFDM schemes as well as hybrid modulation schemes such as HACO-OFDM, ADO-OFDM, and LACO-OFDM are described. 2.1 Conventional Schemes 2.1.1 ACO-OFDM: In ACO-OFDM, only the odd subcarriers carry data while the even subcarriers are set to zeros in the frequency domain. The input signal to the N -point IFFT, X, consists of only odd components and satisfies the Hermitian symmetry as X = [0, X 1 , 0, X 3 , ..., X N /2−1 , 0,

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Fig. 1. Transmitters for hybrid modulation schemes in VLC.

X ∗N /2−1 , ..., X ∗3 , 0, X ∗1 ]. The time-domain signal x n has the anti-symmetric property as x n = −x n+N /2 , (0 ≤ n < N /2). The ACO-OFDM signal, x ACO,n , is ensured non-negative by clipping the negative part without losing any information as x n , x n ≥ 0, x ACO,n = (1) 0, x n < 0. In [11], it has been proved that the clipping noise only falls on the even subcarriers, which will not affect the demodulation of the transmitted data. 2.1.2 PAM-DMT: In PAM-DMT, signals drawn from PAM are used to modulate the imaginary part of each subcarrier except the 0-th and N /2-th subcarriers. The input to the IFFT block can be represented as Y = [0, Y1 , Y2 , ..., YN /2−1 , 0, YN∗ /2−1 , ..., Y1∗ ], where Yk = i b k , b k (k = 1, 2, ..., N /2 − 1) is the real-valued PAM signal and i 2 = −1. As shown in [15], the time-domain signal y n follows the symmetry as y n = −y N −n , (0 ≤ n < N /2). Therefore, PAM-DMT signal y PAM,n can be clipped at zero without any loss of information as y n , y n ≥ 0, y PAM,n = (2) 0, y n < 0. The data could be exactly demodulated from the imaginary part of the subcarriers at the receiver based on the fact that the clipping noise only falls on the real part of each subcarrier [15]. 2.1.3 DCO-OFDM: In DCO-OFDM, the signal z n generated by the IFFT is guaranteed to be positive by adding a DC bias, B DC . After the superposition, the remaining negative signal will be clipped at zero, leading to a clipping noise, c n , which depends on the DC bias. Then, the transmitted DCO-OFDM signal z DCO,n is given by z DCO,n = z n + B DC + c n . Moreover, B DC is usually relative to the electrical power of the signal z n , and B DC

(3) = μ E z 2n , where

μ is a proportional constant and B DC is defined as 10log10 (μ2 + 1) dB. 2.2 Hybrid Schemes Figs. 1 and 2 illustrate the transmitters and receivers of HACO-OFDM, ADO-OFDM, and LACOOFDM, respectively.

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Fig. 2. Receivers for hybrid modulation schemes in VLC.

2.2.1 HACO-OFDM: In HACO-OFDM approach, ACO-OFDM is transmitted on the odd subcarriers while PAM-DMT is conveyed on the even subcarriers. As presented in Fig. 1, the signal from the first block is the same as the conventional ACO-OFDM. The data of the second block is mapped using PAM, which occupies only the even subcarriers. After clipping the negative part individually, the signal from the second block is added to the first one, generating the transmitted HACO-OFDM signal in the time domain, sHACO,n , as sHACO,n = x ACO,n + y PAM,n .

(4)

Considering the fact that the clipping noises caused by ACO-OFDM and PAM-DMT fall on the even subcarriers and the real part of the even subcarriers, respectively, the ACO-OFDM could be demodulated by the conventional method. Thus, at the receiver, the received signal, r HACO , consists of the transmitted signal, sHACO , and the noise. As illustrated in Fig. 2, after the FFT operation, the ACO-OFDM signal can be directly detected by the odd subcarriers multiplied by a factor of 2. Then the clipping noise, C ACO , could be estimated by re-generating the ACO-OFDM signal, which will be then subtracted from the original received signal and assist the demodulation of the PAM signal. The final output data, d HACO , can be obtained once the PAM-DMT and ACO-OFDM signals are decoded. 2.2.2 ADO-OFDM: In ADO-OFDM scheme, ACO-OFDM is combined with DCO-OFDM instead of PAM-DMT in the HACO-OFDM system. As shown in Fig. 1, the time-domain ACO-OFDM and DCO-OFDM signals are generated separately. Then, the transmitted signal, sADO,n , is obtained by adding them together as sADO,n = x ACO,n + z DCO,n .

(5)

At the receiver, the ACO-OFDM signal is first detected as that performed in the conventional ACO-OFDM. Then, the clipping distortion can be estimated and subtracted in order to demodulate the remaining DCO-OFDM signal.

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2.2.3 LACO-OFDM: In [16], a novel hybrid LACO-OFDM scheme is introduced which consists of many layers of ACO-OFDM signals. L -Layer LACO-OFDM denotes a LACO-OFDM with L layers, while l-th ACO-OFDM refers to the l-th layer in LACO-OFDM. In LACO-OFDM, the data signals are divided into different layers, where each layer is achieved by ACO-OFDM scheme in the time-domain with different repeated times. The first layer is the (1) conventional ACO-OFDM, denoted as x ACO,n . If only the 2(l−1) k-th (0 < l < log2 N , k = 0, 1, ..., N /2(l−1) − 1) subcarriers are modulated, the timedomain signal is represented as 1 xn = √ N =√ =√

N /2l−1 −1

1 2l−1 1 2l−1

k=0

1

2π l−1 X 2l−1 k exp j n2 k N

N /2l−1 −1

N /2l−1

X

(l) k

k =0

2π exp j nk N /2l−1

(l)

x mod (n,N /2l−1 ) , n = 0, 1, ...N − 1,

(l)

(6)

(l)

where x n denotes the N /2(l−1) -point IFFT result of X k . Apparently, x n has periodicity and can be (l) (l) generated by repeating x n by 2l−1 times. The l-th ACO-OFDM signals x ACO,n can be obtained by (l)

utilizing the subcarriers with odd indexes of X k and clipping the negative part. Thus, in the l-th ACO-OFDM, only the 2l−1 (2k + 1)-th (k = 0, 1, ..., N /2l−1 ) subcarriers are modulated. As shown in Fig. 1, the time-domain signals from different layers are superposed together and transmitted simultaneously as sL ,n =

L

(l)

x ACO,n .

(7)

l=1

Considering that in conventional ACO-OFDM which utilizes (2k + 1)-th (k = 0, 1, ..., N /2 − 1) subcarriers, the clipping distortion falls on the 2k-th (k = 0, 1, ..., N /2 − 1) subcarriers, in the l-th ACO-OFDM which occupies 2l−1 (2k + 1)-th (k = 0, 1, ..., N /2l − 1) subcarriers, only the 2l−1 (2k)-th (k = 0, 1, ..., N /2l − 1) subcarriers are affected, which are used in higher layers. For the l-th layer, (1) (2) (l−1) the clipping noise from all the lower layers, C ACO , C ACO , ..., C ACO , could be estimated in proper order, (l) (l) and should be subtracted, resulting in R ACO . Then, the final estimation of the l-th layer, X ACO , could be achieved. Therefore, at the receiver, as shown in Fig. 2, the transmitted signals are detected from the 1st layer to the L -th layer sequentially.

3. Analysis of Hybrid Optical Modulation Schemes In VLC systems, one of the main challenges for OFDM modulation is the nonlinearity of LEDs, which can be mitigated by some methods and the LEDs can be considered quasi-linear in a limited range [26]. The comparisons among different modulation schemes are made with the same proportions of out-of-range signals, which depend on the PDFs. Thus, in this section, the PDFs of hybrid optical modulation schemes are calculated and compared theoretically. Besides, a near-optimal power allocation for LACO-OFDM is also investigated for the comparisons of BER performances. For a time-domain signal x n in VLC, the optical power, P op t , is proportional to E {x n } while the electrical power, P elec , depends on E {x 2n }. Thus without loss of generality, it can be defined that P op t = E {x n } and P elec = E {x 2n }.

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3.1 PDFs of ADO-OFDM, HACO-OFDM and LACO-OFDM Based on the central limit theorem, the PDFs of conventional ACO-OFDM, PAM-DMT, and DCOOFDM obey a clipped Gaussian distribution as

f x ACO (w ) = √ f y PAM (w ) = √

1 2πσA 1 2πσP

exp exp

−w 2 2σA 2 −w 2 2σp 2

u(w ) +

1 δ(w ), 2

(8)

u(w ) +

−(w − B DC )2 f zDCO (w ) = √ exp 2σD 2 2πσD 1

1 δ(w ), 2

u(w ) + Q

(9)

B DC σD

δ(w ),

(10)

where σA , σP , and σD are the root mean square (RMS) of the unclipped ACO-OFDM, PAM-DMT, and DCO-OFDM signals, respectively. u(w ) denotes the unit-step function, δ(w ) is the Dirac delta function, and Q (·) is the tail probability of the standard normal distribution given by 1 Q (ξ) = √ 2π

ξ

∞

2 u du. exp − 2

(11)

As described in (4), the PDF of s HACO can be obtained by the convolution of the ACO-OFDM’s and PAM-DMT’s PDF [27], which is given by ⎞ ⎛ ⎞⎤ ⎡ ⎛ σ w w σ w2 A ⎠−Q ⎝ P ⎠⎦ × ⎣Q ⎝ − f sHACO (w ) = exp − 2 2 2 σ + σ 2 2 2 2 2 2 P A 2π(σA + σP ) σP σA + σP σA σA + σP 1 1 1 −w 2 −w 2 + √ + u(w ) + 0.25δ(w ). (12) exp exp σP 2σA2 2σP2 2 2π σA 1

Similarly, as a result of the relationship in (5), the PDF of sADO can be calculated by convolving the PDFs of ACO-OFDM and DCO-OFDM as [23] ⎡ ⎛ ⎞ ⎛ ⎞⎤ −B DC )2 exp −(w 2 2 w σD2 + B DC σA2 w σA2 − B DC σA2 2(σD +σA ) ⎠ − Q ⎝ ⎠⎦ × ⎣Q ⎝ f sADO (w ) = 2 2 2 2 2 2 2 2 2 2 2π(σD + σA ) − σD σA (σD + σA ) σD σA (σD + σA )

1 −(w − B DC )2 1 B DC 1 −w 2 + √ Q + exp exp u(w ) σD 2σD 2σA2 2σD2 2π σA B DC 1 δ(w ). + Q 2 σD

(13)

In LACO-OFDM, the RMS of the unclipped signal for the l-th layer is denoted as σl , i.e., σl2 = (l)

2

E{[x ACO (n)] }. The PDF of 1-Layer LACO-OFDM is the same as the conventional ACO-OFDM shown in (8). For 2-Layer LACO-OFDM, the PDF can be calculated as the convolution of two PDFs of the

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corresponding ACO-OFDM signals. Therefore, the PDF of s2 is represented as f s2 (w ) = f x (1) (w ) ⊗ f x (2) (w ) ACO ACO

∞ 1 −l 2 −(w − l )2 1 1 1 = exp exp u(l ) + δ(l ) × √ u(w − l ) + δ(w − l ) dl √ 2 2 2σ12 2σ22 2πσ1 2πσ2 −∞ ⎞ ⎛ ⎞ ⎤ ⎡ ⎛

2 1 w σ1 w ⎠ − Q ⎝ σ2 w ⎠⎦ × ⎣Q ⎝− = exp − 2 2 2 σ + σ 2 2 2 2 1 2 2π(σ + σ ) σ σ +σ σ σ2 + σ2 1

1 + √ 2 2π

2

2

−w 2 1 exp σ1 2σ12

+

−w 2 1 exp σ2 2σ22

1

1

2

1

2

u(w ) + 0.25δ(w ).

(14)

Moreover, the PDF of s3 is given by f s3 (w ) = f x (1) (w ) ⊗ f x (2) (w ) ⊗ f x (3) (w ) ACO

ACO

ACO

⎡

⎛

⎞

⎛

⎞⎤

σ2 w ⎠ − Q ⎝ σ1 w ⎠⎦ u(w ) 2 2 σ1 σ1 + σ2 σ2 σ12 + σ22 ⎞ ⎛ ⎞⎤

⎡ ⎛ σ w2 w w σ 1 3 1 ⎠−Q ⎝ ⎠⎦ u(w ) × ⎣Q ⎝− exp − 2 + 2 σ1 + σ32 4 2π(σ12 + σ32 ) σ1 σ12 + σ32 σ3 σ12 + σ32 ⎞ ⎛ ⎞⎤

⎡ ⎛ σ w2 w w 1 σ 3 2 ⎠−Q ⎝ ⎠⎦ u(w ) × ⎣Q ⎝− exp − 2 + 2 2 σ + σ 2 2 2 2 2 2 2 3 4 2π(σ2 + σ3 ) σ2 σ2 + σ3 σ3 σ2 + σ3

−w 2 −w 2 −w 2 1 1 1 1 1 (15) exp exp exp + √ + + u(w ) + δ(w )+α, 2 2 2 σ2 σ3 8 2σ1 2σ2 2σ3 4 2π σ1 2

1 w = exp − 2 2 2 σ 2 2 1 + σ2 4 2π(σ1 + σ2 )

where

α=

× ⎣Q ⎝−

−(w − l − v)2 −l 2 exp exp √ 2σ12 2σ22 2π 2πσ1 σ2 σ3

−v 2 × exp u(w − l − v)u(l )u(v) dldv. 2σ32 1

(16)

The PDF of other LACO-OFDM with higher layers can be obtained by recursive method, which can be mathematically formulated as f l (w ) = f l−1 (w ) ⊗ f x (l) (w ).

(17)

ACO

3.2 Near-Optimal Power Allocation for LACO-OFDM In LACO-OFDM, different layers modulate different orthogonal subcarriers, therefore LACO-OFDM with different optical power distributions will lead to diverse BER performances. Without loss of generality, the QAM constellations utilized for all layers in LACO-OFDM are the same, whose orders are denoted as M . The BER performance of conventional ACO-OFDM can be represented as [28], [29] √ ⎛ ⎞ 4 M −1 E 3 s⎠ P b,ACO ≈ √ , (18) Q⎝ M − 1 N0 M log2 M

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where E s denotes ACO-OFDM electrical energy per subcarrier and N 0 represents noise power. In L -Layer LACO-OFDM, E s,l denotes the ACO-OFDM electrical energy per subcarrier in layer l (0 < l ≤ L ). Then, the BER performance of l-th ACO-OFDM is given by P b,l = P b,1∼l−1 P b,l|1∼l−1 + (1 − P b,1∼l−1 ) P b,l|1∼l−1 = P b,l|1∼l−1 + P b,1∼l−1 P b,l|1∼l−1 − P b,l|1∼l−1 ,

(19)

where P b,l|1∼l−1 and P b,l|1∼l−1 denote the conditional probability of error given that the signals from the 1st layer to the (l − 1)-th layer have been demodulated wrongly and successfully, respectively. In general, due to the error propagation in the lower layers, the BER performance will be degraded in the LACO-OFDM with higher layers. However, under high SNR, the error propagation in the lower layers is negligible and the second term in (19) is approximately much smaller than P b,l|1∼l−1 and could be neglected [16]. Thus, the probability is approximately estimated as √ ⎛ ⎞ 4 M −1 E 3 s,l ⎠. (20) P b,l ≈ P b,l|1∼l−1 ≈ √ Q⎝ M − 1 N0 M log2 M Considering the fact that the l-th ACO-OFDM scheme utilizes N /2l subcarriers together with Hermitian constraint, there are only N /2l+1 independent complex input values. Therefore, the total BER performance for L -Layer LACO-OFDM can be derived as L 1 L N l=1 2l+1 log2 M × P b,l l=1 l−1 P b,l = L 2 1 . Pb = (21) L N l=1 2l+1 log2 M l=1 2l−1 The optimal power allocation can be obtained by minimizing the numerator in (21) with the constraint that the sum of the electrical power in the frequency domain from all layers is a constant, β, which is given by L N l=1

2l

E s,l = β.

(22)

Then, the method of Lagrange multipliers is applied to find the local minimum. In this case, the Lagrange function is represented as

L L N 1 P b,l + λ · E s,l − β (23) L (E s,1 , ..., E s,L , λ) = 2l−1 2l l=1

l=1

As a result, the problem is converted by setting the partial derivatives of (23) as zeros, which is given by ∂L (E s,1 , ..., E s,L , λ) 1 ∂P b,l = l−1 +λ ∂E s,l 2 ∂E s,l √ ⎛ ⎞ 3 M −1 E 3 N (M −1)N 0 s,l ⎠ = + lλ Q ⎝ √ l−3 M − 1 N0 2 2 M log2 M = 0,

0BER . 4QAM, 16QAM, 64QAM, and 256QAM constellations are used on the ACO-OFDM subcarriers. As shown in Fig. 3(a), the 2-Layer LACO-OFDM achieves the minimum√< SNR >BER when the proportion of the whole optical power on the 2nd ACO-OFDM is 1/(1 + 2) ≈ 0.41. For 3-Layer LACO-OFDM, variation on the 3rd ACO-OFDM is demonstrated in Fig. 3(b), where of < SNR >BER with the proportion √ σ2 /(σ1 + σ2 ) is kept at√1/(1 + 2). It can be seen that the optimal power allocation on the 3rd ACO-OFDM is 1/(1 + 2 + 2) ≈ 0.23, which verifies the power allocation criteria in (29). In order that no more than 1% signals are out of [0,1] range, extensive computer simulations are carried out to find the proper parameters for the LACO-OFDM based on the relationship in (29), where the simulation results are listed in Table 1. Fig. 4(a) and (b) show the simulated PDFs and the complimentary cumulative distribution function (CCDF) curves of the PAPR for the ADO-OFDM (ACO 16QAM, DCO 4QAM, 5.1dB bias, 0.4 ACO power), HACO-OFDM (ACO 16QAM, PAM 4PAM, 0.6 ACO power), and LACO-OFDM (16QAM) with 2, 3, 4, and 5 layers. It can be seen that the PDFs of the HACO-OFDM and LACO-OFDM with 2 layers are almost the same, and the slight difference is caused by the different RMSs as shown in Tables I and II. The probability of the LACO-OFDM signal with zero values in the time domain will decrease with the increment of the layer number, while the probability of the signal for lower

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Fig. 3. (a) Variation of < SNR >BER with the proportion on optical power on 2nd ACO-OFDM for 2-Layer LACO-OFDM. (b) Variation of < SNR >BER with the proportion on optical power on 3rd ACO-OFDM for 3-Layer LACO-OFDM.

TABLE 1 Parameters for LACO-OFDM

Layer Number L

σ1 , ..., σL

2

0.346, 0.245

3

0.312, 0.221, 0.156

4

0.293, 0.207, 0.147, 0.104

5

0.282, 0.199, 0.141, 0.100, 0.071

Fig. 4. (a) PDFs for ADO-OFDM, HACO-OFDM, and LACO-OFDM. (b) CCDF curves of PAPR for ADO-OFDM, HACO-OFDM, and LACO-OFDM.

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Comparison of Hybrid Optical Modulation Schemes for VLC TABLE 2 Parameters for ADO-OFDM and HACO-OFDM

Schemes

σA

σP or σD

0.203

ACO 4QAM, DCO 4QAM bias = 5.5 dB, ACO power = 0.2 (ADO-OFDM)

0.206


0.3236

0.127


0.3745

0.074


0.3272

0.103


0.3597

0.077

ACO 4QAM, PAM 2PAM, ACO power = 0.6 (HACO-OFDM)

0.352

0.235


0.234

0.156


0.352

0.235


0.385

0.165


0.234

0.156


0.352

0.235

Fig. 5. Comparison of < E b(opt) /N 0 >BER versus bit rate/normalized bandwidth for the ACO-OFDM, DCO-OFDM, ADO-OFDM, HACO-OFDM, and LACO-OFDM.

values will raise, leading to the optical power augment. Due to the DC bias, the ADO-OFDM has a much higher optical power compared with the other two non-DC-biased schemes, which can be inferred from Fig. 4(a). For LACO-OFDM, the PAPR performance is superior with a large number of layers due to the increase of average power, while the power increment becomes slow when the layer number is larger than 4. This can be explained by the small optical power proportion on the 5th ACO-OFDM, which is approximately 3.2% of the total power. Moreover, ADO-OFDM is shown to achieve the best PAPR, which is caused by the higher average optical power due to the DC-bias. As illustrated in Fig. 5, minimum required normalized optical bit energy to noise power for a BER of 10−3 , < E b(opt) /N 0 >BER , versus the average bit rate/normalized bandwidth for the ADOOFDM, HACO-OFDM, and LACO-OFDM systems are simulated. The conventional ACO-OFDM and

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DCO-OFDM with 4QAM, 16QAM, 64QAM, and 256QAM are also included for comparsions. The results of the ADO-OFDM and HACO-OFDM are obtained using the parameters listed in Table 2. Simulations of LACO-OFDM are performed with 4QAM, 16QAM, 64QAM, and 256 QAM for each layer. When the bit rate/normalized bandwidth is small, the < E b(opt) /N 0 >BER of ADO-OFDM is pretty higher than other schemes. This is because ADO-OFDM requires DC bias compared to other nonDC-biased schemes, which is not efficient in optical power, leading to the worst performance among hybrid schemes. Under low SNR, for LACO-OFDM with higher layer, the limited signal powers are allocated to more layers, resulting in high BER. Thus, the LACO-OFDM with higher layers have worse performance in high noise level scenario. It can be seen that when the noise level is high, HACO-OFDM could have similar performance as LACO-OFDM with 2 layers, while 2-Layer LACOOFDM also have better performance than that with higher layers, which is demonstrated in Fig. 5 when the bit rate/normalized bandwidth is less than 2. When the bit rate/normalized bandwidth is around 3.5, 3-Layer LACO-OFDM is shown to be the optimal scheme. Under this SNR condition, the 3rd layer can improve the optical power efficiency with little loss of BER performance. It can also be seen that the < E b(opt) /N 0 >BER performance of LACO-OFDM increases when the layer number raises from 2 to 4, which also outperforms the conventional ADO-OFDM and HACO-OFDM considering the bit rate/normalized bandwidth more than 4. The performance of 4-Layer LACOOFDM is almost the same as that of 5-Layer LACO-OFDM when the bit rate/normalized bandwidth is larger than 5. Considering the error propagation in the lower layers, the BER performance will be degraded for LACO-OFDM with higher layers. Thus, the 5-Layer LACO-OFDM does not show superiority compared with 4-Layer LACO-OFDM in terms of BER performance. In L -Layer LACO-OFDM, the computational complexity at the transmitter would be (2 − 1/2L −1 )O(N log2 (N )) and that would be (5 − 1/2L −3 )O(N log2 (N )) at the receiver [16]. Thus, 4-Layer LACO-OFDM has lower complexity than 5-Layer LACO-OFDM. For synthetical consideration of the performance and complexity, 4-Layer is shown to be the optimal option for LACO-OFDM when the noise level is low. In summary, the optimal layer number of LACO-OFDM varies with the bit rate/normalized bandwidth, which means the best modulation scheme depends on the environment.

5. Conclusion In this paper, three hybrid modulations for VLC are analyzed and compared in terms of PDF and BER performances, which are the LACO-OFDM, ADO-OFDM, and HACO-OFDM. Through both theoretical analysis and simulation verification, LACO-OFDM with higher layers have higher average power, while the electrical powers allocated to each subcarrier among different layers should be equally allocated in order to achieve the best BER performance. When the noise level is high, LACO-OFDM with 2 layers performs slightly better than that with higher layers and HACO-OFDM has similar performance with 2-Layer LACO-OFDM, while ADO-OFDM is less optical power efficient. For low noise level, LACO-OFDM with higher layers is shown to perform better, which also outperforms ADO-OFDM and HACO-OFDM, but the improvement is not significant when the layer number is over 4. As a result, in practice, the optimal choice should be made by considering complexity cost, performance requirement, error propagation, and application environment comprehensively.

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