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Enhanced performance of indoor VLC using anti-periodic asymmetrically clipped OFDM and multiple LEDS
Optics Communications 459 (2020) 124960
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Enhanced performance of indoor VLC using anti-periodic asymmetrically clipped OFDM and multiple LEDS Lijun Deng a ,∗, Yangyu Fan b a b
School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, Shaanxi, China School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, China
ARTICLE
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Keywords: Visible light communication (VLC) Optical OFDM Peak-to-average power ratio (PAPR) Power efficiency Spectral efficiency
ABSTRACT Visible light communication (VLC) systems make use of the available LED lamps to realize a high spatial density of high-speed optical links superposed to their natural illumination function. Orthogonal frequency division multiplexing (OFDM) has been adopted for these intensity modulation/direct-detection optical channels. However, it suffers from low power efficiency or low spectral efficiency. In this paper, we aim to improve the performance of OFDM-based indoor VLC systems. By utilizing the principle of spatial summing, we propose an anti-periodic asymmetrically clipped OFDM scheme to make efficient use of both power and spectrum. In this scheme, the OFDM subcarriers are partitioned into multiple specific groups to form independent unipolar signals. These signals are simultaneously transmitted from different LEDs that are within the same light fixture and are summed in space before being detected by a conventional OFDM receiver. The computer simulation results show that the proposed approach can achieve lower PAPR and more robustness to the clipping distortion caused by the nonlinearities of LED leading to better bit error rate performance for the same spectral efficiency than that of the conventional DCO-OFDM and ACO-OFDM schemes do under both LOS and DOW channels.
1. Introduction Recently, there has been a growing interest in visible light communication (VLC) for advantages such as unlimited bandwidth, environmental friendliness, and immunity to radio frequency interference [1,2]. Orthogonal frequency division multiplexing (OFDM) has been widely adopted in VLC to achieve high-speed transmission due to its inherent advantages such as high spectral efficiency, simple equalization, dynamic bandwidth allocation, and low-complexity implementation [3,4]. The physical properties of LEDs and Photodiodes (PDs) characterize a VLC system as an intensity modulation/direct detection (IM/DD) system. It means that only unipolar OFDM signals can be conveyed. One approach to make OFDM compatible with IM/DD links, termed DC-biased optical OFDM (DCO-OFDM), is to add a DC-bias to the time-domain signal and clip the parts beyond the linear range of the LED [5]. However, the DC-bias depends on the peak-to-average-ratio (PAPR) of the OFDM symbol. It is shown in [6] that the requirement of large DC-bias makes DCO-OFDM optical power inefficient. On the other hand, the use of lower DC-bias can lead to frequent clipping of the negative parts of the time domain signal, which may result in inter-carrier interference and optical power leakage. The transmission of such signal is, thereby, primarily limited by the linearity constraints of LED in the modulation/demodulation process and by the nonlinear
clipping distortion noises. A power-efficient alternative to DCO-OFDM is asymmetrically clipped optical OFDM (ACO-OFDM), which uses the properties of Fourier Transform and asymmetrical clipping to create unipolar signals in the time domain [7]. As shown in [8], clipping the time domain signal does not distort symbols in odd subcarriers, although their amplitude is scaled by a half. ACO-OFDM, however, has half of the spectral efficiency of DCO-OFDM for the same order of M-QAM modulation. In [9], a noise cancellation method is discussed, where the antisymmetry of the time samples of ACO-OFDM is used to identify which samples of the received signal are most likely to be due to the addition of noise. These samples are then set to zero. A maximum gain of 3 dB in optical power can be achieved with this method. In conventional ACO-OFDM, the even subcarriers are discarded, and only odd subcarriers are demodulated. In [10], a diversity combining system for ACO-OFDM is described, where the signal from the received even subcarriers are combined with the signal from the received odd subcarriers. As a result, a gain of up to 3 dB is achieved in electrical power. However, it is vulnerable to the DC offset, which may result from lowfrequency interference and environmental noise. In [11], a new system called asymmetrically clipped DC biased optical OFDM (ADO-OFDM) is proposed, where ACO-OFDM is used for odd subcarriers, and DCOOFDM is used for even subcarriers. It is shown that the bandwidth efficiency is better than ACO-OFDM, and the overall optical power
∗ Corresponding author. E-mail address: [email protected] (L. Deng).
https://doi.org/10.1016/j.optcom.2019.124960 Received 24 June 2019; Received in revised form 9 November 2019; Accepted 13 November 2019 Available online 16 November 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
efficiency is better than DCO-OFDM because all of the subcarriers are used to carry data. However, this method still requires a DC-bias for the generation of DCO-OFDM. A novel unipolar OFDM approach, Flip-OFDM, is proposed in [12], in which the positive and negative parts are extracted from the bipolar OFDM real time-domain signal, and transmitted in two consecutive OFDM symbols. Since the negative parts are flipped before transmission, both subframes have positive samples, Flip-OFDM is thus a unipolar OFDM scheme that can be used in VLC communications. Although Flip-OFDM offers a 50% complexity saving compared to ACO-OFDM, spectral efficiency, and the bit error rate (BER) performance for additive white gaussian noise (AWGN) and diffused optical wireless channels of both Flip-OFDM and ACO-OFDM still are the same. The newly multicarrier modulation scheme, U-OFDM, is inspired by the concept from [13] in an attempt to close the 3 dB gap between OFDM and ACO-OFDM for bipolar signals, whilst generating a unipolar signal without adding a DC-bias for optical wireless communication. An improved decoder for U-OFDM is presented in [14]. This decoder employs a recombination technique for the positive and negative frames, which at each position selects the sample with a higher amplitude between the two frames. Although this ideally removes half of the AWGN, it is still insufficient to make up for the power penalty, which results from the requirement for a higher constellation size compared to DCO-OFDM. In [15], a modified ACO-OFDM with low PAPR via introducing a recoverable upper-clipping (RoC) procedure is presented. It is shown that the system can achieve a significant PAPR reduction while maintaining a competitive bit error rate performance compared with the conventional ACO-OFDM scheme under both LOS and DOW channels. By taking the similar asymmetric structure of both ACO-OFDM and pulse amplitude modulated discrete multitone (PAMDMT), asymmetrically reconstructed optical OFDM scheme is proposed in [16] to enhance the time efficiency of both optical OFDM schemes, and it exhibits a noticeable BER gain compared to the conventional schemes under both LOS and DOW channels by employing an efficient detection. However, the systems in [15] and [16] require higher computational complexity in the demodulation procedure. In this paper, we propose a novel multicarrier modulation scheme, namely, anti-periodic asymmetrically clipped optical OFDM (AP-ACOOFDM), which is inspired by the design principle of ACO-OFDM to make efficient use of both power and spectrum. Most lighting fixtures include multiple LEDs that are modulated by identical signals in conventional VLC systems. In contrast, in this work, the frequency domain OFDM subcarriers are divided into multiple specific groups to form APACO-OFDM signals, which independently modulate the output intensity of groups of LEDs. The signals from each LED group are allowed to sum in space during propagation. At the receiver, the transmitted signals can be recovered noiselessly through a standard OFDM demodulator by employing successive decoding. The idea of spatial summing in VLC has been mentioned in related ways in the literature. Dong et al. [17] presented the concept of spatial summing applied only to the case of a single subcarrier per LED. The concept of spatial summing was mentioned for OFDM in parallel in [18]. However, no analysis, system designs, or performance results were provided. A VLC system based on SC-FDMA and spatial summing has been recently proposed in [19]. Mossaad et al. [20] used spatial summing of the intensities of multiple LEDs to solve the DCO-OFDM PAPR problem for VLC in a given luminary. However, at a lower signal-to-noise ratio (SNR), the BER performance was inferior to that of DCO-OFDM. We use the AP-ACO-OFDM scheme to enhance further the performance of VLC systems based on OFDM in this paper by spatial summing of the intensities of multiple LEDs. The remainder of this paper is organized as follows. Section 2 gives an overview of the principle for the ACO-OFDM-based VLC transmitter. Section 3 provides a description of the system model based on spatialsumming AP-ACO-OFDM. Section 4 shows the result of comparison among three schemes, AP-ACO-OFDM, DCO-OFDM, and ACO-OFDM, in terms of their complementary cumulative distribution function (CCDF) of PAPR. Also, the BER performance of AP-ACO-OFDM is compared with DCO-OFDM and ACO-OFDM schemes. Finally, Section 5 concludes this paper.
Fig. 1. A block diagram of an ACO-OFDM-based VLC transmitter.
2. A review of ACO-OFDM
A block diagram of an ACO-OFDM-based VLC transmitter is shown in Fig. 1. The transmitted binary data stream is first mapped into QAM symbols. After serial-to-parallel (S/P) conversion, loading these QAM symbols on the first half of the odd subcarriers, 𝑋2𝑘+1 , where 𝑘 = 0, 1, 2, … , 𝑁∕4 − 1, and 𝑁 s inverse fast Fourier transform (IFFT) size. The even subcarriers are set to zero, i.e. 𝑋2𝑘 = 0,
𝑘 = 0, 1, 2, … , 𝑁∕4
(1)
Using the above equation, the DC component and the symbol of the subcarrier become zero. After imposing the Hermitian symmetry property in Eq. (2), a bipolar real-time signal 𝑥𝑚 can be generated by the IFFT operation in Eq. (3). 𝑁 th 2
∗ 𝑋𝑘 = 𝑋𝑁−𝑘 ,
𝑥𝑚 =
𝑘 = 1, 2, … , 𝑁∕2 − 1
𝑁−1 ( ) ( ) 1 ∑ 2𝜋 𝑋𝑘𝐼 + 𝑗𝑋𝑘𝑄 exp 𝑗 𝑚𝑘 𝑁 𝑘=0 𝑁
(2)
(3)
where 𝑋𝑘𝐼 +𝑗𝑋𝑘𝑄 is the complex symbol modulated on the 𝑘th subcarrier. During the IFFT process in Eq. (3), each time sample 𝑥𝑚 can be written as a summation of 𝑁 phase rotated QAM symbols from all subcarriers. ( ) Let 𝑥𝑚,𝑘 = 𝑁1 𝑋[𝑘] exp 𝑗 2𝜋 𝑚𝑘 denote the contribution from subcarrier 𝑁 𝑘 to time sample 𝑚. Thus, the IFFT modulation process can be expressed as a summation of contributions from odd and even subcarriers 𝑥𝑚 =
𝑁−1 ∑ 𝑘=0
𝑥𝑚,𝑘 =
∑ 𝑘,odd
𝑥𝑚,𝑘 +
∑
even 𝑥𝑚,𝑘 = 𝑥odd 𝑚 + 𝑥𝑚
(4)
𝑘,even
For each odd subcarrier 𝑘, we have ( ) ( ) 1 2𝜋 2𝜋 𝑁 𝑋[𝑘] exp 𝑗 𝑚𝑘 exp 𝑗 ⋅ 𝑘 𝑥𝑚+ 𝑁 ,𝑘 = 𝑁 𝑁 𝑁 2 2 ( ) 1 2𝜋 = − exp 𝑗 𝑚𝑘 𝑁 𝑁 = −𝑥𝑚,𝑘
(5)
which indicates that 𝑥𝑚 = 𝑥odd 𝑚 is an anti-periodic sequence if only odd subcarriers are loaded with useful symbols. 2
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
⌊ 𝑔 ⌋ 𝑔 ⌋ ⌊ 𝑔 ⌋ 𝑥𝑚2 𝑐 , 𝑥𝑚3 𝑐 , … , 𝑥𝑚𝜇 are created through the zero-bias clipping 𝑐 operation. { 𝑔 𝑔 ⌊ 𝑔 ⌋ 𝑥𝑚𝜇 𝑥𝑚𝜇 > 0 𝑥𝑚𝜇 = (11) 𝑔 𝑐 0 𝑥𝑚𝜇 ≤ 0 ⌊ 𝑔 ⌋ After appending a cyclic prefix (CP), each group signal, 𝑥𝑚𝜇 , is 𝑐 hard-clipped to fit into the dynamic range of the driver. Subsequently, the digital-to-analog conversion is performed on each group clipped signal to form a parallel analog waveform. Finally, these analog waveforms simultaneously drive the corresponding LEDs group for intensity modulation. ⌊
3. Spatial-summing anti-periodic ACO-OFDM system model 3.1. Transmitter model According to Eq. (5), if only even subcarriers carry information, 𝑥𝑚 = 𝑥even is a periodic sequence. Inspired by the principle of ACO𝑚 OFDM, 𝑥even can also be made an anti-periodic sequence with a specific 𝑚 period by carefully loading only some of the even subcarriers. Denote 𝑘 ∈ 𝛺 as those even subcarriers which are loaded with symbols. Let 𝑥even denote the contribution from the 𝑘th even subcarrier 𝑚,𝑘 to the time sample 𝑚. In order to generate an N -point anti-periodic se, where 𝑇 = 2𝜇 for 𝜇 = 1, 2, … , log2 𝑁 − quence with a period equal to 𝑁 𝑇 1, the following relationship must be satisfied. even 𝑥even 𝑁 𝑚,𝑘 = −𝑥
𝑚+ 𝑇 ,𝑘
= 𝑥even2𝑁
𝑚+ 𝑇 ,𝑘
= −𝑥even3𝑁
𝑚+ 𝑇 ,𝑘
= ⋯ = −𝑥even(𝑇 −1)𝑁 𝑚+
𝑇
,𝑘
3.2. Indoor VLC channel model
(6)
Consider that multiple LEDs in a lighting fixture are modeled as having a Lambertian emission pattern and that the line-of-sight (LOS) links are assumed to dominate over all multi-path components from wall and ceiling reflections [2,21]. Therefore, the channel gain from an LED to the photodetector is given by [22] { (𝑚+1)𝐴PD cos𝑚 (𝜙) 𝑇S (𝜓) 𝑔 (𝜓) cos (𝜓) , 0 ≤ 𝜓 ≤ 𝜓c 2𝜋𝑑 2 (12) 𝛺= 0, 𝜓 > 𝜓c
which means ( ) [ ( ) ] 1 2𝜋 1 2𝜋 𝑁 𝑋[𝑘] exp 𝑗 𝑚𝑘 = − 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁 𝑁 𝑁 𝑇 [ ( ) ] 1 2𝜋 2𝑁 = 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁 𝑇 [ ( ) ] 1 2𝜋 3𝑁 = − 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁{ [𝑇 ] } (𝑇 − 1)𝑁 2𝜋 1 𝑚+ 𝑘 = ⋯ = − 𝑋[𝑘] exp 𝑗 𝑁 𝑁 𝑇
where 𝑚 is the Lambertian order given by 𝑚 =
(7) then Eq. (7) can be simplified to ) [ ( ) ] ( 2𝜋 𝑁 2𝜋 𝑚+ 𝑘 exp 𝑗 𝑚𝑘 = − exp 𝑗 𝑁 𝑁 𝑇 [ ( ) ] 2𝜋 2𝑁 = exp 𝑗 𝑚+ 𝑘 𝑁 𝑇 ( ) ] [ 3𝑁 2𝜋 𝑚+ 𝑘 = − exp 𝑗 𝑁{ 𝑇 [ ] } (𝑇 − 1)𝑁 2𝜋 = ⋯ = − exp 𝑗 𝑚+ 𝑘 𝑁 𝑇
− ln 2 ( ( )) , 𝑙𝑛 cos 𝛷1∕2
𝛷1∕2 is the
transmitter semi-angle (at half power), 𝐴PD is the collection area of the detector, 𝑑 is the distance between transmitter and receiver, 𝜙 is the angle of irradiance, 𝜓 is the angle of incidence, 𝑇S (𝜓) is the gain of the optical filter, 𝑔 (𝜓) is the gain of the optical concentrator, and 𝜓c is the field-of-view (FOV) of the receiver. In general, multiple LEDs in an indoor lighting fixture will be placed close to each other. In this case, the difference in path lengths from each LED to the receiver will be on the order of cm’s, while incurring propagation time differences on the order of 10’s ps. Also, the optical channel gains between LEDs will differ on the order of 1% − 2% between different LEDs due to the difference in path lengths. Thus, in this paper, we assume that all LEDs in a given fixture are sufficiently close that they have identical gains and delays to the receiver. Similar assumptions have been widely adopted by many others in a similar context [20,23–25].
(8)
− 1. Therefore, the following two expressions for all 𝑚 = 0, 1, 2, … , 𝑁 𝑇 can be obtained [ ] ( ) ( ) 2(𝑇 − 1)𝑘 2𝑘 6𝑘 exp 𝑗 𝜋 = exp 𝑗 𝜋 = ⋯ = exp 𝑗 𝜋 = −1 (9) 𝑇 𝑇 𝑇 [ ] ( ) ( ) 2(𝑇 − 2)𝑘 4𝑘 8𝑘 exp 𝑗 𝜋 = exp 𝑗 𝜋 = ⋯ = exp 𝑗 𝜋 =1 (10) 𝑇 𝑇 𝑇
3.3. Receiver model
According to Eqs. (9) and (10), the even subcarrier number 𝑘 ∈ 𝛺 would be that is divisible by 2𝜇−1 , but not divisible by 2𝜇 . If we denote this subcarrier group 𝛺 as 𝑔𝜇 , loading symbols separately on the subcarriers belong to 𝑔𝜇 will undoubtedly form an anti-periodic sequence with period 𝑁 . 𝑇 According to the principle of forming the anti-periodic signal above, the implemented scheme of an AP-ACO-OFDM-based spatial summing VLC transmitter is illustrated in Fig. 2. Assume the IFFT size is 𝑁, all subcarriers can be divided into £ = log2 𝑁 − 1 groups. For all 𝜇 = 1, 2, … , £, the subcarrier numbers which are loaded with QAM symbols in each group 𝑔𝜇 are as follows
The total received optical power is the sum of the optical powers received from each LED group. After conducting the photodetection and analogy-to-digital conversion to the received optical signals, the cyclic prefix of the OFDM sequence is removed, and the serial-to-parallel conversion is performed. It is assumed that the LEDs are placed closely enough together so that the optical channel gains and delays in Eq. (12) are almost identical for all LEDs. Thus, the generated photocurrent, 𝑦𝑚 , is proportional to the received power with additive white gaussian noise (AWGN) 𝑤𝑚 introduced by the VLC link and the detector. 𝑦𝑚 = 𝐺
£ ⌊ ⌋ ∑ 𝑔 𝑥𝑚𝜇 + 𝑤𝑚 𝜇=1
𝑔1 ∶ {1, 3, 5, … , 𝑁 − 1}
𝑐
(13)
where 𝐺 = 𝑅𝛺𝑆 is the electrical gain of the system, 𝑅[A∕W] is photodetector responsivity, 𝛺 is channel gain in (12), and 𝑆[W∕A] is conversion factor of the LED [20]. The FFT of 𝑦𝑚 can be expressed as
𝑔2 ∶ {2, 6, 10, … , 𝑁 − 2} 𝑔3 ∶ {4, 12, 20, … , 𝑁 − 4} ⋮ { } 𝑔𝜇 ∶ 2𝜇−1 , 3 ⋅ 2𝜇−1 , 5 ⋅ 2𝜇−1 , … , 𝑁 − 2𝜇−1
𝑌𝑘 = 𝐺
The remaining subcarriers in each group are loaded with zeros and 𝑔𝜇 satisfies Hermitian symmetry property in Eq. (2). After the IFFT 𝑔 𝑔 𝑔 process, 𝜇 groups anti-periodic OFDM signals 𝑥𝑚1 , 𝑥𝑚2 , … , 𝑥𝑚𝜇 can be ⌊ 𝑔 ⌋ obtained. And then, unipolar anti-periodic ACO-OFDM signals 𝑥𝑚1 𝑐 ,
£ {⌊ 𝑔 ⌋ } ∑ F 𝑥𝑚𝜇 + 𝑊𝑘 𝜇=1
𝑐
(14)
{ } where F (⋅) denotes the operator for FFT and 𝑊𝑘 = F 𝑤𝑚 . Assume subcarrier group 𝑔𝜇 is loaded with QAM symbol 𝑋[𝑘], then the output, 3
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
Fig. 2. A block diagram of an AP-ACO-OFDM-based spatial summing VLC transmitter.
𝑋[𝑘]′ , of FFT on subcarrier 𝑘 ∈ 𝑔𝜇 in (14), F as ′
𝑋[𝑘] =
𝑁−1 ∑⌊
𝑔 𝑥𝑚𝜇
⌋
𝑚=0
=
𝑇∑ −1
𝑁 𝑇
𝑔
𝑥𝑚𝜇
⌋ } 𝑐
When the subcarrier number 𝑛 ∉ 𝑔𝜇 , the FFT output 𝑋[𝑛]′ can be written as
, can be expressed
) ( 2𝜋 exp −𝑗 𝑚𝑘 𝑁 𝑐
−1 ⌊
∑
{⌊
𝑇
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑘 𝑁 𝑇 𝑐
=
=
2𝜇−1 ,
According to Eqs. (9) and (10), 𝑘 is divisible by that is, can 𝑘 be divisible by 𝑇2 . The result of 2𝜇−1 is an odd number according to the expression of(𝑔𝜇 . So the in Eq. [ ) ]exponential terms ( ) (15) can be reduced
𝑚+𝑖 𝑁 𝑇
𝑐
⎧ ⌊ 𝑔𝜇 ⌋ ⎪ −𝑥𝑚 = ⎨⌊ ⌋ 𝑐 ⎪ 𝑥𝑔𝜇 ⎩ 𝑚 𝑐
( ) 2𝜋 exp −𝑗 𝑚𝑛 𝑁 𝑐 𝑔𝜇
𝑖=0 𝑚=0
𝑚+𝑖 𝑁 𝑇
𝑥
𝑁 −1 𝑇∑ −1 𝑇∑ ⌊
⌋
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑛 𝑁 𝑇 𝑐
𝑔
(−1)𝑖 𝑥𝑚𝜇
(18)
⌋
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑛 𝑁 𝑇 𝑐
for 𝑖 = 1, 2, … , 𝑇2 − 1, is odd times for 𝜋. Hence, we have ( ) ] [ ( ) ] [ 𝑁 2𝜋 𝑁 2𝜋 𝑚+𝑖 𝑛 = − exp −𝑗 𝑚 + (𝑇 − 𝑖) 𝑛 (19) exp −𝑗 𝑁 𝑇 𝑁 𝑇 In addition, for the first and the middle term, we have ( ) [ ( ) ] 2𝜋 1 2𝜋 exp −𝑗 𝑚𝑛 = − exp −𝑗 𝑚+ 𝑁 𝑛 (20) 𝑁 𝑁 2 Thus, each term in summation in Eq. (18) can be canceled out by the other term that has the same magnitude but opposite sign. Therefore, 𝑋[𝑛]′ = 0, that is, the zero-bias clipping operation at the transmitter has no effect on the subcarrier groups 𝑔1 , 𝑔2 , … , 𝑔𝜇−1 . When 𝑛( ∈ 𝑔𝑟 for) 𝑟 ]= 𝜇 + 1,(𝜇 + 2, …), £, the exponential terms satisfy [ exp −𝑗 2𝜋 𝑚 + 𝑖𝑁 𝑛 = exp −𝑗 2𝜋 𝑚𝑛 due to the fact that 𝑛 is at least 𝑁 𝑇 𝑁
𝑖 is odd number (16) 𝑖 is even number
Therefore, Eq. (16) can be changed into 𝑁 ⎡ 𝑁 −1 ⎤ −1 𝑇 ) 𝑇∑ )⎥ ⌊ ⌋ ( ⌊ 𝑔 ⌋ ( 2𝜋 2𝜋 𝑇 ⎢ ∑ 𝑔𝜇 𝜇 𝑋[𝑘] = ⎢ 𝑥 exp −𝑗 𝑚𝑘 − −𝑥𝑚 exp −𝑗 𝑚𝑘 ⎥ 2 ⎢ 𝑚=0 𝑚 𝑐 𝑁 𝑁 𝑐 ⎥ 𝑚=0 ⎣ ⎦
′
⎡ 𝑁 −1 ⎤ 𝑇 ( )⎥ 𝑇 ⎢ ∑ 𝑔𝜇 2𝜋 = ⎢ 𝑥 exp −𝑗 𝑚𝑘 ⎥ 2 ⎢ 𝑚=0 𝑚 𝑁 ⎥ ⎣ ⎦ ( 𝑔 ) 1 𝜇 ≜ F 𝑥𝑚 2
divisible by 𝑇 . Then the following expression can be obtained 𝑋[𝑛]′ =
(17) ⌊ 𝑔 ⌋ ( 𝑔 ⌊ 𝑔 ⌋ ) where the equation −𝑥𝑚𝜇 = − 𝑥𝑚𝜇 − 𝑥𝑚𝜇 is used, hence, when 𝑐
⌋
𝑁 −1 ⌊ 𝑇∑ −1 𝑇∑
𝑖=0 𝑚=0
to Eq. (6), we have ⌋
𝑔
𝑥𝑚𝜇
When 𝑛 ∈ 𝑔𝑙 for 𝑙 = 1, 2,[ … , 𝜇−1, of the exponential ( the phase ) ] difference [ ( ) ] 𝑁 2𝜋 terms in Eq. (18), e.g. −𝑗 2𝜋 𝑚 + 𝑖 𝑛 and −𝑗 𝑚 + (𝑇 − 𝑖) 𝑁 𝑛 𝑁 𝑇 𝑁 𝑇
to exp −𝑗 2𝜋 𝑚 + 𝑖𝑁 𝑘 = (−1)𝑖 exp −𝑗 2𝜋 𝑚𝑘 . Moreover, according 𝑁 𝑇 𝑁
⌊ 𝑔 𝑥𝜇
𝑁−1 ∑⌊ 𝑚=0
(15)
⌋
𝑥𝑚+𝑖 𝑁
𝑖=0 𝑚=0
𝑋[𝑛]′ =
⎡ 𝑁 −1 ⎤ 𝑇 )⎥ (⌊ 𝑔 ⌋ ⌊ 𝑔 ⌋ ) ( 𝑇 ⎢∑ 2𝜋 𝜇 𝜇 𝑥 + −𝑥 exp −𝑗 𝑚𝑛 ⎥ 𝑚 𝑚 2 ⎢⎢ 𝑚=0 𝑁 𝑐 𝑐 ⎥ ⎣ ⎦
⎡ 𝑁 −1 ⎤ 𝑇 ( )⎥ 𝑇 ⎢ ∑ | 𝑔𝜇 | 2𝜋 𝑥 exp −𝑗 𝑚 | | ⎥ 2 ⎢⎢ 𝑚=0 | 𝑚 | 𝑁 ⎥ ⎣ ⎦ ( 𝑔 ) 1 | 𝜇| ≜ F |𝑥𝑚 | | | 2
(21)
=
𝑐
a single group 𝑔𝜇 which only includes even subcarriers carries QAM symbols, information on any of subcarriers in 𝑔𝜇 can also be perfectly recovered after the receiver FFT in the absence of noise and interference, except for a constant attenuation factor of 2 on the amplitude due to the power leakage.
It is evident that the effect of zero-bias clipping operation at the transmitter goes all to the subcarrier groups 𝑔𝜇+1 , 𝑔𝜇+2 , …, and 𝑔£ according to Eq. (21). 4
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Optics Communications 459 (2020) 124960
Fig. 3. A block diagram of an AP-ACO-OFDM-based VLC receiver with £ = 3.
Therefore, at the transmitter, if the anti-periodic signal which is generated by the subcarrier group 𝑔𝜇 is zero-bias clipped for transmission, then the receiver FFT output without noise and interference finally can be written as ⎧ ⎪0 ⎪ { 𝑔 } 𝑋[𝑘]′ = ⎨ 1 F 𝑥𝑚𝜇 2 ⎪ { } ⎪ 1 F ||𝑥𝑔𝜇 || ⎩2 | 𝑚|
𝑘 ∈ 𝑔𝑙 𝑘 ∈ 𝑔𝜇
(22)
𝑘 ∈ 𝑔𝑟
Fig. 3 shows the detection process and the reconstruction of the OFDM frame for 𝑔1 , 𝑔2 and 𝑔3 subcarrier groups at the receiver end. Through the photodetector and analogy-to-digital convertor, the cyclic prefix of the OFDM sequence is removed, and the serial-to-parallel conversion is performed. According to Eq. (22), information on the 𝑔1 subcarrier group can be recovered with a conventional OFDM receiver, and the clipping distortion form 𝑔1 to all the other subcarriers can be easily estimated. By removing the clipping distortion from 𝑔1 , symbols on 𝑔2 can be determined. Again, information on the 𝑔2 subcarrier group can be recovered by using a conventional OFDM receiver, and the clipping distortion form 𝑔2 to the remaining subcarriers can be estimated. Similarly, once the clipping distortions from 𝑔1 and 𝑔2 are obtained, symbols on 𝑔3 can be recovered. This decoding process undoubtedly can be extended to more than 3 groups.
Fig. 4. The CCDF of the PAPR for AP-ACO-OFDM, DCO-OFDM and ACO-OFDM with 𝑁 = 256 and 𝓁 = 4.
for AP-ACO-OFDM. That is, the numbers of independent modulated 𝑁 𝑁 subcarriers in group 𝑔1 , 𝑔2 , 𝑔3 , and 𝑔4 are 𝑁4 , 𝑁8 , 16 and 32 , respec𝑁 tively, while DCO-OFDM has 2 −1 independent modulated subcarriers. Therefore, from Fig. 4, DCO-OFDM has the largest PAPR, followed by subcarrier groups 𝑔1 , 𝑔2 , and 𝑔3 of AP-ACO-OFDM, and subcarrier group 𝑔4 has the lowest PAPR, which makes the AP-ACO-OFDM system less sensitive to the nonlinear distortions of LEDs. As for ACO-OFDM, the number of independent modulated subcarriers is the same as that of AP-ACO-OFDM when 𝜇 = 1, leading to both of them have an identical PAPR.
4. Simulation results and discussion 4.1. PAPR CCDF results An accurate estimate of continuous-time PAPR is obtained by over𝑔 sampling the discrete-time signals 𝑥𝑚𝜇 . Assume that 𝓁-times oversam𝑔 pling is adopted, and the oversampled version of 𝑥𝑚𝜇 is denoted by [ 𝑔 ]𝓁 𝜇 𝑥𝑚 . In practice, this can be done by adding (𝓁 − 1) 𝑁∕2 zeros to the end of 𝑔𝜇 before applying Hermitian symmetry and taking IFFT. The PAPR of the time-domain OFDM symbol, before clipping, is defined as
4.2. BER results
|[ 𝑔 ]𝓁 |2 [ ]𝓁 max𝑚=0,…,𝓁𝑁−1 || 𝑥𝑚𝜇 || ‖ 𝑥𝑔𝜇 ‖2∞ | | = (23) PAPR𝑔𝜇 = [ ]𝓁 [ ]𝓁 |2 1 ‖ 𝑥𝑔𝜇 ‖22 1 ∑𝓁𝑁−1 || 𝑔𝜇 | 𝓁𝑁 𝑥 𝑚 | | 𝑚=0 𝓁𝑁 | | The simulated CCDFs of PAPR for AP-ACO-OFDM with 𝜇 = 1, 2, 3 and 4, ACO-OFDM, and DCO-OFDM are compared in Fig. 4. All the simulation results are taken from 105 OFDM symbols, wherein the IFFT size is 𝑁 = 256, and 𝓁 = 4 are selected as demonstrated in the previous study [18]. It can be seen that each group OFDM signal of the AP-ACO-OFDM scheme achieves a PAPR reduction gain with respect to DCO-OFDM. A general trend is that the PAPR increases with the number of independent modulated subcarriers in an OFDM frame. 𝑁 independent modulated subcarriers The subcarrier group 𝑔𝜇 has 2𝜇+1
Some numerical comparison results of BER performance between conventional O-OFDM and the proposed AP-ACO-OFDM are displayed in this section. For all BER simulations, the creeQ5 white LED is considered. The number of LEDs is 15, and the LEDs are oriented in the same direction and are placed close to each other. So the channel gain to the receiver is assumed to be the same for each emitter group. The minimum input current 𝐼l and the maximum input current 𝐼u allowed by the LED are 110 mA and 1000 mA, respectively. It is assumed that a digital pre-distortion is used to linearize the relationship between input current and optical power. The direct clipping DCO-OFDM and direct clipping ACO-OFDM two kind of different conventional O-OFDM schemes are considered in our simulation and CR is utilized to indicate 5
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Optics Communications 459 (2020) 124960
In (25), if the number of groups is chosen to be large, such as 5, the formula for a spectral efficiency of AP-ACO-OFDM also becomes approximately 12 log2 𝑀1 . Under the above conditions, the constellation size of AP-ACO-OFDM and DCO-OFDM can be approximated to 𝑀1 = 𝑀2 , and the constellation √ size of AP-ACO-OFDM and ACO-OFDM can be approximated to 𝑀1 = 𝑀3 . It is known that the system performance inevitably suffers from the procedure of clipping due to information loss of clipped signals. Fig. 5 compares the BER performance of our proposed AP-ACO-OFDM scheme with the existing direct clipping DCO-OFDM scheme for the same spectral efficiency, where 𝑀1 = 16, 8 for 𝜇 = 3, 5 and 𝑀2 = 8. In this figure, the optical channel is assumed to be an indoor LOS channel modeled by the AWGN channel and the clipping level CR is set to 7 dB and 10 dB. As depicted, when CR = 7 dB, the BER of direct clipping DCO-OFDM scheme declines very slowly over the whole SNR range under severe clipping scenario, while the BER of the AP-ACO-OFDM scheme declines relatively rapidly with the increasing of 𝜇. Moreover, it can be found that the BER performance of our proposed AP-ACOOFDM scheme for 𝜇 = 3 and direct clipping DCO-OFDM scheme at high SNR values, such as 33 dB and 21 dB, starts exhibiting error floors. The reason for this is that the clipping distortion is negligible compared to AWGN in the low SNR regime, which dominates at high SNR values. Since clipping distortion is smaller for the smaller of the number of modulated subcarriers in an OFDM frame, or equivalently, a larger value of 𝜇, lower BER is achieved by using proposed AP-ACO-OFDM scheme for 𝜇 = 5 compared to AP-ACO-OFDM scheme for 𝜇 = 3 and the direct clipping DCO-OFDM scheme. When 𝜇 = 3 and 𝜇 = 5, we can observe that there does not exist an error floor for the AP-ACO-OFDM scheme by setting a giant CR except for direct clipping DCO-OFDM scheme with a lower error floor. This indicates that signal clipping has a considerable effect on the BER performance of direct clipping DCOOFDM scheme even though under a moderate clipping scenario. In the same low SNR range, it also can be seen that the proposed AP-ACOOFDM scheme for 𝜇 = 5 and direct clipping DCO-OFDM can use a lower order QAM scheme to achieve lower BER than the proposed APACO-OFDM scheme for 𝜇 = 3. Due to the clipping distortion, the BER performance of our proposed AP-ACO-OFDM scheme for both 𝜇 = 3 and 𝜇 = 5 still outperforms direct clipping DCO-OFDM scheme in the same high SNR range, and the power requirement of 𝜇 = 5 is about 1 dB less than the power requirement of 𝜇 = 3 at BER = 10−4 . A BER comparison of the proposed AP-ACO-OFDM and direct clipping ACO-OFDM for the same spectral efficiency is shown in Fig. 6, where 𝑀1 = 16, 8 for 𝜇 = 3, 5, and 𝑀3 = 64. It is shown that at each clipping level, the proposed scheme for both 𝜇 = 3 and 𝜇 = 5 always outperforms the direct clipping ACO-OFDM scheme under an ideal AWGN channel. Since the signal distortion becomes worse with the increasing of SNR, the BER performance saturates when SNR grows high or even without the presence of noise. Therefore, in the case of CR = 7 dB, it is similarly observed that the BERs of AP-ACO-OFDM for 𝜇 = 3 and direct clipping ACO-OFDM exhibit error floors when SNRs are higher than 35 dB and 30 respectively. When CR = 10 dB, the error floor of BER performance for direct clipping ACO-OFDM no longer exists, yet direct clipping ACO-OFDM requires about 5 dB and 6 dB higher SNR than AP-ACO-OFDM for 𝜇 = 3 and 𝜇 = 5 to achieve the BER of 10−4 . This indicates that our proposed AP-ACO-OFDM scheme has high spectral efficiency, thus it can use lower order QAM constellation to achieve higher power efficiency than direct clipping ACO-OFDM. We also study the BER performance under diffused optical wireless channels (DOW) in Figs. 7 and 8 . According to [26], the DOW channel can be express as,
Fig. 5. BER comparisons of AP-ACO-OFDM and DCO-OFDM schemes under LOS channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
the clipping level in dB which is given by ] [ (𝐼u − 𝐼l )∕2 , CR = 20 log 𝜎𝑔
(24) 𝑔
where 𝜎𝑔 is the standard deviation of the sample signals 𝑥𝑚𝜇 , which is √ [ ] 𝑔 2 given by 𝜎𝑔 = 𝐄 |𝑥𝑚𝜇 | . It is obvious that the severity of clipping can be quantified by CR. For instance, smaller CR means more severe clipping, otherwise the opposite. In order to maintain a high indoor luminous efficacy, the standard deviation 𝜎𝑔 of the modulating signal current before clipping is fixed 125 mA in all simulations. The schemes are listed as follows: * Direct clipping DCO-OFDM: The common DCO-OFDM sample values which are larger than the maximum input current or smaller than the minimum input current are direct to be clipped double-sidedly without any other recovery methods. * Direct clipping ACO-OFDM: The common ACO-OFDM sample values which are larger than the upper current are directly clipped without any other manipulations. * AP-ACO-OFDM: The AP-ACO-OFDM sample values are upper clipped, which is similar to the implementation of the direct clipping ACO-OFDM. The spectral efficiencies (SE) of AP-ACO-OFDM, DCO-OFDM and ACO-OFDM in an optical wireless communication system are defined as ( ) 1 1 SEAP−ACO−OFDM = 1 − 𝜇 log2 𝑀1 bps∕Hz, (25) 2 2 SEDCO−OFDM =
𝑁 −2 log2 𝑀2 2𝑁
bps∕Hz,
(26)
1 log2 𝑀3 bps∕Hz, (27) 4 where 𝑀1 , 𝑀2 and 𝑀3 are the order of the QAM modulation in APACO-OFDM, DCO-OFDM and ACO-OFDM, respectively. In (26), if the number of OFDM subcarriers is chosen to be large, such as 2048, the formula for a spectral efficiency of DCO-OFDM becomes approximately 1 log2 𝑀2 . Thus, in order to compare the BER performance between AP2 ACO-OFDM and DCO-OFDM for the same spectral efficiency, 𝑀1 and 𝑀2 should satisfy the following relationship, SEACO−OFDM =
2𝜇 2𝜇 −1
𝑀1 = 𝑀2
.
𝑁𝑡 −1
ℎ (𝑡) =
∑
( ) 𝛼 𝑛 𝛿 𝑡 − 𝜏𝑛
(29)
𝑛=0
where ℎ(𝑡) is the channel response at time slot 𝑡, 𝛼𝑛 is the amplitude, 𝜏𝑛 is the time delay of the 𝑛th path, and 𝑁𝑡 is the number of channel taps. The diffuse fading follows the exponentially decaying and ceiling
(28) 6
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Optics Communications 459 (2020) 124960
Fig. 8. BER comparisons of ACO-OFDM and AP-ACO-OFDM schemes under DOW channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB. Fig. 6. BER comparisons of AP-ACO-OFDM and ACO-OFDM schemes under LOS channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
to the proposed AP-ACO-OFDM scheme as it does to direct doubleside clipping DCO-OFDM scheme and direct upper clipping ACO-OFDM scheme, BER of our proposed scheme can reach the order of magnitude 10−3 for 𝜇 = 5 in the case of severe clipping, while the other schemes cannot attain this level for the transmission power. 5. Conclusion Based on the principle of spatial summing of the intensities of multiple LEDs in the same lighting fixture, this paper proposes a novel method to alleviate many practical issues in the implementation of OFDM in VLC systems, referred to as AP-ACO-OFDM. The approach partitions frequency-domain OFDM subcarriers into multiple specific groups to generate a set of unipolar signals with the possibility of full bandwidth transmission and zero bias power used to drive groups of LEDs and then to rely on spatial summing during propagation. At the receiver side, the symbols on all subcarriers can be effectively estimated through a standard OFDM demodulator. The comparison results with DCO-OFDM and ACO-OFDM show that the PAPR of our proposed AP-ACO-OFDM is effectively reduced with the increasing of the number of groupings. The use of lower DC-bias can lead to frequent clipping of the negative parts in DCO-OFDM. However, there is no signal clipping from below in AP-ACO-OFDM. If a larger DC bias is used in DCO-OFDM, the nonlinear clipping distortion caused by double-side clipping will be smaller, but more power is sacrificed. This indicates that AP-ACO-OFDM can allocate system power more efficiently than DCO-OFDM while maintaining the same spectral efficiency. Since the spectral efficiency of AP-ACO-OFDM is almost double of ACO-OFDM, it can use lower order QAM schemes to achieve higher power efficiency than ACO-OFDM. As a consequence, the BER performance for the same efficiency is effectively improved under both LOS and DOW channels due to both power and spectral efficiency can be achieved at the same time.
Fig. 7. BER comparisons of DCO-OFDM and AP-ACO-OFDM schemes under DOW channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
bounce models, as described in [27] for DOW channels. In the following simulations, we set 𝑁𝑡 = 5 and suppose that the time delay is uniformly distributed from 10 to 20 ns in a conventional room model with dimensions 5 m × 5 m × 3 m. For the case of DOW channels, Figs. 7 and 8 compare the BER performance of the proposed AP-ACO-OFDM scheme with two existing schemes, including direct double-side clipping DCO-OFDM scheme and direct upper clipping ACO-OFDM scheme under different CP values respectively. Note that we tested in Figs. 7 and 8 by setting a CP larger than the multipath delay where no inter-symbol interference exists. From Figs. 7 and 8, although the BER performance of all schemes degrades due to the influence of multipath effect, the AP-ACO-OFDM still outperforms the other two direct clipping schemes, and the SNR gains are more noticeable for larger value of 𝜇. The reason for this is that AP-ACO-OFDM avoids a high nonlinear distortion by clipping while the information loss due to clipping is minimized. As shown, despite multipath effect imposes a similar performance degradation
CRediT authorship contribution statement Lijun Deng: Conceptualization, Methodology, Software, Investigation, Data curation, Writing - original draft. Yangyu Fan: Supervision, Writing - review & editing. 7
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Optics Communications 459 (2020) 124960
Acknowledgments
[12] J. Yong, Modulation and demodulation apparatuses and methods for wired / wireless communication, 2007. [13] D. Tsonev, S. Sinanovic, Enhanced subcarrier index modulation (sim) ofdm, in: GLOBECOM Workshops, 2011, pp. 5–9. [14] D. Tsonev, S. Sinanovic, H. Haas, Novel unipolar orthogonal frequency division multiplexing (u-ofdm) for optical wireless, in: IEEE Vehicular Technology Conference, 2012, pp. 6–9. [15] W. Xu, M. Wu, H. Zhang, Aco-ofdm-specified recoverable upper clipping with efficient detection for optical wireless communications, IEEE Photonics J. 6 (5) (2014) 1081–1089. [16] J.D. Xu, W. Xu, H. Zhang, Asymmetrically reconstructed optical ofdm for visible light communications, IEEE Photonics J. 8 (1) (2016) 1121–1131. [17] H. Dong, H. Zhang, K. Lang, B. Yu, M. Yao, Ofdm visible light communication transmitter based on led array, Chin. Opt. Lett. 12 (5) (2014) 3325–3330. [18] N. Mohammad, B.-P. Maite, Can visible light communications provide gb/s service? Computer Science (2013). [19] C. Wu, H. Zhang, W. Xu, On visible light communication using led array with dft-spread ofdm, in: IEEE International Conference on Communications, 2014, pp. 3325–3330. [20] M.S.A. Mossaad, S. Hranilovic, L. Lampe, Visible light communications using ofdm and multiple leds, IEEE Trans. Commun. 63 (11) (2015) 4304–4313. [21] J. Kahn, J. Barry, Wireless infrared communications, Proc. IEEE 85 (2) (1997) 265–298. [22] T. Fath, H. Haas, Performance comparison of mimo technique for optical wireless communications in indoor environments, IEEE Trans. Commun. 61 (2) (2013) 733–742. [23] T. Fath, C. Heller, H. Haas, Optical wireless transmitter employing discrete power level stepping, J. Lightwave Technol. 31 (11) (2013) 1734–1743. [24] J. Armstrong, Optical domain digital-to-analog converter for visible light communications using led arrays, Photonics Res. 1 (2) (2013) 92–95. [25] R. Mesleh, H. Elgala, H. Haas, Led nonlinearity mitigation techniques in optical wireless ofdm communication systems, J. Opt. Commun. Netw. 4 (11) (2012) 865–875. [26] S.K. Wilson, J.A. Holliday, Scheduling methods for multi-user optical wireless asymmetrically-clipped ofdm, J. Commun. Netw. 13 (6) (2011) 655–663. [27] J.B. Carruthers, J.M. Kahn, Modeling of nondirected wireless infrared channel, IEEE Trans. Commun. 45 (10) (1997) 1260–1268.
This work was sponsored by Xian Science and Technology Planning Project, China (No. 201805037YD15CG21(9)) and Doctoral Starting up Foundation of Xian University of Technology, China (No. 103256081701) and Equipment Pre-Research Fund of the Central Military Commission, China (No.61409230708). The authors wish to thank the anonymous reviewers for their valuable suggestions. References [1] H. Haas, Light fidelity (li-fi): towards all-optical networking, Proc. SPIE -Int. Soc. Opt. Eng. 9007 (5) (2013) 900702–900702–10. [2] T. Komine, M. Nakagawa, Fundamental analysis for visible light communication system using led lights, IEEE Trans. Consum. Electron. 50 (1) (2004) 100–107. [3] J. Armstrong, Ofdm for optical communications, J. Lightwave Technol. 27 (3) (2009) 189–204. [4] J. Armstrong, B. Schmidt, Comparison of asymmetrically clipped optical ofdm and dc-biased optical ofdm in awgn, IEEE Commun. Lett. 12 (5) (2008) 343–345. [5] Z. Yu, R. Baxley, G. Zhou, Peak-to-average power ratio and illumination-tocommunication efficiency considerations in visible light ofdm system, in: IEEE International Conference on Acoustics, 2013, pp. 5397–5401. [6] N. Fernando, Y. Hong, E. Viterbo, Flip-ofdm for unipolar communication system, IEEE Trans. Commun. 60 (12) (2012) 3726–3733. [7] J. Armstrong, A. Lowery, Power efficient optical ofdm, Electron. Lett. 42 (6) (2006) 370–372. [8] M. Sohail, P. Saengudomlert, K.L. Sterckx, Performance analysis of dynamic range limited dco-ofdm, aco-ofdm and flip-ofdm transmissions for visible light communication, IEICE Trans. Commun. 97 (10) (2014) 2192–2202. [9] K. Asadzadeh, A. Dabbo, S. Hranilovic, Receiver design for asymmetrically clipped optical ofdm, in: IEEE Workshop on Optical Wireless Communications, 2011, pp. 777–781. [10] L. Chen, B. Krongold, J. Evans, Diversity combining for asymmetrically clipped optical ofdm in im/dd channel, in: Global Telecommunications Conference, 2010, pp. 681–685. [11] S.D. Dissanayake, K. Panta, J. Armstrong, A novel technique to simultaneously transmit aco-ofdm and dco-ofdm in im/dd systems, in: IEEE Workshop on Optical Wireless Communications, 2011, pp. 782–786.
8
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Enhanced performance of indoor VLC using anti-periodic asymmetrically clipped OFDM and multiple LEDS Lijun Deng a ,∗, Yangyu Fan b a b
School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, Shaanxi, China School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, China
ARTICLE
INFO
Keywords: Visible light communication (VLC) Optical OFDM Peak-to-average power ratio (PAPR) Power efficiency Spectral efficiency
ABSTRACT Visible light communication (VLC) systems make use of the available LED lamps to realize a high spatial density of high-speed optical links superposed to their natural illumination function. Orthogonal frequency division multiplexing (OFDM) has been adopted for these intensity modulation/direct-detection optical channels. However, it suffers from low power efficiency or low spectral efficiency. In this paper, we aim to improve the performance of OFDM-based indoor VLC systems. By utilizing the principle of spatial summing, we propose an anti-periodic asymmetrically clipped OFDM scheme to make efficient use of both power and spectrum. In this scheme, the OFDM subcarriers are partitioned into multiple specific groups to form independent unipolar signals. These signals are simultaneously transmitted from different LEDs that are within the same light fixture and are summed in space before being detected by a conventional OFDM receiver. The computer simulation results show that the proposed approach can achieve lower PAPR and more robustness to the clipping distortion caused by the nonlinearities of LED leading to better bit error rate performance for the same spectral efficiency than that of the conventional DCO-OFDM and ACO-OFDM schemes do under both LOS and DOW channels.
1. Introduction Recently, there has been a growing interest in visible light communication (VLC) for advantages such as unlimited bandwidth, environmental friendliness, and immunity to radio frequency interference [1,2]. Orthogonal frequency division multiplexing (OFDM) has been widely adopted in VLC to achieve high-speed transmission due to its inherent advantages such as high spectral efficiency, simple equalization, dynamic bandwidth allocation, and low-complexity implementation [3,4]. The physical properties of LEDs and Photodiodes (PDs) characterize a VLC system as an intensity modulation/direct detection (IM/DD) system. It means that only unipolar OFDM signals can be conveyed. One approach to make OFDM compatible with IM/DD links, termed DC-biased optical OFDM (DCO-OFDM), is to add a DC-bias to the time-domain signal and clip the parts beyond the linear range of the LED [5]. However, the DC-bias depends on the peak-to-average-ratio (PAPR) of the OFDM symbol. It is shown in [6] that the requirement of large DC-bias makes DCO-OFDM optical power inefficient. On the other hand, the use of lower DC-bias can lead to frequent clipping of the negative parts of the time domain signal, which may result in inter-carrier interference and optical power leakage. The transmission of such signal is, thereby, primarily limited by the linearity constraints of LED in the modulation/demodulation process and by the nonlinear
clipping distortion noises. A power-efficient alternative to DCO-OFDM is asymmetrically clipped optical OFDM (ACO-OFDM), which uses the properties of Fourier Transform and asymmetrical clipping to create unipolar signals in the time domain [7]. As shown in [8], clipping the time domain signal does not distort symbols in odd subcarriers, although their amplitude is scaled by a half. ACO-OFDM, however, has half of the spectral efficiency of DCO-OFDM for the same order of M-QAM modulation. In [9], a noise cancellation method is discussed, where the antisymmetry of the time samples of ACO-OFDM is used to identify which samples of the received signal are most likely to be due to the addition of noise. These samples are then set to zero. A maximum gain of 3 dB in optical power can be achieved with this method. In conventional ACO-OFDM, the even subcarriers are discarded, and only odd subcarriers are demodulated. In [10], a diversity combining system for ACO-OFDM is described, where the signal from the received even subcarriers are combined with the signal from the received odd subcarriers. As a result, a gain of up to 3 dB is achieved in electrical power. However, it is vulnerable to the DC offset, which may result from lowfrequency interference and environmental noise. In [11], a new system called asymmetrically clipped DC biased optical OFDM (ADO-OFDM) is proposed, where ACO-OFDM is used for odd subcarriers, and DCOOFDM is used for even subcarriers. It is shown that the bandwidth efficiency is better than ACO-OFDM, and the overall optical power
∗ Corresponding author. E-mail address: [email protected] (L. Deng).
https://doi.org/10.1016/j.optcom.2019.124960 Received 24 June 2019; Received in revised form 9 November 2019; Accepted 13 November 2019 Available online 16 November 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
efficiency is better than DCO-OFDM because all of the subcarriers are used to carry data. However, this method still requires a DC-bias for the generation of DCO-OFDM. A novel unipolar OFDM approach, Flip-OFDM, is proposed in [12], in which the positive and negative parts are extracted from the bipolar OFDM real time-domain signal, and transmitted in two consecutive OFDM symbols. Since the negative parts are flipped before transmission, both subframes have positive samples, Flip-OFDM is thus a unipolar OFDM scheme that can be used in VLC communications. Although Flip-OFDM offers a 50% complexity saving compared to ACO-OFDM, spectral efficiency, and the bit error rate (BER) performance for additive white gaussian noise (AWGN) and diffused optical wireless channels of both Flip-OFDM and ACO-OFDM still are the same. The newly multicarrier modulation scheme, U-OFDM, is inspired by the concept from [13] in an attempt to close the 3 dB gap between OFDM and ACO-OFDM for bipolar signals, whilst generating a unipolar signal without adding a DC-bias for optical wireless communication. An improved decoder for U-OFDM is presented in [14]. This decoder employs a recombination technique for the positive and negative frames, which at each position selects the sample with a higher amplitude between the two frames. Although this ideally removes half of the AWGN, it is still insufficient to make up for the power penalty, which results from the requirement for a higher constellation size compared to DCO-OFDM. In [15], a modified ACO-OFDM with low PAPR via introducing a recoverable upper-clipping (RoC) procedure is presented. It is shown that the system can achieve a significant PAPR reduction while maintaining a competitive bit error rate performance compared with the conventional ACO-OFDM scheme under both LOS and DOW channels. By taking the similar asymmetric structure of both ACO-OFDM and pulse amplitude modulated discrete multitone (PAMDMT), asymmetrically reconstructed optical OFDM scheme is proposed in [16] to enhance the time efficiency of both optical OFDM schemes, and it exhibits a noticeable BER gain compared to the conventional schemes under both LOS and DOW channels by employing an efficient detection. However, the systems in [15] and [16] require higher computational complexity in the demodulation procedure. In this paper, we propose a novel multicarrier modulation scheme, namely, anti-periodic asymmetrically clipped optical OFDM (AP-ACOOFDM), which is inspired by the design principle of ACO-OFDM to make efficient use of both power and spectrum. Most lighting fixtures include multiple LEDs that are modulated by identical signals in conventional VLC systems. In contrast, in this work, the frequency domain OFDM subcarriers are divided into multiple specific groups to form APACO-OFDM signals, which independently modulate the output intensity of groups of LEDs. The signals from each LED group are allowed to sum in space during propagation. At the receiver, the transmitted signals can be recovered noiselessly through a standard OFDM demodulator by employing successive decoding. The idea of spatial summing in VLC has been mentioned in related ways in the literature. Dong et al. [17] presented the concept of spatial summing applied only to the case of a single subcarrier per LED. The concept of spatial summing was mentioned for OFDM in parallel in [18]. However, no analysis, system designs, or performance results were provided. A VLC system based on SC-FDMA and spatial summing has been recently proposed in [19]. Mossaad et al. [20] used spatial summing of the intensities of multiple LEDs to solve the DCO-OFDM PAPR problem for VLC in a given luminary. However, at a lower signal-to-noise ratio (SNR), the BER performance was inferior to that of DCO-OFDM. We use the AP-ACO-OFDM scheme to enhance further the performance of VLC systems based on OFDM in this paper by spatial summing of the intensities of multiple LEDs. The remainder of this paper is organized as follows. Section 2 gives an overview of the principle for the ACO-OFDM-based VLC transmitter. Section 3 provides a description of the system model based on spatialsumming AP-ACO-OFDM. Section 4 shows the result of comparison among three schemes, AP-ACO-OFDM, DCO-OFDM, and ACO-OFDM, in terms of their complementary cumulative distribution function (CCDF) of PAPR. Also, the BER performance of AP-ACO-OFDM is compared with DCO-OFDM and ACO-OFDM schemes. Finally, Section 5 concludes this paper.
Fig. 1. A block diagram of an ACO-OFDM-based VLC transmitter.
2. A review of ACO-OFDM
A block diagram of an ACO-OFDM-based VLC transmitter is shown in Fig. 1. The transmitted binary data stream is first mapped into QAM symbols. After serial-to-parallel (S/P) conversion, loading these QAM symbols on the first half of the odd subcarriers, 𝑋2𝑘+1 , where 𝑘 = 0, 1, 2, … , 𝑁∕4 − 1, and 𝑁 s inverse fast Fourier transform (IFFT) size. The even subcarriers are set to zero, i.e. 𝑋2𝑘 = 0,
𝑘 = 0, 1, 2, … , 𝑁∕4
(1)
Using the above equation, the DC component and the symbol of the subcarrier become zero. After imposing the Hermitian symmetry property in Eq. (2), a bipolar real-time signal 𝑥𝑚 can be generated by the IFFT operation in Eq. (3). 𝑁 th 2
∗ 𝑋𝑘 = 𝑋𝑁−𝑘 ,
𝑥𝑚 =
𝑘 = 1, 2, … , 𝑁∕2 − 1
𝑁−1 ( ) ( ) 1 ∑ 2𝜋 𝑋𝑘𝐼 + 𝑗𝑋𝑘𝑄 exp 𝑗 𝑚𝑘 𝑁 𝑘=0 𝑁
(2)
(3)
where 𝑋𝑘𝐼 +𝑗𝑋𝑘𝑄 is the complex symbol modulated on the 𝑘th subcarrier. During the IFFT process in Eq. (3), each time sample 𝑥𝑚 can be written as a summation of 𝑁 phase rotated QAM symbols from all subcarriers. ( ) Let 𝑥𝑚,𝑘 = 𝑁1 𝑋[𝑘] exp 𝑗 2𝜋 𝑚𝑘 denote the contribution from subcarrier 𝑁 𝑘 to time sample 𝑚. Thus, the IFFT modulation process can be expressed as a summation of contributions from odd and even subcarriers 𝑥𝑚 =
𝑁−1 ∑ 𝑘=0
𝑥𝑚,𝑘 =
∑ 𝑘,odd
𝑥𝑚,𝑘 +
∑
even 𝑥𝑚,𝑘 = 𝑥odd 𝑚 + 𝑥𝑚
(4)
𝑘,even
For each odd subcarrier 𝑘, we have ( ) ( ) 1 2𝜋 2𝜋 𝑁 𝑋[𝑘] exp 𝑗 𝑚𝑘 exp 𝑗 ⋅ 𝑘 𝑥𝑚+ 𝑁 ,𝑘 = 𝑁 𝑁 𝑁 2 2 ( ) 1 2𝜋 = − exp 𝑗 𝑚𝑘 𝑁 𝑁 = −𝑥𝑚,𝑘
(5)
which indicates that 𝑥𝑚 = 𝑥odd 𝑚 is an anti-periodic sequence if only odd subcarriers are loaded with useful symbols. 2
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
⌊ 𝑔 ⌋ 𝑔 ⌋ ⌊ 𝑔 ⌋ 𝑥𝑚2 𝑐 , 𝑥𝑚3 𝑐 , … , 𝑥𝑚𝜇 are created through the zero-bias clipping 𝑐 operation. { 𝑔 𝑔 ⌊ 𝑔 ⌋ 𝑥𝑚𝜇 𝑥𝑚𝜇 > 0 𝑥𝑚𝜇 = (11) 𝑔 𝑐 0 𝑥𝑚𝜇 ≤ 0 ⌊ 𝑔 ⌋ After appending a cyclic prefix (CP), each group signal, 𝑥𝑚𝜇 , is 𝑐 hard-clipped to fit into the dynamic range of the driver. Subsequently, the digital-to-analog conversion is performed on each group clipped signal to form a parallel analog waveform. Finally, these analog waveforms simultaneously drive the corresponding LEDs group for intensity modulation. ⌊
3. Spatial-summing anti-periodic ACO-OFDM system model 3.1. Transmitter model According to Eq. (5), if only even subcarriers carry information, 𝑥𝑚 = 𝑥even is a periodic sequence. Inspired by the principle of ACO𝑚 OFDM, 𝑥even can also be made an anti-periodic sequence with a specific 𝑚 period by carefully loading only some of the even subcarriers. Denote 𝑘 ∈ 𝛺 as those even subcarriers which are loaded with symbols. Let 𝑥even denote the contribution from the 𝑘th even subcarrier 𝑚,𝑘 to the time sample 𝑚. In order to generate an N -point anti-periodic se, where 𝑇 = 2𝜇 for 𝜇 = 1, 2, … , log2 𝑁 − quence with a period equal to 𝑁 𝑇 1, the following relationship must be satisfied. even 𝑥even 𝑁 𝑚,𝑘 = −𝑥
𝑚+ 𝑇 ,𝑘
= 𝑥even2𝑁
𝑚+ 𝑇 ,𝑘
= −𝑥even3𝑁
𝑚+ 𝑇 ,𝑘
= ⋯ = −𝑥even(𝑇 −1)𝑁 𝑚+
𝑇
,𝑘
3.2. Indoor VLC channel model
(6)
Consider that multiple LEDs in a lighting fixture are modeled as having a Lambertian emission pattern and that the line-of-sight (LOS) links are assumed to dominate over all multi-path components from wall and ceiling reflections [2,21]. Therefore, the channel gain from an LED to the photodetector is given by [22] { (𝑚+1)𝐴PD cos𝑚 (𝜙) 𝑇S (𝜓) 𝑔 (𝜓) cos (𝜓) , 0 ≤ 𝜓 ≤ 𝜓c 2𝜋𝑑 2 (12) 𝛺= 0, 𝜓 > 𝜓c
which means ( ) [ ( ) ] 1 2𝜋 1 2𝜋 𝑁 𝑋[𝑘] exp 𝑗 𝑚𝑘 = − 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁 𝑁 𝑁 𝑇 [ ( ) ] 1 2𝜋 2𝑁 = 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁 𝑇 [ ( ) ] 1 2𝜋 3𝑁 = − 𝑋[𝑘] exp 𝑗 𝑚+ 𝑘 𝑁 𝑁{ [𝑇 ] } (𝑇 − 1)𝑁 2𝜋 1 𝑚+ 𝑘 = ⋯ = − 𝑋[𝑘] exp 𝑗 𝑁 𝑁 𝑇
where 𝑚 is the Lambertian order given by 𝑚 =
(7) then Eq. (7) can be simplified to ) [ ( ) ] ( 2𝜋 𝑁 2𝜋 𝑚+ 𝑘 exp 𝑗 𝑚𝑘 = − exp 𝑗 𝑁 𝑁 𝑇 [ ( ) ] 2𝜋 2𝑁 = exp 𝑗 𝑚+ 𝑘 𝑁 𝑇 ( ) ] [ 3𝑁 2𝜋 𝑚+ 𝑘 = − exp 𝑗 𝑁{ 𝑇 [ ] } (𝑇 − 1)𝑁 2𝜋 = ⋯ = − exp 𝑗 𝑚+ 𝑘 𝑁 𝑇
− ln 2 ( ( )) , 𝑙𝑛 cos 𝛷1∕2
𝛷1∕2 is the
transmitter semi-angle (at half power), 𝐴PD is the collection area of the detector, 𝑑 is the distance between transmitter and receiver, 𝜙 is the angle of irradiance, 𝜓 is the angle of incidence, 𝑇S (𝜓) is the gain of the optical filter, 𝑔 (𝜓) is the gain of the optical concentrator, and 𝜓c is the field-of-view (FOV) of the receiver. In general, multiple LEDs in an indoor lighting fixture will be placed close to each other. In this case, the difference in path lengths from each LED to the receiver will be on the order of cm’s, while incurring propagation time differences on the order of 10’s ps. Also, the optical channel gains between LEDs will differ on the order of 1% − 2% between different LEDs due to the difference in path lengths. Thus, in this paper, we assume that all LEDs in a given fixture are sufficiently close that they have identical gains and delays to the receiver. Similar assumptions have been widely adopted by many others in a similar context [20,23–25].
(8)
− 1. Therefore, the following two expressions for all 𝑚 = 0, 1, 2, … , 𝑁 𝑇 can be obtained [ ] ( ) ( ) 2(𝑇 − 1)𝑘 2𝑘 6𝑘 exp 𝑗 𝜋 = exp 𝑗 𝜋 = ⋯ = exp 𝑗 𝜋 = −1 (9) 𝑇 𝑇 𝑇 [ ] ( ) ( ) 2(𝑇 − 2)𝑘 4𝑘 8𝑘 exp 𝑗 𝜋 = exp 𝑗 𝜋 = ⋯ = exp 𝑗 𝜋 =1 (10) 𝑇 𝑇 𝑇
3.3. Receiver model
According to Eqs. (9) and (10), the even subcarrier number 𝑘 ∈ 𝛺 would be that is divisible by 2𝜇−1 , but not divisible by 2𝜇 . If we denote this subcarrier group 𝛺 as 𝑔𝜇 , loading symbols separately on the subcarriers belong to 𝑔𝜇 will undoubtedly form an anti-periodic sequence with period 𝑁 . 𝑇 According to the principle of forming the anti-periodic signal above, the implemented scheme of an AP-ACO-OFDM-based spatial summing VLC transmitter is illustrated in Fig. 2. Assume the IFFT size is 𝑁, all subcarriers can be divided into £ = log2 𝑁 − 1 groups. For all 𝜇 = 1, 2, … , £, the subcarrier numbers which are loaded with QAM symbols in each group 𝑔𝜇 are as follows
The total received optical power is the sum of the optical powers received from each LED group. After conducting the photodetection and analogy-to-digital conversion to the received optical signals, the cyclic prefix of the OFDM sequence is removed, and the serial-to-parallel conversion is performed. It is assumed that the LEDs are placed closely enough together so that the optical channel gains and delays in Eq. (12) are almost identical for all LEDs. Thus, the generated photocurrent, 𝑦𝑚 , is proportional to the received power with additive white gaussian noise (AWGN) 𝑤𝑚 introduced by the VLC link and the detector. 𝑦𝑚 = 𝐺
£ ⌊ ⌋ ∑ 𝑔 𝑥𝑚𝜇 + 𝑤𝑚 𝜇=1
𝑔1 ∶ {1, 3, 5, … , 𝑁 − 1}
𝑐
(13)
where 𝐺 = 𝑅𝛺𝑆 is the electrical gain of the system, 𝑅[A∕W] is photodetector responsivity, 𝛺 is channel gain in (12), and 𝑆[W∕A] is conversion factor of the LED [20]. The FFT of 𝑦𝑚 can be expressed as
𝑔2 ∶ {2, 6, 10, … , 𝑁 − 2} 𝑔3 ∶ {4, 12, 20, … , 𝑁 − 4} ⋮ { } 𝑔𝜇 ∶ 2𝜇−1 , 3 ⋅ 2𝜇−1 , 5 ⋅ 2𝜇−1 , … , 𝑁 − 2𝜇−1
𝑌𝑘 = 𝐺
The remaining subcarriers in each group are loaded with zeros and 𝑔𝜇 satisfies Hermitian symmetry property in Eq. (2). After the IFFT 𝑔 𝑔 𝑔 process, 𝜇 groups anti-periodic OFDM signals 𝑥𝑚1 , 𝑥𝑚2 , … , 𝑥𝑚𝜇 can be ⌊ 𝑔 ⌋ obtained. And then, unipolar anti-periodic ACO-OFDM signals 𝑥𝑚1 𝑐 ,
£ {⌊ 𝑔 ⌋ } ∑ F 𝑥𝑚𝜇 + 𝑊𝑘 𝜇=1
𝑐
(14)
{ } where F (⋅) denotes the operator for FFT and 𝑊𝑘 = F 𝑤𝑚 . Assume subcarrier group 𝑔𝜇 is loaded with QAM symbol 𝑋[𝑘], then the output, 3
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
Fig. 2. A block diagram of an AP-ACO-OFDM-based spatial summing VLC transmitter.
𝑋[𝑘]′ , of FFT on subcarrier 𝑘 ∈ 𝑔𝜇 in (14), F as ′
𝑋[𝑘] =
𝑁−1 ∑⌊
𝑔 𝑥𝑚𝜇
⌋
𝑚=0
=
𝑇∑ −1
𝑁 𝑇
𝑔
𝑥𝑚𝜇
⌋ } 𝑐
When the subcarrier number 𝑛 ∉ 𝑔𝜇 , the FFT output 𝑋[𝑛]′ can be written as
, can be expressed
) ( 2𝜋 exp −𝑗 𝑚𝑘 𝑁 𝑐
−1 ⌊
∑
{⌊
𝑇
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑘 𝑁 𝑇 𝑐
=
=
2𝜇−1 ,
According to Eqs. (9) and (10), 𝑘 is divisible by that is, can 𝑘 be divisible by 𝑇2 . The result of 2𝜇−1 is an odd number according to the expression of(𝑔𝜇 . So the in Eq. [ ) ]exponential terms ( ) (15) can be reduced
𝑚+𝑖 𝑁 𝑇
𝑐
⎧ ⌊ 𝑔𝜇 ⌋ ⎪ −𝑥𝑚 = ⎨⌊ ⌋ 𝑐 ⎪ 𝑥𝑔𝜇 ⎩ 𝑚 𝑐
( ) 2𝜋 exp −𝑗 𝑚𝑛 𝑁 𝑐 𝑔𝜇
𝑖=0 𝑚=0
𝑚+𝑖 𝑁 𝑇
𝑥
𝑁 −1 𝑇∑ −1 𝑇∑ ⌊
⌋
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑛 𝑁 𝑇 𝑐
𝑔
(−1)𝑖 𝑥𝑚𝜇
(18)
⌋
[ ( ) ] 2𝜋 𝑁 exp −𝑗 𝑚+𝑖 𝑛 𝑁 𝑇 𝑐
for 𝑖 = 1, 2, … , 𝑇2 − 1, is odd times for 𝜋. Hence, we have ( ) ] [ ( ) ] [ 𝑁 2𝜋 𝑁 2𝜋 𝑚+𝑖 𝑛 = − exp −𝑗 𝑚 + (𝑇 − 𝑖) 𝑛 (19) exp −𝑗 𝑁 𝑇 𝑁 𝑇 In addition, for the first and the middle term, we have ( ) [ ( ) ] 2𝜋 1 2𝜋 exp −𝑗 𝑚𝑛 = − exp −𝑗 𝑚+ 𝑁 𝑛 (20) 𝑁 𝑁 2 Thus, each term in summation in Eq. (18) can be canceled out by the other term that has the same magnitude but opposite sign. Therefore, 𝑋[𝑛]′ = 0, that is, the zero-bias clipping operation at the transmitter has no effect on the subcarrier groups 𝑔1 , 𝑔2 , … , 𝑔𝜇−1 . When 𝑛( ∈ 𝑔𝑟 for) 𝑟 ]= 𝜇 + 1,(𝜇 + 2, …), £, the exponential terms satisfy [ exp −𝑗 2𝜋 𝑚 + 𝑖𝑁 𝑛 = exp −𝑗 2𝜋 𝑚𝑛 due to the fact that 𝑛 is at least 𝑁 𝑇 𝑁
𝑖 is odd number (16) 𝑖 is even number
Therefore, Eq. (16) can be changed into 𝑁 ⎡ 𝑁 −1 ⎤ −1 𝑇 ) 𝑇∑ )⎥ ⌊ ⌋ ( ⌊ 𝑔 ⌋ ( 2𝜋 2𝜋 𝑇 ⎢ ∑ 𝑔𝜇 𝜇 𝑋[𝑘] = ⎢ 𝑥 exp −𝑗 𝑚𝑘 − −𝑥𝑚 exp −𝑗 𝑚𝑘 ⎥ 2 ⎢ 𝑚=0 𝑚 𝑐 𝑁 𝑁 𝑐 ⎥ 𝑚=0 ⎣ ⎦
′
⎡ 𝑁 −1 ⎤ 𝑇 ( )⎥ 𝑇 ⎢ ∑ 𝑔𝜇 2𝜋 = ⎢ 𝑥 exp −𝑗 𝑚𝑘 ⎥ 2 ⎢ 𝑚=0 𝑚 𝑁 ⎥ ⎣ ⎦ ( 𝑔 ) 1 𝜇 ≜ F 𝑥𝑚 2
divisible by 𝑇 . Then the following expression can be obtained 𝑋[𝑛]′ =
(17) ⌊ 𝑔 ⌋ ( 𝑔 ⌊ 𝑔 ⌋ ) where the equation −𝑥𝑚𝜇 = − 𝑥𝑚𝜇 − 𝑥𝑚𝜇 is used, hence, when 𝑐
⌋
𝑁 −1 ⌊ 𝑇∑ −1 𝑇∑
𝑖=0 𝑚=0
to Eq. (6), we have ⌋
𝑔
𝑥𝑚𝜇
When 𝑛 ∈ 𝑔𝑙 for 𝑙 = 1, 2,[ … , 𝜇−1, of the exponential ( the phase ) ] difference [ ( ) ] 𝑁 2𝜋 terms in Eq. (18), e.g. −𝑗 2𝜋 𝑚 + 𝑖 𝑛 and −𝑗 𝑚 + (𝑇 − 𝑖) 𝑁 𝑛 𝑁 𝑇 𝑁 𝑇
to exp −𝑗 2𝜋 𝑚 + 𝑖𝑁 𝑘 = (−1)𝑖 exp −𝑗 2𝜋 𝑚𝑘 . Moreover, according 𝑁 𝑇 𝑁
⌊ 𝑔 𝑥𝜇
𝑁−1 ∑⌊ 𝑚=0
(15)
⌋
𝑥𝑚+𝑖 𝑁
𝑖=0 𝑚=0
𝑋[𝑛]′ =
⎡ 𝑁 −1 ⎤ 𝑇 )⎥ (⌊ 𝑔 ⌋ ⌊ 𝑔 ⌋ ) ( 𝑇 ⎢∑ 2𝜋 𝜇 𝜇 𝑥 + −𝑥 exp −𝑗 𝑚𝑛 ⎥ 𝑚 𝑚 2 ⎢⎢ 𝑚=0 𝑁 𝑐 𝑐 ⎥ ⎣ ⎦
⎡ 𝑁 −1 ⎤ 𝑇 ( )⎥ 𝑇 ⎢ ∑ | 𝑔𝜇 | 2𝜋 𝑥 exp −𝑗 𝑚 | | ⎥ 2 ⎢⎢ 𝑚=0 | 𝑚 | 𝑁 ⎥ ⎣ ⎦ ( 𝑔 ) 1 | 𝜇| ≜ F |𝑥𝑚 | | | 2
(21)
=
𝑐
a single group 𝑔𝜇 which only includes even subcarriers carries QAM symbols, information on any of subcarriers in 𝑔𝜇 can also be perfectly recovered after the receiver FFT in the absence of noise and interference, except for a constant attenuation factor of 2 on the amplitude due to the power leakage.
It is evident that the effect of zero-bias clipping operation at the transmitter goes all to the subcarrier groups 𝑔𝜇+1 , 𝑔𝜇+2 , …, and 𝑔£ according to Eq. (21). 4
L. Deng and Y. Fan
Optics Communications 459 (2020) 124960
Fig. 3. A block diagram of an AP-ACO-OFDM-based VLC receiver with £ = 3.
Therefore, at the transmitter, if the anti-periodic signal which is generated by the subcarrier group 𝑔𝜇 is zero-bias clipped for transmission, then the receiver FFT output without noise and interference finally can be written as ⎧ ⎪0 ⎪ { 𝑔 } 𝑋[𝑘]′ = ⎨ 1 F 𝑥𝑚𝜇 2 ⎪ { } ⎪ 1 F ||𝑥𝑔𝜇 || ⎩2 | 𝑚|
𝑘 ∈ 𝑔𝑙 𝑘 ∈ 𝑔𝜇
(22)
𝑘 ∈ 𝑔𝑟
Fig. 3 shows the detection process and the reconstruction of the OFDM frame for 𝑔1 , 𝑔2 and 𝑔3 subcarrier groups at the receiver end. Through the photodetector and analogy-to-digital convertor, the cyclic prefix of the OFDM sequence is removed, and the serial-to-parallel conversion is performed. According to Eq. (22), information on the 𝑔1 subcarrier group can be recovered with a conventional OFDM receiver, and the clipping distortion form 𝑔1 to all the other subcarriers can be easily estimated. By removing the clipping distortion from 𝑔1 , symbols on 𝑔2 can be determined. Again, information on the 𝑔2 subcarrier group can be recovered by using a conventional OFDM receiver, and the clipping distortion form 𝑔2 to the remaining subcarriers can be estimated. Similarly, once the clipping distortions from 𝑔1 and 𝑔2 are obtained, symbols on 𝑔3 can be recovered. This decoding process undoubtedly can be extended to more than 3 groups.
Fig. 4. The CCDF of the PAPR for AP-ACO-OFDM, DCO-OFDM and ACO-OFDM with 𝑁 = 256 and 𝓁 = 4.
for AP-ACO-OFDM. That is, the numbers of independent modulated 𝑁 𝑁 subcarriers in group 𝑔1 , 𝑔2 , 𝑔3 , and 𝑔4 are 𝑁4 , 𝑁8 , 16 and 32 , respec𝑁 tively, while DCO-OFDM has 2 −1 independent modulated subcarriers. Therefore, from Fig. 4, DCO-OFDM has the largest PAPR, followed by subcarrier groups 𝑔1 , 𝑔2 , and 𝑔3 of AP-ACO-OFDM, and subcarrier group 𝑔4 has the lowest PAPR, which makes the AP-ACO-OFDM system less sensitive to the nonlinear distortions of LEDs. As for ACO-OFDM, the number of independent modulated subcarriers is the same as that of AP-ACO-OFDM when 𝜇 = 1, leading to both of them have an identical PAPR.
4. Simulation results and discussion 4.1. PAPR CCDF results An accurate estimate of continuous-time PAPR is obtained by over𝑔 sampling the discrete-time signals 𝑥𝑚𝜇 . Assume that 𝓁-times oversam𝑔 pling is adopted, and the oversampled version of 𝑥𝑚𝜇 is denoted by [ 𝑔 ]𝓁 𝜇 𝑥𝑚 . In practice, this can be done by adding (𝓁 − 1) 𝑁∕2 zeros to the end of 𝑔𝜇 before applying Hermitian symmetry and taking IFFT. The PAPR of the time-domain OFDM symbol, before clipping, is defined as
4.2. BER results
|[ 𝑔 ]𝓁 |2 [ ]𝓁 max𝑚=0,…,𝓁𝑁−1 || 𝑥𝑚𝜇 || ‖ 𝑥𝑔𝜇 ‖2∞ | | = (23) PAPR𝑔𝜇 = [ ]𝓁 [ ]𝓁 |2 1 ‖ 𝑥𝑔𝜇 ‖22 1 ∑𝓁𝑁−1 || 𝑔𝜇 | 𝓁𝑁 𝑥 𝑚 | | 𝑚=0 𝓁𝑁 | | The simulated CCDFs of PAPR for AP-ACO-OFDM with 𝜇 = 1, 2, 3 and 4, ACO-OFDM, and DCO-OFDM are compared in Fig. 4. All the simulation results are taken from 105 OFDM symbols, wherein the IFFT size is 𝑁 = 256, and 𝓁 = 4 are selected as demonstrated in the previous study [18]. It can be seen that each group OFDM signal of the AP-ACO-OFDM scheme achieves a PAPR reduction gain with respect to DCO-OFDM. A general trend is that the PAPR increases with the number of independent modulated subcarriers in an OFDM frame. 𝑁 independent modulated subcarriers The subcarrier group 𝑔𝜇 has 2𝜇+1
Some numerical comparison results of BER performance between conventional O-OFDM and the proposed AP-ACO-OFDM are displayed in this section. For all BER simulations, the creeQ5 white LED is considered. The number of LEDs is 15, and the LEDs are oriented in the same direction and are placed close to each other. So the channel gain to the receiver is assumed to be the same for each emitter group. The minimum input current 𝐼l and the maximum input current 𝐼u allowed by the LED are 110 mA and 1000 mA, respectively. It is assumed that a digital pre-distortion is used to linearize the relationship between input current and optical power. The direct clipping DCO-OFDM and direct clipping ACO-OFDM two kind of different conventional O-OFDM schemes are considered in our simulation and CR is utilized to indicate 5
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Optics Communications 459 (2020) 124960
In (25), if the number of groups is chosen to be large, such as 5, the formula for a spectral efficiency of AP-ACO-OFDM also becomes approximately 12 log2 𝑀1 . Under the above conditions, the constellation size of AP-ACO-OFDM and DCO-OFDM can be approximated to 𝑀1 = 𝑀2 , and the constellation √ size of AP-ACO-OFDM and ACO-OFDM can be approximated to 𝑀1 = 𝑀3 . It is known that the system performance inevitably suffers from the procedure of clipping due to information loss of clipped signals. Fig. 5 compares the BER performance of our proposed AP-ACO-OFDM scheme with the existing direct clipping DCO-OFDM scheme for the same spectral efficiency, where 𝑀1 = 16, 8 for 𝜇 = 3, 5 and 𝑀2 = 8. In this figure, the optical channel is assumed to be an indoor LOS channel modeled by the AWGN channel and the clipping level CR is set to 7 dB and 10 dB. As depicted, when CR = 7 dB, the BER of direct clipping DCO-OFDM scheme declines very slowly over the whole SNR range under severe clipping scenario, while the BER of the AP-ACO-OFDM scheme declines relatively rapidly with the increasing of 𝜇. Moreover, it can be found that the BER performance of our proposed AP-ACOOFDM scheme for 𝜇 = 3 and direct clipping DCO-OFDM scheme at high SNR values, such as 33 dB and 21 dB, starts exhibiting error floors. The reason for this is that the clipping distortion is negligible compared to AWGN in the low SNR regime, which dominates at high SNR values. Since clipping distortion is smaller for the smaller of the number of modulated subcarriers in an OFDM frame, or equivalently, a larger value of 𝜇, lower BER is achieved by using proposed AP-ACO-OFDM scheme for 𝜇 = 5 compared to AP-ACO-OFDM scheme for 𝜇 = 3 and the direct clipping DCO-OFDM scheme. When 𝜇 = 3 and 𝜇 = 5, we can observe that there does not exist an error floor for the AP-ACO-OFDM scheme by setting a giant CR except for direct clipping DCO-OFDM scheme with a lower error floor. This indicates that signal clipping has a considerable effect on the BER performance of direct clipping DCOOFDM scheme even though under a moderate clipping scenario. In the same low SNR range, it also can be seen that the proposed AP-ACOOFDM scheme for 𝜇 = 5 and direct clipping DCO-OFDM can use a lower order QAM scheme to achieve lower BER than the proposed APACO-OFDM scheme for 𝜇 = 3. Due to the clipping distortion, the BER performance of our proposed AP-ACO-OFDM scheme for both 𝜇 = 3 and 𝜇 = 5 still outperforms direct clipping DCO-OFDM scheme in the same high SNR range, and the power requirement of 𝜇 = 5 is about 1 dB less than the power requirement of 𝜇 = 3 at BER = 10−4 . A BER comparison of the proposed AP-ACO-OFDM and direct clipping ACO-OFDM for the same spectral efficiency is shown in Fig. 6, where 𝑀1 = 16, 8 for 𝜇 = 3, 5, and 𝑀3 = 64. It is shown that at each clipping level, the proposed scheme for both 𝜇 = 3 and 𝜇 = 5 always outperforms the direct clipping ACO-OFDM scheme under an ideal AWGN channel. Since the signal distortion becomes worse with the increasing of SNR, the BER performance saturates when SNR grows high or even without the presence of noise. Therefore, in the case of CR = 7 dB, it is similarly observed that the BERs of AP-ACO-OFDM for 𝜇 = 3 and direct clipping ACO-OFDM exhibit error floors when SNRs are higher than 35 dB and 30 respectively. When CR = 10 dB, the error floor of BER performance for direct clipping ACO-OFDM no longer exists, yet direct clipping ACO-OFDM requires about 5 dB and 6 dB higher SNR than AP-ACO-OFDM for 𝜇 = 3 and 𝜇 = 5 to achieve the BER of 10−4 . This indicates that our proposed AP-ACO-OFDM scheme has high spectral efficiency, thus it can use lower order QAM constellation to achieve higher power efficiency than direct clipping ACO-OFDM. We also study the BER performance under diffused optical wireless channels (DOW) in Figs. 7 and 8 . According to [26], the DOW channel can be express as,
Fig. 5. BER comparisons of AP-ACO-OFDM and DCO-OFDM schemes under LOS channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
the clipping level in dB which is given by ] [ (𝐼u − 𝐼l )∕2 , CR = 20 log 𝜎𝑔
(24) 𝑔
where 𝜎𝑔 is the standard deviation of the sample signals 𝑥𝑚𝜇 , which is √ [ ] 𝑔 2 given by 𝜎𝑔 = 𝐄 |𝑥𝑚𝜇 | . It is obvious that the severity of clipping can be quantified by CR. For instance, smaller CR means more severe clipping, otherwise the opposite. In order to maintain a high indoor luminous efficacy, the standard deviation 𝜎𝑔 of the modulating signal current before clipping is fixed 125 mA in all simulations. The schemes are listed as follows: * Direct clipping DCO-OFDM: The common DCO-OFDM sample values which are larger than the maximum input current or smaller than the minimum input current are direct to be clipped double-sidedly without any other recovery methods. * Direct clipping ACO-OFDM: The common ACO-OFDM sample values which are larger than the upper current are directly clipped without any other manipulations. * AP-ACO-OFDM: The AP-ACO-OFDM sample values are upper clipped, which is similar to the implementation of the direct clipping ACO-OFDM. The spectral efficiencies (SE) of AP-ACO-OFDM, DCO-OFDM and ACO-OFDM in an optical wireless communication system are defined as ( ) 1 1 SEAP−ACO−OFDM = 1 − 𝜇 log2 𝑀1 bps∕Hz, (25) 2 2 SEDCO−OFDM =
𝑁 −2 log2 𝑀2 2𝑁
bps∕Hz,
(26)
1 log2 𝑀3 bps∕Hz, (27) 4 where 𝑀1 , 𝑀2 and 𝑀3 are the order of the QAM modulation in APACO-OFDM, DCO-OFDM and ACO-OFDM, respectively. In (26), if the number of OFDM subcarriers is chosen to be large, such as 2048, the formula for a spectral efficiency of DCO-OFDM becomes approximately 1 log2 𝑀2 . Thus, in order to compare the BER performance between AP2 ACO-OFDM and DCO-OFDM for the same spectral efficiency, 𝑀1 and 𝑀2 should satisfy the following relationship, SEACO−OFDM =
2𝜇 2𝜇 −1
𝑀1 = 𝑀2
.
𝑁𝑡 −1
ℎ (𝑡) =
∑
( ) 𝛼 𝑛 𝛿 𝑡 − 𝜏𝑛
(29)
𝑛=0
where ℎ(𝑡) is the channel response at time slot 𝑡, 𝛼𝑛 is the amplitude, 𝜏𝑛 is the time delay of the 𝑛th path, and 𝑁𝑡 is the number of channel taps. The diffuse fading follows the exponentially decaying and ceiling
(28) 6
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Optics Communications 459 (2020) 124960
Fig. 8. BER comparisons of ACO-OFDM and AP-ACO-OFDM schemes under DOW channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB. Fig. 6. BER comparisons of AP-ACO-OFDM and ACO-OFDM schemes under LOS channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
to the proposed AP-ACO-OFDM scheme as it does to direct doubleside clipping DCO-OFDM scheme and direct upper clipping ACO-OFDM scheme, BER of our proposed scheme can reach the order of magnitude 10−3 for 𝜇 = 5 in the case of severe clipping, while the other schemes cannot attain this level for the transmission power. 5. Conclusion Based on the principle of spatial summing of the intensities of multiple LEDs in the same lighting fixture, this paper proposes a novel method to alleviate many practical issues in the implementation of OFDM in VLC systems, referred to as AP-ACO-OFDM. The approach partitions frequency-domain OFDM subcarriers into multiple specific groups to generate a set of unipolar signals with the possibility of full bandwidth transmission and zero bias power used to drive groups of LEDs and then to rely on spatial summing during propagation. At the receiver side, the symbols on all subcarriers can be effectively estimated through a standard OFDM demodulator. The comparison results with DCO-OFDM and ACO-OFDM show that the PAPR of our proposed AP-ACO-OFDM is effectively reduced with the increasing of the number of groupings. The use of lower DC-bias can lead to frequent clipping of the negative parts in DCO-OFDM. However, there is no signal clipping from below in AP-ACO-OFDM. If a larger DC bias is used in DCO-OFDM, the nonlinear clipping distortion caused by double-side clipping will be smaller, but more power is sacrificed. This indicates that AP-ACO-OFDM can allocate system power more efficiently than DCO-OFDM while maintaining the same spectral efficiency. Since the spectral efficiency of AP-ACO-OFDM is almost double of ACO-OFDM, it can use lower order QAM schemes to achieve higher power efficiency than ACO-OFDM. As a consequence, the BER performance for the same efficiency is effectively improved under both LOS and DOW channels due to both power and spectral efficiency can be achieved at the same time.
Fig. 7. BER comparisons of DCO-OFDM and AP-ACO-OFDM schemes under DOW channels with 𝑁 = 64, SE = 1.5 bps∕Hz and CR = 7, 10 dB.
bounce models, as described in [27] for DOW channels. In the following simulations, we set 𝑁𝑡 = 5 and suppose that the time delay is uniformly distributed from 10 to 20 ns in a conventional room model with dimensions 5 m × 5 m × 3 m. For the case of DOW channels, Figs. 7 and 8 compare the BER performance of the proposed AP-ACO-OFDM scheme with two existing schemes, including direct double-side clipping DCO-OFDM scheme and direct upper clipping ACO-OFDM scheme under different CP values respectively. Note that we tested in Figs. 7 and 8 by setting a CP larger than the multipath delay where no inter-symbol interference exists. From Figs. 7 and 8, although the BER performance of all schemes degrades due to the influence of multipath effect, the AP-ACO-OFDM still outperforms the other two direct clipping schemes, and the SNR gains are more noticeable for larger value of 𝜇. The reason for this is that AP-ACO-OFDM avoids a high nonlinear distortion by clipping while the information loss due to clipping is minimized. As shown, despite multipath effect imposes a similar performance degradation
CRediT authorship contribution statement Lijun Deng: Conceptualization, Methodology, Software, Investigation, Data curation, Writing - original draft. Yangyu Fan: Supervision, Writing - review & editing. 7
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Optics Communications 459 (2020) 124960
Acknowledgments
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