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16-QAM modulation for OFDM-VLC system
Optics Communications 424 (2018) 154–158
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
A MB-CAZAC precoding combined with 128/64/32/16-QAM modulation for OFDM-VLC system Jie Ma a , Jing He a, *, Qinghui Chen a , Jin Shi a , Zhihua Zhou a , Yun Cheng b , Yaoqiang Xiao a a b
College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China Department of Information Science and Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, China
ARTICLE
INFO
Keywords: Visible light communication (VLC) Orthogonal frequency division multiplexing (OFDM) Constant amplitude zero autocorrelation sequence (CAZAC) precoding Signal-to-noise ratio (SNR) Peak-to-average power ratio (PAPR)
ABSTRACT In this paper, multi-band constant amplitude zero autocorrelation sequence (MB-CAZAC) precoding combined with the 128/64/32/16-quadrature amplitude modulation (QAM) technology is proposed and experimentally demonstrated in the orthogonal frequency-division multiplexing-based visible light communication (OFDM-VLC) system. By using the MB-CAZAC precoding, it can equalize the uneven signal-to-noise ratio (SNR) and reduce the PAPR compared with the traditional OFDM system. The experimental results show that the 128/64/32/16QAM MB-CAZAC precoding outperforms the traditional scheme at different data rates for OFDM-VLC system. The spectral efficiency (SE) of the proposed scheme is up to 5.28 b/s/Hz. Meanwhile, it can be successfully transmitted 50-cm free-space at the bit error rate (BER) of 3.82 × 10−4 .
1. Introduction Nowadays, visible light communication (VLC) systems have become a research hotspot, thanks to its license-free spectrum, immunity to electromagnetic interference, security of indoor transmission and flexibility in installation. Light emitting diode (LED) based VLC, has been considered to be a promising technology for high-speed indoor communication [1–3]. By modulating LED-based VLC, channel access configurations to support different applications can be facilitated for users, including electronic payment, navigation & position, smart homes and vehicle-to-vehicle communication [4,5]. However, due to the limited bandwidth of LED, it is the main challenge of achieving high speed VLC transmission [6]. Orthogonal frequency-division multiplexing (OFDM) is proposed to take full advantage of the limited bandwidth of LED and thereby improve the spectrum efficiency (SE) [7–10]. Moreover, high-order quadrature amplitude modulation (QAM) technology is applied to increase data rate effectively [11,12]. Hence, OFDM has been one of the attractive candidates for VLC system. However, the key factor that limits performance of OFDM-VLC system is the critical low-passlike fading. Fortunately, several precoding techniques are proposed to combat severe frequency-selective fading effectively [13–17]. In [13], it has been demonstrated that orthogonal circulant matrix transform (OCT) precoding outperforms traditional scheme for mitigating the signal-to-noise ratio (SNR) fluctuation. As a multi-carrier system, OFDM *
has a high peak-to-average power ratio (PAPR). It can cause serious distortion to the transmitted signal. Hence, besides equalizing the uneven SNR across the subcarriers, precoding technique can also reduce the PAPR [18–20]. Currently, constant amplitude zero autocorrelation sequence (CAZAC) precoding technology is extensively applied to direct detection optical OFDM (DDO-OFDM) communication to improve the dispersion tolerance of the system, in terms of equalizing the uneven SNR and reducing the PAPR [21,22]. In addition, the 128/64/32/16-QAM modulation scheme is utilized to provide flexible data rates for multiple users and thereby enhance the network flexibility [23,24]. Nevertheless, to the best of our knowledge, the performance of the 128/64/32/16-QAM modulation scheme combination with CAZAC precoding method, has never been studied in OFDM-VLC system. In this paper, the 128/64/32/16-QAM OFDM combined with the multi-band CAZAC (MB-CAZAC) precoding is proposed and experimentally demonstrated for LED-based VLC. The CAZAC precoding is employed to reduce the PAPR and achieve a relatively flat SNR curve. By utilizing different level of QAM to the MB-CAZAC precoding, the BER performance is improved significantly. The experimental results show that, a 519.8 Mb/s signal transmission over 50-cm free-space is successfully implemented, and the BER is lower than the 7% hard-decision forward-error-correction (HD-FEC) limitation of 3.8 × 10−3 .
Corresponding author. E-mail address: [email protected] (J. He).
https://doi.org/10.1016/j.optcom.2018.04.047 Received 4 March 2018; Received in revised form 19 April 2018; Accepted 19 April 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
J. Ma et al.
Optics Communications 424 (2018) 154–158
Fig. 1. The schematic block diagram of the MB-CAZAC precoding.
Fig. 2. The schematic block diagram of the K sub-band transmission system.
2. Principle
where Z represents the precoded signal symbol vector on all subbands. There are 4*m data-modulated subcarriers in total, and each sub-band contains m data-modulated subcarriers. In this way, m-point CAZAC precoding is only performed on each sub-band. All sub-bands share the same precoding modules and thereby the space that stores large precoding matrices is saved. Thus, its complexity is O (4*m2 ). For the conventional CAZAC precoding, it requires 4*m -point CAZAC precoding, of which complexity is O (16*m2 ). Consequently, the MBCAZAC precoding can reduce the complexity of the system. After precoding, the modulated data carried by each subcarrier is multiplied by a phase rotation factor and then summed up. Therefore, the phase among the subcarriers is disordered and the energies become diverse. As a result of precoding, it can reduce the correlation among the input sequences. Hence, the PAPR can be significantly reduced compared with the traditional scheme.
2.1. MB-CAZAC precoding In this paper, precoding technique is used to improve PAPR and BER performance without destroying the orthogonality between subcarriers or adding much complexity. The precoding is implemented by multiplying a mapped data with the precoding matrix before IFFT operation in each OFDM symbol. Fig. 1 depicts the schematic block diagram of MB-CAZAC precoding for OFDM-VLC system. After QAM mapping, the data-modulated subcarriers are allocated to four subbands. There are 4*m data-modulated subcarriers in total, and each subband contains m data-modulated subcarriers. It can be written as 𝑆 = [ ]𝑇 [ ]𝑇 𝑆1 , 𝑆2 , 𝑆3 , 𝑆4 = 𝑋1 , … , 𝑋𝑚 ; 𝑋𝑚+1 , … , 𝑋2𝑚 ; ⋯ ; 𝑋3𝑚+1 , … , 𝑋4𝑚 . To improve the spectrum efficiency and system capacity, the 128∕64∕32∕16 QAM modulation scheme is applied from the first sub-band to the last sub-band respectively. Before IFFT, each sub-band with same mapping scheme is fed into a CAZAC block for CAZAC precoding implementation. The precoding matrix C is derived from a CAZAC sequence [22]. It can be expressed as: ⎡𝑐11 ⎢𝑐 1 ⎢ 12 𝐶 = √ ⎢⋮ 𝑁 ⎢𝑐 ⎢ 1𝑁−1 ⎣𝑐1𝑁
2.2. Noise equalization The schematic block diagram of the K sub-band transmission system through free space channel is depicted in Fig. 2. 𝑍𝑘 = [ ]𝑇 𝑍1𝑘 , 𝑍2𝑘 , … , 𝑍𝑚𝑘 denotes the K transmitted sub-band precoded signal [ ]𝑇 symbol vector, 𝑌𝑘 = 𝑌1𝑘 , 𝑌2𝑘 , … , 𝑌𝑚𝑘 denotes the K received sub-band precoded signal symbol vector. Their dimensions are both 𝑁𝑚 × 1. 𝐻𝑘 denotes the channel ( ) transfer matrix, and it can be expressed by diag 𝐻1𝑘 , 𝐻2𝑘 , … , 𝐻𝑚𝑘 , of which dimension is 𝑁𝑚 × 𝑁𝑚 . Supposing the inter-carrier interference (ICI) is free, the K received sub-band precoded signal symbol vector can be expressed as:
𝑐𝑁1 ⎤ 𝑐𝑁2 ⎥ ⎥ (1) ⋮ ⎥, 𝑐𝑁𝑁−1 ⎥ ⎥ 𝑐𝑁𝑁 ⎦ √ where 𝑐𝑖𝑗 = 𝑐𝑎𝑧𝑎𝑐𝑁∗(𝑖−1)+𝑗 , 𝑖, 𝑗 = 1, 2, … , 𝑁. 1∕ 𝑁 denotes a constant power during the precoding process. { exp[𝑗𝜋𝑘(𝑘 − 1)∕𝑁 2 ], 𝑁 is odd 𝑐𝑎𝑧𝑎𝑐𝑘 = , 𝑘 = 1, 2, … , 𝑁 2 . (2) exp[𝑗𝜋(𝑘 − 1)2 ∕𝑁 2 ], 𝑁 is even 𝑐21 𝑐22 ⋮ 𝑐2𝑁−1 𝑐2𝑁
⋯ ⋯ ⋯ ⋯ ⋯
𝑐𝑁−11 𝑐𝑁−12 ⋮ 𝑐𝑁−1𝑁−1 𝑐𝑁−1𝑁
𝑌𝑘 = 𝐻𝑘 𝑍𝑘 + 𝑛𝑘 (5) [ ]𝑇 where 𝑛𝑘 = 𝑛1𝑘 , 𝑛2𝑘 , … , 𝑛𝑚𝑘 denotes the noise vector, of which dimension is 𝑁𝑚 × 1. At the receiver, after symbol synchronization, channel equalization and decoding, the recovered symbol is given by:
Due to that CAZAC has an ideal periodic autocorrelation property, C is an orthogonal matrix, for 𝐶 𝐻 𝐶 = 𝐼. And the inverse matrix of C is its conjugate transpose 𝐶 𝐻 . The matrix C is used to equalize the parallel input symbols modulated on subcarriers. In MB-CAZAC precoding scheme, the precoding matrix is applied to each sub-band individually. As shown in Fig. 1, in the first sub-band, the OFDM symbols multiplying by C can be transposed as: [ ]𝑇 𝑍𝑏𝑎𝑛𝑑1 = 𝐶 × 𝑋1 , 𝑋2 , … , 𝑋𝑚
=
1 √ 𝑁𝑚
⎡ 𝑐11 𝑋1 + 𝑐21 𝑋2 + ⋯ + 𝑐𝑁 1 𝑋𝑚 ⎤ ⎢ 𝑐 𝑋 +𝑐 𝑋 +⋯+𝑐 𝑚 𝑋 ⎥ 12 1 22 2 𝑁𝑚 2 𝑚 ⎢ ⎥ ⎢ ⎥ ⋮ ⎢𝑐 ⎥ ⎣ 1𝑁𝑚 𝑋1 + 𝑐2𝑁𝑚 𝑋2 + ⋯ + 𝑐𝑁𝑚 𝑁𝑚 𝑋𝑚 ⎦
[ ] ′ 𝑆𝐾 = 𝑋1′ , … , 𝑋𝑚′ = 𝐶 −1 𝐻𝐾−1 𝑌𝐾 = 𝑆𝐾 + 𝐶 𝐻 𝐻𝐾−1 𝑛𝐾
It is assumed that different subcarriers have independent noises. For the 𝑖th subcarrier in K sub-band, the noise power is expressed as: ) (𝑁 )∗ (𝑁 2 𝑁𝑚 𝑚 𝑚 ∑ ∑ 𝑛 𝑛 1 ∑ || 𝑛𝑝 || ∗ 𝑞 ∗ 𝑝 ⋅ = (7) 𝑐𝑞𝑖 𝑃𝑁,𝑖 = 𝑐𝑝𝑖 | | | | 𝐻𝑝 𝐻𝑞 𝑁𝑚 𝑝=1 | 𝐻𝑝 | 𝑞=1 𝑝=1 | |2 where |𝑐𝑝𝑖 | = 1∕𝑁𝑚 . Accordingly, the noise equalization effect of each | | sub-band is demonstrated. The SNR of 𝑖th subcarrier in the K received sub-band can be expressed as:
(3)
𝑃𝑆,𝑖
|𝑋𝑖 |2 | |
(8) ∑𝑁𝑚 || 𝑛𝑝 ||2 𝑝=1 | 𝐻𝑝 | | | where 𝑃𝑠,𝑖 and 𝑃𝑁,𝑖 denote the signal power and noise power in K subband, respectively. Consequently, the effect of the uniform distribution of SNR is confirmed.
𝑆𝑁𝑅𝑖 =
where 𝑍𝑏𝑎𝑛𝑑1 denotes the 𝑁𝑚 × 1 precoded signal symbol vector. Its residual side-band has similar processing. Thus, we can get a precoding column vector, which can be expressed as: [ ] 𝑍 = 𝐶 ⋅ 𝑆1𝑇 ; 𝐶 ⋅ 𝑆2𝑇 ; 𝐶 ⋅ 𝑆3𝑇 ; 𝐶 ⋅ 𝑆4𝑇
(6)
(4) 155
𝑃𝑁,𝑖
=
1 𝑁𝑚
J. Ma et al.
Optics Communications 424 (2018) 154–158
Fig. 3. The schematic block diagram of the proposed MB-CAZAC precoding for OFDM-VLC system.
Table 1 Key parameters of the 128/64/32/16-QAM MB-CAZAC precoding scheme. Parameter
Value
Modulation scheme IFFT/FFT size Cyclic prefix length DAC sampling rate ADC sampling rate Number of data subcarriers Number of TS per OFDM frame OFDM symbols per frame Oversampling factor Raw signal bit rate Net signal bit rate Spectral efficiency
128/64/32/16-QAM 1024 32 800 MS/s 2.5 GS/s 504 1 100 4 126*(7+6+5+4)/(1024*0.005)=541.41 Mb/s 126*(7+6+5+4)*100/(101*1056*0.005)=519.8 Mb/s 519.8/(504/512*100)=5.28 bit/s/Hz
3. Experimental setup Fig. 3 depicts the experimental setup of the proposed MB-CAZAC precoding combined with the 128/64/32/16-QAM modulation scheme for OFDM-VLC system. At the transmitter, the DSP for OFDM modulation can be depicted as follows. Firstly, the data stream containing a pseudorandom binary sequence (PRBS) is generated. Secondly, we assign the each OFDM symbol for four sub-bands to realize the MB-CAZAC precoding scheme. For each sub-band, the length of data subcarrier is 126. The 128/64/32/16-QAM modulation scheme is adopted. The complex-value 128/64/32/16-QAM symbols are filled into independent MB-CAZAC precoding modules. Then, the complex values are converted into real values by adopting Hermitian symmetry. Thirdly, a 1024-point IFFT is used for the real data to generate a digital time-domain OFDM data. In order to resist the inter-symbol-interference (ISI), a cyclic prefix (CP) is added as the header of each OFDM symbol. Subsequently, one training sequence (TS) is inserted as the header of each OFDM frame to realize symbol synchronization. The key parameters of the 128/64/32/16QAM MB-CAZAC precoding scheme for OFDM-VLC system are given in Table 1. The FFT size is 1024, the CP length is 32, and the length of data-carrying subcarriers is 504. In this paper, the proposed MB-CAZAC precoding OFDM signal is fed into an arbitrary waveform generator (AWG, Tektronix 7122C) to produce an electrical OFDM signal. And the sampling rate of AWG is worked from 100 MS/s to 200 MS/s. The peak-to-peak voltage and bias voltage for input signal are optimized to 0.5 V and 3.328 V, respectively. Then, the electrical signal from the AWG is magnified by an electrical amplifier (EA). Afterwards, the 450-nm LED is directly driven by the transmitted signal to achieve optical signal. After 50-cm free-space transmission, the optical signal from the LED is detected by the PD integrated with trans-impedance amplifier (TIA) circuit to achieve electrical signal. Subsequently, a digital storage oscilloscope (DSO) is utilized to capture the received signal. Finally, the offline processing is utilized for experimental analysis. At the receiver, the demodulation processes of the detected signal include: timing synchronization, CP removal, 1024point FFT operation, channel estimation, equalization, CAZAC decoding, the 128/64/32/16-QAM de-mapping, and BER analysis.
Fig. 4. The CCDF curves versus PAPR for the four kinds of OFDM.
4. Experimental results and discussions We compare the PAPR of the 128/64/32/16-QAM OFDM signal with the 64QAM OFDM signal, in the case of with and without CAZAC precoding. Fig. 4 gives the complementary cumulative distribution function (CCDF) curves over PAPR for four kinds of OFDM signal. As is shown in Fig. 4, the PAPR of the MB-CAZAC precoding for the 128/64/32/16QAM OFDM is the lowest. And the PAPR with MB-CAZAC precoding schemes is lower than that without MB-CAZAC schemes. The results indicate that the 128/64/32/16-QAM MB-CAZAC precoding technology can reduce PAPR and will improve the tolerance of frequency-selective fading effect efficiently in OFDM-VLC system. Fig. 5 shows the average SNR over total data subcarriers index for OFDM-VLC system (a) with the 128/64/32/16-QAM MB-CAZAC precoding (b) without precoding. As we can see from Fig. 5(a), a ladder-like SNR profile for each sub-band is achieved. It indicates that the SNR curve of each sub-band is relatively flat by using MB-CAZAC precoding scheme 156
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Optics Communications 424 (2018) 154–158
Fig. 5. The average SNR over total data subcarrier index for the OFDM-VLC system (a) with the 128/64/32/16-QAM MB-CAZAC precoding; (b) without precoding.
Fig. 6. Sampling rate versus BER with MB-CAZAC precoding and without precoding: (a) 1-band, (b) 2-band, (c) 3-band and (d) 4-band.
comparing with the conventional scheme. When the sampling rate is 150 MS/s, the BER of the conventional scheme is 2.0 × 10−3 , while the BER of the 128/64/32/16-QAM MB-CAZAC precoding scheme is 3.82 × 10−4 . It is lower than the hard-decision forward error correlation (HDFEC) limitation of 3.8 × 10−3 . Fig. 5 also depicts the corresponding signal constellation using MB-CAZAC precoding. In practice, the VLC system is a frequency selective fading channel. By using the 128/64/32/16-QAM MB-CAZAC precoding technology, the performance of the system can be improved remarkably. Fig. 6 shows the BER performance of sub-bands with different number, running at different sampling rates with the MB-CAZAC precoding and the traditional scheme. As is shown in Fig. 6, when the sampling rate is 150 MS/s, the measured BER of four sub-bands can be reduced from 3.40 × 10−3 to 3.00 × 10−4 , 3.84 × 10−4 to 1.32 × 10−5 , 1.27 × 10−4 to 2.22 × 10−4 , and 4.00 × 10−3 to 1.60 × 10−3 . This results verify that, the proposed MB-CAZAC precoding can improve the BER performance on each sub-band significantly. Moreover, the BER of the 128/64/32/16-QAM OFDM scheme and the 64-QAM OFDM scheme on different sampling rate are depicted in
Fig. 7. It can be seen that a more obvious BER performance improvement can be achieved by utilizing the 128/64/32/16-QAM modulation scheme with MB-CAZAC precoding for the OFDM-VLC system. 5. Conclusion In this paper, the 128/64/32/16-QAM MB-CAZAC precoding scheme for OFDM-VLC system is proposed. The 128/64/32/16-QAM modulation technology is utilized to improve the system performance and enhance the network flexibility. Based on the proposed MB-CAZAC precoding scheme, the PAPR of OFDM-VLC system could be reduced compared with the conventional scheme. In addition, the MB-CAZAC precoding can not only reduce the complexity of the system but also equalize the uneven SNR on each sub-band. Hence, it is more conducive to the implementations of practical OFDM-VLC. Meanwhile, the proposed scheme could achieve better BER performance with a data rate of 541.41 Mb/s and higher spectral efficiency of 5.28 bit/s/Hz in OFDMVLC system. 157
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Optics Communications 424 (2018) 154–158
Fig. 7. Sampling rate versus BER with MB-CAZAC precoding and without precoding: (a) the 128/64/32/16-QAM OFDM scheme; (b) the 64QAM OFDM scheme.
Acknowledgments
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A MB-CAZAC precoding combined with 128/64/32/16-QAM modulation for OFDM-VLC system Jie Ma a , Jing He a, *, Qinghui Chen a , Jin Shi a , Zhihua Zhou a , Yun Cheng b , Yaoqiang Xiao a a b
College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China Department of Information Science and Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, China
ARTICLE
INFO
Keywords: Visible light communication (VLC) Orthogonal frequency division multiplexing (OFDM) Constant amplitude zero autocorrelation sequence (CAZAC) precoding Signal-to-noise ratio (SNR) Peak-to-average power ratio (PAPR)
ABSTRACT In this paper, multi-band constant amplitude zero autocorrelation sequence (MB-CAZAC) precoding combined with the 128/64/32/16-quadrature amplitude modulation (QAM) technology is proposed and experimentally demonstrated in the orthogonal frequency-division multiplexing-based visible light communication (OFDM-VLC) system. By using the MB-CAZAC precoding, it can equalize the uneven signal-to-noise ratio (SNR) and reduce the PAPR compared with the traditional OFDM system. The experimental results show that the 128/64/32/16QAM MB-CAZAC precoding outperforms the traditional scheme at different data rates for OFDM-VLC system. The spectral efficiency (SE) of the proposed scheme is up to 5.28 b/s/Hz. Meanwhile, it can be successfully transmitted 50-cm free-space at the bit error rate (BER) of 3.82 × 10−4 .
1. Introduction Nowadays, visible light communication (VLC) systems have become a research hotspot, thanks to its license-free spectrum, immunity to electromagnetic interference, security of indoor transmission and flexibility in installation. Light emitting diode (LED) based VLC, has been considered to be a promising technology for high-speed indoor communication [1–3]. By modulating LED-based VLC, channel access configurations to support different applications can be facilitated for users, including electronic payment, navigation & position, smart homes and vehicle-to-vehicle communication [4,5]. However, due to the limited bandwidth of LED, it is the main challenge of achieving high speed VLC transmission [6]. Orthogonal frequency-division multiplexing (OFDM) is proposed to take full advantage of the limited bandwidth of LED and thereby improve the spectrum efficiency (SE) [7–10]. Moreover, high-order quadrature amplitude modulation (QAM) technology is applied to increase data rate effectively [11,12]. Hence, OFDM has been one of the attractive candidates for VLC system. However, the key factor that limits performance of OFDM-VLC system is the critical low-passlike fading. Fortunately, several precoding techniques are proposed to combat severe frequency-selective fading effectively [13–17]. In [13], it has been demonstrated that orthogonal circulant matrix transform (OCT) precoding outperforms traditional scheme for mitigating the signal-to-noise ratio (SNR) fluctuation. As a multi-carrier system, OFDM *
has a high peak-to-average power ratio (PAPR). It can cause serious distortion to the transmitted signal. Hence, besides equalizing the uneven SNR across the subcarriers, precoding technique can also reduce the PAPR [18–20]. Currently, constant amplitude zero autocorrelation sequence (CAZAC) precoding technology is extensively applied to direct detection optical OFDM (DDO-OFDM) communication to improve the dispersion tolerance of the system, in terms of equalizing the uneven SNR and reducing the PAPR [21,22]. In addition, the 128/64/32/16-QAM modulation scheme is utilized to provide flexible data rates for multiple users and thereby enhance the network flexibility [23,24]. Nevertheless, to the best of our knowledge, the performance of the 128/64/32/16-QAM modulation scheme combination with CAZAC precoding method, has never been studied in OFDM-VLC system. In this paper, the 128/64/32/16-QAM OFDM combined with the multi-band CAZAC (MB-CAZAC) precoding is proposed and experimentally demonstrated for LED-based VLC. The CAZAC precoding is employed to reduce the PAPR and achieve a relatively flat SNR curve. By utilizing different level of QAM to the MB-CAZAC precoding, the BER performance is improved significantly. The experimental results show that, a 519.8 Mb/s signal transmission over 50-cm free-space is successfully implemented, and the BER is lower than the 7% hard-decision forward-error-correction (HD-FEC) limitation of 3.8 × 10−3 .
Corresponding author. E-mail address: [email protected] (J. He).
https://doi.org/10.1016/j.optcom.2018.04.047 Received 4 March 2018; Received in revised form 19 April 2018; Accepted 19 April 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
J. Ma et al.
Optics Communications 424 (2018) 154–158
Fig. 1. The schematic block diagram of the MB-CAZAC precoding.
Fig. 2. The schematic block diagram of the K sub-band transmission system.
2. Principle
where Z represents the precoded signal symbol vector on all subbands. There are 4*m data-modulated subcarriers in total, and each sub-band contains m data-modulated subcarriers. In this way, m-point CAZAC precoding is only performed on each sub-band. All sub-bands share the same precoding modules and thereby the space that stores large precoding matrices is saved. Thus, its complexity is O (4*m2 ). For the conventional CAZAC precoding, it requires 4*m -point CAZAC precoding, of which complexity is O (16*m2 ). Consequently, the MBCAZAC precoding can reduce the complexity of the system. After precoding, the modulated data carried by each subcarrier is multiplied by a phase rotation factor and then summed up. Therefore, the phase among the subcarriers is disordered and the energies become diverse. As a result of precoding, it can reduce the correlation among the input sequences. Hence, the PAPR can be significantly reduced compared with the traditional scheme.
2.1. MB-CAZAC precoding In this paper, precoding technique is used to improve PAPR and BER performance without destroying the orthogonality between subcarriers or adding much complexity. The precoding is implemented by multiplying a mapped data with the precoding matrix before IFFT operation in each OFDM symbol. Fig. 1 depicts the schematic block diagram of MB-CAZAC precoding for OFDM-VLC system. After QAM mapping, the data-modulated subcarriers are allocated to four subbands. There are 4*m data-modulated subcarriers in total, and each subband contains m data-modulated subcarriers. It can be written as 𝑆 = [ ]𝑇 [ ]𝑇 𝑆1 , 𝑆2 , 𝑆3 , 𝑆4 = 𝑋1 , … , 𝑋𝑚 ; 𝑋𝑚+1 , … , 𝑋2𝑚 ; ⋯ ; 𝑋3𝑚+1 , … , 𝑋4𝑚 . To improve the spectrum efficiency and system capacity, the 128∕64∕32∕16 QAM modulation scheme is applied from the first sub-band to the last sub-band respectively. Before IFFT, each sub-band with same mapping scheme is fed into a CAZAC block for CAZAC precoding implementation. The precoding matrix C is derived from a CAZAC sequence [22]. It can be expressed as: ⎡𝑐11 ⎢𝑐 1 ⎢ 12 𝐶 = √ ⎢⋮ 𝑁 ⎢𝑐 ⎢ 1𝑁−1 ⎣𝑐1𝑁
2.2. Noise equalization The schematic block diagram of the K sub-band transmission system through free space channel is depicted in Fig. 2. 𝑍𝑘 = [ ]𝑇 𝑍1𝑘 , 𝑍2𝑘 , … , 𝑍𝑚𝑘 denotes the K transmitted sub-band precoded signal [ ]𝑇 symbol vector, 𝑌𝑘 = 𝑌1𝑘 , 𝑌2𝑘 , … , 𝑌𝑚𝑘 denotes the K received sub-band precoded signal symbol vector. Their dimensions are both 𝑁𝑚 × 1. 𝐻𝑘 denotes the channel ( ) transfer matrix, and it can be expressed by diag 𝐻1𝑘 , 𝐻2𝑘 , … , 𝐻𝑚𝑘 , of which dimension is 𝑁𝑚 × 𝑁𝑚 . Supposing the inter-carrier interference (ICI) is free, the K received sub-band precoded signal symbol vector can be expressed as:
𝑐𝑁1 ⎤ 𝑐𝑁2 ⎥ ⎥ (1) ⋮ ⎥, 𝑐𝑁𝑁−1 ⎥ ⎥ 𝑐𝑁𝑁 ⎦ √ where 𝑐𝑖𝑗 = 𝑐𝑎𝑧𝑎𝑐𝑁∗(𝑖−1)+𝑗 , 𝑖, 𝑗 = 1, 2, … , 𝑁. 1∕ 𝑁 denotes a constant power during the precoding process. { exp[𝑗𝜋𝑘(𝑘 − 1)∕𝑁 2 ], 𝑁 is odd 𝑐𝑎𝑧𝑎𝑐𝑘 = , 𝑘 = 1, 2, … , 𝑁 2 . (2) exp[𝑗𝜋(𝑘 − 1)2 ∕𝑁 2 ], 𝑁 is even 𝑐21 𝑐22 ⋮ 𝑐2𝑁−1 𝑐2𝑁
⋯ ⋯ ⋯ ⋯ ⋯
𝑐𝑁−11 𝑐𝑁−12 ⋮ 𝑐𝑁−1𝑁−1 𝑐𝑁−1𝑁
𝑌𝑘 = 𝐻𝑘 𝑍𝑘 + 𝑛𝑘 (5) [ ]𝑇 where 𝑛𝑘 = 𝑛1𝑘 , 𝑛2𝑘 , … , 𝑛𝑚𝑘 denotes the noise vector, of which dimension is 𝑁𝑚 × 1. At the receiver, after symbol synchronization, channel equalization and decoding, the recovered symbol is given by:
Due to that CAZAC has an ideal periodic autocorrelation property, C is an orthogonal matrix, for 𝐶 𝐻 𝐶 = 𝐼. And the inverse matrix of C is its conjugate transpose 𝐶 𝐻 . The matrix C is used to equalize the parallel input symbols modulated on subcarriers. In MB-CAZAC precoding scheme, the precoding matrix is applied to each sub-band individually. As shown in Fig. 1, in the first sub-band, the OFDM symbols multiplying by C can be transposed as: [ ]𝑇 𝑍𝑏𝑎𝑛𝑑1 = 𝐶 × 𝑋1 , 𝑋2 , … , 𝑋𝑚
=
1 √ 𝑁𝑚
⎡ 𝑐11 𝑋1 + 𝑐21 𝑋2 + ⋯ + 𝑐𝑁 1 𝑋𝑚 ⎤ ⎢ 𝑐 𝑋 +𝑐 𝑋 +⋯+𝑐 𝑚 𝑋 ⎥ 12 1 22 2 𝑁𝑚 2 𝑚 ⎢ ⎥ ⎢ ⎥ ⋮ ⎢𝑐 ⎥ ⎣ 1𝑁𝑚 𝑋1 + 𝑐2𝑁𝑚 𝑋2 + ⋯ + 𝑐𝑁𝑚 𝑁𝑚 𝑋𝑚 ⎦
[ ] ′ 𝑆𝐾 = 𝑋1′ , … , 𝑋𝑚′ = 𝐶 −1 𝐻𝐾−1 𝑌𝐾 = 𝑆𝐾 + 𝐶 𝐻 𝐻𝐾−1 𝑛𝐾
It is assumed that different subcarriers have independent noises. For the 𝑖th subcarrier in K sub-band, the noise power is expressed as: ) (𝑁 )∗ (𝑁 2 𝑁𝑚 𝑚 𝑚 ∑ ∑ 𝑛 𝑛 1 ∑ || 𝑛𝑝 || ∗ 𝑞 ∗ 𝑝 ⋅ = (7) 𝑐𝑞𝑖 𝑃𝑁,𝑖 = 𝑐𝑝𝑖 | | | | 𝐻𝑝 𝐻𝑞 𝑁𝑚 𝑝=1 | 𝐻𝑝 | 𝑞=1 𝑝=1 | |2 where |𝑐𝑝𝑖 | = 1∕𝑁𝑚 . Accordingly, the noise equalization effect of each | | sub-band is demonstrated. The SNR of 𝑖th subcarrier in the K received sub-band can be expressed as:
(3)
𝑃𝑆,𝑖
|𝑋𝑖 |2 | |
(8) ∑𝑁𝑚 || 𝑛𝑝 ||2 𝑝=1 | 𝐻𝑝 | | | where 𝑃𝑠,𝑖 and 𝑃𝑁,𝑖 denote the signal power and noise power in K subband, respectively. Consequently, the effect of the uniform distribution of SNR is confirmed.
𝑆𝑁𝑅𝑖 =
where 𝑍𝑏𝑎𝑛𝑑1 denotes the 𝑁𝑚 × 1 precoded signal symbol vector. Its residual side-band has similar processing. Thus, we can get a precoding column vector, which can be expressed as: [ ] 𝑍 = 𝐶 ⋅ 𝑆1𝑇 ; 𝐶 ⋅ 𝑆2𝑇 ; 𝐶 ⋅ 𝑆3𝑇 ; 𝐶 ⋅ 𝑆4𝑇
(6)
(4) 155
𝑃𝑁,𝑖
=
1 𝑁𝑚
J. Ma et al.
Optics Communications 424 (2018) 154–158
Fig. 3. The schematic block diagram of the proposed MB-CAZAC precoding for OFDM-VLC system.
Table 1 Key parameters of the 128/64/32/16-QAM MB-CAZAC precoding scheme. Parameter
Value
Modulation scheme IFFT/FFT size Cyclic prefix length DAC sampling rate ADC sampling rate Number of data subcarriers Number of TS per OFDM frame OFDM symbols per frame Oversampling factor Raw signal bit rate Net signal bit rate Spectral efficiency
128/64/32/16-QAM 1024 32 800 MS/s 2.5 GS/s 504 1 100 4 126*(7+6+5+4)/(1024*0.005)=541.41 Mb/s 126*(7+6+5+4)*100/(101*1056*0.005)=519.8 Mb/s 519.8/(504/512*100)=5.28 bit/s/Hz
3. Experimental setup Fig. 3 depicts the experimental setup of the proposed MB-CAZAC precoding combined with the 128/64/32/16-QAM modulation scheme for OFDM-VLC system. At the transmitter, the DSP for OFDM modulation can be depicted as follows. Firstly, the data stream containing a pseudorandom binary sequence (PRBS) is generated. Secondly, we assign the each OFDM symbol for four sub-bands to realize the MB-CAZAC precoding scheme. For each sub-band, the length of data subcarrier is 126. The 128/64/32/16-QAM modulation scheme is adopted. The complex-value 128/64/32/16-QAM symbols are filled into independent MB-CAZAC precoding modules. Then, the complex values are converted into real values by adopting Hermitian symmetry. Thirdly, a 1024-point IFFT is used for the real data to generate a digital time-domain OFDM data. In order to resist the inter-symbol-interference (ISI), a cyclic prefix (CP) is added as the header of each OFDM symbol. Subsequently, one training sequence (TS) is inserted as the header of each OFDM frame to realize symbol synchronization. The key parameters of the 128/64/32/16QAM MB-CAZAC precoding scheme for OFDM-VLC system are given in Table 1. The FFT size is 1024, the CP length is 32, and the length of data-carrying subcarriers is 504. In this paper, the proposed MB-CAZAC precoding OFDM signal is fed into an arbitrary waveform generator (AWG, Tektronix 7122C) to produce an electrical OFDM signal. And the sampling rate of AWG is worked from 100 MS/s to 200 MS/s. The peak-to-peak voltage and bias voltage for input signal are optimized to 0.5 V and 3.328 V, respectively. Then, the electrical signal from the AWG is magnified by an electrical amplifier (EA). Afterwards, the 450-nm LED is directly driven by the transmitted signal to achieve optical signal. After 50-cm free-space transmission, the optical signal from the LED is detected by the PD integrated with trans-impedance amplifier (TIA) circuit to achieve electrical signal. Subsequently, a digital storage oscilloscope (DSO) is utilized to capture the received signal. Finally, the offline processing is utilized for experimental analysis. At the receiver, the demodulation processes of the detected signal include: timing synchronization, CP removal, 1024point FFT operation, channel estimation, equalization, CAZAC decoding, the 128/64/32/16-QAM de-mapping, and BER analysis.
Fig. 4. The CCDF curves versus PAPR for the four kinds of OFDM.
4. Experimental results and discussions We compare the PAPR of the 128/64/32/16-QAM OFDM signal with the 64QAM OFDM signal, in the case of with and without CAZAC precoding. Fig. 4 gives the complementary cumulative distribution function (CCDF) curves over PAPR for four kinds of OFDM signal. As is shown in Fig. 4, the PAPR of the MB-CAZAC precoding for the 128/64/32/16QAM OFDM is the lowest. And the PAPR with MB-CAZAC precoding schemes is lower than that without MB-CAZAC schemes. The results indicate that the 128/64/32/16-QAM MB-CAZAC precoding technology can reduce PAPR and will improve the tolerance of frequency-selective fading effect efficiently in OFDM-VLC system. Fig. 5 shows the average SNR over total data subcarriers index for OFDM-VLC system (a) with the 128/64/32/16-QAM MB-CAZAC precoding (b) without precoding. As we can see from Fig. 5(a), a ladder-like SNR profile for each sub-band is achieved. It indicates that the SNR curve of each sub-band is relatively flat by using MB-CAZAC precoding scheme 156
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Optics Communications 424 (2018) 154–158
Fig. 5. The average SNR over total data subcarrier index for the OFDM-VLC system (a) with the 128/64/32/16-QAM MB-CAZAC precoding; (b) without precoding.
Fig. 6. Sampling rate versus BER with MB-CAZAC precoding and without precoding: (a) 1-band, (b) 2-band, (c) 3-band and (d) 4-band.
comparing with the conventional scheme. When the sampling rate is 150 MS/s, the BER of the conventional scheme is 2.0 × 10−3 , while the BER of the 128/64/32/16-QAM MB-CAZAC precoding scheme is 3.82 × 10−4 . It is lower than the hard-decision forward error correlation (HDFEC) limitation of 3.8 × 10−3 . Fig. 5 also depicts the corresponding signal constellation using MB-CAZAC precoding. In practice, the VLC system is a frequency selective fading channel. By using the 128/64/32/16-QAM MB-CAZAC precoding technology, the performance of the system can be improved remarkably. Fig. 6 shows the BER performance of sub-bands with different number, running at different sampling rates with the MB-CAZAC precoding and the traditional scheme. As is shown in Fig. 6, when the sampling rate is 150 MS/s, the measured BER of four sub-bands can be reduced from 3.40 × 10−3 to 3.00 × 10−4 , 3.84 × 10−4 to 1.32 × 10−5 , 1.27 × 10−4 to 2.22 × 10−4 , and 4.00 × 10−3 to 1.60 × 10−3 . This results verify that, the proposed MB-CAZAC precoding can improve the BER performance on each sub-band significantly. Moreover, the BER of the 128/64/32/16-QAM OFDM scheme and the 64-QAM OFDM scheme on different sampling rate are depicted in
Fig. 7. It can be seen that a more obvious BER performance improvement can be achieved by utilizing the 128/64/32/16-QAM modulation scheme with MB-CAZAC precoding for the OFDM-VLC system. 5. Conclusion In this paper, the 128/64/32/16-QAM MB-CAZAC precoding scheme for OFDM-VLC system is proposed. The 128/64/32/16-QAM modulation technology is utilized to improve the system performance and enhance the network flexibility. Based on the proposed MB-CAZAC precoding scheme, the PAPR of OFDM-VLC system could be reduced compared with the conventional scheme. In addition, the MB-CAZAC precoding can not only reduce the complexity of the system but also equalize the uneven SNR on each sub-band. Hence, it is more conducive to the implementations of practical OFDM-VLC. Meanwhile, the proposed scheme could achieve better BER performance with a data rate of 541.41 Mb/s and higher spectral efficiency of 5.28 bit/s/Hz in OFDMVLC system. 157
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Fig. 7. Sampling rate versus BER with MB-CAZAC precoding and without precoding: (a) the 128/64/32/16-QAM OFDM scheme; (b) the 64QAM OFDM scheme.
Acknowledgments
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