 Research
 Open Access
Compressed sensingbased channel estimation for ACOOFDM visible light communications in 5G systems
 Muhammad Tabish Niaz^{1},
 Fatima Imdad^{1},
 Waleed Ejaz^{2} and
 Hyung Seok Kim^{1}Email author
https://doi.org/10.1186/s1363801607742
© The Author(s). 2016
Received: 29 April 2016
Accepted: 14 November 2016
Published: 25 November 2016
Abstract
In this paper, we propose a compressive sensing (CS)based channel estimation technique for asymmetrically clipped opticalorthogonal frequency division multiplexing (ACOOFDM) visible light communications (VLC) in 5G systems. We proposed a modified version of sparsity adaptive matching pursuit (SAMP) algorithm which is named as selfaware step size sparsity adaptive matching pursuit (SSSAMP) algorithm. It utilizes the builtin features of SAMP and with additional ability to select step size according to the present situation, hence term selfaware, can provide better accuracy and low computational cost. It also does not require any prior knowledge of the sparsity of the signal which makes it selfsufficient. CSbased algorithms such as orthogonal matching pursuit (OMP), SAMP, and our proposed SSSAMP were implemented on ACOOFDM VLC. The paper is supported by simulation results which demonstrate performance of proposed scheme in terms of bit error rate (BER), mean square error (MSE), computational complexity, and key VLC parameter (LED nonlinearity, shot noise, thermal noise, channel response, and peaktoaverage power ratio (PAPR). It is shown that the SSSAMP is a good candidate for ACOOFDMbased VLC that are mobile and have limited processing power, based on its performance and computational complexity.
Keywords
 Biterrorrate
 Channel estimation
 Compressed sensing
 Visible light communication
1 Introduction
Visible light communication (VLC) is a promising optical wireless communication (OWC) technology which is paving its way to reality very quickly [1]. VLC uses LED emitted light which fulfills the dual functionality of illuminance and data transmission. VLC has shown potential to be an integral part of upcoming 5G networks. The market is continuously pushing the limits of the network data rate and capacity; it is very difficult for the wireless communication industry to meet these demands. It is estimated that for 5G networks, there will be a 1000fold increase in data traffic [2]. In order to meet these demands, 5G networks will have to rely on other more efficient technologies. It is highly likely that it will incorporate smaller cells (attocells), additional spectrum, energy efficient communication, and heterogeneous networks (HetNet) integration [3].

Spectrum of visible light is free.

Light that cannot penetrate solid objects makes it secure for indoor transmission.

It can be deployed wherever LEDs are installed [5].

The signaltonoise ratio (SNR) is usually high because of high illumination requirements.
The fact that VLC can provide high bandwidth density can help in solving the demand of high bandwidth problem faced by upcoming RFbased networks. VLC can resolve supply and demand issue in 5G networks. Considering the positive traits of VLC at its present state can be best suited as a supplemental technology to assist HetNets in 5G networks. These main features of VLC make it a promising supplementary technology for 5G systems; however, it comes with various new challenges which open new research topics [6, 7].
Recently, optical orthogonal frequency division multiplexing (OFDM) systems have gained a lot of popularity due to high bandwidth, power efficiency, flexibility, and use of licensefree spectrum [8]. The optical OFDM works on the technique of intensity modulation and direct detection (IM/DD) [9]. There are many proposed methods utilizing the optical OFDM in VLC systems [10–15]. In [11], Armstrong and Lowery have proposed asymmetrically clipped optical OFDM (ACOOFDM) which is a very efficient technique to be used with VLC system. Instead of sending all subcarriers, ACOOFDM sends only odd subcarriers. ACOOFDM has been shown to be more efficient in terms of optical power than the systems that use DCbiasing as it utilizes a large dynamic range of the LED. The ACOOFDM technique performs well under interferences caused by intersymbol interference (ISI) and intercarrier interference (ICI). It requires less optical power for a given data rate than other variants of optical OFDM if the constellation size is lower than 1024QAM. In addition, ACOOFDM is a good candidate for dimming systems because of its better performance at lowSNR regime. Due to these features, ACOOFDM is used in this paper.
In VLC systems, due to interference from ambient light sources, estimating the channel for correct signal recovery is of utmost importance. Among studies on ACOOFDM VLC systems, there have been proposals for channel estimation, which is an important part of wireless communication systems. In [12], authors have proposed a technique to find channel state information (CSI) in the ACOOFDM communication system for better channel estimation. A study has proposed a least square (LS)based channel estimator to achieve highly accurate result in ACOOFDM VLC systems [13]. Another study proposed the use of minimum mean square error (MMSE) and least minimum mean square error (LMMSE) based methods to improve the channel estimation of ACOOFDM VLC systems [14, 15]. There is an alternate approach for channel estimation, which utilizes the technique of compressed sensing (CS). The CSbased technique exploits the signal sparsity and incoherency to achieve best results [16–20]. It relies on finding sparse solutions to underdetermined linear systems and can estimate signals from fewer samples rather than using the Nyquist sampling rate [21]. The positive aspect of using CS technology is to have more accurate, fast ,and reliable channel estimation techniques, which are inexpensive and have low complexity.
2 Related work
The CS algorithms, which recover a sparse signal, are generally divided into two branches: linear programming (LP) and dynamic programming (DP). This paper focuses on the DP algorithm because most of the LP algorithms tend to have high computational complexity. Due to the high complexity of LP algorithms, they do not perform well in real largescale applications. The orthogonal matching pursuit (OMP) algorithm [22] is by far the most popular algorithm in DP category [23, 24]. The major drawback in DP algorithms is that they rely on the knowledge of channel sparsity beforehand, which is not always possible in real practical applications. To counter the problem of channel sparsity information, sparsity adaptive matching pursuit (SAMP) was proposed in [25]. The SAMP algorithm uses an iterative method to estimate the signal sparsity, with a fixed step size to be used in each stage. This was an improvement over OMP algorithm, which usually requires the level of sparsity as a priori information to estimate the original signal. The research in [25] showed that SAMP outperforms OMP and its variants, but its drawback is that the MSE performance and complexity are directly related to the initial step size. Since mobile devices equipped with VLC modules have limited resources, the high computational complexity is a huge disadvantage.
There is no such literature that has worked on CSbased channel estimation in ACOOFDM VLC systems. To the best of our knowledge, one article claims to improve the channel bandwidth of simple OFDM VLC system using CS [26]. The authors propose a new technique that can compensate the lack of channel bandwidth in an opticalOFDM link by using compressive sensing. The positive aspect of using CS technology is to have more accurate, fast, and reliable channel estimation techniques that are inexpensive and have low complexity.
To summarize the current trend of research, most of the CSbased techniques are devised for RFbased channel estimation. CS is very new in VLC domain, and there are very few literatures available which makes it a very open field for research.
3 Contribution

SSSAMP can adaptively adjust the step size.

Due to the adaptive adjustment of step size, convergence is faster.

SSSAMP does not require a priori knowledge of sparsity as in the case of other mentioned algorithms.
The paper is organized as follows: Section 2 describes the system model used in the paper; Section 3 presents the proposed CSbased channel estimation techniques; Section 4 discusses the effect of various VLC key parameter impact; Section 5 presents simulation for the performance comparison with existing CSbased channel estimation algorithms; finally, Section 6 concludes the paper.
4 System model
The main requirement of a VLC system to work is to have real and positive values from the optical modulator. This property usually employs the presence of IM/DD technique. ACOOFDM also works on the IM/DD technique and thus is simple to implement. The main problem here lies with the OFDM signal. Since they are complex and bipolar, simple OFDM system cannot be used with VLC system. It is necessary to make it unipolar and real. The ACOOFDM modulator inherently does this work.
To ensure that the output of ACOOFDM is real and unipolar, the following procedure is followed [14]. There are N subcarriers out of which only odd ones will be used to send data. At the transmitter, the source bits are first modulated using Graycoded Mary quadrature amplitude modulation (QAM) mapping block. This will produce a complex bit stream. Then to maintain real OFDM symbols in time domain, the encoded data is passed through the Hermitian symmetry block. The data is then passed on to inverse fast Fourier transform (IFFT) block and clipping block so that the data is on odd subcarriers and positive. Cyclic prefix (CP) is later added to avoid ISI. The addition of CP has a negligible impact on the SNR and spectral efficiency of the VLC system. To reduce the peaktoaverage power ratio (PAPR), clipping is performed to combat two types of distortions: firstly the outofband distortion which is reduced by applying filtering and secondly the inband distortion which is reduced by adding the CP. It is to be noted that in ACOOFDM signal, only odd subcarriers are sent [14]. The signal is converted from analog to digital using an analogtodigital converter (ADC) and later, using optical intensity modulation (IM), the data is sent over the optical wireless channel.
There are two more types of interference noises, the narrowband interference (NBI) and impulse interference, which have to be taken into consideration. To solve these interferences, there are two methods that are commonly used in ultrawideband communication systems. One method is based on frequency domain and the other is based on timedomain schemes [27]. While keeping strictly within the scope of this paper, the frequency domain will be discussed. For frequencydomain schemes, OFDM is used to combat these interference noises. One of the most prominent methods is the frequency threshold excision (FTE), in which the excess interference is clipped from the signal. The advantage of using ACOOFDM is the intrinsic immunity to interferences like NBI. It is shown in [11] that the interference component lies in the even subcarriers while the odd subcarrier’s components are affected by the multiplication of a constant 0.5. ACOOFDM also mitigates these interferences by clipping the signal before transmission. This helps in containing the signal within the time frame hence minimize the interference. To further reduce the effects of these interferences, a narrowband optical filter can be used at the receiver [28–32]. CS has many applications, one of these applications is of channel estimation, which is discussed in this paper. One of the other applications of CS is the noise cancellation in which the sparsity is used to mitigate the effect of interference noises including NBI and impulse noise. This discussion is out of the scope of this paper, since the scheme used in this paper strictly deals with the channel estimation. The intrinsic immunity of ACOOFDM towards the interference noise tries to minimize the effect of these interferences.
At the receiver’s end, using direct detection (DD), the signal is received using photodiode (PD). This will convert the signal to digital electrical domain. The received signal is first recovered using different CS channel estimation techniques. The estimated signal is then passed to the ACOOFDM demodulator block. After demodulation, the signal goes through the demapping block and original data stream is recovered.
5 CSbased channel estimation method
In this section, the different channel estimation algorithms are discussed and the proposed scheme is given.
5.1 Least square channel estimation
The LS channel estimation is the simplest one. The only catch with this estimation is that the optimal solution is only achieved when there is no noise and interference is considered in the received signal. The mean square error (MSE) is high, hence accuracy is limited. Thus, concluding the LS estimation technique is not the best solution for this CSbased channel estimation.
5.2 OMP channel estimation algorithm
One of the earliest greedy iterative algorithm is orthogonal matching pursuits (OMP). It is one of the main stepping stones on which the other greedy algorithm is based on. The basic working of an OMP algorithm revolves under the conditions of a given iteration number. Since it is an iterative process, it is required to stop after certain iterations. To make accurate estimation of the original signal, OMP requires a lot of measurement data. One of the drawbacks of the OMP is that, as it requires a large number of measurement data to estimate the signal, any increase in the degree of sparse or the number of samples would increase the time it takes to obtain the results. The basic working of OMP algorithm is shown in Algorithm 1.
5.3 SAMP channel estimation algorithm
The OMP algorithm is not adaptive. A preestimate of the sparse degree of the signal should be known and also the estimation accuracy is not so good. In an actual scenario, the sparse degree is not known; hence, to make things easier and less complex the adaptive algorithm like sparsity adaptive matching pursuit (SAMP) was proposed in [24]. With this adaptive algorithm, the signal estimation does not require any information of signal sparse degree beforehand. The working of SAMP requires to choose a step size s, which should satisfy s ≤ K. The tradeoff of choosing the step size is that if it is too small the algorithm will take long time to converge. Hence the choice of the step size is very important in this algorithm. The SAMP algorithm has a high computational complexity and more computational time than OMP algorithm. The basic working of SAMP algorithm is shown in Algorithm 2.
5.4 SSSAMP channel estimation algorithm
The choice of step size is the main parameter which defines the performance of the proposed selfaware step size sparsity matching pursuit (SAMP) algorithm. If the chosen step size is small, SAMP algorithm leads to better estimation accuracy but increases the computational complexity. On the other hand, if the step size is large, the computational complexity decreases but at the cost of low estimation accuracy. By making the algorithm selfaware with respect to step size, a better tradeoff can be maintained between the estimation accuracy and computational complexity. The selfaware step size in this particular case depends on the current state of signal estimation from the original signal. The current state of estimation can be the current estimated signal energy or the estimated sparsity of the current signal. Since the estimation of sparse elements is done with large values at the initial stages of the algorithm, the values are reduced as the later stages come. This means that the energy tends to stabilize as the estimated sparsity is close to true sparsity K. Utilizing this property of sparse signals, the proposed SSSAMP algorithm starts by choosing step size which is large and, as the algorithm progresses, the energy of the signal decreases at a certain rate which defines by how much the step size will be reduced. To specify the finetuning process, an additional threshold γ is specified. The proposed algorithm is shown in Algorithm 3. The algorithm is stagewise with a variable size of the final support set F _{ k } in different stages. During each stage, F _{ k } adapts to two correlation test. These tests are the candidate test and final test, which searched a certain number of coordinates corresponding to the largest correlation values between the signal residual and the columns of the measurement matrix. In the next stage the algorithm runs until the recovered signal is found which has the least residual. The SSSAMP uses two threshold values for halting criterion. These two values are tolerance ε and γ. The SSSAMP algorithm comes to a halt when the residual’s norm is smaller than ε. On the other side, the values of the step size are decreased as the difference in energy of the estimated signal and original signal falls below γ.
6 Discussion on different VLC characteristics
In this section, different VLC characteristics are discussed such as LED nonlinearity, shot noise, and PAPR calculation. The effects of the proposed scheme on these parameters are discussed, and the results are shown in Section 5.
6.1 LED nonlinearity, shot noise, and thermal noise
Due to the directly proportional relationship between the radiated optical power and the forward current of the LED, the signal and constraints are described in terms of optical power. There are two main points on concern in the dynamic range imposed by the LED. One is the minimum optical power point, termed as \( {P}_{Tx,\mathsf{min}} \) _{,} and the other point is the maximum optical power point, termed as \( {P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{max}} \). The point at which the optical power bias is indicated is termed as \( {P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{bias}} \). The signal is clipped at the top level, to ensure the maximum power driving limit of the LED. The clipping at the top level can be expressed as \( {\epsilon}_{\mathrm{top}}={P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{max}}  {P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{min}} \). If the LED is insufficiently forward biased, then it should be clipped at the bottom level, \( {\epsilon}_{\mathrm{bottom}}={P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{min}}  {P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{bias}} \), this condition will only hold true if \( {P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{bias}}<{P}_{\mathit{\mathsf{T}}\mathit{\mathsf{x}},\mathsf{min}} \). The signal after the conversion is then transmitted over the optical wireless channel h.
The analysis of the nonlinearity is done in Section 5.
6.2 PAPR
PAPR is usually presented in the form of CCDF. In this, we find the probability that PAPR value is higher than a certain PAPR value PAPR_{0}, i.e., P _{ r }(PAPR > PAPR_{0}). The simulation results are analyzed in Section 5.
7 Performance evaluation
In this section, the performance of different channel estimation techniques is simulated and later the proposed scheme performance is analyzed on the basis of the key VLC parameters. The comparison of LS, OMP, SAMP, and proposed SSSAMP are shown in two parameters, BER and MSE, since the main parameter that defines the accuracy of estimation signals is based on the step size. To simulate, three different step sizes are chosen: small, medium, and large step size. The MSE and BER are used to measure the channel estimation accuracy and the system performance, respectively. To measure the computational complexity, CPU running time was computed. Simulations were performed in MATLAB R2015a using the i5 CPU with 4 GB of memory. The results were averaged using 1000 MonteCarlo trials. Later, the proposed scheme is analyzed on how it will tackle the LED nonlinearity, shot noise, and thermal noise. Also, the channel response and the modulation constellation are analyzed to give a clear picture on how the proposed scheme will perform in an indoor VLC environment.
Simulation parameters
Parameter  Value 

Room dimensions (m)  5 × 5 × 3 
Height of receiving plane (m)  0.8 
Number of LEDs  256 
Center luminous intensity, I _{0} (cd)  30 
Minimum optical power, P _{ Tx,min} (mW)  90 
Maximum optical power, P _{ Tx,max} (mW)  400 
Semiangle at half power (°)  60 
Photodiode responsivity  0.3 
Field of view at the receiver (°)  85 
Reflective index of concentrator  1.5 
A _{ r } (cm^{2})  1 
Background noise current, I _{ bg } (mA)  0.62 
Load resistance, R _{ L }(KΩ)  10 
Absolute temperature, T (°K)  295 
Reflectivity, ρ walls and floor  0.8 and 0.3 
Modulation  64QAM ACOOFDM 
8 Conclusions
In this paper, a new modified CSbased channel estimation algorithm SSSAMP was proposed for the ACOOFDM VLC system. The performance was evaluated in terms of BER, MSE, computational complexity, and key parameters of VLC system (nonlinearity, noise, channel response). The results show that CSbased techniques: OMP, SAMP, and SSSAMP perform better than the traditional LSbased method. SSSAMP stood out to be the best among the algorithms applied to the VLCbased system. The OMP algorithm requires the knowledge of sparsity beforehand. The SAMP algorithm is an improved adaptive version of OMP, but the computational cost is on the higher side due to the fact that the SAMP algorithm has to start with a random step size. It is shown through the performance analysis that SSSAMP can improve the channel estimation accuracy without significantly increasing the computational complexity. It can be said that CStechnologybased algorithms can be used with the ACOOFDM VLC system and can give accurate estimation of the original signal and still can manage to have an acceptable computation time.
Declarations
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. 2016R1A2B4008457) and by the Strengthening R & D Capability Program of Sejong University.
Authors’ contributions
The research presented in this paper was a collaborative effort among all authors. MTN conceived, implemented and simulated the results along with the paper writeup. FI and WE wrote the paper and discussed the results. HSK revised the manuscript critically. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Z Ghassemlooy, W Popoola, S Rajbhandari, Optical wireless communications: system and channel modelling with MATLAB®. (CRC Press, 2012)Google Scholar
 Qualcomm incorporated: the Qualcomm 1000x challenge (2013), HYPERLINK “https://www.qualcomm.com/invention/1000x” https://www.qualcomm.com/invention/1000x. Accessed 24 Apr 2016
 MB Rahaim, L TDC, Towards practical integration of dualuse VLC within 5G networks. IEEE Wirel Commun. 22, 97–103 (2015)View ArticleGoogle Scholar
 L Garber, Turning on the lights for wireless communications. Computer 44, 11–14 (2011)View ArticleGoogle Scholar
 H Elgala, R Mesleh, H Hass, Indoor optical wireless communication: potential and stateoftheart. IEEE Commun. Mag. 49, 56–62 (2011)View ArticleGoogle Scholar
 DC O’Brien, L Zeng, H LeMinh, G Faulkner, JW Walewski, S Randel, In IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, 2008. PIMRC 2008. Visible light communications: Challenges and possibilities, (2008), pp. 1–5.Google Scholar
 J Armstrong, RJ Green, MD Higgins, Comparison of three receiver designs for optical wireless communications using white LEDs. IEEE Commun Lett 16, 748–751 (2012)View ArticleGoogle Scholar
 J Armstrong, OFDM for optical communications. J Light Technol 27, 189–204 (2009)View ArticleGoogle Scholar
 SD Dissanayake, J Armstrong, Comparison of ACOOFDM, DCOOFDM and ADOOFDM in IM/DD systems. J Light Technol 31, 1063–1072 (2013)View ArticleGoogle Scholar
 JM Kahn, JR Barry, , Wireless infrared communications. Proc IEEE 85, 265–298 (1997)View ArticleGoogle Scholar
 J Armstrong, AJ Lowery, Power efficient optical OFDM. Electron Lett 42, 370–372 (2006)View ArticleGoogle Scholar
 P Errong, C Fang, L Jibi, Optimal power allocation for OFDMbased cognitive radio systems with fair protection against primary users. J Comput Inf Syst 8, 9831–9837 (2012)Google Scholar
 D Wu, Z Wang, R Wang, J He, Q Zuo, H Zhao, Channel estimation for asymmetrically clipped optical orthogonal frequency division multiplexing optical wireless communications. IET Commun 6, 532–540 (2012)MathSciNetView ArticleGoogle Scholar
 H Zhao, M Li, R Wang, D Wu, Channel estimation for asymmetrically clipped optical orthogonal frequency division multiplexing communication system. Opt Eng 52, 076111 (2013)View ArticleGoogle Scholar
 S Qaisar, RM Bilal, W Iqbal, M Naureen, S Lee, Compressive sensing: from theory to applications, a survey. J Commun Netw 15, 443–456 (2013)View ArticleGoogle Scholar
 EJ Candes, MB Wakin, An introduction to compressive sampling. IEEE Signal Proc Mag 25, 21–30 (2008)View ArticleGoogle Scholar
 S Ji, Y Xue, L Carin, Bayesian compressive sensing. IEEE Trans Signal Proc 56, 2346–2356 (2008)MathSciNetView ArticleGoogle Scholar
 EJ Candes, J Romberg, Sparsity and incoherence in compressive sampling. Inverse Probl 23, 969 (2007)MathSciNetView ArticleMATHGoogle Scholar
 EJ Candes, The restricted isometry property and its implications for compressed sensing. C. R. Math 346, 589–592 (2008)MathSciNetView ArticleMATHGoogle Scholar
 EJ Candes, J Romberg, T Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52, 489–509 (2006)MathSciNetView ArticleMATHGoogle Scholar
 YY Won, SM Yoon, Compressive sensingbased channel bandwidth improvement in optical wireless orthogonal frequency division multiplexing link using visible light emitting diode. Optics Express 22, 19990 (2014)View ArticleGoogle Scholar
 J Tropp, A Gilbert, Signal recovery from random measurment via orthogonal matching pursuit. IEEE Trans Inf Theory 53, 4655–4666 (2007)MathSciNetView ArticleMATHGoogle Scholar
 C Berger, S Zhou, J Preisig, P Willett, Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Trans Signal Proc 58, 1708–1721 (2010)MathSciNetView ArticleGoogle Scholar
 C Berger, Z Wang, J Huang, S Zhou, Aplication of compressive sensing to sparse channel estimation. IEEE Commun Mag 48, 164–174 (2010)View ArticleGoogle Scholar
 T Do, NNG Lu, T Tran, Proceedings of the 42nd Asilomar Conference on Signals, Systems and Computer (Sparsity adaptive matching pursuit algorithm for practical compressed sensing, Pacific Grove, CA, 2008), pp. 581–587Google Scholar
 CN Reinhardt, S Jaruwatanadilok, Y Kuga, A Ishimaru, JA Ritcey, Investigation of multilevel amplitude modulation for a dualwavelength freespace optical communications system using realistic channel estimation and minimum meansquarederror linear equalization. Appl. Opt 47, 5378–5389 (2008)View ArticleGoogle Scholar
 S Liu, F Yang, J Song, Narrowband interference cancelation based on priori aided compressive sensing for DTMB systems. IEEE Trans Broadcast 61(1), 66–74 (2015)View ArticleGoogle Scholar
 AJC Moreira, RT Valadas, AM Oliveira Duarte, IET Conference Proceedings, Reducing the Effects of Artificial Light Interference in Wireless Infrared Transmission Systems, 1996, p. 5Google Scholar
 RP Jimenez, J Rabadan, FL Hernandez, Filtered modulation schemes for short distance infrared wireless communications. IEEE Trans Consum Electron 46(2), 275–282 (2000)View ArticleGoogle Scholar
 F Delgado, RP Jiménez, J Rabadán, FL Hernández, Design of fast frequencyhopping spreadspectrum system for wireless infrared communications. Electron Lett 36(17), 1510 (2000)View ArticleGoogle Scholar
 J Rabadan, M Bacallado, F Delgado, S Perez, RP Jimenez, Experimental characterization of a directsequence spreadspectrum optical wireless system based on pulseconformation techniques for inhouse communications. IEEE Trans Consum Electron 50(2), 484–490 (2004)View ArticleGoogle Scholar
 O Gonzalez, RP Jimenez, S Rodriguez, J Rabadan, A Ayala, OFDM over indoor wireless optical channel. IEE Proc  Optoelectron 152(4), 199 (2005)View ArticleGoogle Scholar
 J Barry, Wireless Infrared Communications (Kluwer Academic, Boston, MA, (2004)Google Scholar
 R Gagliardi, S Karp, Optical Communications (Wiley, New York, 1984)Google Scholar
 M Wang, J Wu, W Yu, H Wang, J Li, J Shi, C Luo, Efficient coding modulation and seamless rate adaptation for visible light communications. IEEE Wirel Commun 22(2), 86–93 (2015)View ArticleGoogle Scholar
 C Berger, Z Shengli, J Preisig, P Willett, Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Trans Signal Proc 58(3), 1708–1721 (2010)MathSciNetView ArticleGoogle Scholar
 W Li, J Preisig, Estimation of rapidly timevarying sparse channels. IEEE J Ocean Eng 32(4), 927–939 (2007)View ArticleGoogle Scholar
 W Bajwa, J Haupt, A Sayeed, R Nowak, Compressed channel sensing: a new approach to estimating sparse multipath channels. Proc IEEE 98(6), 1058–1076 (2010)View ArticleGoogle Scholar
 S Cotter, B Rao, Sparse channel estimation via matching pursuit with application to equalization. IEEE Trans Commun 50(3), 374–377 (2002)View ArticleGoogle Scholar
 R Prasad, C Murthy, B Rao, Joint approximately sparse channel estimation and data detection in OFDM systems using sparse Bayesian learning. IEEE Trans Signal Proc 62(14), 3591–3603 (2014)MathSciNetView ArticleGoogle Scholar
 H Elgala, R Mesleh, H Haas, Indoor broadcasting via white LEDs and OFDM. IEEE Trans Consum Electron 55, 1127–1134 (2009)View ArticleGoogle Scholar
 O Gonzalez, RP Jimenez, A Ayala, OFDM over indoor wireless optical channel. IEE Proc  Optoelectron 152, 199–204 (2005)View ArticleGoogle Scholar
 L Weihao, Z Difan, X Zhengyuan, Modelling of optical wireless scattering communication channels over broad spectra. J Opt Soc Am A 32, 486–490 (2015)View ArticleGoogle Scholar
 European Standard EN 124641, Lighting of indoor Work Places, 2009Google Scholar