Improved TKM-TR methods for PAPR reduction of DCO-OFDM visible light communications

The dc-biased optical orthogonal frequency division multiplexing (DCO-OFDM) system is experimentally demonstrated as an appealing candidate in future visible light communication (VLC) system. However, the intrinsic high PAPR drawback that the DCO-OFDM system suffers from still needs to be addressed and few effective approach has been found so far. To deal with this problem, in this paper, the tone reservation (TR) technique based the time domain kernel matrix (TKM-TR) schemes for reducing the PAPR are studied and applied to DCO-OFDM system. Aiming at the drawback of its severe tailing in previous TKM-TR schemes, first an improved TKM-TR scheme is proposed, in which the peak regrowth caused by severe tailing is eliminated by optimizing the scaling factors. In addition, considering the clipping ratio (CR) value in TKM-TR scheme is greatly related to the PAPR reduction performance, an extensively used heuristic global optimization algorithm, the particle swarm optimization (PSO) method is employed in TKM-TR to obtain a better CR for more PAPR reduction. Simulation results show that the improved TKM-TR scheme can efficiently address the tailing problem in previous TKM-TR schemes and achieve better PAPR reduction. Moreover, due to the powerful searching ability, PSO based TKM-TR scheme achieves more PAPR reduction and lower bit error rate (BER). © 2017 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.4510) Optical communications. References and links 1. H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011). 2. D. OBrien, L. Zeng, H. Le-Minh, G. Faulkner, J. W. Walewski, and S. 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Introduction
Owing to the advantages of huge bandwidth, unlicensed frequency, immune to electromagnetic interference and high security [1][2][3], visible light communication (VLC) technology is considered as a potential candidate to complement the conventional radio frequency (RF) communication.By using the white light emitting diodes (LEDs), both illumination and communication can be realized simultaneously in the VLC system.Hence it has become an active research topic for decades.However, one issue that the practical VLC system suffers from is the single carrier pulsed modulation technique, such as on-off Keying (OOK), variable pulse position modulation (VPPM) or pulse amplitude modulation (PAM) [4], which can cause severe inter symbol interference (ISI).To deal with this problem, orthogonal frequency division multiplexing (OFDM) based VLC system has been proposed, such as direct current (DC)-biased optical OFDM (DCO-OFDM) [5], Flip-OFDM [6], asymmetrically clipped optical OFDM (ACO-OFDM) [7] and so on.They can effectively combat the ISI induced by multi-path in the VLC system, at the same time enhancing the spectrum efficiency.Among those OFDM based VLC system, the DCO-OFDM system is extensively investigated because of the easily configurable DC component and the high spectral efficiency.However, the intrinsic high PAPR problem of the DCO-OFDM system is still a challenge.The signals with high PAPR, on one hand, can cause the nonlinear distortion passing through power amplifier and light emitting diode (LED) [8] emitter.On the other hand, they require a large DC bias in DCO-OFDM system, and hence deteriorate the system power efficiency.Thus, efficient measures or techniques have to be developed to reduce PAPR in VLC OFDM system.
So far, several available methods have been proposed for the PAPR reduction of the DCO-OFDM system.In [9], an exponential nonlinear PAPR reduction algorithm was proposed for the VLC OFDM system by compressing large signals and expanding the small signals simultaneously.An iterative clipping method without in-band distortion was put forward in [10] for the VLC OFDM system.Unfortunately, due to the nonlinear distortion of signals, BER performance degradation could be caused in both methods mentioned above.Recently, several tone injection (TI) technique based different methods, i.e., the semidefinite relaxation method [11], the linear programming algorithm [12] and the branch and bound method [13] were proposed to reduce the PAPR of the VLC OFDM system.Nevertheless, these TI based methods can effectively reduce the PAPR at the sacrifice of computational complexity and energy consumption.In RF-OFDM systems, another popular technique in reducing the PAPR is the tone reservation (TR) scheme, which is regarded as a distortionless technique and hence attracts considerable interests.According to the derivation in [14], the PAPR reduction problem in conventional RF OFDM system was formulated as a quadratically constrained quadratic program (QCQP) problem [15].A signal to clipping noise ratio (SCR) maximization based on TR (SCR-TR) method [14] was proposed to deal with this optimization problem by using the gradient algorithm.However, one drawback of SCR-TR is its slow convergence speed.To accelerate the convergence speed and reduce the computational complexity, several improved TR methods were proposed in [15][16][17][18], among which the TKM-TR algorithm [15] owned much better PAPR reduction performance and lower complexity.Moreover, an enhanced TKM-TR scheme [19] was applied to the RF-OFDM system to address the problem of the peak regrowth, however, the result still seems not so satisfied after multiple iterations.
In this paper, to further eliminate the peak regrowth of the TKM-TR schemes applied in RF-OFDM system, first an improved TKM-TR scheme is proposed for the DCO-OFDM system by optimizing the scaling factors.In addition, considering the PAPR reduction performance of the TKM-TR method is largely affected by the CR value, the PSO method in [20] is introduced to search the better CR to further reduce the PAPR.The simulation results reveal that the improved TKM-TR scheme can effectively reduce the probability of peak regrowth and the PSO based TKM-TR method can further suppress the peak regrowth, with much better PAPR reduction performance and lower BER than other existing TR algorithms.

System model and tone reservation
In this section, a general DCO-OFDM VLC system is considered, as shown in Fig. 1  For the DCO-OFDM system with N subcarriers, the discrete-frequency signals where 0 2 0 N X X = = and ( ) * ⋅ represents the conjugation operation.Then, the equivalent discrete-time baseband signal is expressed as: where L is the oversampling factor.Therefore, the PAPR of the DCO-OFDM system is: where [ ] E ⋅ represents the expected value operation.
In TR, r N subcarriers are reserved as the peak reduction tones (PRT) set to carry the frequency-domain peak reduction signals where  represents the positions of the PRT set and c R is the corresponding complementary subcarriers set.Then, the PAPR of OFDM signals with TR is redefined as: Following the derivations in [14], minimizing the PAPR in ( 6) is a QCQP optimization problem [15].

Improved TKM-TR schemes and PSO based TKM-TR schemes
To deal with the problem of minimizing the PAPR in (6), the TKM-TR scheme in [15] and the enhanced-TKM-TR scheme in [19] were proposed, respectively.However, it is found that the TKM-TR scheme has the drawback of peak growth during the PAPR reduction, which will result in the severe tailing.Although the severe tailing has been greatly suppressed in the enhanced-TKM-TR, the result seems not so satisfied after multiple iterations.Towards this end, superior TKM-TR schemes are proposed in this section.

Improved TKM-TR schemes
As a low complexity suboptimal iterative clipping and compensating technique, the TKM-TR scheme constructs the time-domain kernel matrix scaled by a scaling vector β .The time-domain kernel is obtained by: [ ] , , , ( ) where the frequency-domain kernel , , , In TKM-TR, the clipping ratio (CR) is defined as CR A σ = , where A is the clipping threshold and 2 σ represents the average power of the input OFDM signal.Then the clipping noise is obtained by: , 0, The corresponding clipping noise positions are expressed as: The time-domain OFDM signals are updated by: where the time-domain kernel matrix It is found that in the TKM-TR scheme, the lower the clipped signals, the more the kernels are.Hence, a higher probability of peak regrowth is caused in each iteration.However, this drawback has not received enough attention in previously proposed TKM-TR methods.Despite their good PAPR reduction performance, this problem has to be addressed in order to further improve the performance.Motivated by that, in the proposed improved-TKM-TR method, we propose the idea that the small clipping ratio signals are just kept as their original state without clipping.In particular, if the time-domain peak reduction signals c generated by β cannot reduce the peak value of signals, the scaling factor i β at the location of the minimum clipping noise is set to zero, i.e., the signal at the corresponding location is not clipped.If the newly generated time-domain peak reduction signals c still have the peak regrowth problem, the scaling factor corresponding to the second-smallest clipping noise is also set to zero until the peak regrowth does not take place again or each element of β is zero.
In summary, the specific operation steps of the improved TKM-TR scheme are provided in Table 1.
Table 1.The improved TKM-TR scheme Initialization: 1) Set the CR, peak reduction tones location R , and the number of iterations K .2) Calculate the time-domain kernel p according to Eq. ( 7).
The specific steps of implementation: 3) Calculate the clipping noise f by Eq. ( 9) and obtain S by using Eq.(10).Sort f in descending order.

PSO based TKM-TR schemes
Figure 2 shows the average PAPR reduction performance of different TR schemes with 256 subcarriers, 4 times oversampling and 50 reserved tones.As can be seen, the improved TKM-TR scheme in the appropriate clipping zone performs better than the other TR schemes in terms of the reduced PAPR performance, which therefore proves its benefit.From Fig. 2, it is also observed that these TR schemes are very sensitive to the CR value.Considering the CR value is greatly related to the PAPR reduction performance, in this paper, a heuristic optimization method, i.e, the particle swarm optimization (PSO) in [20], is employed to optimize the CR to achieve more PAPR reduction.For convenience, we call it PSO based TKM-TR method.In PSO based TKM-TR method, first the particle swarm of CR are initialized as follows: q lower upper lower rand t Original Moore-Penrose [15] Least-Squares [15] Enhanced TKM-TR [19] TKM-TR [15] Improved TKM-TR TKM-TR+PSO Fig. 3. PAPR reduction comparison of different TR methods.
Figure 3 compares the PAPR reduction performance achieved by different TR methods.It is observed that the problem of peak regeneration is well addressed by the improved TKM-TR scheme, which achieves better PAPR reduction performance than the enhanced TKM-TR method [19].Additionally, the PSO based TKM-TR scheme obtains much better PAPR reduction performance when compared with the other TR methods and effectively addresses the problem of severe tailing caused by the peak regrowth.
In the following, the BER performance of the proposed schemes applied in DCO-OFDM system is evaluated.Without loss of generality, a simplified LED nonlinear model is employed in the DCO-OFDM system, in which the linear range of LED is [ ] 0, m A and the DC bias is 2 Figure 4 shows the BER performance achieved by different TR schemes in the additive white Gaussian noise (AWGN) channel with LED.Simulation results indicate that the improved TKM-TR scheme has the same BER performance as the TKM-TR scheme, but better than the enhanced TKM-TR method.In addition, the PSO based TKM-TR scheme obtains the best BER performance among the other TR methods, which is in accordance with the PAPR reduction results in Fig. 3.
to transmit the data symbols.The TR based time-domain OFDM signals are: -domain peak reduction signals.The frequency-domain peak reduction signals C are reserved on the PRT set, i.e., , , circularly shifting p to the right in accordance with the clipping noise positions S new time-domain peak reduction signals obtained by new β are expressed as: x and terminate.Otherwise, go to step 3.
If c generated by β cannot reduce the peak value, set the scaling factor corresponding to the minimum clipping noise to zero and update β .Otherwise, go to step 6. ≤ or iteration number is larger than K ,transmit x and terminate.Otherwise, go to step 3.