Optical Orthogonal Frequency Division Multiplexing Schemes Research Articles

Distortion-Elimination Hybrid OFDM With Low Complexity for Optical Wireless Communications

In optical wireless communications (OWC), hybrid optical orthogonal frequency division multiplexing (O-OFDM) schemes, such as hybrid asymmetrically clipped O-OFDM (HACO-OFDM) and layered asymmetrically clipped O-OFDM (LACO-OFDM), enjoy both high power and spectral efficiency. However, due to the non-orthogonal transmission of signal components induced by the clipping distortion, successive interference cancellation (SIC) is required in these hybrid O-OFDM schemes, leading to notably increased complexity. In this paper, we conceive novel hybrid O-OFDM schemes to offer both high spectral and power efficiency, whilst possessing low complexity. By elaborately designing a time-domain (TD) distortion elimination methodology at the transmitter, a novel distortion-elimination hybrid O-OFDM (DEHO-OFDM) is first proposed, which combines asymmetrically clipped O-OFDM (ACO-OFDM) and pulse-amplitude-modulated discrete multitone (PAM-DMT) in an interference-free manner. In order to further improve the spectral efficiency, an enhance DEHO-OFDM (EDEHO-OFDM) is designed by activating the remaining subcarrier resources. Both DEHO-OFDM and EDEHO-OFDM can be realized through a single-IFFT transmitter and standard OFDM receiver, leading to much lower complexity than the existing hybrid O-OFDM schemes. Simulation results have demonstrated the superiorities of the proposed schemes over HACO-OFDM and LACO-OFDM in terms of peak-to-average-power ratio (PAPR) and bit error rate (BER).

Improved Receivers for Optical Wireless OFDM: An Information Theoretic Perspective

We consider performance enhancement of asymmetrically-clipped optical orthogonal frequency division multiplexing (ACO-OFDM) and related optical OFDM schemes, which are variations of OFDM in intensity-modulated optical wireless communications. Unlike most existing studies on specific designs of improved receivers, this paper investigates information theoretic limits of all possible receivers. For independent and identically distributed (IID) complex Gaussian inputs, we obtain an exact characterization of information rate of ACO-OFDM with improved receivers for all SNRs. It is proved that the high-SNR gain of improved receivers asymptotically achieve 1/4 bits per channel use, which is equivalent to 3 dB in electrical SNR or 1.5 dB in optical SNR; as the SNR decreases, the maximum achievable SNR gain of improved receivers decreases monotonically to a non-zero low-SNR limit, corresponding to an information rate gain of 36.3%. For practically used constellations, we derive an upper bound on the gain of improved receivers. Numerical results demonstrate that the upper bound can be approached to within 1 dB in optical SNR by combining existing improved receivers and coded modulation. We also show that our information theoretic analyses can be extended to Flip-OFDM and PAM-DMT. Our results imply that, for the considered schemes, improved receivers may reduce the gap to channel capacity significantly at low-to-moderate SNR.

Signal clipping at transmitter and receiver of O-OFDM for VLC under optical power constraint

Visible light communications (VLC) is considered as an effective supplement technology for next-generation (6G) communications due to its abundant spectrum, high power efficiency and easy deployment. Optical orthogonal frequency division multiplexing (O-OFDM) is a common technology to obtain further promotion. In this paper, two typical O-OFDM schemes direct current biased O-OFDM (DCO-OFDM) and asymmetrically clipped O-OFDM (ACO-OFDM) are analyzed in terms of signal clipping at both transmitter and receiver under the constraints of maximum optical power and non-negative optical power. And effective electrical SNR models after signal clipping are proposed and verified by link simulation. Then a noise cancellation scheme is proposed based on received signal clipping and is proved to bring a significant gain for ACO-OFDM. By system simulation, we find that under a certain optical power limitation, most users can achieve above 4Gbps in indoor scenario when modulation bandwidth of the light emit diode (LED) or laser diode (LD) is 1GHz. Therefore, it can be expected that the throughput could reach tens Gbps when the LED/LD modulation bandwidth is increased and multiple LEDs/LDs are deployed.

Machine-Learning-Aided Optical OFDM for Intensity Modulated Direct Detection

End-to-end learning systems are conceived for Orthogonal Frequency Division Multiplexing (OFDM)-aided optical Intensity Modulation paired with Direct Detection (IM/DD) communications relying on the Autoencoder (AE) architecture in deep learning. We first propose an AE-aided Layered ACO-OFDM (LACO-OFDM) scheme, termed as LACONet, for exploiting the increased bandwidth efficiency of LACO-OFDM. LACONet employs a Neural Network (NN) at the transmitter for bit-to-symbol mapping, and another NN at the receiver for recovering the data bits, which together form an AE and can be trained in an end-to-end manner for simultaneously minimizing both the BER and PAPR. Moreover, the detection architecture of LACONet is drastically simplified compared to classical LACO-OFDM, since the Fast Fourier Transform (FFT) operation is applied only once at the receiver. We further propose a generalized AE-aided optical OFDM scheme for IM/DD communications, termed as IMDD-OFDMNet, where the unipolarity of the Time Domain (TD) signal is no longer guaranteed by the Hermitian Symmetry, but rather by taking the absolute square value of the complex TD signal. As such, all available subcarriers of IMDD-OFDMNet are used for carrying useful information, hence it has a higher throughput than the LACO-based schemes. As a further benefit, its transceiver requires only a single Inverse FFT or FFT. Finally, simulation results are provided to show that our learning schemes achieve better BER and PAPR performance than their conventional counterparts.

Deep Learning-Aided Optical IM/DD OFDM Approaches the Throughput of RF-OFDM

Deep learning-aided optical orthogonal frequency division multiplexing (O-OFDM) is proposed for intensity modulated direct detection transmissions, which is termed as O-OFDMNet. In particular, O-OFDMNet employs deep neural networks (DNNs) for converting a complex-valued signal into a non-negative signal in the time-domain at the transmitter and vice versa at the receiver. The associated frequency-domain signal processing remains the same as in conventional radio frequency (RF) OFDM. As a result, our scheme achieves the same spectral efficiency as the RF scheme, which has never been attained by the existing O-OFDM schemes, because they have relied on the Hermitian symmetry of the spectral-domain signal to guarantee that the time-domain signal becomes real-valued. We show that O-OFDMNet can be viewed as an autoencoder architecture, which can be trained in an end-to-end manner in order to simultaneously improve both the bit error ratio (BER) and the peak-to-average power ratio (PAPR) for transmission over both additive white Gaussian noise and frequency-selective channels. Furthermore, we intrinsically integrate a soft-decision aided channel decoder with our O-OFDMNet and investigate its coded performance relying on both convolutional and polar codes. The simulation results show that our scheme improves both the uncoded and coded BER as well as a reducing the PAPR compared to the benchmarks at the cost of a moderate additional DNN complexity. Furthermore, our scheme is capable of approaching the throughput of RF-OFDM, which is notably higher than that of conventional O-OFDM. Finally, our complexity analysis shows that O-OFDMNet is suitable for real-time operation.

Hybrid Adaptive Bias OFDM-Based IM/DD Visible Light Communication System

Conventional optical orthogonal frequency division multiplexing (OFDM) schemes, such as adaptively biased optical OFDM (ABO-OFDM) and hybrid asymmetrically clipped optical OFDM (HACO-OFDM), are unable to tap all the resources of the subcarriers and only achieve relatively high power efficiency. In this paper, a hybrid adaptive bias optical OFDM (HABO-OFDM) scheme for visible light communication (VLC) is proposed to improve spectral efficiency and power efficiency. In the proposed HABO-OFDM scheme, different optical OFDM components are combined for transmission at the same time, and the adaptive bias is designed to ensure the non-negativity, as well as obtaining significantly high power efficiency. Meanwhile, the implementation complexity of the HABO-OFDM receiver is notably lower than the conventional superimposed optical OFDM schemes. Simulation results show that the proposed HABO-OFDM scheme outperforms ABO-OFDM and HACO-OFDM in terms of both peak-to-average-power ratio (PAPR) and power efficiency. The PAPR performance of HABO-OFDM is about 3.2 dB lower than that of HACO-OFDM and 1.7 dB lower than that of ABO-OFDM. Moreover, we can see that the Eb(elec)/N0 required for HABO-OFDM to reach the BER target is lower than the other two schemes at the Bit rate/Normalized bandwidth range of 3.5 to 8.75, which means that the power efficiency of HABO-OFDM is higher in this range.

Performance enhancement for visible light communication based ADO-OFDM

The increasing demand for bandwidth through modern applications and multimedia services has led to high-speed wireless communications. Optical wireless communications (OWC) encourages solutions that provide a higher data rate due to the large bandwidth available. In this paper, performance enhancement approaches are studied and simulated for visible light communication (VLC) as a case study. The orthogonal frequency division multiplexing (OFDM) systems are used to investigate Intensity modulation/direct detection (IM/DD) to improve the performance of VLC. The IM/DD in OWC requires positive real OFDM symbols, so there are many approaches to satisfy this requirement. This paper proposes a model of Asymmetrically Clipped DC-Biased Optical (ADO-OFDM) to use in OWC/VLC environment. The proposed system has avoided the use of the noise cancellation technology that is used in traditional ADO-OFDM. The results show that the ADO-OFDM has the best spectral efficiency than DC-biased optical (DCO-OFDM) and Asymmetrically clipped optical (ACO-OFDM). Also, it has better optical efficiency than DCO-OFDM with the equally overall bit error rate (BER) at the same signal-to-noise ratio. Hamming channel coding/decoding with different code lengths is applied in various optical OFDM schemes for BER improvements. Furthermore, we simulate and analyze these optical OFDM systems with many modulation orders.

Joint Dimming Control and Optimal Power Allocation for THO-OFDM Visible Light Communications

Layered or hybrid optical orthogonal frequency division multiplexing (OFDM) has been proposed for use in optical communications due to its excellent spectral and power efficiencies, especially in visible light communications (VLC). However, most of the current works concentrate on transmitter and receiver design as well as the quality of service in communication networks. In this paper, we propose a spectrum-efficient dimmable triple-layer hybrid optical OFDM (DTH-OFDM) scheme to tackle the illumination requirements, considering different practical indoor VLC scenarios from low illumination to high illumination intensities. In the proposed DTH-OFDM scheme, the required dimming level is achieved by jointly adjusting the dimming factors and direct current bias. We investigate the comprehensive performance analysis of the proposed DTH-OFDM in detail, including probability density function, bit error rate (BER), spectral and energy efficiencies. In addition, a joint dimming control and optimal power allocation problem for DTH-OFDM is formulated and solved using convex optimization under the constraints of light emitting diode (LED) nonlinearity, dimming target and communications reliability. Numerical results show that, the proposed DTH-OFDM can offer continuous and arbitrary dimming target with higher spectral efficiency and lower BER compared with its counterparts, as well as an enhanced tolerance to the LED nonlinearity.

The Evolution of Optical OFDM

Optical Orthogonal Frequency-Division Multiplexing (O-OFDM) is eminently suitable for mitigating the multi-path and chromatic dispersion in both Visible Light Communications (VLC) and Optical Fiber Communications. We commence our discourse by surveying the conception and historic evolution of O-OFDM designed for both VLC and optical fiber, culminating in the birth of its most flexible design alternative, namely Layered Asymmetrically Clipped Optical OFDM (LACO-OFDM). We demonstrate that it is eminently suitable for intensity-modulation and direct-detection aided optical communication systems and characterize its design flexibility. It is also shown that given its flexibility, it subsumes a wide range of optical OFDM schemes conceived over the past two decades or so. The LACO-OFDM transmitter and receiver designs strike a compelling compromise between the features of the popular Asymmetrically Clipped Optical OFDM (ACO-OFDM) and Direct-Current-biased Optical OFDM (DCO-OFDM). The pivotal role of forward error correction designs is also surveyed with the objective of striking a coding gain versus complexity trade-off. We conclude by highlighting a suite of promising techniques capable of further improving the system performance, but require further research. The take-away message of the paper crystallized in the associated design guidelines.

Enhanced Optical OFDM/OQAM for Visible Light Communication Systems

Orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) has the advantage of high spectral efficiency due to non-requirement of cyclic prefix (CP) and guard band. However, the high direct current (DC) used in OFDM/OQAM is power inefficient for visible light communication (VLC). In this letter, an enhanced OFDM/OQAM (EO-OFDM/OQAM) scheme is proposed for VLC, which is inspired by the idea of the pulse-amplitude-modulation based hybrid optical OFDM (PHO-OFDM) scheme. In this system, the half of subcarriers of the normal branch carry useful data while the remaining subcarriers are selected to carry negative clipping noise instead of useful data for improving the power efficiency, and a flexible power allocation method is introduced. The simulation results show that compared with the PHO-OFDM, the proposed scheme has a better bit error rate (BER) performance under the same average bit rate without additional operations of interference regeneration and cancellation.

Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links.

Underwater optical wireless systems have dual requirements of high data rates and long ranges in harsh scattering and attenuation conditions. In this paper, we investigate the advantages and limitations of optical orthogonal frequency-division multiplexing (O-OFDM) signaling when a silicon photo-multiplier (SiPM) is used at the receiver in order to ensure high sensitivity. Considering a light-emitting diode (LED) transmitter and taking into account the limited dynamic range imposed by the transmitter and the SiPM receiver, we study the performance of three popular O-OFDM schemes, i.e., DC-biased, asymmetrically-clipped, and layered asymmetrically-clipped O-OFDM (DCO-, ACO-, and LACO-OFDM, respectively). We consider a constraint on transmit electrical power and take into account the required DC bias for the three considered schemes in practice, showing the undeniable advantage of ACO- and LACO-OFDM in terms of energy efficiency. For instance, for the considered SiPM and LED components, a spectral efficiency of ∼1 bps/Hz with a data rate of 20 Mbps, a link range of 70 m, and a target bit-error-rate (BER) of , ACO and LACO allow a reduction of about 10 and 6 mW, respectively, in the required , compared to DCO-OFDM. Meanwhile, we show that when relaxing the constraint, DCO-OFDM offers the largest operational link range within which a target BER can be achieved. For instance, for a target BER of and a data rate of 20 Mbps, and considering of 185, 80, and 50 mW for DCO-, LACO-, and ACO-OFDM, respectively, the corresponding intervals of operational link range are about 81, , and m. Lastly, we show that LACO-OFDM makes a good compromise between energy efficiency and operational range flexibility, although requiring a higher computational complexity and imposing a longer latency at the receiver.

Unipolar-pulse amplitude modulation frequency division multiplexing for visible light communication systems

Asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) has been proposed in visible light communication (VLC) systems to overcome the dc-biased optical OFDM power consumption issue at the cost of the available electrical spectral efficiency. Due to the implementation of inverse fast Fourier transform, all the optical OFDM schemes including ACO-OFDM suffer from large peak-to-average power ratio (PAPR), which degrades the performance in VLC systems as the light-emitting diodes used as the transmitter have a limited optical power-current linear range. To address the PAPR issue in ACO-OFDM, we introduce a unipolar-pulse amplitude modulation frequency division multiplexing by adopting the single carrier frequency division multiple access (SC-FDMA). This is achieved by considering a PAM as an SC-FDMA data symbol and inserting a conjugate copy of the middle and first SC-FDMA FFT output subcarriers after the middle and last subcarriers, respectively. Simulation results show that, for the proposed scheme, the PAPR is 3.6 dB lower compared with ACO-OFDM. The PAPR improvement is further analyzed with the simulation results demonstrating that the proposed scheme offers 2.5 dB more average transmitted power compared to ACO-OFDM.

High-speed multi-layer coded adaptive LACO-OFDM and its experimental verification

In this work, we review the proposition and development history of intensity modulation and direct detection optical orthogonal frequency division multiplexing (OOFDM), as well as of its evolved versions, the layered asymmetrically clipped OOFDM (LACO-OFDM) scheme. We conceive and characterize the first experimental demonstration of a LACO-OFDM link relying on sophisticated adaptive bit-loading. The transmission scheme can be adopted for the development of low-cost high speed unrepeatered optical connections. Unrepeatered and uncompensated transmission tests over single mode fiber (0-20 km) are reported, achieving transmission rates up to 72 Gb/s. Moreover, we characterize both uncoded and channel coded waveforms, using a multi-class coding scheme, which has specifically been developed to benefit from the layered structure of LACO-OFDM.

A Novel Transceiver Model for Polar Transform Optical (PTO --) OFDM for V isible L ight C ommunication (VLC) Based on Peak to Average Power Ratio Reduction u sing Precoding

Indoor visible light communication (VLC) has the potential of providing high data rates for short-range wireless communication with a relative spatial elevated security in contrast to a radiofrequency wireless one. To support that high data stream, Orthogonal Frequency Division Multiplexing (OFDM) is used; however, due to the limited operational bandwidth of the commercial white light-emitting diode (LED), signal processing techniques are used to increase the efficiency of the OFDM and to adapt OFDM to VLC systems. As a major concern, the intensity modulation direct detection necessary for VLC requires positive real signal, this is dealt with by imposing Hermitian pre-possessing or Cartesian to polar conversion post-processing to the OFDM. The use of the Cartesian to polar converter allows the transmission of complex OFDM symbols through the intensity modulation channel. A polar transform optical (PTO-) OFDM presented here as an improvement and simplification of previous polar optical OFDM schemes gives an efficient transceiver architecture. Nevertheless, both OFDM transmission techniques for Visible optical links, similar to radiofrequency (RF), suffer greatly from irregular excessive Peak-to-Average power ratio (PAPR). Higher PAPR reduces the power efficiency of the On-Off Keying (OOK) based on pulse amplitude modulation (PAM). Furthermore, it also is recommendable to reduce the PAPR for conformity with eye safety. A precoding technique is proposed to reduce the PAPR of intensity-modulated for direct detectability of the OFDM signal destined for the wireless optical link using Cartesian-to-Polar conversion. Based on the enhanced processing at the front ends and using MATLAB simulation, it is proven that the presented model can improve the link parameters including the bit error rate (BER) and signal to noise ratio (SNR) and bandwidth efficient compared to Hermitian modified ones.

Residual Clipping Noise in Multi-Layer Optical OFDM: Modeling, Analysis, and Applications

Optical orthogonal frequency division multiplexing (O-OFDM) schemes are variations of OFDM schemes that produce non-negative signals. Asymmetrically-clipped O-OFDM (ACO-OFDM) is a single-layer O-OFDM scheme, whose spectral efficiency can be enhanced by adopting multiple ACO-OFDM layers or a combination of ACO-OFDM and other O-OFDM schemes. However, since symbol detection in such enhanced ACO-OFDM (eACO-OFDM) is done iteratively, erroneous detection leads to residual clipping noise (RCN) which can degrade performance in practice. Thus, it is necessary to develop an accurate model for RCN in designing RCN-aware eACO-OFDM schemes. To this end, this paper provides a mathematical analysis of RCN leading to an accurate model of RCN power. The obtained model is used to analyse the performance of various eACO-OFDM schemes. It is shown that the model provides an accurate evaluation of symbol error rate (SER), which would be underestimated if RCN is ignored. Moreover, the model is shown to be useful for designing an RCN-aware resource allocation that increases the robustness of the system in terms of meeting a target SER, compared to an RCN-unaware design.

Spectrum-efficient hybrid PAM-DMT for intensity-modulated optical wireless communication.

In optical wireless communication (OWC), the superimposed optical orthogonal frequency division multiplexing (O-OFDM), such as layered asymmetrically clipped O-OFDM (LACO-OFDM), can improve spectrum efficiency by appropriately combining multiple O-OFDM signals for simultaneous transmission. However, it suffers from increased receiver complexity and latency. Therefore, a novel architecture of hybrid pulse-amplitude-modulated discrete multitone modulation (HPAM-DMT) is proposed in this paper to support a spectrum-efficiency OWC link. In HPAM-DMT, a PAM-DMT signal is carefully designed by using the real parts of subcarriers and is then superimposed on the classic PAM-DMT signal for simultaneous transmission, which fully exploits the spectrum in terms of subcarriers. Moreover, thanks to the well-designed aritecture of the two superimposed PAM-DMT signals, the proposed HPAM-DMT achieves the same spectrum efficiency as the LACO-OFDM, with much lower complexity and latency. Notable improvement of the bit-error rate (BER) performance is observed for the proposed HPAM-DMT compared to LACO-OFDM under the corruption of the transmitter nonlinearity. Moreover, HPAM-DMT achieves a relatively higher power efficiency than conventional O-OFDM schemes, which makes it a competitive O-OFDM scheme for IM/DD-based OWC.

PWM‐based dimmable hybrid optical OFDM for visible‐light communications

In visible-light communication (VLC) system, hybrid asymmetrically clipped optical orthogonal frequency division multiplexing (HACO-OFDM) is an attractive multi-carrier modulation to achieve high power and spectrum efficiency. Dimming control is deemed to be an essential technique in VLC since it can meet diverse luminance demands. However, severe non-linear distortion occurs when dimming the HACO-OFDM VLC system, especially with the pulse-width modulation (PWM) dimming technique. In this work, a novel PWM-based dimmable hybrid optical OFDM (DHO-OFDM) scheme is proposed to simultaneously support different illumination requirements and realise a spectral-efficient VLC link. The transmitted symbols in the authors' proposed DHO-OFDM can be readily estimated by the standard HACO-OFDM receiver without requiring the additional detecting the PWM signal, thus reducing the receiver complexity compared to the other PWM-based dimmable schemes. Moreover, the proposed DHO-OFDM scheme can support a broad dimming range with a relatively stable communication performance, which makes it more suitable for broadband data transmission. Numerical results have verified the superiorities of DHO-OFDM over the conventional OFDM schemes in terms of achievable spectral efficiency and bit-error rate.

Triple-layer hybrid optical OFDM scheme for passive optical network

Orthogonal frequency division multiplexing (OFDM) based on intensity modulation and direct detection (IM/DD) is a promising candidate for future passive optical network (PON). As the IM/DD system requires the output to be unipolar, a direct current (DC) is required but with a reduced energy efficiency. Asymmetrically clipped optical OFDM (ACO-OFDM) has been proposed to improve the energy efficiency at the cost of a lower spectral efficiency. With infinite layers’ superimposition, layered ACO-OFDM (LACO-OFDM) can significantly improve the spectral efficiency while the computation complexity is very high. In this paper, we propose a triple-layer hybrid optical OFDM (THO-OFDM) scheme for PON, which combines N-point ACO-OFDM, N/2-point ACO-OFDM and N/2-point PAM-DMT signals for simultaneously transmission. Compared with LACO-OFDM, the proposed THO-OFDM offers better spectral and energy efficiency, reduced peak-to-average power ratio and computation complexity. The simulation results show that the transmitted THO-OFDM-PON can attain a ∼1.2 dB power gain compared with the LACO-OFDM-PON over 20 km fiber link.

A PAPR reduction scheme combining superimposed O-OFDM and [formula omitted]-law mapping for VLC-OFDM systems

Due to the high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals, the inherent nonlinearity of light emitting diodes (LEDs) is a challenge for optical OFDM (O-OFDM) schemes in visible light communication (VLC) systems. In order to reduce PAPR to mitigate the effects of the nonlinearity of LEDs, and avoid the asymmetric clipping interference in the conventional hybrid O-OFDM schemes, a novel superimposed O-OFDM scheme is proposed in this paper, which reduce the PAPR by combining the μ-law mapping and the superposition modulation. Moreover, at the transmitter, the hybrid O-OFDM components are superimposed in an interference-free way, the receiver does not require the operation of interference cancellation, and the symbols of each branch can be demodulated independently. Simulation results verify that the proposed scheme can significantly reduce the PAPR. At the same time, the comprehensive performance of the proposed scheme outperforms other competing schemes under the constraints of the nonlinearity and limited dynamic range of LEDs.

Adaptive Power Allocation for Distortion Minimization in Generalized Polar Optical Wireless Communications

In this paper, we investigate adaptive power allocation for generalized polar optical wireless communications (OWC), where a general complex bipolar signal is converted into magnitude and phase signals for intensity modulation. Mean square errors (MSE) between the input complex signals and the re-constructed complex signals are derived to characterize signal distortion. Optimal power scaling factors and power allocation are investigated to minimize the distortion. Under a sole average intensity constraint, closed-form optimal power scaling factors are derived and found to be input-dependent. Specifically, they are determined by the first and second moments of the magnitude signals, the first moment of the phase signals as well as the channel state. Under both average and peak intensity constraints, the expression of MSE regarding the power scaling factors is derived but it is too complicated to find the optimal power allocation. Thus, we propose to use a small-scale numerical search for practical power allocation. As an example, we adopt the proposed power allocation to polar optical orthogonal frequency division multiplexing (P-OFDM) systems and analyze its achievable bit error rate (BER). Numerical simulations are presented to validate the analysis. It is shown that the proposed power allocation greatly improves the performance in terms of MSE and BER and the proposed power allocation-enhanced P-OFDM (EP-OFDM) outperforms existing optical OFDM schemes over various channels in the high signal-to-noise ratio (SNR) regime, especially in the systems with a peak intensity constraint.