## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) is regarded as a promising modulation candidate for optical wireless communication (OWC) and polymer optical fiber (POF) as it provides a high data rate, high spectral efficiency, and high tolerance to multi-path interference [1; 2]. A baseband OFDM with Hermitian symmetry property, as in [3; 4], is also called discrete multi-tone (DMT). For simple and low cost consideration, the DMT can be employed in optical communications using the intensity modulation with direct detection (IM/DD) technique and bit-loading algorithm to maximize the system capacity [4; 5; 6]. However, the DMT suffers from a high peak-to-average power ratio (PAPR) and is more susceptible to nonlinear distortions. Since the light-emitting diode (LED) has a limited linear dynamic range, the DMT signals with high PAPRs drive the LED at the transmitter to saturation, producing a greater number of nonlinear distortions and degrading the overall system performance [7; 8; 9]. Therefore, the PAPR of the DMT should be reduced so that the LED can operate linearly and power efficiently [10]. Several PAPR reduction techniques have been proposed for wireless communication systems [11; 12; 13; 14; 15; 16; 17; 18]. In general, these techniques can be broadly categorized into signal distortion, distortionless, and coding schemes. Clipping, filtering and companding are well-known varieties of signal distortion schemes that directly limit the peak envelope of the transmitting signals to a desired value [13; 14; 15]. However, these signal processing schemes result in both in-band distortion and out-of-band high frequency components, which further degrades the bit error rate (BER) performance and reduces the spectral efficiency. Selective mapping (SLM), and partial transmit sequence (PTS) are typical distortionless schemes [16; 17; 18] that improve the PAPR distribution statistically and provide pretty good PAPR performance. However, they all have very high computational complexities and require the receivers to know the side information to retrieve the original data blocks. In addition, it is complicated to design the phase vectors for both SLM and PTSs. The coding changes their original codewords to reduce their PAPRs with high operational complexities. Tone reservation and tone injection are effective approaches to mitigate the PAPR problem [11]. However, due to their computational complexity, the challenge is to find the optimal subset and it becomes intractable for OFDM systems with a large number of subcarriers. In addition, the transmission rate is also degraded. Schemes such as active constellation extension introduce redundancy as well [12]. In particular, these methods used in radio wireless communication cannot be directly adopted in optical systems because of the real value property in IM/DD implementation. In contrast, discrete Fourier transform spreading (DFT-S) is an efficient method of reducing the PAPR without causing any distortion noise [8]. Nevertheless, DFT-S-DMT still exhibits a high PAPR because of the Hermitian symmetry requirement of the IM/DD channel. In addition, each subcarrier of DFT-S-DMT obtains the same signal-to-noise ratio (SNR) after the equalization and dispreading procedure, indicating that it is unsuited to apply the bit-loading with DFT-S-DMT in the frequency selective channel to achieve overall system capacity. Moreover, DFT-S-DMT is extremely sensitive to LED nonlinearity, which limits its practical applications. The discrete Hartley transform (DHT)-spread approach exhibits a lower PAPR compared to DFT-spread techniques. However, it is only applicable to real constellations such as pulse amplitude modulation (PAM) and the PAPR reduction capability decreases with an increase in size of the PAM alphabet. In this paper, an efficient low-complexity PAPR reduction scheme combining both multi-band (MB)-Hadamard precoding and clipping is proposed in DMT systems.