# Pilot-Aided Frame Synchronization in Optical OFDM Systems
## 1 Introduction  
Synchronization at the receiver of a practical orthogonal frequency division multiplexing (OFDM) system design is one of the most crucial data detection stages that must be performed accurately in order to avoid system performance degradation due to symbol timing and carrier frequency offset [1]. A number of studies have been presented on synchronization techniques in both radio frequency OFDM (RF-OFDM) and optical OFDM (O-OFDM) systems [2, 3]. The RF-OFDM synchronization schemes include the well-known training symbol-based method proposed by [PERSON] and [PERSON] in [2]. The timing metric of this method has a form of plateau as a result of the cyclic prefix concatenated to the OFDM symbols, thereby making it difficult to detect the precise start of the training symbol at the receiver. To reduce this ambiguity, [PERSON] et al. proposed a synchronization timing metric which has an impulse-like shape with a principal peak indicating the start of the training symbol [4]. Synchronization methods in O-OFDM include the modified versions of the RF-OFDM techniques to make them applicable to optical communication systems and a number of techniques specially designed for O-OFDM [5, 6, 7, 8, 9]. In optical communication system based on intensity modulation and direct detection (IM/DD) scheme, carrier frequency offset is not an issue because the O-OFDM signal is baseband [10]. Hence, the synchronization problems in the IM/DD O-OFDM receivers are due to symbol frame timing offset and sampling clock frequency offset [10]. Sampling clock frequency offset may occur when there is a mismatch between the clock frequency of the digital-to-analog converter (DAC) at the transmitter and analog-to-digital converter (ADC) at the receiver. Precise O-OFDM framesynchronization is important to avoid the symbol timing offset that may occur when the start of the O-OFDM symbol detected at the receiver either leads or lags behind the original transmitted O-OFDM symbol. Hence, proper symbol synchronization is required before demodulation in order to align the fast Fourier transform (FFT) window at the correct position within the transmitted sequence of each received O-OFDM symbol samples. Our previous studies proposed and demonstrated the use of a pilot signal for peak-to-average power ratio (PAPR) reduction in pilot-assisted (PA) O-OFDM [11; 12]. The PA technique embeds the pilot signal in the original O-OFDM signal for the purpose of PAPR reduction at the transmitter. The PA technique is based on data symbol phase rotation with several iterations of a randomly generated pilot symbol sequence in the frequency domain prior to inverse fast Fourier transform (IFFT) operation to generate the time domain signal. The phase rotation makes the data symbols statistically quasi-independent in order to reduce the probability of having subcarriers adding up coherently to produce high peaks. Thereafter, the PA time domain O-OFDM frame with the pilot phase sequence that gives the minimum PAPR is selected for transmission. The empirical evaluation of the PA PAPR reduction technique in a real indoor optical wireless communication (OWC) channel also shows the usefulness of the transmitted pilot signal for channel estimation at the receiver [12]. Furthermore, full use can still be made of the transmitted pilot symbol by utilizing it for symbol synchronization at the PA O-OFDM receiver. In this paper, we present a frame synchronization technique in the PA O-OFDM system. The PA O-OFDM frame consists of data and pilot symbols where a cluster of \(U\) complex data symbols is allocated to subcarriers using the direct-current biased O-OFDM (DCO-OFDM) or asymmetrically clipped O-OFDM (ACO-OFDM) scheme. However, the randomly generated pilot sequence is allocated to odd indexed subcarriers only while even indexed subcarriers are set to zero in both schemes.