# Pilot-Aided Frame Synchronization in Optical OFDM Systems
## 2 Frame Synchronization in a Pilot-Assisted Optical OFDM System  
Transmitted OFDM signals usually have preamble/header and payload. Thus, one approach used in categorizing synchronization methods in OFDM is based on the portion of the transmitted signal utilized for the purpose of symbol timing offset estimation at the receiver. The two broad classifications under this category are called blind and preamble-based techniques [5]. The blind techniques exploit the unique properties of the transmitted OFDM payload to perform synchronization. For instance, the blind technique in [8] leverages the time domain symmetry in ACO-OFDM to achieve symbol timing synchronization at the receiver. On the other hand, the preamble-based techniques involve the use of predefined synchronization sequence appended in the frequency or time domain. A preamble-based method in [5] utilizes the switching signs pattern of a time domain training sequence to perform synchronization in order to reduce the computational complexity in O-OFDM system. Another approach of categorizing the synchronization methods is based on the type of operationsperformed by the synchronization algorithm at the receiver. This category includes correlation and cross-correlation techniques. Cross-correlation methods require prior knowledge of the transmitted synchronization sequence at the receiver in order to make a comparison between such a sequence and the received signal [3]. The correlation methods simply perform synchronization by searching for a portion of the received signal that best satisfies specific criteria of the timing metric correlation term [6]. The vital criteria for preamble used for synchronization timing in O-OFDM include ability to generate the preamble using the same hardware utilized for the O-OFDM data symbols, ability to use the preamble for other signal detection stage like channel estimation and the preamble is expected to have low peak-to-average power ratio (PAPR) because of the performance degradation effects of high PAPR in O-OFDM. All these criteria are greatly influenced by the intended applications. The PA frame synchronization presented in this work is a correlation-based method that utilizes preamble called the pilot symbol. The PA frame has \(U\) clusters of data symbols, \(\mathbf{X}_{s}^{u}\), \(u=1,2,\ldots,U\) and randomly generated pilot sequence, \(\mathbf{X}_{p}\), as illustrated in Figure 1a,b for DCO-OFDM and ACO-OFDM respectively. The clusters of data symbols, \(\mathbf{X}_{s}^{u}\), are drawn from \(M\)-QAM (M-ary quadrature amplitude modulation) constellation. The pilot symbol in both cases is generated using the IFFT by modulating odd indexed subcarriers only while zeros are used on the even indexed subcarriers, that is, \(\mathbf{X}_{p}(i)=0\) for even \(i\) where \(i=0,1,\ldots,N-1\) and \(N\) is the IFFT size. The real-valued time domain signal required in the IM/DD optical communication system is obtained by constraining the frequency domain subcarriers of the PA frame to have Hermitian symmetry. For the purpose of PAPR reduction, the phase of the data symbols is rotated with \(R\) iterations of pilot symbol sequence. Thereafter, the IFFT output that gives the minimum PAPR value is selected for further processing. The PAPR reduction capability of the PA technique in O-OFDM with a complementary cumulative distribution function (CCDF) of \(10^{-3}\) and \(R=5\) is about 2.2 dB. The process of activating odd indexed subcarriers only of the pilot symbol in this work is similar to the concept outlined in [2], while a novel timing metric algorithm for the PA frame synchronization at the receiver is introduced.