# A Novel Data-Aided Frame Synchronization Method Based on Hough Transform for Optical Communications
## 1 Introduction  
In optical communication systems, frame synchronization is indispensable to subsequent signal processing, such as error correction and information extraction [1, 2]. It can be considered as a type of reverse engineering problem in the field of information theory, which has received increased attention over the past few decades [3]. There are mainly two categories of frame synchronization techniques: data-aided frame synchronization and code-aided frame synchronization. For the former, synchronization is attained through recognizing the synchronization word, while for the latter, synchronization is achieved through exploiting the properties of error correction code. In cooperative communications, data-aided frame synchronization is commonly applied, and there are two main types of methods, correlation rule and maximum-likelihood (ML) rule [4]. In 1953, [PERSON] first proposed a correlation-based recognizer to detect the given frame synchronization sequence in received bit stream [5]. This method is simple to implement, but it has a poor performance and a narrow application scope. Some improved schemes have also been put forward in succession, such as double correlation [6, 7], which is robust to carrier frequency and phase errors. A method based on the ML rule for frame synchronization was first proposed by [PERSON] in 1972 over additive white Gaussian noise (AWGN) channel [8], and he concluded that ML-based detection has a better performance than traditional correlation detection. The conclusion was subsequently confirmed in the environmentof high SNR by [PERSON] [9], and was further extended to the M-ary phase shift keying modulation by [PERSON] and [PERSON] [10]. Later, ML-based frame synchronization algorithms for flat fading channels and frequency-selective channels were proposed successively [11; 12; 13]. In addition to the correlation and ML rule, some other schemes have also been offered in recent years. [PERSON] and [PERSON] applied the likelihood ratio test (LRT) in the hypothesis test theory to frame synchronization detection [14; 15; 16], and their method performs better than correlation in AWGN channels. [PERSON] exploited post-detection integration (PDI) to provide coarse frame alignment with limited complexity with respect to ML solutions [17]. More recently, another novel algorithm called balanced generalized PDI (B-GPDI), which combines the ML rule and PDI for synchronization detection, was reported in [18]. In non-cooperative communications, a synchronization word needs to be recognized blindly for data-aided frame synchronization. [PERSON] proposed a blind recognition algorithm based on the peak characteristic of the partial third-order correlation function for the synchronization word being m-sequence [19]. A joint recognition algorithm based on correlation filtering and Hadamard transform is proposed in [20], and it performs well with a high bit error rate. [PERSON] used the auto-correlation function to blindly recover the synchronization word and frame length in a satellite system, and proposed another two algorithms based on hardware equipment, in case auto-correlation cannot determine the exact frame length [21]. The blind recognition algorithm of the synchronization word based on soft-decision for QPSK signals was proposed in [22], and it can clearly enhance the accuracy of blind recognition. [PERSON] proposed a cumulative filtering algorithm to identify the frame header [23], but it is difficult to determine the decision threshold with a complex frame structure or uncertain synchronization word length. To resolve this issue, an improved algorithm based on autocorrelation (AC) was proposed by [PERSON] [24]. Peak-to-average ratio (PAR) is calculated in his algorithm to overcome high bit-error-rate (BER). In recent years, code-aided frame synchronization has received considerable attention, due to the advantages of saving bandwidth and high spectral efficiency [25; 26; 27; 28].