## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) is an effective modulation technique for high-speed data communication due to its high spectral efficiency and robustness to channel distortions. Due to its its attractive features, OFDM has been the dominant technology in a number of wireless transmission standards such as Digital Video Broadcasting-Terrestrial-Second Generation (DVB-T2), Long-Term Evolution (LTE) and wireless local area networks (WLAN) [1; 2; 3]. Recently, OFDM has attracted much attention for Visible Light Communication (VLC) systems. The wavelength division multiplexing (WDM) scheme is widely used in VLC systems to increase the transmission rate [4; 5; 6; 7]. Furthermore, OFDM has been considered for many cable communication standards such as HomePlug AV, IEEE1901 and a second generation digital transmission system for cable systems (DVB-C2) [8; 9; 10]. DVB-C2 has been designed for innovative multimedia services that require a high bandwidth, such as high definition television (HDTV) and 3D-TV [10]. In DVB-C2, high-speed cable transmission has been obtained using low density parity check (LDPC)-coded OFDM along with higher quadrature amplitude modulation (QAM) [11; 12]. As proven in many wireless transmission systems, substantial advances have been made in the field of OFDM-based cable communications thanks to its ability to not only achieve high spectral efficiency, but also provide better immunity to channel impairments [13]. However, OFDM is vulnerable to receiver synchronization imperfections such as carrier frequency offset (CFO) and sampling frequency offset (SFO) [14; 15; 16]. The CFO and SFO give rise to inter-symbol interference (ISI) and inter-carrier interference (ICI), which lead to the loss of orthogonality and have a harmful effect on the system performance. If not compensated accurately, they can limit the performance of an OFDM system. Hence, it is of primary interest to keep the orthogonality between the transmitter and receiver in the DVB-C2 system [11; 12]. A number of pilot-assisted estimation methods have been presented to obtain accurate CFO and SFO estimates in the literature, from maximum likelihood estimation (MLE) to least-squares estimation (LSE) strategies [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. Although the MLE is known to provide the optimal estimate of CFO and SFO, its complexity tends to be prohibitively expensive to be applied to practical systems [17; 18; 19; 20]. In order to account for this issue, its low-complexity versions have been investigated in many works [21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. In [21; 22; 23; 24; 25], the joint CFO and SFO estimation scheme was presented, observing the phase difference between two pilots located in consecutive OFDM symbols based on a decision-directed estimation or linear LSE (LLSE). In [26; 27; 28], a weighted least-squares estimation (WLSE) technique has been suggested using the frequency-domain channel estimate to enhance the estimation performance. In [29; 30], a low-complexity CFO and SFO estimation method was proposed in a decoupled fashion, which still may impose severe computational demands in real-time implementation. Hence, accurate and computationally-efficient frequency-offset estimation is a crucial challenge in realizing high-performance OFDM receivers. To address this issue, this paper proposes a reduced-complexity and accurate CFO and SFO estimation scheme in the DVB-C2 OFDM system using continual pilots (CPs) for synchronization. To avoid bias from non-symmetrically-distributed CPs, we adopt the LSE strategy, which performs the frequency-offset estimation on a block-by-block basis. For this purpose, \(N_{b}\) observation symbols are divided into two successive correlation blocks with sizes \(N_{a}\) and \(N_{b}-N_{a}\). The received CP symbols within each correlation block are sequentially summed, and the result is conjugated.