## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) has been successfully applied in many high data rate communication systems because of its attractive spectrum usage efficiency. Due to its benefits of wide available bandwidth, OFDM has been considered for optical communication systems. Optical OFDM can be used for short and long distance applications such as optical access networks, multimode fiber transmissions, free space optical systems, and indoor visible light communications [1; 2; 3; 4; 5]. In the broadcasting domain, the use of OFDM modulation facilitates the deployment of single frequency networks (SFN) in numerous broadcast systems such as digital radio monadie (DRM), digital video broadcasting-terrestrial-second generation (DVB-T2), DVB next-generation handheld (DVB-NGH) systems, integrated services digital broadcasting-terrestrial (ISDB-T) systems, and the advanced television systems committee (ATSC) 3.0 [6; 7; 8; 9; 10]. DVB-T2 was designed primarily to provide interactive content that requires high bandwidth, such as HDTV and 3D TV [11]. To support these requirements, the DVB-T2 standard has incorporated a widely used multiple-input single-output (MISO) antenna scheme [7]. The DVB-NGH system is the first broadcast standard to integrate a multiple-input multiple-output (MIMO) scheme in order to increase bandwidth efficiency without any need for extra wireless bandwidth [12]. Recently, ATSC 3.0 and ISDB-T have adopted MIMO to achieve higher throughput and increase coverage [13; 14]. Many studies have been carried out to improve MIMO configurations and transceivers in digital terrestrial broadcast systems [14; 15; 16]. Despite many advantageous features, the OFDM-based ATSC 3.0 system has a few key issues that have to be addressed. One of the biggest weaknesses of OFDM is its vulnerability to synchronization mismatches, including symbol timing offset (STO), carrier frequency offset (CFO), and sampling frequency offset (SFO) in a frequency-selective fading environment [17]. If these effects are not properly compensated, OFDM systems can suffer from severe inter-symbol interference (ISI) or inter-channel interference (ICI), which downgrades the performance of OFDM and MIMO-OFDM systems. To eliminate ICI and ISI effects, the receiver must first estimate the correct STO [18; 19]. Second, it is essential that the frequency offset on the OFDM block is estimated and corrected to remove ICI. In particular, the performance of OFDM receivers is greatly affected by SFO as the fast Fourier transform (FFT) size becomes larger [20], which usually occurs in a typical broadcast system. Therefore, the challenges in the MIMO-OFDM-based ATSC 3.0 system are its susceptibility to the frequency synchronization between the transmitter and the receiver. In order to help acquire synchronization, the ATSC 3.0 system provides several types of pilot symbols such as scattered pilots (SPs), edge pilots (EPs), continual pilots (CPs), and subframe boundary pilots (SBPs) [10]. The SPs, EPs, and SBPs are mainly dedicated to estimate the channel, whereas CPs are present to assist time and frequency estimation [21]. To maximize the advantages of MIMO-OFDM, it is therefore of crucial importance to accurately estimate the CFO and SFO [22; 23]. In the literature, a number of pilot-assisted approaches, from maximum likelihood estimation (MLE) to linear least-squares estimation (LSE) strategies [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35], have been presented to obtain accurate CFO and SFO estimates. The MLE is well known to be capable of achieving high accuracy in joint estimation of CFO and SFO, but its high complexity limits its practical use [22; 23; 24; 25]. To solve the complexity issue, a considerable amount of research has been devoted to the low complexity variants of joint MLE [26; 27; 28; 29; 30; 31; 32; 33; 34; 35].