## 1 Introduction  
Power line communication (PLC) technology has received significant attention as a highly competitive candidate for smart grid applications since the PLC infrastructure is already widely deployed and the use of the power line network for communication purposes does not demand any extra cost. Due to the rapid development of communication technology, the power line network is fully considered as high-speed data communication [1]. Though the high data rates are being achieved using other data networks, PLC network offers many attractive benefits of cost-effective access network installation using the pre-deployed electrical network infrastructure by which the network coverage can be widely extended to the remote areas. Recently, there is a trend towards deploying power lines as physical medium for data communication, which eliminates the need for dedicated communication links [2; 3]. Since the power line network is not designed for data communication, PLC technology has some problems such as cable attenuation, narrowband interference, frequency-selective fading, and dynamic impedance across the network [4; 5; 6; 7]. Orthogonal frequency division multiplexing (OFDM) has been widely used as a key transmission technology for narrowband and broadband communication over power lines. Recently, OFDM has been adopted by many industrial associations such as the high-definition power line communication (HD-PLC) alliance [8], the HomePlug powerline alliance (HPA) [9], and the universal powerline association (UPA) [10]. Among them, HomePlug Green PHY (HomePlug GP) is a new PLC technology for smart grid applications [11]. HomePlug GP is a low-rate version of the HomePlug AV standard with an emphasis on a robust communication, which is achieved by utilizing exclusively QPSK modulation and adopting robust OFDM (ROBO) modes. Specifically, ROBO mode is a form of repetition code and its throughput relies on the degree to which coding is repeated across streams. As in other communication systems, OFDM has been employed to effectively address the hardness of PLC channels because of its capability to mitigate frequency selectivity of the channel and to notch segment of the transmitted spectrum [12; 13]. However, a potential drawback of OFDM is also inherent in the PLC applications. A widely known problem of OFDM is its vulnerability of the receiver to oscillator instabilities such as carrier frequency offset (CFO) and sampling frequency offset (SFO). Both CFO and SFO bring about inter-carrier interference (ICI) and inter-symbol interference (ISI), which may severely deteriorate system performance [14; 15]. Therefore, it is crucial to keep the synchronization between the transmitter and the receiver. The frequency synchronization can be performed either by the use of pilot symbols or in a blind way [16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Although maximum likelihood estimation (MLE) is known to provide optimal estimates of CFO and SFO, its complexity tends to be prohibitively expensive for use in practical systems [16; 17; 18; 19]. In order to account for this issue, its low complexity versions have been investigated in many literature [20; 21; 22]. Commonly used synchronization algorithms take advantage of repetitive patterns of pilot symbols to estimate CFO and SFO [16; 17; 18; 19; 20; 21; 22]. However, a lot of pilot symbols should be embedded to help acquire synchronization in a time-variant PLC channel, leading to a decrease of the spectral efficiency. In indoor PLC environments, the decision-directed (DD) method is more appropriate than the pilot-assisted estimation method because the location of the notch in the channel frequency response (CFR) is unknown [23; 24; 25]. Besides some advantageous features, the DD method has a long processing delay and high computational burden due to tentative decoding.