## 1 Introduction  
In wireless communications, the carrier frequency offset (CFO) [1,2] is primarily caused when the frequencies of the oscillators between the transmitting and receiving ends do not match or there is a Doppler frequency shift that is proportional to the carrier frequency, as well as to the moving speed of the mobile unit. For orthogonal frequency division multiplexing (OFDM) systems [3,4], the quality of the signal transmission is liable to degrade in the case of the existence of CFO. This is because CFO destroys the orthogonality between the subcarriers and, thus, brings about the signal distortion in OFDM systems. Since multi-carrier systems are very sensitive to the subcarrier synchronization error, it is essential to provide an accurate estimation for compensating the CFO. Otherwise, it is difficult to develop an OFDM system that is able to meet the elementary requirement of acceptable communication link quality. Therefore, CFO estimation for OFDM attracts much attention and is an active area of research. In the past, a number of works (e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]) have been devoted to the CFO estimation techniques. The least square (LS) criterion is used in [8] for CFO estimation. [PERSON] [7] presented a CFO estimator based on the maximum-likelihood (ML) criterion while assuming the training sequences and channel statistics are known. In [9], the ML criterion is further employed for the joint estimation of channel and CFO. In [1,10,11], CFO estimators were developed using a training sequence with two or multiple identical components. By using one OFDM symbol with \(M\) identical components, the CFO estimation scheme in [11] expands the estimation range to \(M\) subcarrier spacing for reducing the implementation cost, since the wider the estimation range is, the lower the precision of the employed oscillator will be. However, the expense of the scheme [11] is the increase of the computational complexity, especially for a large \(M\). The estimation range can be further expanded by using one more OFDM symbol [12] while sacrificing the transmission efficiency. The CFO estimation algorithms with the cyclic prefix (CP) technique [13], which either use a special training sequence [14] or a pilot signal [15], have been presented. One of the most commonly used is to employ the subspace estimation algorithm of the singular value decomposition (SVD) [16] and the ML criterion [17]. On the other hand, it is commonly assumed that the channel side information is unavailable to the CFO estimator, and CFO estimation can also be reached by employing the inherent structure of OFDM signals. This is generally categorized into the field of blind approaches. For instance, the ML-based CFO estimator is implemented by using correlation operations, as the training signals are periodic and unknown [1,10]. The blind CFO estimation has received a great amount of attention because of its bandwidth efficiency. However, the blind schemes degrade in performance significantly, especially when the length of the channel impulse response is large. In practice, many channel estimation and space-time coding schemes [18] require the channel statistics information. For these systems, the availability of channel statistics information can be expected for CFO estimation in OFDM. The objective of this paper is to present a CFO estimation technique, which is aided with pilot symbols, for OFDM transmission. The results obtained from this novel approach would provide two major contributions. For the traditional line search methods of CFO, it is often assumed that the channel order is known prior to the CFO estimate. However, this assumption may not be realistic, while the channel characteristic is difficult to be acquired promptly. First, we discard the assumption and modified the traditional CFO line search method by introducing an interpolation technique to attempt reconstructing full-dimensional channel frequency responses for an OFDM system with pilots.