# A Low-Complexity Channel Estimation Based on a Least-Squares Algorithm in OFDM Systems
###### Abstract  
As the channel frequency responses (CFRs) at virtual pilot subcarriers are assumed to be zero, the estimated CFRs will have a leakage effect for discrete Fourier transform (DFT)-based channel estimation in OFDM systems. The CFRs at odd pilot subcarriers and even pilot subcarriers are related if the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilots). According to this correlation, we propose a low-complexity least-squares (LS) method to estimate the CFRs at virtual even and odd pilot subcarriers, respectively. This will solve the problem of the leakage effect in DFT-based channel estimation. The proposed method does not need to know the statistical properties of the channel or insert extra pilots as with some estimation methods. Furthermore, although this method has less computation than the LS method, both have almost the same channel estimation efficiency in simulation. The channel estimation efficiency of our proposed method is still similar to that of the LS method, even if the number of maximum channel delay points is greater than half the number of pilots. Therefore, the  
method. However, in the present communication specifications, there is a guard band in the spectrum to reduce the interference from neighboring bands. This leads to large errors in the estimated CFRs near the guard band based on the DFT-based channel estimation (i.e., the leakage effect [6; 7; 8; 9]). In [6; 7; 8], the CFRs at the virtual pilot subcarriers were estimated with different methods. The method proposed in [6] inserts extra pilots at the specific subcarriers on both sides of the guard band. Then, the CFRs at the virtual pilot subcarriers are estimated using the inserted pilots. However, as the pilot signal arrangement used by this method is not applicable to any communication specification, it cannot be used in actual communication systems. The optimal linear estimator for leakage suppression is proposed in [7]. The method [7] must determine the statistical properties of a channel. However, in practical application, the statistical properties of a channel are unknown and unlikely to be estimated. In [8], the estimated CFRs at the two pilot subcarriers at both ends of the guard band were used to estimate CFRs at the virtual pilot subcarriers by linear interpolation. However, linear interpolation may not provide a good estimate. The three methods can estimate the overall CFR using the conventional DFT-based channel estimation after estimating the CFRs at the virtual pilot subcarriers. The two estimating channel impulse response (CIR) methods of [9; 11] are very similar, and their computational complexities are the same.  
The method proposed in this paper does not require any statistical properties of a channel or the insertion of extra pilots. This method is applicable to the pilot signals in a comb arrangement. When the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilots), the CFRs at the virtual pilot subcarriers can be estimated. The method proposed in this paper has lower computational complexity and stored complex numbers than the LS method [11]. The channel estimation efficiency of our proposed method is still similar to that of the LS method, even if the number of maximum channel delay points is greater than half the number of pilots. Therefore, this paper performed simple system simulations in the time-varying channel to verify the channel estimation efficiency of the proposed method.  
The system architecture is outlined in Section 2 and the proposed method is introduced in Section 3. The computational complexity is compared with the LS method in Section 4. Furthermore, Section 5 shows the simulation and discussion, while Section 6 shows the conclusions of this paper.