nal can be written as (1.15) where Wn is the additive white Gaussian noise (AWGN) and n = 0, 1, ...,N ..., - 1. After DFT, the received signals in the frequency domain can be expressed as m=0,1,...,N , - 1, (1.16) 1.3 Carrier Frequency Offset Effect where Wm is the noise in the frequency domain, and (1.17) is the ICI coefficient [5, 5,6]. 1.3.1 Properties of ICI Coefficients The ICI coefficient Sk is a periodic function with period N. The amplitude of Sk is plotted in Figure 1.4 with E=0.1 and N = 1000. It can be observed that for large values of |k|, ISkI goes to 0. This means that ICI mainly comes from neighboring subcarriers. The phase of Sk is O<E< 1, which is plotted in Figure 1.5 with N = 1000. From its expression or Figure 1.5, it is obvious that for small values of |k|, LSk THE and LS_k 22 TE - . This implies Sk +S-k =0. In addition, for small values of E, , LSk ~ 0 and <S_k 22 -. This means Sk+S-k~0 It is worth noting that Sk + S_k 22 0 is a more accurate approximation than Sk+S-k As we will see in Section 1.4, the mirror-mapping-based schemes are designed on the basis of the aforementioned properties. 1.3.2 Carrier-to-Interference Power Ratio The carrier-to-interference power ratio (CIR) is a widely used metric for evaluating the sys- tem ICI power level without considering the noise power. Suppose that the transmitted data symbols are mutually independent. According to Eq. (1.16), the instantaneous CIR of the OFDM system can be derived as Figure 1.4 The amplitude of Sk. 1 ICI Cancellation Techniques Based on Data Repetition for OFDM Systems Figure 1.5 The phase of Sk. (1.18) k=0,k#m The average CIR can be calculated by averaging the above instantaneous CIR expression over the distribution of the channel gains. However, the calculation of the average CIR using multiple integral is overly complicated. Therefore, an approximate average CIR expression can be derived by taking the average of the numerator and the denominator of Eq. (1.18) separately. It is a good predictor of the average CIR and is simple e