 Physical Layer Aspects (Part 1) 327 where NFFT and NCP denote the number of data samples and CP samples, respectively. The OFDM symbol xm(n) is transmitted through a channel hm(n) and is perturbed by a Gaussian noise Zm(n). The channel hm(n) is assumed to be block-stationary, that is, it is time-invariant over each OFDM symbol. With this assumption, the output ym(n) of the channel can be represented as ym(n) = hm(n)*xm(n) + Zm(n), where hm(n)*xm(n) = hm(k)xm(k-, n) and Zm(n) is a zero-mean additive white Gaussian noise (AWGN) k=-00 with variance 02. Since the channel impulse response hm(n) is assumed to be block- stationary, the channel response does not change over each OFDM symbol; however, the channel response hm(n) may vary across different OFDM symbols; thus it is a func- tion of the OFDM symbol index m. When the receiver oscillator is not perfectly synchronized to the transmitter oscillator, there can be a carrier frequency offset = fTX - fRX between the transmitter carrier fre- quency fTx and the receiver carrier frequency fRX. Furthermore, there may be a phase offset Ao between the transmitter carrier and the receiver carrier. The mth received symbol ym(n) can be represented as ym(n) = [hm(n)*xm(n)]exp(j{2fFon + m(NFFT + NCP) |Ts + 00}) + Zm(n) where Ts is the sampling period. The carrier frequency offset can be represented relative to the subcarrier bandwidth 1/(NFFTTs) by defining the relative fre- quency offset 8CFO = AfcfoNFFTTs. The carrier frequency offset attenuates the desired sig- nal and introduces ICI, thus decreasing the SNR. The SNR of the kth subcarrier can be expressed as where ONFFT = of the SNR on the frequency offset. In the latter equation, Ph, oz and o2 denote the total average power of channel impulse response, variance of the signal, and variance of the addi- tive noise, respectively. The subcarrier index k is dropped since the SNR is the same for all subcarriers. From this SNR expression, it is clearly seen that the effect of the frequency off- set is to decrease the signal power b