y ONEET (8CFO) and to convert the decreased power to interference power. The SNR depends not only on the frequency offset ECFO, but also on the number of subcarriers; however, as NFFT increases, converges to sinc2(8CFO). Therefore, the SNR converges to SNR(8CFO) = sinc2(8CFo)Pho2/([1- as NFFT becomes increasingly large. In the above equations, the power of inter-carrier interference as a function of relative carrier frequency offset is defined as PICI(8CFO) = [1 - (8CFO)]Pho2. In practice, the subcarrier spacing is not the same among different subcarriers due to mismatched oscillators (i.e., frequency offset), Doppler shift, and timing synchronization errors, resulting in inter-carrier interference and loss of orthogonality. It can be seen that the ICI increases with the increase of the OFDM symbol duration (or alternatively decrease of subcarrier spacing) and the frequency offset. The effects of timing offset are typically less than that of the frequency offset, provided that 328 Chapter 3 the CP is sufficiently large. It can be shown that the ICI power can be calculated as a func- tion of generic Doppler power spectrum A(v) as follows [30]: where Vmax denotes the maximum Doppler frequency. We further assume that the transmit- ted signal power is normalized. It can be noted that the ICI generated as a result of carrier frequency offset is a special case of the above equation when A(f) = s(f - fCFO) in which 8(f) represents the Dirac delta function. Using classic Jakes' model of Doppler spread where the spaced-time correlation function is defined as (t) = Jo(2) in which J0(x) denotes the zeroth-order Bessel function of the first kind, the ICI power can be written as follows: which approximately gives an upper bound on the ICI power due to Doppler spread. Comparison of the power of ICI generated by carrier frequency offset and Doppler spread suggests that the ICI impairment due to the former is higher than the latter. 3.2.1.6 Phase Noise Oscillators are used in typical radio circuits to drive the mixer used for th