expression of the signal in time-domain can be expressed as follows: s(t) = Re of (NFFT -1)/2 mT,<t<(m+1)T, (9-11) k=-(NFFT-1)/2 Where s(t) denotes the OFDM signal in time-domain, Ak is the complex-valued data that is QAM- modulated and transmitted over sub-carrier k, NFFT is the number of sub-carriers in frequency-domain, Wc is the RF carrier frequency, and T g is the guard interval or Cyclic Prefix (CP). For a large number of sub-carriers, direct generation and demodulation of the OFDM signal would require arrays of coherent CHAPTER 9 The IEEE 802. 16m Physical Layer (Part I) Sub-Carrier Index FIGURE 9-5 The OFDM signal in the frequency-domain sinusoidal generators, which can become excessively complex and expensive. However, one can notice that the OFDM signal is actually the real part of the Inverse Discrete Fourier Transform (IDFT) of the original complex-valued data symbols Ak. It can be seen that there are N < NFFT sub-carriers, each carrying the corresponding data Ak. The inverse of the sub-carrier spacing 1/T is defined as the OFDM useful symbol duration, which is NFF times longer than that of the original input data symbol duration. Since IDFT is used in the OFDM modulator, the original data is defined in the frequency-domain, while the OFDM signal s(t) is defined in the time-domain. The IDFT can be implemented via a computationally efficient Fast Fourier Transform (FFT) algorithm. The orthogonality of sub-carriers in OFDM can be maintained, and individual sub-carriers can be completely separated and demodu- lated by an FFT at the receiver when there is no ISI introduced by the communication channel. In practice, linear distortions, such as multipath delay, cause ISI between OFDM symbols, resulting in loss of orthogonality and an effect that is similar to co-channel interference. However, when delay spread is small, i.e., within a fraction of the OFDM useful symbol length, the impact of ISI is insignificant, although it depends on the order of modulation implemented by the sub-carriers. A simple solutio