alized through the Discrete Fourier Transform (DFT) and its inverse (IDFT). The computation of DFT and IDFT are themselves performed by Fast Fourier Transform (FFT) techniques. Figure 2.4 shows the transmitter and receiver chain of an OFDM modem. Contrary to SCM, the OFDM modulation is performed on a block-by-block basis. At the transmitter, a block of source symbols in the frequency domain is first serial-to-parallel converted onto K sub-carriers. These sub-carriers are input to an IFFT (Inverse FFT) block that brings the signal into a time domain. The orthogonal waveform is carried out using an IFFT and a parallel to serial converter. The output of the converter is the summation of all sub-carriers. Following the converter, certain points (symbols) are appended to the beginning of the sequence as a cyclic prefix. The purpose is to allow multipath to settle before the main data arrives at the receiver. The length of the cyclic prefix is often equal to the guard interval. The resulting samples are then shaped, converted to analog and transmitted. Each transmitted block over the channel is referred to as on OFDM symbol [4,5]. At the receiver, an FFT block is used to reverse the operation. In particular, the sampled signals are first processed to determine the starting point of a block and the proper demodulation window. Next, CP which also contains ISI (Inter symbol interference) is removed and then the sequence is serial to 7 subcarriers Frequency Figure 2.3 OFDM with seven sub-carriers OFDM and OFDMA add CP shaping CP removal timing Figure 2.4 OFDM system model. Reproduced with permission from Li and Li C 2005 John Wiley and Sons, Ltd [5] parallel converted. The converted sequence is input to the FFT. The output of the FFT are the symbols are modulated on the K sub-carriers, each multiplied by a complex channel gain. Finally, different demodulation schemes can be used to recover the information bits. 2.3.2 OFDM Mathematical Realization As stated earlier, the computation of DFT and IDFT are themselves performed b