synchronous transmissions are allowed in the uplink. The inclusion of he cyclic prefix adds redundancy to the transmission since the same con- tent is transmitted twice as the CP is a copy of the tail of a symbol placed at its beginning. This overhead can be expressed as a function of symbol duration and duration of the CP as OH = TCP/(TCP OFDM is a flexible waveform that can support diverse services in a wide range of frequencies when properly selecting subcarrier spacing and CP. Further dis- cussion on OFDM numerology design that fulfills a wide range of requirements is given in the next section. Since IDFT is used in the OFDM modulator, the original data are 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 FFT algorithm. The orthogonality of subcar- riers in OFDM can be maintained and individual subcarriers can be completely separated and demodulated by an FFT at the receiver when there is no ISI introduced by communi- cation 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 cochan- nel interference. However, when delay spread is small, that is, within a fraction of the OFDM useful symbol length, the impact of ISI is negligible, although it depends on the order of modulation implemented by the subcarriers (see Fig. 3.10). A simple solution to mitigate multipath delay is to increase the OFDM effective symbol duration such that it is much larger than the delay spread; however, when the delay spread is large, it requires a large number of subcarriers and a large FFT size. Meanwhile, the system might become sensitive to Doppler shift and carrier frequency offset. An alternative approach to mitigate multipath distortion is to generate a cyclically extended guard interval, where each OFDM symbol is prefixed with a periodic extension of the signal itself, as shown in Fig. 3.10 where the tail of the symbo