o enable low latency. Maximal spectral efficiency, that is, P = (8T8F)-1 with P denoting the spectral effi- ciency in data symbols per second per Hertz. However, it is shown in the literature [38,46], that it is not possible to satisfy these three requirements at the same time and certain tradeoffs are necessary. This con- clusion has an impact on the waveform selection in wireless communication systems. 3.2.1 OFDM Basics and Transmission Characteristics OFDM was selected in LTE/LTE-A due to its efficiency and simplicity using baseband modulation and demodulation stages based on FFT. Mathematically, the nth OFDM symbol can be described as where k denotes the subcarrier index and n denotes symbol index, NFFT is the total number of subcarriers, rect(.) is a rectangular pulse with the symbol period of , and Sk,n is the data symbol [e.g., quadrature amplitude modulation (QAM) symbol] of the kth subcarrier at the nth time instant. A CP is appended to the beginning of each symbol. The inserted CP serves as a guard time between symbols which protects against ISI. In addition, it preserves the orthogonality between subcarriers after passing through a channel provided that the CP 316 Chapter 3 duration is longer than the channel RMS delay spread. The CP acts as a buffer region where delayed information from the previous symbols can be stored. The receiver must exclude samples from the CP which might be corrupted by the previous symbol when choosing the samples for an OFDM symbol. When demodulating the received symbol, the receiver can choose Tu/Ts samples from a region which is not affected by the previous symbol. In a conventional serial data transmission system the information bearing symbols are trans- mitted sequentially, with the frequency spectrum of each symbol occupying the entire avail- able bandwidth. An unfiltered QAM signal spectrum can be described in the form of sin(7fTu)/Tff" with zero-crossing points at integer multiples of 1/Tu, where Tu is the QAM symbol period. The concept of OFDM is to transmit the dat