ency-domain equalizer (FDE) and the signal at the FDE output can be described as V = Cz where CNFFT) is the diagonal matrix of FDE coefficients. The FDE complex coefficients can be derived using minimum mean square error (MMSE) criterion as Ck = 02/02) where k denotes the subcarrier index, o2 denotes the variance of the additive noise, and o2 is the variance of the transmitted pilot symbol. Following the subcarrier demapping function and IDFT despreading, an NDFT X 1 vector X containing NDFT QAM-modulated symbols as an estimate to the input vector X is obtained at the receiver. The IDFT despreading block in the receiver averages the noise over each subcarrier. A particular subcarrier may experience deep fading in a frequency-selective fad- ing channel. The IDFT despreading averages and spreads the fading effect, which results in a noise enhancement to all the QAM symbols. Therefore the IDFT despreading makes DFT-S-OFDM more sensitive to the noise. As shown in Fig. 3.14, the modulation symbols in blocks of NDFT symbols are processed through an NDFT-point DFT processor, where NDFT denotes the number of subcarriers assigned to the transmission of the data/control block. The rationale for the use of DFT pre- coding is to reduce the cubic metric of the transmitted signal. From an implementation point of view, the DFT size should ideally be a power of 2. However, such a constraint would limit the scheduler flexibility in terms of the amount of resources that can be assigned for an uplink transmission. In LTE, the DFT size and the size of the resource allocation is lim- ited to products of the integers 2, 3, and 5. For example, the DFT sizes of 60, 72, and 96 are allowed, but a DFT size of 42 is not allowed [30]. Therefore, the DFT can be implemen- ted as a combination of relatively low-complexity radix-2, radix-3, and radix-5 FFT proces- sing blocks. The subcarrier mapping in DFT-S-OFDM determines which part of the 332 Chapter 3 spectrum is used for transmission by inserting a number of zeros (i.e., null subcarriers in