eam input to the M-QAM/M-PSK symbols represented by the vector Xm of length Nd. The OFDM system then constructs smas Sm=FmXxm (6.1) where Fm m is a matrix that performs an N--point inverse fast Fourier transform (IFFT) operation. N is the number of IFFT output samples. N is the length of the guard interval samples, and Ng=Ng N is the length of the total time domain symbol. D,0[0] Dm,N -1[0] D. m = Dmkkn (6.3) Dm.,O[Nd-1] The mth transmitted symbol in a DFT-S OFDM system can be expressed as a vector of length Ngs samples, defined by (6.2) 0.5 ms LB #1 LB #2 SB #1 LB #4 LB #5 LB #6 Figure 6.2 LTE uplink slot structure with one short block. © 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology SC-FDMA M-PSK/ M-QAM Carrier DAC RF Spreading Insertion Modulator Alloc. Transmitter Structure SC-FDMA M-PSK/ M-QAM IDFT De- Carrier Remo- Demo- spreading Equalizer Dealloc. dulator Channel Estimation Receiver Structure Figure 6.3 OFDMA and SC-FDMA basic transmitter and receiver structures. Dm m is a matrix which performs an Nd-point DFT operation. The DFT-S matrix element is expressed as (6.4) where k is the M-QAM/PSK symbol index. Tm m is an Ns X N mapping matrix for the subcarrier allocation. The subcarrier allocation can be classified in two allocation modes: distributed and localized allocation [6] (see also Figure 6.16). In distributed mode, N = Sf X N with Sf defined as the spreading factor. The matrix of subcar- rier allocation in localized mode is defined as Fm,0[0] Fm,N,-1[0] Fm./[n] (6.7) Fm,O[Ngs-1] (6.5) where q is the localized chunk index. Jab is an axb matrix of ones. For the distrib- uted mode, the subcarrier allocation matrix is defined as (6.6) © 2009 by Taylor & Francis Group, LLC Single-Carrier Transmission for UTRA LTE Uplink Finally, Fm has a matrix element given by (6.8) where l is the subcarrier index. After the multipath channel and adding the additive white Gaussian noise (AWGN), removing the cyclic prefix, and going through the N point FFT at the receiver,