g split into blocks of the size M x N , i.e. the data blocks X, located on the grid points of the delay-Doppler plane. To arrive at a simplified OTFS receiver structure, we replace WTx,c and WTx,r[n] in (6.12) with I'M and 1, respectively. Thus, Z, i.e. the OFDM receiver output signal, can be expanded Z = V = FM[H,XfN(0),. (6.23) where the M x N matrix V =[v(0),...,V(N - 1)] includes the noise samples at the output of the OFDM receiver. Replacing WRx,c with IM in (6.13), while using (6.23), one realizes that similar to the transmitter, the DFT operation at the OFDM demodulator and the IDFT in the SFFT block cancel out. As a result, (6.13) can be rearranged as (6.24) where the M x 1 vectors n) are the OFDM received symbols after CP removal and V = FHVEN Equation (6.24) shows that after discarding the CP, OTFS receiver only requires scaling the OFDM symbols n with the scalar WRx,r[n] and performs M number of N-point DFT operations. Therefore, the OTFS demodulator that is shown in Figure 6.1 boils down to the structure that is presented in Figure 6.3 where the (M + Mcp) X 1 vector r(n) includes the samples of the nth time domain OTFS received symbol and dk is the high rate data stream at the output of the OTFS demodulator. As was pointed out earlier, the OTFS demodulator output can be fed into a channel equalizer for data detection while taking advantage of full channel diversity. WRx,r[n] N-point Removal N-point N-point Figure 6.3 Simplified OFDM-based OTFS demodulator structure. 6.6 Complexity Analysis Table 6.1 Computational complexity of different modem structures. Structure Number of modulator CMs Number of demodulator CMs OTFS mod./demod. in Section 6.5 (1+log,N) OTFS mod./demod. in [4] MN log2M+MN10B2N MN log,M+ OFDM mod./demod. log2M Complexity Analysis This section focuses on the computational complexity of the presented modem structure in Section 6.5 and compares it with the conventional modem structure in [4] as well as that of OFDM. Let us consider transmission of a data block with the total number of M 