Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

MC-CDMA 73L corresponds to the spreading code length and in the case of OFDM (OFDMA, MC-TDMA), L is equal to the number of sub-carriers N c . The pre-equalized sequence s isfed to the OFDM operation and transmitted.In the receiver, the signal after inverse OFDM operation results inr = Hs + n= HGs + n (2.58)where H represents the channel matrix with the diagonal components H l,l and n representsthe noise vector. It can be observed from Equation (2.58) that by choosingG l,l = 1H l,l(2.59)the influence of the fading channel can be compensated and the signal is only disturbed byAWGN. In practice, this optimum technique cannot be realized since this would requiretransmission with very high power on strongly faded sub-channels. Thus, in the followingsection we focus on pre-equalization with a power constraint where the totaltransmission power with pre-equalization is equal to the transmission power without preequalization[37].The condition for pre-equalization with power constraint isL−1∑L−1∑|G l,l S l | 2 = |S l | 2 . (2.60)l=0When assuming that all symbols S l are transmitted with the same power, the conditionfor pre-equalization with power constraint becomesl=0L−1∑L−1∑|G l,l | 2 = |G l,l C| 2 = L, (2.61)l=0l=0where G l,l is the pre-equalization coefficient without power constraint and C is a normalizingfactor that keeps the transmit power constant. The factor C results inC =L. (2.62)L−1∑√|G l,l | 2l=0By applying the equalization criteria introduced in Section 2.1.5.1, the following preequalizationcoefficients are obtained.Maximum Ratio Transmission (MRT)G l,l = Hl,l∗L. (2.63)L−1∑√|H n,n | 2n=0