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

MC-CDMA 65After inverse OFDM the received sequence r is equalized by employing a bank ofadaptive one tap equalizers to combat the phase and amplitude distortions caused by themobile radio channel on the sub-channels. The one tap equalizer is simply realized byone complex-valued multiplication per sub-carrier. The received sequence at the outputof the equalizer has the formu = Gr = (U 0 ,U 1 ,...,U L−1 ) T . (2.31)The diagonal equalizer matrix⎛⎞G 0,0 0 ··· 00 G 1,1 0G = ⎜⎝.. ..⎟. ⎠0 0 ··· G L−1,L−1(2.32)of dimension L × L represents the L complex-valued equalizer coefficients of the subcarriersassigned to s. The complex-valued output u of the equalizer is de-spread bycorrelating it with the conjugate complex user-specific spreading code c (k)∗ . The complexvaluedsoft decided value at the output of the despreader isThe hard decided value of a detected data symbol is given byv (k) = c (k)∗ u T . (2.33)ˆd (k) = Q{v (k) }, (2.34)where Q{·} is the quantization operation according to the chosen data symbol alphabet.The term equalizer is generalized in the following, since the processing of the receivedvector r according to typical diversity combining techniques is also investigated using thesingle-user detection scheme shown in Figure 2-6.In the uplink G and H are user-specific.Maximum Ratio Combining (MRC)MRC weights each sub-channel with its respective conjugate complex channel coefficient,leading toG l,l = Hl,l ∗ , (2.35)where H l,l ,l = 0,...,L− 1, are the diagonal components of H. The drawback of MRCin MC-CDMA systems in the downlink is that it destroys the orthogonality between thespreading codes and, thus, additionally enhances the multiple access interference. In theuplink, MRC is the most promising single-user detection technique since the spreadingcodes do not superpose in an orthogonal fashion at the receiver and maximization of thesignal-to-interference ratio is optimized.Equal Gain Combining (EGC)EGC compensates only for the phase rotation caused by the channel by choosing theequalization coefficients asG l,l = H l,l∗|H l,l | . (2.36)