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

66 MC-CDMA and MC-DS-CDMAEGC is the simplest single-user detection technique, since it only needs information aboutthe phase of the channel.Zero Forcing (ZF)ZF applies channel inversion and can eliminate multiple access interference by restoringthe orthogonality between the spread data in the downlink with an equalization coefficientchosen asG l,l =H l,l∗|H l,l | 2 . (2.37)The drawback of ZF is that the equalizer enhances noise, especially for small amplitudesof H l,l .Minimum Mean Square Error (MMSE) EqualizationEqualization according to the MMSE criterion minimizes the mean square value of theerrorε l = S l − G l,l R l (2.38)between the transmitted signal and the output of the equalizer. The mean square errorJ l = E {|ε l | 2 } (2.39)can be minimized by applying the orthogonality principle, stating that the mean squareerror J l is minimum if the equalizer coefficient G l,l is chosen such that the error ε l isorthogonal to the received signal R ∗ l ,i.e.E {ε l Rl ∗ }=0. (2.40)The equalization coefficient based on the MMSE criterion for MC-CDMA systems results inG l,l =H ∗l,l|H l,l | 2 + σ 2 . (2.41)The computation of the MMSE equalization coefficients requires knowledge about theactual variance of the noise σ 2 .ForSNR→∞, the MMSE equalizer becomes identicalto the ZF equalizer. To overcome the additional complexity for the estimation of σ 2 ,alow complex sub-optimum MMSE equalization can be realized [24].With sub-optimum MMSE equalization, the equalization coefficients are designed suchthat they perform optimally only in the most critical cases for which successful transmissionshould be guaranteed. The variance σ 2 is set equal to a threshold λ at which theoptimal MMSE equalization guarantees the maximum acceptable BER. The equalizationcoefficient with sub-optimal MMSE equalization results inG l,l =H ∗l,l|H l,l | 2 + λ(2.42)