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

142 Implementation Issuesthe received signal at sub-carrier m is made up of four terms as follows:r m (lT s + τ error ) = d m,l A m (τ error )e j2πf error lT s+ ISI m,l + ICI m,l + n ′ (lT s + τ error ), (4.18)where the first term corresponds to the transmitted data d m,i which is attenuated and phaseshifted. The second and third terms are the ISI and ICI, given byISI m,l =+∞∑i=−∞i≠ld m,i A m [(l − i)T s + τ error ] e j2πf error iT s, (4.19)ICI m,l =+∞∑i=−∞N∑c −1n=0n≠md n,i A n [(l − i)T s + τ error ] e j2πf error iT s, (4.20)whereA n (t) =) (g(t) e j2πf error t (n−m)tj2πe T s ⊗ h(t), (4.21)g(t) is the impulse response of the transmitter filter, and A n (lT s ) represents the sampledcomponents of Equation (4.21), i.e. samples after convolution.4.2.2.1 Analysis of the SNR in the Presence of a Frequency ErrorHere we consider only the effect of a frequency error; i.e. we put τ error = 0 in the aboveexpressions. For simplicity, the guard time is omitted. Then Equation (4.21) becomes [73]{A n (t) =e jπf error t n−m) ]( )jπe T st sinc[(f error + n−mT s(T s − t) 1 − tT s0