Simulation of Third Generation CDMA Systems - Virginia Tech

(t)R i ’(t)R i (t)e -jϕ i C SC * (t-τ i )Figure 3.15: Descrambling at a Rake BranchR () t = r()t e’ - jφi ( t)i= { r‡ ( t) + n( t)}e- jφi () tφi= r‡ () t e + n()t e- j () t - jφi()t(3.26)The second term in equation (3.12) is the complex Gaussian noise with a rotation. Let usdenote that as n i ’(t). So,’ - jφi( t)R () t = r‡ () t e + n () tiNÊijφl() t - jφi()t= h ( t-τ) s( t - τ ) e e + n ‡ ( t)l = 1l l ljφl() t - jφi()t= h( t-τ ) st ( - τ ) + h( t-τ ) st ( - τ ) e e + n ‡ ( t)i i i l l ll = 1lžiNÊii(3.27)The first term in equation (3.13) is the desired signal. Let us call that m i ’(t). Thesecond term is interference due to other paths or the Inter Symbol Interference (ISI). Let usdenote that as I i ’(t). So we haveR‡ () t = m‡ () t + I ‡ () t + n ‡ () t(3.28)i i i i’ *\ R() t = R () t C ( t-τ)i i SC i’ * ’ * ’ *= m() t C ( t- τ ) + I () t C ( t- τ ) + n () t C ( t-τ)i SC i i SC i i SC i(3.29)The first term representing the desired signal m i (t) is given by’ *m() t = m() t C ( t-τ)i i SC i*= h( t-τ ) s( t-τ ) C ( t-τ)i i i SC i*= h( t-τ ) d ( t-τ ) C ( t-τ ) C ( t-τ)i i s i SC i SC i= h( t-τ) d ( t-τ)i i s i(3.30)45