TAILIEUCHUNG - Adaptive WCDMA (P5)

Modulation and demodulation MAXIMUM LIKELIHOOD ESTIMATION We start again with the ML principle defined in Section of Chapter 3. After the signal despreading, vector of parameters θ to be estimated includes timing of the received symbols τ0 , phase of the received carrier θ0 , frequency offset of the received signal ν0 , amplitude of the signal A0 and data symbols an θ (τ0 , θ0 , ν0 , A0 , an ) After despreading, the narrowband signal can be represented as r(t) = s(t, θ ) + w(t) The likelihood becomes ˜ L(θ ) = C1 exp − C2. | Adaptive WCDMA Theory And Practice. Savo G. Glisic Copyright 2003 John Wiley Sons Ltd. ISBN 0-470-84825-1 5 Modulation and demodulation MAXIMUM LIKELIHOOD ESTIMATION We start again with the ML principle defined in Section of Chapter 3. After the signal despreading vector of parameters 0 to be estimated includes timing of the received symbols t0 phase of the received carrier 90 frequency offset of the received signal v0 amplitude of the signal A0 and data symbols an 0 T0 d0 v0 A0 an After despreading the narrowband signal can be represented as r t s t 0 w t The likelihood becomes - L 0 C1 exp -C2 l r t - s f l2dt N0 JTq In the sequel we will use a linear-modulated complex-signal format given by s t 0 expj a0h t - nT - T0 jbnh t - nT - sT - TOJ 5-1 5-2 5-3 5-4 where h is the pulse shape and for s 0 or 1 2 we have quadrature phase shift keying QPSK or offset QPSK OQPSK signals respectively. The likelihood function defined by equation now becomes T0 1 r t s t 0 dt 0 If we define the filters matched to the pulse shape in I and Q channel as W p n T i r t h t nT t dt J œ q n T e i r t h t nT eT t dt J œ 5-5 124 MODULATION AND DEMODULATION then equation becomes R N 9 Re N exp -j i 2 änp n t n 1 Im N exp -j i 2 bnq n t e n 1 In the special important case of nonstaggered signals e 0 we find q p. If we define cn an jbn the correlation integral becomes R N 9 Re exp - Tl-p n 1 Phase and frequency correction phase rotations and NCOs For a given phase error 0 n the complex signal sample sampling index n zin n is corrected by multiplying the sample by a complex correlation factor exp j0 n as follows Zin n Xin n jyn n Zo n zin n x exp j0 n By using exp j0 cos 0 j sin 0 we get Zo xin cos 0 - yin sin 0 j xin sin 0 yin sin 0 The operation is known as phase rotation and the block diagram for the realization of equation is shown in Figure . Frequency corrections translations can be performed by the same circuitry but now the phase .

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