lect14 - Kevin Buckley - 2007 1 ECE 8770 Topics in Digital...

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Unformatted text preview: Kevin Buckley - 2007 1 ECE 8770 Topics in Digital Communications - Sp. 2007 Lecture 14 6 Spread Spectrum & Multiuser Communications 6.3 Multiuser CDMA This discussion corresponds to Section 15.3 of the course text. We will consider the simultaneous reception of CDMA signals form K users, all sharing a common symbol interval T = T b = 1 R , carrier frequency f c , and modulations scheme. Each is using its oen CDMA signature signal of L = L c chips, with chip duration T c = T b L . Following the Course Text, we will use k as our user index and a k ( n ) = 1 as the n-th chip for the k-th user. That is, a k ( n ); n = 0 , 1 , 2 , , L 1 is the k-th users code sequence. The signature signal of the k th user is g k ( t ) = L 1 summationdisplay n =0 a k ( n ) p ( t nT c ) t T b , (1) where the pulse p ( t ) is nonzero over 0 t T c and designed such that the signature signal has energy E g = 1 (e.g. p ( t ) = 1 T b [ u ( t ) u ( t T c )] ). That is, integraldisplay T b g 2 k ( t ) dt = 1 . (2) Since the receiver will employ filters matched to the different user signature signals, we will be interested in the following signature signal correlations and cross correlations. The correlation of the k-th user signature signal is defined as kk ( ) = integraldisplay g k ( t ) g k ( t ) dt (3) = integraltext T b g k ( t ) g k ( t ) dt T b integraltext g k ( t ) g k ( t ) dt T b | | > T b . The shape of this function will depend on the code sequence. Figure 1 illustrates a typical signature correlation function. Note that kk (0) = 1. From a performance point of view, we will see that for asynchronous processing, kk ( ) = ( ) would be ideal, but this in not possible. The cross correlation between the signature signals of users j and k is defined as jk ( ) = integraldisplay g k ( t ) g j ( t ) dt (4) = integraltext T b g k ( t ) g j ( t ) dt T b integraltext g k ( t ) g j ( t ) dt T b | | > T b . Kevin Buckley - 2007 2 ( 29 kk T b-T b T c Figure 1: Typical CDMA users signature signal correlation function. Note that kj ( ) = jk ( ). Ideally, for multiuser reception, when k negationslash = j , kj ( ) = 0 for all . Again, the ideal is not possible. Consider N symbols transmitted per user. Let the k-th users symbol vector be denoted as b k = [ b k (1) , b k (2) , , b k ( N ) ] T , (5) where b k ( i ) is the k-th users i-th symbol. For the k-th user, the received signal (lowpass equivalent) is s k ( t k ) = radicalBig E k N summationdisplay i =1 b k ( i ) g k ( t iT b ) , (6) k is the propagation delay for the k th user and E k is the received energy per signature signal. Given all K users observed in noise, the corresponding received signal is r ( t ) = K summationdisplay...
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lect14 - Kevin Buckley - 2007 1 ECE 8770 Topics in Digital...

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