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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 user’s 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 ρ kk ( τ ) = integraldisplay ∞ −∞ g k ( t ) g k ( t − τ ) dt (3) = integraltext T b τ g k ( t ) g k ( t − τ ) dt ≤ τ ≤ T b integraltext τ g k ( t ) g k ( t − τ ) dt − T b ≤ τ ≤ | τ | > T b . The shape of this function will depend on the code sequence. Figure 1 illustrates a typical signature correlation function. Note that ρ kk (0) = 1. From a performance point of view, we will see that for asynchronous processing, ρ kk ( τ ) = δ ( τ ) would be ideal, but this in not possible. The cross correlation between the signature signals of users j and k is defined as ρ jk ( τ ) = integraldisplay ∞ −∞ g k ( t ) g j ( t − τ ) dt (4) = integraltext T b τ g k ( t ) g j ( t − τ ) dt ≤ τ ≤ T b integraltext τ g k ( t ) g j ( t − τ ) dt − T b ≤ τ ≤ | τ | > T b . Kevin Buckley - 2007 2 ρ(τ 29 kk T b-T b T c τ Figure 1: Typical CDMA user’s signature signal correlation function. Note that ρ kj ( τ ) = ρ jk ( τ ). Ideally, for multiuser reception, when k negationslash = j , ρ kj ( τ ) = 0 for all τ . Again, the ideal is not possible. Consider N symbols transmitted per user. Let the k-th user’s 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 user’s i-th symbol. For the k-th user, the received signal (lowpass equivalent) is s k ( t − τ k ) = radicalBig E k N summationdisplay i =1 b k ( i ) g k ( t − iT b ) , (6) τ 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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This document was uploaded on 10/12/2009.
- Spring '09