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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 nth chip for the kth user. That is, a k ( n ); n = 0 , 1 , 2 , ··· , L − 1 is the kth 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 kth 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 bT 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 kth 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 kth user’s ith symbol. For the kth 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

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