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Figure 10.2. Base station architecture of DS-CDMA/MISO transmitter with nT antennas.
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where tr(LkL* ) = pk is the total power allocated to user k. We assume that the k total transmit power in the base station is constrained to P0
k A
tr( L
L* ) = P0 k
where A = {k [1, K] : pk > 0} is the active user set. Consider frequency-selective fading channels with Lp resolvable multipaths. The impulse response between the mth transmit antenna and the kth mobile is given by hk ,m (t ) =
h( ) d (t - t ( ) )
p k ,m p k ,m p=1
where t (p) denotes the delay of the pth path for the kth user from the mth k,m transmit antenna. We assume NSFTc > maxk,m,pt (p) . In addition, for the sake of > k,m simplicity, we assume that all paths are synchronous, although in practice, these paths will arrive at slightly different delays [39, 97]. Hence, the NSF 1 received signal at user k is given by Yk =
k A
+ Zk
where Bj is the nT 1 transmitted vector of user j, Zk is the NSF 1 complex Gaussian noise vector with covariance matrix s 2INSF z S j = C(j p ) H (j p ) L j ,
p =1 Lp
where H(p) is the nT nT diagonal matrix consisting of the complex fading gains k from the nT transmit antennas along path p
( p)
hk p1 , = M 0
K 0 O M ( ) K hk pnT ,
and C(p) is the NSF nT spreading sequence matrix (assigned to user j) along j the pth path. We assume that the channel gains across different paths, different antennas, and different users are i.i.d. complex Gaussian random processes with zero
mean and variance s 2 (p) set according to the power-delay pro le such that h SLp=1s 2 (p) = 1. To decouple the physical layer performance from speci c p h spreading sequence design, we assume random sequence. The spreading sequence matrix C(p) consists of i.i.d. entries with zero mean and variance j 1/NSF. In practice, sequences across different paths are related through shifts. However, we assume small autocorrelation of the sequence and therefore, the sequence matrices C(p) are independent for p = 1, . . . , Lp. This shall greatly j simplify the analysis, and it is shown [39] to be quite accurate through simulations. Without loss of generality, we consider the receive processing for user k. The received signal can be written as follows: Yk = Sk Bk + S j B j + Zk { 13 2 j k Desired signal 12 3 Noise 4 4
For low-complexity implementations, we assume linear processing. Specifically, the received vector Yk is premultiplied by a linear vector F* : k * * * Vk = Fk Yk = Fk Sk Bk + Fk * S j B j + Fk Zk
j k
In particular, we shall focus on the conventional matched- lter approach where Fk = Sk. In this case, the matched- lter (MF) output is given by Vk (MF) = S*Sk Bk + Sk * S j B j + S*Zk k k
j k
Note that
( Vk (MF) = S*Yk = L* H kp )*C(j p )*Yk k k
p =1 Lp
indicates that the matched- lter processing is the same as the standard RAKE receiver processing as illustrated in Figure 10.3. In much the same way as we did in previous chapters, we shall model the performance of the multiuser physical layer using the information-theoretic approach. The maximum data rate of user k (bits per channel use) based on matched- lter processing and perfect CSIR is given by Ck = max I (Bk ; Vk S)
p ( Bk )
= log I nT + S*QSk k where P = SkS*, Q is given by k
S*PSk k
Path 1
(1 N SF )
H (1)*k,1
Despreading (w.r.t. antenna 1) . . .