B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

11 .7 Multiuser Detection (MUD) 641
optimum matrix Gk :
(11.46)
This G still represents a linear detector. Once G has been determined, the MUD receiver simply
takes a hard decision on the linearly transformed signal, that is,
(11.47)
The optimum matrix G can be deten11ined by applying the principle of orthogonality
[Eq. (8. 84), Sec. 8.5]. The principle of orthogonality requires that the error vector
be orthogonal to the received signal vector rk . In other words,
Thus, the optimum receiver matrix G can be found as
(11.48)
Because the noise vector Dk and the signal vector Sk are independent,
(11.49)
is their cross-correlation.
In addition, we have earlier established equalities
Sksf = I M xM
where we use IM xM to denote the M x M identity matrix. Hence, we have
The optimum linear receiver matrix is therefore
(11.50a)
( 11.50b)
(11.51)
It is clear that when the channel noise is zero (i.e., N = 0), then the optimum matrix given by
Eq. ( 11.51) degenerates into
which is essentially the decorrelator receiver.
The MMSE linear MUD receiver is shown in Fig. 11.15. Similar to the decorrelator
receiver, the major computational requirement comes from the matrix multiplication of Gk ,
The MMSE linear receiver is also near-far resistant. 11