Adaptive Beamforming for Multiantenna Communications - Adaptive Signal Processing in Wireless Communications - page 215

Obviously, there is a strong similarity between the vectorized MIMO model in (8.56)
and the beamforming snapshot model in (8.1).
The established similarity between the models (8.1) and (8.56) opens an avenue for
extending MV beamforming techniques to MIMO communications. A linear MIMO
space-time receiver can be expressed as [57, 59]

ˆ sWX

= T , (8.60)

where s is the receiver estimate of the vector s , and W  [ w 1 , w 2 , …, w 2 J ] is the 2 M r T × 2 J
matrix of the receiver weights. Note that each entry of s requires a separate weight vector
for estimation and subsequent decoding. For example, the vector w l can be interpreted
as the space-time receiver weight vector for the l th entry of s .
The MIMO receiver counterpart of the MRC technique is commonly referred to as the
matched-filter (MF) receiver, and can be written as [59, 62]

1

s

2 A T

= X . (8 . 61)

H

The MF receiver (8.61) corresponds to the following weight matrix:

1

W

MF =

2 A

. (8.62)

H

When followed by the simple nearest-neighbor symbol-by-symbol decoder, this receiver
is known to be equivalent to the maximum likelihood (ML) space-time decoder for the
single-user (point-to-point) case [62].
In the multiuser case (when multiple multiantenna transmitters simultaneously com-
municate with a multiantenna receiver; see Figure 8.2 ), the models in (8.54) and (8.56)
can be straightforwardly modified to account for multiple users. For example, if all the
transmitters use the same OSTBC, (8.56) can be rewritten as [59]

L

l

X = A s + N , (8.63)

l l

= 1

where s l is the J × 1 vector of information symbols of the l th user,

   

A l = CH , , , ,, … CH DH … DH

1 l J l 1 l J l

(8.64)

 [ aa  a

,, 2 J ],

l , , 1 l 2 l

and H l is the matrix channel between the l th user and the receiver.