Adaptive Beamforming for Multiantenna Communications - Adaptive Signal Processing in Wireless Communications - page 219

Certain combinations of space-time coding and beamforming at the transmitter are
also possible, that may require only partial CSI [68, 69].
In the sequel, we will consider the transmit beamforming problem that includes the
following (related) cases:

1. Unicasting . Different data streams should be delivered to different users.

2. Broadcasting . The same data content should be delivered to all users.

3. Multicasting . The same data content should be broadcasted to a selected group of
users, but different data streams should be transmitted to different groups of users.

Clearly, the first two cases represent two extremes of the most general multicasting case.
In particular, broadcasting and unicasting can be viewed as single-group multicasting
and multicasting with single-user groups, respectively.

8.4.1 Unicast Transmit Beamforming
8.4.1.1 Traditional Techniques
Early formulations of the transmit beamforming problem were mostly developed in the
context of voice services in a cellular mobile radio network, where from the operator
perspective, the system should provide an acceptable QoS for each user and serve as
many users as possible, while radiating as low power as possible [11, 14].
The QoS requirements can be set up in the form of the lowest admissible value of
the received SINR at each mobile. Using (8.7), the receive SNR of the i th user can be
expressed as [14]

H

wr w

i ici , () i

SINR =

,,

(8.80)

i

L

∑

σ 2

H

+ wr w

i m icmm , ()

mmi =; ≠ 1

where σ i 2 is the noise power of the i th user, r i,c ( m ) is the correlation matrix of the downlink
channel between the BS serving the m th mobile and the i th mobile, and the other param-
eters used in (8.80) have been defined in section 8.2.
The numerator of (8.80) represents the receive signal power at the i th mobile, whereas
the denominator of (8.80) contains the noise and interference powers at the same mobile.
The interference terms are given by the sum of powers of transmissions that are intended
for other than the i th mobile but which are received by the i th mobile. Clearly, this is a
crosstalk type of interference that should be avoided to guarantee an acceptable quality
of the voice message.
Equation (8.80) views all channels as stochastic random vectors. This representation
is suitable for the case of fast fading where the downlink channel vectors themselves are
unavailable at the transmitter, and only their correlation matrices are known. In the
opposite case of slow channel fading, it is more natural to view the downlink channels as
deterministic vectors. In the latter case, the downlink channel correlation matrix is rank
one and is given by r i,c ( m ) = h i,c ( m ) h i,c ( m ) . Then, (8.80) can be rewritten in a simpler form: