Adaptive Beamforming for Multiantenna Communications - Adaptive Signal Processing in Wireless Communications - page 200

transmit (downlink) beamforming techniques used at multiantenna base stations (BSs)
have been shown to enable efficient mitigation of multiuser interference and offer sub-
stantial improvements in system capacity and performance [6, 7, 14, 19].
In this chapter, we provide an overview of fundamentals and recent advances in the
field of receive and transmit beamforming for multiantenna communication systems.
The chapter is organized as follows. In section 8.2, the basic receive and transmit signal
models are introduced. Section 8.3 is devoted to the receive beamforming problem and
methods. In the same section, applications of receive adaptive beamforming to space-
time multiuser multiple-input multiple-output (MIMO) receivers are highlighted. The
transmit beamforming problem and methods are overviewed in section 8.4, and conclu-
sions are given in section 8.5.

8.2 Basic Signal Models

Let us consider a receive (transmit) M -element BS array depicted in Figure 8.1, whose
sensors are weighted by the weight vector w = [ w 1 , w 2 , …, w M ] T , where (·) T denotes the
transpose. Assume that there are L single-antenna users with flat fading channels.
he M × 1 uplink user channel vectors (hereafter referred to as user spatial signatures )
are denoted by a l , l = 1, …, L , while the M × 1 downlink channel vectors are denoted by
h l , l = 1, …, L . Note that for each user, the uplink and downlink channel vectors may dif-
fer from each other because the difference
in the uplink and downlink frequencies in
the frequency division duplex (FDD) mode
and channel variability in the time divi-
sion duplex (TDD) mode may violate the
uplink-downlink reciprocity property [14].
In the sequel, we assume without any loss
of generality that the first user is the user
of interest.

w 1 w 2 w 3 w M

FIgure 8.1 Receive/transmit beamformer.

8.2.1 The Uplink Case
In the uplink case, the baseband M × 1 complex signal vector received at the BS array
can be written as

L

∑ 1

x () t = s t () a + = + n () t s () t n () t , (8 .1)

l l

l =

where s l ( t ) is the baseband receive signal waveform of the l th user, n ( t ) is the M × 1 vector
of additive sensor noise, a  [ a 1 , a 2 , …, a L ], s ( t )  [ s 1 ( t ), s 2 ( t ), …, s L ( t )] T , and t is the time
index. The additive noise is assumed to be zero mean and spatially white, that is, its cor-
relation matrix is given by