
122 Energy-Efficient Cooperative Wireless Communication and Networks
the relay; that is, user i transmits F
i
x
i
where F
i
∈ C
M×M
is the transmit
beamforming matrix of user
i and x
i
∈ C
M×1
is the information bearing
vector of user
i with normalized covariance (i.e., E[x
i
x
H
i
]=I
M
). The de-
sign of
F
i
will be discussed in the following section. The signal observed by
the relay can be expressed as
r = H
1
F
1
x
1
+ H
2
F
2
x
2
+ n
r
, (9.1)
where H
i
∈ C
M×M
is the channel from user i to the relay and n
r
∈ C
M×1
is the noise vector observed by the relay. In the second time slot, the relay
broadcasts the linear precoded observation to both users, that is, Wr where
W ∈ C
M×M
is the joint