Space-Time Block Codes for Wireless Systems - The ...

lock decoder analysis. We will consider two decoder structures, the jointly optimal ML
decoder for all users and a single user ML–based decoder. The key difference between the
uplink and the downlink is the fact that in the downlink, all users experience the same
channel, thus resulting in a multiuser coding problem. Note that the following downlink
model is general enough to encompass the case where different transmit antennae of the
same user employ distinct spreading codes, s (k)
i
(t) ≠ s (k)
i
(t), and the case where different
transmit antennae of the same user employ identical spreading codes, s (k)
i
(t) = s (k)
i
(t).
2.3.1 The Downlink Model
At the base station, each user’s information is encoded in the same way as shown in
Figure 2.1, but the transmitted signal for each user is combined on each transmit antenna,
and the sum signals are transmitted. We will initially assume that user 1 knows all users’
spreading codes and the common channel state information, while this assumption is
impractical, the decoder will provide a bench mark for the suboptimal decoder discussed
in the sequel.
information.
The matched filter outputs are constructed using the spreading code
At symbol time t, the received signal due to d (k)
i
(t) is,
r(t) = √ σ t
∑
∑
K ∑L t L c
k=1 i=1 l=1
g l(k)
i
(t)d (k)
i
(t)h l i(t) + n(t) ∈ C (Lu+τmax)×1 . (2.56)
A single set of channel coefficients h l i (t) appear in (2.56), this is due to the fact that each
user experiences the same channel in the downlink. Written in matrix form
r(t) = √ σ t G(t)D(t)h(t) + n(t) ∈ C (Lu+τmax)×1 , (2.57)
where
G(t) = [G (1) (t), . . . , G (K) (t)] ∈ R (Lu+τmax)×KLcLt , (2.58)
and G (k) (t) is defined in Equation (2.9). The codeword matrix D(t) is
⎡ ⎤
D (1) (t)
D(t) = ⎢ . ⎥
⎣ ⎦ ∈ CKLcLt×LcLt , (2.59)
D (K) (t)
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