ARAPOGLOU et al.: MIMO OVER SATELLITE: A REVIEW 31
period are transmitted. This is usually carried out employing
one of the variants of BLAST coding that follow:
◦ Diagonal encoding (D-BLAST) [36], where the data
stream is first serial-to-parallel dem ultiplexed on to M
T
separate streams. Each stream undergoes independent
temporal coding, interleaving and symbol mapping and,
then, it is fed into a stream rotator that rotates the symbols
diagonally across antennas and time.
◦ Parallel encoding (V-BLAST) [37] is a simplified version
of D-BLAST aiming at a lower computational complexity
by removin g the stream rotator.
◦ Serial encoding is another variant of D-BLAST, where
the input bit stream is first SISO encoded, interleaved
and mapp ed to a constellation point and then serial-to -
parallel demultiplexed o nto the M
T
antennas.
◦ Tu rbo-BLAST [38], [39] combines layered STC with the
Turbo coding principle. It overcomes the limitation of
V-BLAST of having more transmit than receive antennas
and it is based on a random layered STC scheme and a
Turbo-like decoder of the random layered STC.
Full-Rate Full-Diversity 2x2 Space-Time Codes: Practical
reasons limit current wireless communication system s to
small dimensions, typically 2 ×2. In this regard, various 2 ×2
STC have been proposed in the literature that, in contrast
to Alamouti and BLAST, obtain the full-rate, full-diversity
frontier. The most characteristic is the 2 × 2 Golden STBC
code introduced in [40], although also studied independently
in [41], [42]. Golden codes, based on cyclic division algebra,
possess many desired properties: full rate (2 symbols per
channel use), full diversity (equal to 4), non-vanishing
minimum determinant independent of the constellation
size and preserve the spectral efficiency. I n fact, the IEEE
802.16e-2005 specification includes a variant of the Golden
codes dubbed as Matrix C, since Matrix A and B correspond
to Alamouti and spatial multiplexing. The main drawback of
Golden codes is the high decoding complexity, which grows
with the fourth power of the signal constellation size.
Receivers for Spatial Multiplexing: In the analysis of
MIMO techniques over satellite various kin d s of receivers
appear. To reduce the complexity of the optimal (full search-
based) ML receivers, researchers have resorted to linear
techniques, such as ZF and MMSE. Furthermore, the key
idea of the SIC decoder is layer peeling, i.e. symbol streams
are successively decoded and stripped away layer by layer.
This strategy, called interference nulling and canceling,is
detailed in [36], [43], [44] and gives a reasonable tradeoff
between complexity and performance. Iterative receivers may
approach optimum performance at an affordable receiver
complexity. Iterative receivers for MIMO are based on a
combination of iterative interfe rence cancelation and coding.
Finally, sphere decoding aims at reducing the computational
complexity of ML by narrowing down the size of the
lattice searched. Though the worst case complexity remains
exponential with respect to the constellation size (as in ML),
the expected complexity of sphere decoding has been shown
to be cubic or even sub-cubic at high SNR [45].
B. Multi-User MIMO
MU-MIMO System Model & Assumptions: Multiple
antenna techniques in point-to-multipoint systems are com-
monly referred to as a MU-MIMO. MU-MIMO exhibits key
advantages over SU-MIMO, such as [14]:
◦ In additio n to stream m ultiplexing, MU-MIMO schemes
offer MU mu ltiplexing, resulting in a direct capacity
gain proportional to the number of BS antennas and the
number of users.
◦ MU-MIMO appears more immune to most of the adverse
propagation phenomena resulting in a low rank SU-
MIMO channel matrix, such as LOS or antenna correla-
tion. Although increased correlation affects the diversity
achieved by each user, MU d iversity can be extracted
instead.
◦ MU-MIMO allows for spatial multiplexing gain at the BS
without necessitating terminals with multiple antennas.
This is especially significant from a commercial point of
view, since cost is kept in the infrastructure side.
The above advantages of MU-MIMO come at a certain cost:
◦ Perhaps the most important drawback is that MU-MIMO
requires CSIT to perform spatial multiplexing. While not
essential in SU-MIMO, CSIT is of utmost importance in
this case.
◦ The users in MU systems may significantly d iffer with
respect to the channel conditions. This gives rise to
fairness issues related to the selection of the subgroup
of users that will be served −scheduling.
◦ In SU-MIMO, co ding at the transmitter and decoding at
the receiver can be done in a cooperative fashion, since
the respective multiple an tennas a re co-located, whereas
in MU-MIMO users are geographically dispersed.
The MU channels can be distinguished into: the broadcasting
channel (BC), which is the downlink from the BS to the
mobile terminals, and the multiple access channel (MAC),
which is the corresponding uplink (see Fig. 3). The rest of
this article will focus on the BC. Consider a system with
M antennas at the BS and K users, each equipped with
N
k
antennas, k =1,...,K. Assuming frequency flat fading,
the downlink (BC) channel from the BS to the kth user is
represented by a complex Gaussian N
k
×M matrix H
k
.The
N
k
× 1 signal vector received at the kth user can be written
as:
y
k
= H
k
s + n
k
, (10)
where s represents the M × 1 signal vector transmitted from
the BS and n
k
is the N
k
× 1 ZMCSCG additive noise at
receiver k. The transmit covariance matrix of the input signal
is Q = E
ss
H
and the BS is subject to an average power
constraint P , which implies Tr(Q) ≤ P .
Capacity Region of the Broadcasting Channel: The
region of all user rates that are simultaneously achievable
is the capacity region [46]. A rate vector [R
1
,...,R
K
] is
achievable if a coding scheme exists assuring that the error
probability of all users goes to zer o as the code bloc k length
becomes long enough. An important point on the boundary of
the capacity region is the sum rate point, which corresponds
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