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Antenna Selection for Space-Time Coded Systems
with Imperfect Channel Estimation
Qian Ma and Cihan Tepedelenlio˘glu, Member, IEEE
Abstract—This paper studies the performance of antenna
selection (AS) for space-time (ST) coded systems with noisy
channel estimates. For coherent AS systems over Rayleigh flat
fading channels, we derive the pairwise error probability (PEP) in
the presence of imperfect channel estimation, where the channel
is estimated using training insertion and minimum mean square
error (MMSE) estimation. Multiplexed training is employed, where
the antennas are multiplexed to the small number of RF chains
available in the AS system. AS is performed only at the receiver,
using the maximum estimated channel power selection rule. Both
the maximum likelihood (ML) decoder taking into account the
channel estimation error, and the minimum distance decoder
are considered, and full diversity gain is shown to be preserved
for both cases. Based on the derived training-based PEP, the
effective SNR and the coding gain loss due to training are
quantified for square unitary and orthogonal codes. The optimal
power allocation between the training and data symbols is
obtained by minimizing the PEP. For AS systems employing
orthogonal designs, we further derive the exact PEP expression
in closed-form. We also show that when square unitary training
is employed, AS using the norm of MMSE channel estimates is
equivalent to AS using the norm (power) of the received signal.
Exploiting this fact, we propose an alternate training scheme
which avoids multiplexing, has higher spectral efficiency, and
better performance compared to the multiplexed training scheme.
Simulations are shown to validate our analysis.
Index Terms—Antenna selection, channel estimation, diversity,
pairwise error probability (PEP), multiple-antenna communications,
multiplexed training, space-time (ST) coding. |
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