IEEE Signal Processing - May 2018 - 55
information is then used to form the weighted factors and
design a weighted block optimization algorithm to estimate
the channel matrix. The authors of [59] proposed a spatial
sparsity-based compression mechanism to reduce the load of
the channel feedback. In this mechanism, they used random
projection with an unknown sparsity basis and direct com-
pression based on known sparsity. Since the spatial sparsity
will reduce channel rank, to obtain the compressed channel
estimation, they proposed a dictionary-learning method that
captures the communication environment and the anten-
na property.
After researchers designed the compressed hierarchical
multiresolution codebook [51]-[54], the corresponding chan-
nel estimation schemes could be developed. In these approach-
es, the hierarchical multiresolution codebook was capable of
generating variable beamwidth radiation patterns to facilitate
the use of robust adaptive multipath channel estimation algo-
rithms. Meanwhile, the exploitation of adaptive CS algorithms
would also reduce implementation complexity and estima-
tion error.
With spatial-temporal sparsity
In the aforementioned schemes, the investigators independent-
ly exploited both the temporal- and spatial-domain sparsities.
In practice, they can be jointly used to further reduce the cost
of channel estimation and feedback.
In [60], Shen et al. proposed a structured CS-enabled dif-
ferential joint channel training and feedback scheme, where a
structured compressive sampling matching pursuit algorithm
uses the structured spatial-time sparsity of wireless MIMO
channels to reduce the training and feedback overhead. In [61],
Huang et al. proposed a Bayesian CS-based feedback mecha-
nism for time-varying spatially and temporally correlated vec-
tor autoregression wireless channels, where the feedback rate
can be adaptively adjusted.
With spatial-frequency sparsity
Besides the spatial-temporal sparsity, the spatial-frequency one
can also be exploited to reduce the cost of channel estimation
and feedback. In [62], the researchers first exploited the sparsi-
ty in the spatial-frequency domain and proposed an adaptive
CS-enabled feedback scheme to reduce the feedback over-
head. In this approach, the feedback can be dynamically
configured based on the channel conditions to improve the
efficiency. Because of sharing sparse common support for the
adjacent subcarriers in orthogonal frequency-division modula-
tion (OFDM), the investigators developed an approximate
message passing with the nearest-neighbor sparsity pattern-
learning algorithm to adaptively learn the underlying structure
to obtain better performance.
Precoding and detection
The precoder design based on the estimated CSI is a very
important problem in massive MIMO systems, especially in
the mm-wave wide-band systems. Since the wide-band mm-
wave massive MIMO channel generally exhibits frequency-
selective fading, the precoder design based on the estimated
CSI becomes challenging. Generally, the sparse structure of
mm-wave massive MIMO channels in angle domain or beam
space can be used to simplify the precoder design [63], [64]. In
[63], Venugopal et al. used compressive subspace estimation to
get the full channel information and then design the precoder
to maximize the system SE. To reduce the CSI acquisition cost
and address the mismatch between few RF chains and many
antennas, the authors used the hybrid precoding design with
baseband and RF precoders in mm-wave massive MIMO sys-
tems. However, this hybrid precoding introduces performance
loss. To mitigate this, [64] utilized an iterative OMP to refine
the quality of the hybrid precoders. Meanwhile, a limited feed-
back technique was also proposed for hybrid precoding to
reduce the feedback cost.
CS can be also used in signal detection of massive MIMO
with spatial modulation (SM). In massive SM-MIMO, the
maximum likelihood detector has a prohibitively high com-
plexity. Thanks to the structured sparsity of multiple SM
signals, a low-complexity signal detector based on CS was
introduced to improve signal detection performance. In [65],
Gao et al. developed a joint SM transmission scheme for user
equipment and a structured CS-enabled multiuser detector for
the BS. The proposed detector can reliably detect the resultant
SM signals with low complexity by exploiting the intrinsic
sparse features.
CSI acquisition and precoding based on CS theory in FDD
massive MIMO systems have been mainly discussed so far. In
practice, the CS theory can also be applied to TDD massive
MIMO systems. Investigators developed a channel estimation
approach based on block-structured CS [66], where the com-
mon support in sparse channels and the channel reciprocity in
TDD mode are used simultaneously so that the computational
complexity and pilot overhead can be significantly reduced.
Potential research
Researchers have successfully used CS in massive MIMO to
improve the performance of channel estimation and precod-
ing. However, there are still many open topics that need to be
explored before CS can be implemented in massive MIMO
systems. We will discuss some of them in this section.
Effect of antenna deployment
Because of space limitations, large-scale antennas may be
deployed in various topologies, i.e., centralized or distributed.
Since the different antenna topologies correspond to different
channel sparsities, the effect of antenna configuration on the
performance of CS-enabled channel estimation is still an open
research question.
Measure of channel sparsity
As mentioned previously, channel sparsity is very important
for CS-enabled channel estimation. In current research,
investigators have assumed and exploited various sparsity
models in channel acquisition. Many of these assumed spar-
sity models lack verification by measured results. Thus,
IEEE Signal Processing Magazine
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Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018
Contents
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