IEEE Signal Processing - May 2018 - 41

how to exploit sparsity properties to process wireless signals
in different applications.

Introduction
Sparse representation expresses some signals as a linear com-
bination of a few atoms from a prespecified and overcomplete
dictionary [1]. This form of sparse (or compressible) structure
arises naturally in many applications [2]. For example, audio
signals are sparse in the frequency domain, especially for the
sounds representing tones. Image processing can exploit a
sparsity property in the discrete cosine domain, i.e., many
images' discrete cosine transform (DCT) coefficients are zero
or small enough to be regarded as zero. This type of sparsity
property has enabled intensive research on signal and data
processing, such as dimension reduction in data science, wide-
band sensing in CRNs, data collection in large-scale wireless
sensor networks (WSNs), and channel estimation and feed-
back in massive MIMO.
Traditionally, signal acquisition and transmission adopt the
procedure with sampling and compression. As massive con-
nectivity is expected to be supported in the 5G and IoT net-
works, the amount of generated data becomes huge. Therefore,
signal processing has been confronted with challenges regard-
ing high sampling rates for data acquisition and large amounts
of data for storage and transmission, especially in IoT applica-
tions with power-constrained sensor nodes. Except for devel-
oping more advanced sampling and compression techniques,
it is natural to ask whether there is an approach to achieving
signal sampling and compression simultaneously.
As an appealing approach to employing sparse represen-
tation, Candès proposed CS for reducing data acquisition
costs by enabling sub-Nyquist sampling [3]. Based on his
advanced theory [4], CS has been widely applied in many
areas. The key idea in CS is to enable exact signal reconstruc-
tion from far fewer samples than required by the Nyquist-
Shannon sampling theorem, provided that the signal admits a
sparse representation in a certain domain. In CS, compressed
samples are acquired via a small set of nonadaptive, linear,
and usually randomized measurements, and signal recovery
is usually formulated as an l 0 -norm minimization problem
to find the sparsest solution satisfying the constraints. Since
l 0 -norm minimization is an NP-hard problem, most of the
existing CS research contributions solve it by either approxi-
mating it to a convex l 1-norm minimization problem [4] or
adopting greedy algorithms, such as orthogonal match pur-
suit (OMP).
It is often the case that the sparsifying transformation is
unknown or difficult to determine. Therefore, projecting a
signal to its proper sparse domain is essential in many appli-

cations that invoke CS. In 5G and IoT networks, the identi-
fied sparse domains mainly include the frequency, spatial,
wavelet, and DCT domains. CS can be used to improve the
SE and EE for these networks. By enabling the unlicensed use
of spectrum, CRNs exploit spectral opportunities over a wide
frequency range to enhance the network SE. In wide-band
spectrum sensing, spectral signals naturally exploit a sparsity
property in the frequency domain because of the low utiliza-
tion of spectrum [5], [6], which enables sub-Nyquist sampling
on cognitive devices.
Another interesting scenario is a small amount of data col-
lection in large-scale WSNs with power-constrained sensor
nodes, such as smart meters monitoring infrastructure in IoT
applications. In particular, the monitoring readings usually
have a sparse representation in the DCT domain because of
the temporal and spatial correlations [7]. CS can be applied
to enhance the EE of WSNs and to extend the lifetime of
sensor nodes.
Moreover, massive MIMO is a critical technique for 5G
networks. In massive MIMO systems, channels correspond-
ing to different antennas are correlated. Furthermore, a huge
number of channel coefficients can be represented by only a
few parameters because of a hidden joint sparsity property
from the shared local scatterers in the radio propagation envi-
ronment. Therefore, CS can be potentially used in massive
MIMO systems to reduce the overhead for channel estimation
and feedback and facilitate precoding [8]. Even though various
applications have different characters, it is worth noting that the
signals in different scenarios share a common sparsity prop-
erty, even though the sparse domains can be different, which
enables CS to enhance the SE and EE of wireless communica-
tions networks.
There have been some interesting surveys on CS [9] and
its applications [10]-[12]. One of the most popular articles
[9] provided an overview on the theory of CS as a novel sam-
pling paradigm that goes against the common wisdom in
data acquisition. The study in [10] summarized CS-enabled
sparse channel estimation. In [11], the authors provided a
comprehensive review of the application of CS in CRNs.
Other researchers presented a more specific survey on com-
pressive covariance sensing [12] that included the reconstruc-
tion of second-order statistics even in the absence of prior
sparsity information. These existing surveys serve different
purposes. Some cover the basic principles for beginners,
and others focus on specific aspects of CS. In contrast to
the existing literature, our article provides a comprehensive
overview of the recent contributions to CS-enabled wireless
communications from the perspective of adopting different
sparse domain projections.

IEEE Signal Processing Magazine

|

May 2018

|

41



Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018

Contents
IEEE Signal Processing - May 2018 - Cover1
IEEE Signal Processing - May 2018 - Cover2
IEEE Signal Processing - May 2018 - Contents
IEEE Signal Processing - May 2018 - 2
IEEE Signal Processing - May 2018 - 3
IEEE Signal Processing - May 2018 - 4
IEEE Signal Processing - May 2018 - 5
IEEE Signal Processing - May 2018 - 6
IEEE Signal Processing - May 2018 - 7
IEEE Signal Processing - May 2018 - 8
IEEE Signal Processing - May 2018 - 9
IEEE Signal Processing - May 2018 - 10
IEEE Signal Processing - May 2018 - 11
IEEE Signal Processing - May 2018 - 12
IEEE Signal Processing - May 2018 - 13
IEEE Signal Processing - May 2018 - 14
IEEE Signal Processing - May 2018 - 15
IEEE Signal Processing - May 2018 - 16
IEEE Signal Processing - May 2018 - 17
IEEE Signal Processing - May 2018 - 18
IEEE Signal Processing - May 2018 - 19
IEEE Signal Processing - May 2018 - 20
IEEE Signal Processing - May 2018 - 21
IEEE Signal Processing - May 2018 - 22
IEEE Signal Processing - May 2018 - 23
IEEE Signal Processing - May 2018 - 24
IEEE Signal Processing - May 2018 - 25
IEEE Signal Processing - May 2018 - 26
IEEE Signal Processing - May 2018 - 27
IEEE Signal Processing - May 2018 - 28
IEEE Signal Processing - May 2018 - 29
IEEE Signal Processing - May 2018 - 30
IEEE Signal Processing - May 2018 - 31
IEEE Signal Processing - May 2018 - 32
IEEE Signal Processing - May 2018 - 33
IEEE Signal Processing - May 2018 - 34
IEEE Signal Processing - May 2018 - 35
IEEE Signal Processing - May 2018 - 36
IEEE Signal Processing - May 2018 - 37
IEEE Signal Processing - May 2018 - 38
IEEE Signal Processing - May 2018 - 39
IEEE Signal Processing - May 2018 - 40
IEEE Signal Processing - May 2018 - 41
IEEE Signal Processing - May 2018 - 42
IEEE Signal Processing - May 2018 - 43
IEEE Signal Processing - May 2018 - 44
IEEE Signal Processing - May 2018 - 45
IEEE Signal Processing - May 2018 - 46
IEEE Signal Processing - May 2018 - 47
IEEE Signal Processing - May 2018 - 48
IEEE Signal Processing - May 2018 - 49
IEEE Signal Processing - May 2018 - 50
IEEE Signal Processing - May 2018 - 51
IEEE Signal Processing - May 2018 - 52
IEEE Signal Processing - May 2018 - 53
IEEE Signal Processing - May 2018 - 54
IEEE Signal Processing - May 2018 - 55
IEEE Signal Processing - May 2018 - 56
IEEE Signal Processing - May 2018 - 57
IEEE Signal Processing - May 2018 - 58
IEEE Signal Processing - May 2018 - 59
IEEE Signal Processing - May 2018 - 60
IEEE Signal Processing - May 2018 - 61
IEEE Signal Processing - May 2018 - 62
IEEE Signal Processing - May 2018 - 63
IEEE Signal Processing - May 2018 - 64
IEEE Signal Processing - May 2018 - 65
IEEE Signal Processing - May 2018 - 66
IEEE Signal Processing - May 2018 - 67
IEEE Signal Processing - May 2018 - 68
IEEE Signal Processing - May 2018 - 69
IEEE Signal Processing - May 2018 - 70
IEEE Signal Processing - May 2018 - 71
IEEE Signal Processing - May 2018 - 72
IEEE Signal Processing - May 2018 - 73
IEEE Signal Processing - May 2018 - 74
IEEE Signal Processing - May 2018 - 75
IEEE Signal Processing - May 2018 - 76
IEEE Signal Processing - May 2018 - 77
IEEE Signal Processing - May 2018 - 78
IEEE Signal Processing - May 2018 - 79
IEEE Signal Processing - May 2018 - 80
IEEE Signal Processing - May 2018 - 81
IEEE Signal Processing - May 2018 - 82
IEEE Signal Processing - May 2018 - 83
IEEE Signal Processing - May 2018 - 84
IEEE Signal Processing - May 2018 - 85
IEEE Signal Processing - May 2018 - 86
IEEE Signal Processing - May 2018 - 87
IEEE Signal Processing - May 2018 - 88
IEEE Signal Processing - May 2018 - 89
IEEE Signal Processing - May 2018 - 90
IEEE Signal Processing - May 2018 - 91
IEEE Signal Processing - May 2018 - 92
IEEE Signal Processing - May 2018 - 93
IEEE Signal Processing - May 2018 - 94
IEEE Signal Processing - May 2018 - 95
IEEE Signal Processing - May 2018 - 96
IEEE Signal Processing - May 2018 - 97
IEEE Signal Processing - May 2018 - 98
IEEE Signal Processing - May 2018 - 99
IEEE Signal Processing - May 2018 - 100
IEEE Signal Processing - May 2018 - 101
IEEE Signal Processing - May 2018 - 102
IEEE Signal Processing - May 2018 - 103
IEEE Signal Processing - May 2018 - 104
IEEE Signal Processing - May 2018 - 105
IEEE Signal Processing - May 2018 - 106
IEEE Signal Processing - May 2018 - 107
IEEE Signal Processing - May 2018 - 108
IEEE Signal Processing - May 2018 - 109
IEEE Signal Processing - May 2018 - 110
IEEE Signal Processing - May 2018 - 111
IEEE Signal Processing - May 2018 - 112
IEEE Signal Processing - May 2018 - 113
IEEE Signal Processing - May 2018 - 114
IEEE Signal Processing - May 2018 - 115
IEEE Signal Processing - May 2018 - 116
IEEE Signal Processing - May 2018 - 117
IEEE Signal Processing - May 2018 - 118
IEEE Signal Processing - May 2018 - 119
IEEE Signal Processing - May 2018 - 120
IEEE Signal Processing - May 2018 - 121
IEEE Signal Processing - May 2018 - 122
IEEE Signal Processing - May 2018 - 123
IEEE Signal Processing - May 2018 - 124
IEEE Signal Processing - May 2018 - 125
IEEE Signal Processing - May 2018 - 126
IEEE Signal Processing - May 2018 - 127
IEEE Signal Processing - May 2018 - 128
IEEE Signal Processing - May 2018 - 129
IEEE Signal Processing - May 2018 - 130
IEEE Signal Processing - May 2018 - 131
IEEE Signal Processing - May 2018 - 132
IEEE Signal Processing - May 2018 - Cover3
IEEE Signal Processing - May 2018 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com