IEEE Signal Processing - May 2018 - 45
pressed data to the sink. Then, the sink is responsible for
recovering the original reading using CS algorithms because
the readings across all of the sensor nodes exhibit both spa-
tial and temporal correlations, as we can see from the discus-
sion in the "CS-Enabled Large-Scale WSNs" section.
■ Angular-time domain: Massive MIMO channels between
some users and the massive base station (BS) antennas
appear to have spatial common sparsity in both the time
domain and the angular domain, as we will discuss in detail
in the "Channel Acquisition and Precoding in Massive
MIMO" section.
In Table 1, we summarize the different sparse domains and
their application in 5G and IoT networks. In addition to the
list, it is worth noting that the core of applying CS is to identi-
fy how to exploit the sparse property in 5G and IoT networks.
...
...
...
...
I Channels
J Sensors at Different Locations
...
frequency, wavelet, discrete cosine, and angular domains, to
name a few.
■ Frequency domain: Because of low spectrum utilization,
the wide-band spectrum signal shows a sparse property
when it is converted into the frequency domain.
■ Discrete cosine domain: Because of temporal correlation,
signals in some applications, such as environmental infor-
mation monitoring, show a sparse property in the discrete
cosine domain, as the readings normally do not change too
much within a short period.
■ Spatial domain: As the number of paths and the angle of
arrival are much smaller than the number of antennas in
massive MIMO systems, the channel conditions can be
represented by a limited number of parameters. In this
case, the spatial domain turns into the angular domain.
For multinode cases, because of the spatial correlation, joint
sparsity is exploited to apply DCS in spatial-x domains, where
x can be any of the aforementioned domains. Here, we give
some examples of how joint sparsity is utilized in different
scenarios in 5G and IoT networks:
■ Spatial-frequency domain: We provide an illustration of a
DCS-enabled cooperative CRN in Figure 3, where the joint
sparsity in the spatial-frequency domain is utilized. Specifically,
each column represents the signal received at each loca-
tion, which is sparse in the frequency domain, as only a
few channels are occupied. At different locations, the same
frequency bands may be occupied, but the signal powers
for each frequency band are various, because of fading and
shadowing. Therefore, different columns of the matrix
share the common sparse support, though each node oper-
ates without cooperation. With the DCS framework, each
node performs sub-Nyquist sampling individually first, and
then the original signals can be recovered simultaneously.
More details on this issue will be discussed in the
"CS-Enabled CRNs" section.
■ Spatial-temporal domain: In WSNs, sensor nodes are
deployed to periodically monitor data and send the com-
Joint Sparsity
Unoccupied
Occupied
FIGURE 3. Spatial-frequency correlation.
Table 1. Some common sparse domains and their applications in 5G and IoT networks.
Sparse Domain
Sparsifying Transform
Applications
Why Sparse?
Sparsity Property
Frequency domain
FT
Wide-band spectrum sensing
Low spectrum utilization in practice
Single sparsity
Spatial domain
-
Channel estimation in massive
MIMO
Number of paths is much fewer than
the number of antennas
Single sparsity
Discrete cosine domain
DCT
Sensor data gathering
Temporal correlation
Single sparsity
Wavelet domain
WT
Sensor data gathering
Temporal correlation
Single sparsity
Spatial-frequency domain
FT
Cooperative wide-band
spectrum sensing
Spatial correlation and low
spectrum utilization
Joint sparsity
Spatial-discrete cosine/wavelet
domain
DCT/WT
Active node detection/data
gathering
Spatial and temporal correlation
Joint sparsity
Angular-time domain
-
Channel estimation in massive
MIMO
Number of paths and degrees of
arrival are much fewer than the
number of antennas
Joint sparsity
WT: wavelet transform.
IEEE Signal Processing Magazine
|
May 2018
|
45
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