IEEE Signal Processing - May 2018 - 48
could attain high sensing performance at a reasonable compu-
tational cost and power overhead by utilizing the joint sparsity
property. In decentralized approaches, signal recovery or matrix
completion is performed at each individual node. Compared with
centralized approaches, decentralized ones are more robust, as
they adopt an FC-free network structure. Another advantage of
decentralized approaches is that they allow the recovery of indi-
vidual sparse components at each node as well as the common
sparse components shared by all of the participating nodes.
Furthermore, the authors of [38] investigated CSS privacy
and security issues by exploiting joint sparsity in the frequency
and spatial domains. In their work, they removed measure-
ments corrupted by malicious users during the signal recovery
process at the FC so that the recovery accuracy and security of
the considered networks could be improved.
Compressive spectrum sensing with prior information
In conventional compressive spectrum sensing, only the spar-
sity property is utilized. Certain prior information is available
in some scenarios and can be exploited to improve the perfor-
mance of wide-band spectrum sensing in CRNs. For example,
in the case of spectrum sensing over TV white space (TVWS),
where the PUs are TV signals and the transmitted waveforms
are determined by the standard, this prior information,
together with the specifications dictated by the spectrum regu-
latory bodies, i.e., carrier frequencies and bandwidths, can
also be utilized to enhance signal recovery performance. Thus,
it is reasonable to assume that the PSD of the individual trans-
mission is known up to a scaling factor.
As discussed in the "Reweighted CS" section, reweighted CS
normally introduces weights to provide different penalties on
large and small coefficients, which naturally inspires the appli-
cation of reweighted CS in wide-band spectrum sensing with
available prior information. In [39], Liu and Wan divided the
whole spectrum into different segments, as the bounds between
different types of primary radios were known in advance.
Within each segment, they proposed an iteratively reweighted
, 1 /, 2 formulation to recover the original signals. In [5], the
researchers suggested a low-complexity wide-band spectrum-
sensing algorithm for the TVWS spectrum to improve signal
recovery performance, in which they constructed the weights
by utilizing the prior information from the geolocation data-
base. For example, in the TVWS spectrum, there are 40 TV
channels, each spanning 8 MHz, which can be either occupied
or not. Hence, the TV signals show a group sparsity property
in the frequency domain, as the nonzero coefficients show up
in clusters.
The authors of [40] developed a more efficient approach by
utilizing such a group sparsity property. Moreover, the signals in
wide-band spectrum sensing have the following two characteristics:
1) The input signals are stationary so that their covariance
matrices are redundant.
2) Most information in signals is, in practice, concentrated on
the first few lags of the autocorrelation.
Inspired by these characteristics, [41] proposed a spectral prior
information-assisted structured covariance estimation algo-
48
rithm with low computational complexity that especially fits
with applications on low-end devices.
Potential research
We have reviewed some research results in CS-enabled CRNs,
but there are still many open research issues in the area, espe-
cially when practical constraints are considered. In this section,
we will introduce a couple of important points of focus.
Performance limitations under practical constraints
Although there exist many research contributions in the field
of compressive spectrum sensing, most of them have assumed
some ideal operating conditions. In practice, there may exist
various imperfections, such as noise uncertainty, channel
uncertainty, dynamic spectrum occupancy, and transceiver
hardware imperfection [11]. For example, centralized com-
pressive spectrum sensing normally considers ideal reporting
channels, which is not the case in practice. This imperfection
may lead to significant performance degradation in real life.
Another example comes from the measurement matrix design.
As shown in Figure 2, the Gaussian distributed matrix
achieves better performance but with a higher implementation
cost. Even though investigators have proposed some structured
measurement matrices, such as the random demodulator, with
a lower cost and acceptable recovery performance degradation
to enable the implementation of CS as a replacement for high-
speed ADCs, the nonlinear recovery process limits their imple-
mentation. Therefore, a big challenge exists in further exploring
compressive spectrum sensing in the presence of practical
imperfections and to develop a common framework to combat
their aggregate effects in CS-enabled CRNs.
Generalized platform for compressive spectrum sensing
The existing hardware implementation of sub-Nyquist sam-
pling systems follows the procedure that the theoretic algo-
rithm is specifically designed for currently available hardware
devices. However, it is very difficult or sometimes even impos-
sible to extend current hardware architectures to implement
other existing compressive spectrum-sensing algorithms. Thus,
it is desired to have a generalized hardware platform that can
be easily adjusted to implement different compressive spec-
trum-sensing algorithms with different types of measurement
matrices and recovery algorithms.
CS-enabled large-scale WSNs
WSNs provide the ability to monitor diverse physical character-
istics of the real world, such as sound, temperature, and humi-
dity, by incorporating information and communication
technologies that are especially important to various IoT appli-
cations. In the typical WSN setup, a large number of inexpen-
sive and maybe individually unreliable sensor nodes with
limited energy storage and low computational capability are
distributed in a smart environment to perform a variety of data
processing tasks, such as sensing, data collection, classification,
modeling, and tracking. Cyberphysical systems (CPSs) merge
wireless communication technologies and environmental
IEEE Signal Processing Magazine
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May 2018
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