IEEE Signal Processing - May 2018 - 47
signals are then sampled at a sub-Nyquist rate. Because of low
spectrum utilization, s f can be recovered from the undersam-
pled measurements. Then, the energy of each channel can be
calculated, and so the spectrum occupancy can be determined.
Recently, the authors of [29] identified that the CS-enabled
system is somewhat sensitive to noise, exhibiting a 3-dB signal-
to-noise ratio loss per octave of subsampling, which parallels
the classic noise-folding phenomenon. To improve robustness to
noise, [6] proposed a denoised compressive spectrum-sensing
algorithm. It requires the sparsity level to determine in advance
the lower sampling rate locally at SUs without loss of any infor-
mation. However, the sparsity level is dependent on spectrum
occupancy, which is usually unavailable in dynamic CR net-
works. To solve this problem, the researchers in [30] proposed
a two-step CS scheme to minimize the sampling rates when the
sparsity level is changing. This approach estimates the actual
sparsity level first, along with the number of compressed mea-
surements to be collected, and then makes adjustments before
sampling. But this algorithm introduces extra computational
complexity by performing the sparsity-level estimation.
To avoid this estimation, Sun et al. [31] proposed adjust-
ing the number of compressed measurements adaptively by ac-
quiring compressed measurements step by step in continuous
sensing slots. However, this iterative process incurs higher com-
putational complexities at the SU, as (4) has to be solved sever-
al times until the exact signal recovery is achieved. The work in
[5] proposed a low-complexity compressive spectrum-sensing
algorithm by alleviating the iterative signal recovery process.
More specifically, the study showed that geolocation data pro-
vided a rough estimation of the sparsity level to minimize the
sampling rates. Subsequently, the authors utilized data from a
geolocation database as the prior information for signal recov-
ery. By doing so, signal recovery performance was improved,
with a significant reduction in the computational complexity
and a minimal number of measurements.
Compressive power spectral density estimation
In contrast to the aforementioned approaches that concentrate on
spectral estimation with perfect reconstruction of the original sig-
nals, compressive power spectral density (PSD) estimation pro-
vides another approach for spectrum detection, without requiring
the complete recovery of the original signals. Compressive PSD
estimation has been widely applied, as the original signals are not
actually required in many signal processing applications. For
wide-band spectrum-sensing applications with spectrally sparse
signals, only the PSD or, equivalently, the autocorrelation func-
tion needs to be recovered, as only the spectrum occupancy status
is required for each channel.
Polo et al. [32] proposed reconstructing the autocorrelation
of the compressed signal to provide an estimate of the signal
spectrum by utilizing the sparsity property of the edge spec-
trum, in which the CS is performed directly on the wide-band
analog signal. Nevertheless, [32] assumed the compressive
measurements to be wide-sense stationary, which is not true
for some compressive measurement matrices. Subsequently,
Lexa et al. [33] proposed a multicoset sampling-based power
spectrum estimation method to exploit the fact that a wide-
sense stationary signal corresponds with a diagonal covariance
matrix of the frequency domain representation of the signal.
Additionally, Leus et al. [34] solved the power spectrum blind-
sampling problem based on a periodic sampling procedure and
further proposed a simple LS reconstruction method for power
spectrum recovery.
Beyond sparsity
For spectrum blind sampling, the goal is to perfectly reconstruct
the spectrum, and sub-Nyquist rate sampling is possible only if
the spectrum is sparse. However, sub-Nyquist rate sampling
could be achieved in [34] without making any constraints on the
power spectrum, though the LS reconstruction required some
rank conditions to be satisfied. Leus et al. [35] further proposed
an efficient power spectrum reconstruction and a novel multico-
set sampling implementation by exploiting the spectral correla-
tion properties without requiring any sparsity constraints on the
power spectrum. More recently, Cohen and Eldar [36] devel-
oped a compressive power spectrum estimation framework for
both sparse and nonsparse signals as well as blind and nonblind
detection in the sparse case. For each of those scenarios, the
researchers derived the minimal sampling rate allowing per-
fect reconstruction of the signal's power spectrum in a noise-
free environment.
Cooperative spectrum sensing with joint sparsity
In spectrum sensing, the performance is degraded by noise
uncertainty, deep fading, shadowing, and hidden nodes.
Cooperative spectrum sensing (CSS) was proposed to im-
prove sensing performance by exploiting the collaboration
among all of the participating nodes. In CRNs, a CSS network
constructs a multinode network. As mentioned previously, the
joint sparsity and low-rank properties can be utilized to recov-
er the original signals simultaneously with fewer measure-
ments; DCS is employed, as it fits the CSS model perfectly.
In the existing literature, cooperative compressive spec-
trum sensing mainly includes two categories: centralized
and decentralized.
A centralized approach involves a fusion center (FC) per-
forming signal recovery by utilizing the compressed measure-
ments contributed by the spatially distributed SUs. The work in
[6] proposed a robust wide-band spectrum-sensing algorithm
for centralized CSS. Specifically, each SU senses a segment of
the spectrum at a sub-Nyquist rate to reduce the sensing bur-
den. With the collected compressive measurements, CS recov-
ery algorithms are performed at the FC to recover the original
signals by exploiting the sparse nature of spectrum occupancy.
Note that the sparse property of signals received at the SUs
can be transformed into the low-rank property of the matrix
constructed at the FC. In the case of CSS with sub-Nyquist
sampling, the measurements collected by the participating SUs
are sent to the FC, which exploits the joint sparsity or low-rank
property to recover the complete matrix.
Zeng et al. proposed a typical decentralized approach in [37],
in which the decentralized consensus optimization algorithm
IEEE Signal Processing Magazine
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May 2018
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47
Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018
Contents
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