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In this paper we present a unified comparison of the performance of four detection techniques for centralized datafusion cooperative spectrum sensing in cognitive radio networks under impulsive noise, namely, the eigenvaluebased generalized likelihood ratio test (GLRT), the maximumminimum eigenvalue detection (MMED), the maximum eigenvalue detection (MED), and the energy detection (ED). We consider two system models: an implementationoriented model that includes the most relevant signal processing tasks realized by a real cognitive radio receiver, and the theoretical model conventionally adopted in the literature. We show that under the implementationoriented model, GLRT and MMED are quite robust under impulsive noise, whereas the performance of MED and ED is drastically degraded. We also show that performance under the conventional model can be too pessimistic if impulsive noise is present, whereas it can be too optimistic in the absence of this impairment. We also discuss the fact that impulsive noise is not such a severe problem when we take into account the more realistic implementationoriented model.
Spectrum scarcity in the fixed allocation policy is one of the main obstacles to the deployment of existing wireless communication systems and services, and to the development of new ones. With the advent of the cognitive radio (CR) paradigm [
Cooperative spectrum sensing can be classified as centralized and distributed, with the possibility of being relayassisted [
It is worth mentioning that the role of an FC in a centralized cooperative spectrum sensing can be assigned to a clusterhead in the context of clustered network topologies [
Conventionally, the wellknown memoryless linear discretetime multipleinput multipleoutput (MIMO) fading channel model has been indistinctively adopted for modeling the received samples for singlereceiver, multisensor and for multiplereceiver, singlesensor cognitive devices in datafusion cooperative spectrum sensing. However, this model, henceforth called conventional model (
Moreover, we investigate the performance of four eigenvaluebased sensing schemes under impulsive noise (IN) circumstances using the conventional MIMO channel model and the implementationoriented model. Specifically, we assess the performance of the eigenvaluebased generalized likelihood ratio test (GLRT); the maximumminimum eigenvalue detection (MMED), also known as the eigenvalue ratio detection (ERD); the maximum eigenvalue detection (MED), also known as Roy’s largest root test (RLRT); and the energy detection (ED) [
Impulsive noise in wireless systems may arise from several different sources, such as lightning, electrical switches, motors, vehicle ignition circuits, and reflections from sea waves, and it is known that it can severely degrade the performance of communications systems [
In [
Motivated by the above issues, this paper aims at contributing with investigations on the performance of eigenvaluebased spectrum sensing algorithms in view of two important issues, namely, the effect of impulsive noise and the behavior in a realistic implementation oriented model.
Although it is known that IN can severely degrade the performance of communication receivers, little effort has been put into investigations about the influence of IN in cognitive radio receivers in the context of spectrum sensing. This paper also aims to contribute with such investigations.
This paper presents a unified analysis about the influence of IN in four important detection techniques for datafusion cooperative spectrum sensing, namely, GLRT, MMED, MED, and ED, not only regarding the conventional model that is often adopted in the literature, but also considering a more realistic approach in which an implementationoriented CR receiver model is taken into account.
We show that GLRT and MMED are quite robust in the IN environment, while MED and ED performance is drastically affected. We also show that the sensing performance under the conventional model can be rather pessimistic if IN is present, while it can be optimistic in the absence of such impairment. We further show that the implementationoriented model is intrinsically able to combat IN.
Given the large differences in performance attained by these models in some situations, our main conclusion is that the implementationoriented model should be preferred for spectrum sensing design and assessment, as it more closely reflects the reality. Furthermore, this model shows that sensing can be more robust than expected with the conventional model under impulsive noise circumstances. To the best of our knowledge, no publication so far has considered such a unified approach.
Many papers in the literature, such as [
The rest of the paper is organized as follows.
In what concerns the baseband memoryless linear discretetime MIMO fading channel model, assume that there are
In eigenvaluebased sensing, spectral holes are detected using test statistics based on the eigenvalues of the sample covariance matrix of the received signal matrix
All the eigenvalue based methods rely on the fact that the covariance matrix in the presence of noise only is a diagonal matrix with all its elements equal to
In the conventional model, when a centralized cooperative sensing with singlesensor (e.g., single antenna) CRs is considered, matrix
The analog radiofrequency frontend is made up of a wideband antenna, a wideband bandpass filter (BPF), a lownoise amplifier (LNA), and quadrature local oscillators (LO) and mixers responsible for noncoherent direct conversion of the target channel to inphase and quadrature (I&Q) baseband signals. These signals are amplified using an AGC, which is responsible for maintaining its output signal within the dynamic range of the analogtodigital converters (ADC) in the I&Q signal paths. I&Q channel lowpass filters (LPF) select the desired bandwidth to be sampled and avoid aliasing. A noisewhitening process takes place to guarantee that noise components are kept uncorrelated when the received signal matrix is built at the fusion center. This is done because the detection techniques considered here assume, for optimum operation, that the noise samples are uncorrelated.
CR receiver diagram (adapted from [
Remembering that the samples are quantized at the ADC with
It is well known that the DC offset is one of the most relevant problems in a directconversion receiver [
Impulsive noise can be (i) generated from the electrical mains or by direct induction on the receiver; or (ii) captured by the receiver antenna. In the first category, the main noise sources are the ignition system of ovens, the control system of dishwasher machines, thermostats of heaters, and switches of fluorescent and incandescent lamps. In the second category, typical sources are lightning and the ignition system of cars.
Several models are available in the literature for characterizing IN [
Gating waveform (top) and impulsive noise waveform (bottom).
To adhere the above parameters to the context of spectrum sensing, we translated them into five other parameters:
The simulation setup under the conventional discretetime memoryless MIMO model (
The received matrix
The simulation setup under the realistic implementationoriented model (
Matrices
The elements in the channel matrix
To take into account the effect of the CR receive filters on the thermal and impulsive noises the entries in
A normalization of filtered samples was done to guarantee the desired received signaltonoise ratio (SNR), in dB, and the desired average IN power. Specifically,
The effect of the LNA and the AGC on the samples processed by the
From above one can see that the AGC will affect not only the noise level that corrupts the received samples in the
Back to the description of the implementationoriented model based on
Assuming no bit errors in the reporting channels, the modified received matrix
In this section we present simulation results and discussions concerning the influence of the system parameters under the
The ROC curves shown hereafter were obtained with a minimum of 5,000 runs in Monte Carlo simulations implemented according to the setup described in
Reference System Parameters.
Signaltonoise ratio  SNR = −10 dB 
Number of primary transmitters  
Number of CRs  
Number of samples collected by each CR  
Impulsive to thermal noise power ratio  
Signaltonoise ratio  SNR = −10 
MAfilter length  
ADC dynamic range  
ADC overdrive factor  
Number of quantization levels 
ROC curves for GLRT under parameter variations.
Since the influence of increasing the number
In what concerns the effect of increasing the SNR, we also know that it has no influence on
ROC curves for MMED (or ERD) under parameter variations.
From the results in
We now turn our attention to MED (or RLRT) and ED. In both cases the noise variance is assumed to be known.
ROC curves for MED (or RLRT) and ED under parameter variations.
The first big difference between the
3D plots of matrices
3D plots of matrices
System Parameters for IN Analysis.
Matrices plots 



Moderate IN  Strong IN  
Signaltonoise ratio (SNR) in dB  −10  −10  −10 
Number of primary transmitters ( 
1  1  1 
Number of CRs ( 
50  6  6 
Samples collected by each CR ( 
50  50  50 
Impulsive to thermal noise power ratio ( 
2  1  10 
Probability of impulsive noise ( 
1  1  0.2 
Fraction of CRs hit by impulsive noise ( 
0.1  0.5  0.5 
Samples affected by impulsive noise ( 
3  10  10 
Number of impulsive noise bursts ( 
1  1  1 


MAfilter length  
AGC dynamic range  
AGC overdrive fac  
Number of quantization levels 
We now analyze the spectrum sensing performance under IN. We show that the low influence of this noise on
The ROC curves referred to in this subsection were inserted in
As we can see in
ROC curves for the eigenvaluebased GLRT with and without (w/o) moderate or strong, concentrated IN.
ROC curves for MMED (or ERD) with and without (w/o) moderate or strong, concentrated IN.
ROC curves for MED (or RLRT) with and without (w/o) moderate or strong, concentrated IN.
ROC curves for ED with and without (w/o) moderate or strong, concentrated IN.
The bad performance of MED and ED under the
Although some eigenvaluebased sensing schemes are robust against IN, particularly with the
Detecting and removing IN influence is an active research topic in audio, image processing, and radio communications [
In the second countermeasure, the effective number of cooperating CRs is found as
Effect of muting samples and CR elimination under moderate or strong concentrated IN on GLRT.
Effect of muting samples and CR elimination under moderate or strong concentrated IN on MMED (or ERD).
Effect of muting samples and CR elimination under moderate or strong concentrated IN on MED (or RLRT).
Effect of muting samples and CR elimination under moderate or strong concentrated IN on ED.
In what concerns GLRT, we compare all ROC curves in
The above comparisons and conclusions closely hold for MMED (or ERD), as can be seen by comparing all ROC curves in
For MED (or RLRT), we compare all ROC curves in
In the case of ED, we compare all ROC curves in
From the results presented in this paper we can conclude that typical signalprocessing tasks performed at each cognitive radio before the collected samples are sent to the fusion center must be taken into account when investigating softvalues fusion algorithms, as the performance results may vary significantly between an idealized and a realistic model. Furthermore, the realistic model shows that the impact of impulsive noise is not as negative in real life as it could be implied from an idealized model.
We also conclude that GLRT performs better under IN circumstances, closely followed by MMED. The performance of MED and ED is drastically degraded by the effect of IN, with a clear advantage of MED over ED, since the latter did not work at all in any of the simulated scenarios. The superior performance of GLRT and MMED is attributed to the inherent ability of the eigenvalues of the covariance matrix
Last but not least, we conjecture that the performance of MED and ED under the implementationoriented model can be improved if the known normalization gains before the ADC are taken into account for the design of new test statistics and for producing the estimate of the thermal noise power in each cognitive radio. ED has a stronger demand for such improvement, since it simply does not work based on the test statistic (6). As already stated, this remains an open problem for future investigation
From the impulsive noise model described in
The number of CRs under cooperation resulting from the CR elimination IN countermeasure will be the random variable
The average number of CRs under cooperation,
The values of
Supplementary Material (XMCD, 414 KB)
IEEE Standard for Information Technology–Telecommunications and information exchange between systems Wireless Regional Area Networks (WRAN)–Specific requirements Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: Policies and Procedures for Operation in the TV Bands. IEEE Std 802.222011, 2011, pp. 1–680