Spectrum sensing for cognitive radio exploiting spectrum discontinuities detection
 Wael Guibene^{1}Email author,
 Monia Turki^{2},
 Bassem Zayen^{1} and
 Aawatif Hayar^{3}
https://doi.org/10.1186/1687149920124
© Guibene et al; licensee Springer. 2012
Received: 6 July 2011
Accepted: 9 January 2012
Published: 9 January 2012
Abstract
This article presents a spectrum sensing algorithm for wideband cognitive radio exploiting sensed spectrum discontinuity properties. Some work has already been investigated by wavelet approach by Giannakis et al., but in this article we investigate an algebraic framework in order to model spectrum discontinuities. The information derived at the level of these irregularities will be exploited in order to derive a spectrum sensing algorithm. The numerical simulation show satisfying results in terms of detection performance and receiver operating characteristics curves as the detector takes into account noise annihilation in its inner structure.
Keywords
1. Introduction
During the last decades, we have witnessed a great progress and an increasing need for wireless communications systems due to costumers demand of more flexible, wireless, smaller, more intelligent, and practical devices explaining markets invaded by smartphones, personal digital assistant (PDAs), tablets and netbooks. All this need for flexibility and more "mobile" devices lead to more and more needs to afford the spectral resources that shall be able to satisfy costumers need for mobility. But, as wide as spectrum seems to be, all those needs and demands made it a scarce resource and highly misused.
Trying to face this shortage of radio resources, telecommunication regulators, and standardization organisms recommended sharing this valuable resource between the different actors in the wireless environment. The federal communications commission (FCC), for instance, defined a new policy of priorities in the wireless systems, giving some privileges to some users, called primary users (PU) and less to others, called secondary users (SU), who will use the spectrum in an opportunistic way with minimum interference to PU systems.
Cognitive radio (CR) as introduced by Mitola [1], is one of those possible devices that could be deployed as SU equipments and systems in wireless networks. As originally defined, a CR is a self aware and "intelligent" device that can adapt itself to the Wireless environment changes. Such a device is able to detect the changes in wireless network to which it is connected and adapt its radio parameters to the new opportunities that are detected. This constant track of the environment change is called the "spectrum sensing" function of a CR device.
Thus, spectrum sensing in CR aims in finding the holes in the PU transmission which are the best opportunities to be used by the SU. Many statistical approaches already exist. The easiest to implement and the reference detector in terms of complexity is still the energy detector (ED). Nevertheless, the ED is highly sensitive to noise and does not perform well in low signal to noise ratio (SNR). Other advanced techniques based on signals modulations and exploiting some of the transmitted signals inner properties were also developed. For instance, the detector that exploits the builtin cyclic properties on a given signal is the cyclostationary features detector (CFD). The CFD do have a great robustness to noise compared to ED but its high complexity is still a consequent draw back. Some other techniques, exploiting a wavelet approach to efficient spectrum sensing of wideband channels were also developed [2].
The rest of the article is organized as following. In Section 2, we introduce the state of the art and the motivations behind our proposed approach. In Section 3, we state the problem as a detection problem with the formalism related to both sensing and detection theories. The derivation of the proposed technique and some key points on its implementation are introduced in Section 4. In Section 5, we give the results and the simulation framework in which the developed technique was simulated. Finally, Section 6 summarizes about the presented work and concludes about its contributions.
2. State of the art
As previously stated, CR is presented [3] as a promising technology in order to handle this shortage and misuse of spectral resources. The main functions of CRs are:

Spectrum sensing: which is an important requirement towards CR implementation and feasibility. Three main strategies do exist in order to perform spectrum sensing: transmitter detection (involving PU detection techniques), cooperative detection (involving centralized and distributed schemes) and interference based detection.

Spectrum management: which captures the most satisfying spectrum opportunities in order to meet both PU and SU quality of service (QoS).

Spectrum mobility: which involves the mechanisms and protocols allowing frequency hopes and dynamic spectrum use.

Spectrum sharing: which aims at providing a fair spectrum sharing strategy in order to serve the maximum number of SUs.
The presented work fits in the context of spectrum sensing framework for CR networks (CRN) and more precisely single node detection or transmitter detection. In this context, many statistical approaches for spectrum sensing have been developed. The most performing one is the cyclostationary features detection technique [4, 5]. The main advantage of the cyclostationarity detection is that it can distinguish between noise signal and PU transmitted data. Indeed, noise has no spectral correlation whereas the modulated signals are usually cyclostationary with non null spectral correlation due to the embedded redundancy in the transmitted signal. The CFD is thus able to distinguish between noise and PU.
The reference sensing method is the ED [4], as it is the easiest to implement. Although the ED can be implemented without any need of apriori knowledge of the PU signal, some difficulties still remain for implementation. First of all, the only PU signal that can be detected is the one having an energy above the threshold. So, the threshold selection in itself can be problematic as the threshold highly depends on the changing noise level and the interference level. Another challenging issue is that the energy detection approach cannot distinguish the PU from the other SU sharing the same channel. CFD is more robust to noise uncertainty than an ED. Furthermore, it can work with lower SNR than ED.
More recently, a detector based on the signal space dimension based on the estimation of the number of the covariance matrix independent eigenvalues has been developed [6–8]. It was presented that one can conclude on the nature of this signal based on the number of the independent eigenvectors of the observed signal covariance matrix. The Akaike information criterion (AIC) was chosen in order to sense the signal presence over the spectrum bandwidth. By analyzing the number of significant eigenvalues minimizing the AIC, one is able to conclude on the nature of the sensed subband. Specifically, it is shown that the number of significant eigenvalues is related to the presence or not of data in the signal.
Some other techniques, exploiting a wavelet approach to efficient spectrum sensing of wideband channels were also developed [2]. The signal spectrum over a wide frequency band is decomposed into elementary building blocks of subbands that are well characterized by local irregularities in frequency. As a powerful mathematical tool for analyzing singularities and edges, the wavelet transform is employed to detect and estimate the local spectral irregular structure, which carries important information on the frequency locations and power spectral densities of the subbands. Along this line, a couple of wideband spectrum sensing techniques are developed based on the local maxima of the wavelet transform modulus and the multiscale wavelet products.
The proposed method was inspired from algebraic spike detection in electroencephalograms (EEGs) [9] and the recent work developed by Giannakis based on wavelet sensing [2]. Originally, the algebraic detection technique was introduced [9, 10] to detect spike locations in EEGs. And thus it can be used to detect signals transients. Given Giannakis work on wavelet approach, and its limitations in complexity and implementation, we suggest in this context of wideband channels sensing, a detector using an algebraic approach to detect and estimate the local spectral irregular structure, which carries important information on the frequency locations and power spectral densities of the subbands.
This article summarizes the work we've been conducting in spectrum sensing for CRN. A complete description of the reported work can be found in [11–15].
3. System model
where A_{ n }being the transmission channel gain, s_{ n }is the transmit signal sent from primary user and e_{ n }is an additive corrupting noise.
which represents the probability of the detector having detected a signal under hypothesis H_{1}, where P_{ M }indicates the probability of missed detection.
where ${F}_{{H}_{0}}$ denote the cumulative distribution function (CDF) under H_{0}. In this article, the threshold is determined for each of the detectors via a Monte Carlo simulation.
4. Mathematical background
 (1)
The frequency boundaries f_{1} and f_{ K }= f_{1} + B are known to the CR. Even though the actual received signal may occupy a larger band, this CR regards [f_{1}, f_{ K }] as the wide band of interest and seeks white spaces only within this spectrum range.
 (2)
The number of bands N and the locations f_{2},..., f_{K1}are unknown to the CR. They remain unchanged within a time burst, but may vary from burst to burst in the presence of slow fading.
 (3)
The PSD within each band B_{ n }is smooth and almost flat, but exhibits discontinuities from its neighboring bands B_{n1}and B_{n+1}. As such, irregularities in PSD appear at and only at the edges of the K bands.
 (4)
The corrupting noise is additive white and zero mean.
where: χ_{ i }[f_{i1}, f_{ i }]: the characteristic function of the interval [f_{i1}, f_{ i }], (p_{ i })_{i∈[1,K]}: an N th order polynomials series, (f_{ i })_{i∈[1,K]}: the discontinuity points resulting from multiplying each p_{ i }by a χ_{ i }and n(f): the additive corrupting noise.
And let b, the frequency band, given such as in each interval I_{ b }= [f_{i1},f_{i}] = [ν,ν + b], ν ≥ 0 maximally one change point occurs in the interval I_{ b }.
with μ_{ k }= 0⌋_{k = 1...N}if there is no change point and μ_{ k }≠ 0⌋ _{k = 1...N}if the change point is in I_{ b }.
[X_{ ν }(f)]^{(N)}is the regular derivative part of the N th derivative of the signal.
where: ${h}_{k+1}\left(f\right)=\left\{\begin{array}{cc}\frac{{\left({f}^{l}{\left(bf\right)}^{N+k}\right)}^{\left(k\right)}}{\left(l1\right)!}\hfill & 0<f<b\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}\right.$
4.1. Implementation issues
Then, we process by detecting spectrum discontinuities and to find the intervals of interest.
4.2. Algorithm discrete implementation
5. Performance evaluation
5.1. Performance metrics
where N_{ cd }is the number of correct detections per iteration and N_{ a }is number of generated change points per iteration (it's the same in every iteration).
where $\overline{{N}_{FAk}}$ is the average number of falsely detected change points given that the number of detected ones is k with n different realizations.
5.2. Simulations results
where M is the number of samples of the received signal x_{ n }. Traditional ED can be simply implemented as a spectrum analyzer. A threshold used for PU detection is highly susceptible to unknown or changing noise levels. Even if the threshold would be set adaptively, presence of any inband interference would confuse the ED.
Complexity comparison of the different sensing techniques
Sensing technique  Complexity 

Energy detector  M 
Algebraic detector  NM 
The transmitted DVBT primary user signal parameters
Bandwidth  8MHz 

Mode  2K 
Guard interval  1/4 
Frequencyflat  Single path 
Sensing time  1.25 ms 
Location variability  10dB 
6. Conclusion
In this article, we presented a new standpoint for spectrum sensing emerging in detection theory, deriving from differential algebra, noncommutative ring theory, and operational calculus. The proposed algebraic based algorithm for spectrum sensing by change point detections in order to emphasizes "spikelike" parts of the given noisy amplitude spectrum. Simulations results showed that the proposed approach is very efficient to detect the occupied subbands in the the primary user transmissions. We have shown how very simple sensing algorithm with good robustness to noise can be devised within the framework of such unusual mathematical chapters in signal processing. A probabilistic interpretation, in the sense of ROC curve, probability of detection and probability of false alarm, is shown to be attached to the presented approach. It has allowed us to give a first step towards a more complete analysis of the proposed sensing algorithms.
Appendix 1. Annihilating jumps in the derivatives
Given the fact the initial conditions and the jump of the derivatives of X_{ ν }(f) are unknown parameters to the problem, in a first time we are going to annihilate the jump values μ_{0},μ_{1},..., μ_{N1}then the initial conditions. In order to make further calculations easier and shorter to write, let:
where, $\left({}_{k}^{N}\right)={\scriptscriptstyle \frac{N!}{k!(Nk)!}}:$: denotes the binomial coefficient.
Now, given the fact that the initial conditions in:
Now, given that:
Appendix 2. Annihilating initial conditions
where each time:
where: ${h}_{k+1}\left(f\right)=\left\{\begin{array}{cc}\frac{{\left({f}^{l1}{\left(bf\right)}^{N+k}\right)}^{\left(N\right)}}{\left(l1\right)!},\hfill & 0<f<b\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}\right.$
And the estimator is deduced by assuming as input the real amplitude spectrum Y(f) instead of X(f).
Declarations
Acknowledgements
The research work was carried out at EURECOM's Mobile Communications leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/20072013) under grant agreement SACRA n◦249060.
Authors’ Affiliations
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