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Schemes for spectrum holes sensing for cognitive radio based on the estimation of the Stokes parameters of monochromatic and quasimonochromatic polarized electromagnetic waves are developed. Statistical information that includes the variations of the polarization state in both cases (present and absent) of Primary User (PU) is accounted for. A detector based on the fluctuation of the Stokes parameters is analyzed, and
its performance is compared with that of energy detectors, which use only the scalar amplitude information to sense the PU signal. The cooperative spectrum sensing based on the polarization in which the reporting channels are noisy will be investigated. The cluster technique is proposed to reduce the bit error probability due to channel impairment. A closed-form expression for the polarization detection is derived using

Cognitive radio (CR) technology has witnessed a growing interest over the past decade, as it promises more efficient use of the available spectrum [

It is possible, however, to improve the spectrum sensing process by exploiting the polarization state of the signal. In radar systems [

Recent research on polarization detection in CR was concerned with completely polarized waves. A Virtual Polarization Detection (VPD) method based on the vector signal processing was presented for effective spectrum sensing of cognitive radios [

In this paper, the above constraint is addressed by proposing a polarization-based spectrum sensing scheme where a statistical model for the PU signal polarization parameters is adopted. This model takes into account the channel backscatter and the partial polarization nature of the PU signal, with the assumption that the channel experiences slow fading. Cooperative polarization spectrum sensing is proposed to mitigate the effects of fading and shadowing, which can seriously degrade the sensing performance. A cluster-based cooperation scheme is proposed to decrease bit error probability. All SUs are grouped into few clusters and one cluster head is set for each cluster to collect the sensing results, make cluster decisions, and forward measurements to the central unit. Thus the bit error probability will be reduced greatly because most of SUs will be closer to the cluster heads than to the central unit. Analytical results show that significant improvement can be achieved with our proposed method.

The rest of this paper is organized as follows. In Section

The polarization of a monochromatic plane wave is completely specified by constant amplitude and relative phase of the two orthogonal electric-field components.

In a cognitive radio system, the SU uses orthogonally dual polarized antennas to detect the PU signal

Alternatively, the polarization is determined by the geometrical parameters, namely the ellipticity angle

However, if the amplitudes and phases encounter slow fluctuations with time, which is the case if the polarization of primary signal suffers from either noise or fading, the components of the Jones vector are said to be quasimonochromatic or narrowband. The polarization of a quasimonochromatic wave is quantified using an average polarization state vector, which may be defined in terms of four measurable components; namely,

The component

Alternatively, the average polarization state can be obtained from the coherence matrix

The relationship of the SPs to the geometrical parameters

Thus far, the orientation of a polarization vector on the unit Poincare sphere can completely represent the polarization state of the received signal.

Spectrum sensing is essentially a binary hypothesis testing problem, which indicates the PU’s absence or presence, respectively, such that

In this paper, we propose two schemes which use the degree of polarization and the axial ratio to detect the PU signal.

The degree of polarization (

The estimate of the ratio of the polarized power to the total power in the received signal is used as detection statistics in radar systems [

The proposed spectrum sensing system model.

The distribution that governs the statistic

By substituting (

Using [

where

The polarized portion of the PU signal represents a net polarization ellipse traced by the electric field vector as a function of time. The ellipse has a magnitude (

The ellipticity is the ratio of the minor to the major axis of the corresponding electric field polarization ellipse and varies from

Figure

For a fixed threshold

Using binomial theorem and [

It is worth mentioning that the restriction for this scheme is that the polarization information of the primary signal must be known a priori. If the PU signal is linearly polarized, then

The fading and noisy nature of a wireless communication channel places a major challenge on the accuracy of spectrum sensing. Sensing decisions that is based on measurements of a single SU may be unreliable. Cooperative spectrum sensing is one possible solution to overcome this unreliability. In Figure

System model of the cooperative network.

Two cases are considered, namely, cooperative spectrum sensing with perfect and imperfect reporting channels.

If the channels between each SU and the central unit are noise free, then the overall probability of false alarm

In practical systems, the reporting channels between the SUs and the central unit will experience fading. This, in turn, will degrade transmission reliability of the sensing results that are reported from the SUs to the central unit. Let

Consequently, the overall probability of false alarm

Substituting (

where

Therefore, for AND rule, the overall probability of false alarm and detection are given by

The clustering method is proposed in the cooperative spectrum sensing scheme in order to improve the sensing performance by decreasing the reporting channel error, which is proved to exploit a selection diversity gain [

Cluster-based spectrum sensing mode.

Substituting

where

and substituting

Results obtained using the proposed methods are presented. Monte Carlo simulation consisting of 100000 independent trials was performed. The degree of freedom is set to 3.5 to make fair comparison between the proposed methods and the energy detection method [

Figure

Probability of detection versus SNR for directional and DoP methods.

Figure

ROC of the DoP method in AWGN.

The case of Rayleigh fading channel is considered in Figure

ROC of the DoP method under Rayleigh fading channel.

ROC of the DoP method under Nakagami fading channel.

It can be noticed that at fading conditions, the depolarization effect increases, which means higher dispersion of polarization states. Therefore, the detection performance decreases. Thus, the smaller the depolarization effect on the primary signal, the more constant the polarization state and thus the better the detection performance.

To demonstrate the performance of the axial ratio (AR) method, Figure

ROC of the DoP method under different

Figure

ROC of the AR method under Rayleigh fading channel.

ROC of the AR method under Nakagami fading channel.

A comparison between both approaches is drawn in Figure

ROC of the two methods (AR, DoP) at SNR=0 dB under Nakagami fading channel.

Figure

ROC of the cooperative scheme of the DoP method under imperfect Nakagami fading channel.

Spectrum sensing based on Stokes parameters was thoroughly analyzed using new detection statistics, namely, the degree of polarization and the axial ratio. The proposed approaches were studied under different fading scenarios and the obtained results demonstrated superior performance relative to the conventional energy detection method. An extensive study is reported on the two methods and their performance under

Cooperative spectrum sensing was then considered and shown to be a powerful method for dealing with the hidden terminal problem. Simulation results show that the cluster rule gives superior performance for a wide range of SNR.

The authors declare that there is no conflict of interests regarding the publication of this paper.