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In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. This combining strategy is applied to variants of four test statistics for binary hypothesis test, namely: the eigenvalue-based generalized likelihood ratio test (GLRT), the maximum-minimum eigenvalue detection (MMED), the maximum eigenvalue detection (MED) and the energy detection (ED). It is shown that the eigenvalue fusion can outperform schemes based on decision fusion and sample fusion. A tradeoff is also established between complexity and volume of data sent to the fusion center in all combining strategies.

Due to the increased demand for wireless communication services and the adoption of a fixed spectral allocation policy that designates a specific band for primary systems in a given geographical region and on a long-term basis, spectral scarcity has become of main concern. The spectral scarcity is one of the greatest obstacles to the deployment of existing and new wireless communication systems and services. With the advent of the concept of cognitive radio (CR) [

Spectrum sensing is the fundamental task performed by a CR in order to gain access to a band of interest. As the name suggests, it is the task of monitoring a given band of interest in order to find spectral holes for subsequent opportunistic occupation. CRs with spectrum sensing capability have to identify spectrum holes efficiently and avoid harmful interference to primary users by either switching to an unoccupied band or keeping the interference below a maximum acceptable level [

Third-generation (3G) broadband systems are mostly based on direct-sequence spread spectrum (DSSS), such as Evolution-Data Optimized (EV-DO) or High-Speed Packet Access (HSPA). Fourth-generation (4G) systems, however, predominately use multicarrier systems, like orthogonal frequency division multiplexing (OFDM), combined with or without its access counterpart, the orthogonal frequency division multiple access (OFDMA) [

Due to the high importance of OFDMA signals in wireless communication systems and the high importance of spectral sensing in the context of cognitive radio networks, ongoing researches are proposing new methods of wideband spectral sensing and existing ones are being combined to improve the performance of cognitive radio networks. This paper aims at contributing to this research effort by proposing a new approach to the spectrum sensing of OFDMA and other wideband signals.

Several spectrum sensing techniques have been proposed so far, which can be classified as narrowband and wideband according to the bandwidth of the spectrum sensed. Narrowband sensing techniques are limited to detect the presence of primary signals in a single band, while wideband techniques aim at jointly or sequentially monitoring multiple bands.

In what concerns narrowband sensing, energy detection (ED) [

In wideband ED, the presence of the primary signal is detected from the energy of the received signal in each pre-defined band. The spectral partition can be done by using a filter bank approach [

Wavelet detection uses the wavelet transform to detect discontinuities in the power spectrum density (PSD) of the signal received by a CR, thus defining the frequency boundaries in the primary signal [

Compressed sensing uses a procedure of parameter estimation from a sampling with rate below the Nyquist rate (sub-Nyquist sampling) [

In eigenvalue-based spectrum sensing, the test statistic is computed from the eigenvalues of the received signal covariance matrix [

Although spectrum sensing can be performed by each CR individually and independently from others CRs, cooperative spectrum sensing is being considered as a possible solution for problems experienced by cognitive networks with a non-cooperative spectrum sensing, such as receiver uncertainty, multipath fading and correlated shadowing [

Cooperative spectrum sensing can be centralized, distributed or relay-assisted [

It is worth mentioning that the role of an FC in a centralized cooperative spectrum sensing can be assigned to a cluster-head in the context of clustered network topologies [

This paper proposes a new eigenvalue-based centralized cooperative spectrum sensing approach for OFDMA and other wideband signals. In this approach, the energy detection in [

Three forms of data fusion were addressed: (i) the fusion of samples from each CR, but in the frequency domain; (ii) the fusion of binary decisions made by all cooperating CRs and (iii) the new fusion approach in which the eigenvalues estimated by each CR are combined at the FC.

Simulation results show that the new eigenvalue fusion scheme can overcome the performance of the sample and decision fusion for detection of unoccupied sub-bands in a general wideband signal and for detection of unoccupied subchannels in an OFDMA signal.

The eigenvalue fusion scheme demands less transmitted data to the FC when compared with sample fusion schemes with similar performances. However, the amount of data transmitted to the FC in eigenvalue fusion and sample fusion can be, by far, greater than those in decision fusion schemes with similar system parameters.

The remaining of the paper is organized as follows.

Consider a discrete-time memoryless multiple input multiple output (MIMO) model, where each of the m sensors (antennas) in a CR or each single-sensor CR collects n samples of the received signal from ^{m×n}. Analogously, consider that the signals transmitted by the ^{p×n}. Let H ∈ ℂ^{m×p} be the channel matrix with elements ^{m×n} be the matrix with thermal noise samples corrupting the signal received by the

In eigenvalue-based cooperative spectrum sensing, a spectral hole is detected by applying a binary hypothesis test where the test statistic is built from the eigenvalues of the received signal ensemble covariance matrix ^{†} denotes the conjugate and transpose operations. The eigenvalues {λ_{1} ≥ λ_{2} ≥ · · · λ_{m} } of ^{2} is thermal noise variance at the input of each sensor, and tr(·) and ║·║_{F} correspond to the trace and the Frobenius norm of the matrix, respectively. The sensing process is then concluded by comparing the test statistic with a threshold pre-defined according to the desired performance of the sensing process. If the test statistic is greater than the threshold, the channel is deemed occupied; otherwise the channel is declared vacant.

The performance of a sensing technique is usually measured in terms of the probability of false alarm (_{fa} ) and the probability of detection (_{d} ). _{fa} is the probability of inferring that a sensed band is occupied when it is in fact vacant, _{fa} is minimized and _{d} is maximized. However, these objectives are conflicting ones: increasing the threshold decreases _{fa} , but also decreases _{d}. As a consequence, a tradeoff must be adopted so that the correct threshold is established. The tradeoff is usually determined with the aid of receiver operating characteristic (ROC) curves that show the variation of _{fa} versus _{d} with changes in the threshold value.

The eigenvalue-based detection for narrowband signals can be used to detect wideband signals as well. To this end, the model considered in the previous section has to be adapted to a situation in which received samples are represented in the frequency domain. Therefore, before going into the specifics of the proposed eigenvalue fusion scheme, we first address the channel and signal models in the frequency domain. Then we discuss how the sample fusion process works when samples are in the frequency domain. The proposed eigenvalue fusion is presented in the sequel. For the sake of completeness, the section ends with the description of the decision fusion process in the context of general wideband signals.

Consider a wideband communication system in which the overall bandwidth is partitioned into

Assume a multipath frequency-selective fading channel, where _{ℓ}, _{t} is the primary transmitted signal samples and _{t} is the complex additive white Gaussian noise (AWGN) samples with zero mean and variance

In a multipath fading channel, a wideband signal undergoes frequency-selective fading. The frequency-selective behavior of the channel in a given observation instant (snapshot) can be unveiled from its frequency response, which can be obtained by a _{t}, _{k} is the primary signal in the frequency domain and _{k} is the thermal noise in the frequency domain at the ^{2}, as the FFT operation is a linear transformation and the samples of a Gaussian noise in the time domain are Gaussian distributed. We also model the primary signal samples as a Gaussian random signal, since most of the modulated signals, especially OFDM signals, can be accurately modeled as having Gaussian distributed amplitudes. We also assume a slow fading channel, meaning that the channel frequency response is constant during a sensing period, but independent from one period to another.

Traditional data fusion cooperative spectrum sensing combines the samples collected by each CR at the FC, as described in

The

The eigenvalues of Rk are also computed at the FC and the test statistic for the k-th sub-band of a general wideband signal with sample fusion is formed via Equations (3)–(6).

We now propose a new eigenvalue fusion scheme, where each CR is responsible for computing its own sample covariance matrix, estimating its eigenvalues and transmitting these eigenvalues to the FC. The aim is to detect the presence of a primary signal to the level of subcarriers in OFDM systems, or to the level of predefined channels or sub-bands in general wideband signals. The adaptation of the eigenvalue combining is discussed in the next section.

Again, let

The sample covariance matrices in this case are computed in each CR and are given by

The eigenvalues of these covariance matrices are then computed and sent to the FC. The next part of the sensing process is to combine the eigenvalues received by the FC for the computation of the test statistic. For a quantity _{1,k,i} ≥ λ_{2,k,i} ≥ · · · λ_{J,k,i}} are the

Notice that the difference between the sample fusion and the eigenvalue fusion schemes goes beyond a simple shift of the eigenvalue computations from the FC to the CRs. In sample fusion, samples collected by the CRs are sent to the FC, where one sample covariance matrix from all CR samples is formed. The eigenvalues of this matrix are computed and then the desired test statistic is formed. In the proposed scheme, each CR forms one covariance matrix based solely on its samples and computes its eigenvalues. The eigenvalues from different CRs are then sent to the FC, where they are combined to form the test statistic. Notice that this approach aims at reducing the volume of data sent in the reporting channel (from the CRs to the FC) when compared with the sample fusion scheme.

It is worth mentioning that the modified test statistics Equations (14)–(17), as well as other ones defined later in this paper, were determined empirically. This means that it is not guaranteed that they are the optimal versions of the corresponding hypothesis tests derived from a likelihood ratio test. Then, all the modified test statistics from this point on can be cast as GLRT-like, MMED-like, MED-like and ED-like tests.

In

The final decision at the FC related to a given band is arrived at as follows: let _{i} represent the decision made by the _{i}, u_{i} = 1 for _{i} = 1 for any _{i} > _{i} < _{i} =

Individual CR decisions can be made by applying any of the detection techniques discussed so far. The test statistics for the _{1,k,i} ≥ λ_{2,k,i} ≥ · · · λ_{J,k,i}} are the

The proposed eigenvalue fusion scheme can be applied to any wideband signal. From the previous section we saw that it can be directly applied to the level of subcarriers in OFDM signals, for example, or to the level of predefined sub-bands in general wideband signals. Moreover, it can be adapted to sense an OFDMA signal to a subchannel level. This adaptation is described in this section. For the sake of completeness, the sample fusion and the decision fusion are also described in the context of OFDMA signals.

While OFDM assigns an entire block of frequencies to one user, OFDMA is a multiple access technique that allocates to a given user a set or multiple sets of subcarriers, allowing for simultaneous access to the overall band by several users. A set of frequencies is called a subchannel. The formation of a subchannel can be classified in two types: adjacent subcarrier method (ASM), which groups a set of contiguous subcarriers to form a subchannel, and diversity subcarrier method (DSM), in which non-contiguous subcarriers are chosen to form a subchannel [

Suppose a single OFDMA signal with _{1,s,i} ≥ λ_{2,s,i} ≥ · · · λ_{K ′ ,s,i}} are the

Here we describe how the sample fusion strategy can be adapted to detect the occupancy of an OFDMA subchannel. Several sample combining rules can be implemented in this case; below we describe two alternatives that produce a sample covariance matrix at the FC with the same order as in the case of eigenvalue combining. These alternatives are designated as concatenation and maximum-ratio-combining.

A number of

In another situation, the rows corresponding to all CRs are maximum-ratio-combined, resulting in _{1,s} ≥ λ_{2,s} ≥ · · · λ_{K ′ ,s}} are estimated. The test statistics Equations (3)–(6) are now modified to detect the

The decision upon the occupancy of the s-th OFDMA subchannel is then reached at the FC after comparing the adopted test statistic with the decision threshold.

Now we describe how the decision fusion strategy was adapted to detect the occupancy of an OFDMA subchannel. A matrix with sample values at each CR and for each subchannel will be formed according to Equation (22), from where the corresponding sample covariance matrices are computed via Equation (23). From each of the resulting _{1,s} ≥ λ_{2,s} ≥ · · · λ_{K ′,s}}. The occupation of each subchannel is determined by comparing any of the test statistics Equations (31)–(34) with the decision threshold. The resulting decisions are then sent to the FC for binary arithmetic combining and final decisions upon each subchannel.

In this section, we compare the proposed eigenvalue fusion scheme with schemes using sample and decision fusions. Two types of primary signal were considered: a general wideband signal and an OFDMA signal. In the case of a general wideband signal, the performance is relative to sensing at the level of sub-bands. In the case of OFDMA, the performance is relative to sensing at the subchannel level. In all cases, the ROC curves were built from the average of _{fa} and _{d} in all frequency sub-bands of general wideband signals, or in all subchannels of OFDMA signals. The curves were obtained via Monte Carlo simulations, counting a minimum of 100 false alarm or detection events (which occurs first) or a maximum of 5000 runs. The code was implemented in MATLAB according to the models and test statistics described throughout the paper. The primary radio signal activity in each sub-band and subchannel was modeled as a Bernoulli random variable with 50% of the time in the ON state (for _{d} computations) and 50% in the OFF state (for _{fa} computations).

To simulate the detection of a general wideband signal, we have considered a single primary transmitter whose total bandwidth was partitioned into K = 8 sub-bands. We have also considered:

It is known that the number of collected samples and the order of the sample matrix used in the computation of the covariance matrix influence the sensing performance of eigenvalue-based spectrum sensing. Then, for a fair comparison, both should be the same in all fusion schemes analyzed here. However, this is only possible in the case of the eigenvalue and decision fusion, as can be verified in

For the eigenvalue and decision fusion schemes, the total number of samples collected by each CR was

From

ROCs for sample fusion, decision fusion and eigenvalue fusion using GLRT for sensing a general wideband signal.

ROCs for sample fusion, decision fusion and eigenvalue fusion using MMED for sensing a general wideband signal.

ROCs for sample fusion, decision fusion and eigenvalue fusion using MED for sensing a general wideband signal.

ROCs for sample fusion, decision fusion and eigenvalue fusion using ED for sensing a general wideband signal.

When

Still referring to the results in

To simulate the application of the eigenvalue fusion technique for detecting subchannels of a single OFDMA signal, we have considered a primary network with

The test statistics Equations (31)–(34) were used for the sample fusion (using concatenation and MRC) and for individual CR decisions. The test statistics Equations (24)–(27) were considered for the eigenvalue fusion.

As in the case of a general wideband signal, the eigenvalue fusion scheme delivered the best performance among all fusion methods under analysis, for all test statistics, closely followed by the sample fusion using the concatenation approach for constructing the sample matrices. The performance of the sample fusion using the MRC approach produced a worse performance than the concatenation approach, also having the drawback of needing to know the channel gains. The better performance of the concatenation approach can be accredited to the large number of columns in the matrices used to compute the sample covariance matrices, as shown by Equation (28). We conjecture that the poor performance of the sample fusion for sensing OFDMA signals can be accredited to the different channel gains affecting each row of the sample matrices used for covariance matrices computations: notice in Equation (28) that the concatenated matrices come from different CRs and, thus, result from different channel gains. This is in contrast with the model presented in

ROCs for sample fusion, decision fusion and eigenvalue fusion using GLRT for sensing OFDMA subchannels.

ROCs for sample fusion, decision fusion and eigenvalue fusion using MMED for sensing OFDMA subchannels.

ROCs for sample fusion, decision fusion and eigenvalue fusion using MED for sensing OFDMA subchannels.

ROCs for sample fusion, decision fusion and eigenvalue fusion using ED for sensing OFDMA subchannels.

The ranking of the performances considering different test statistics still has ED in the first position, followed by MED, GLRT and MMED. Again it is observed the inversion of the behaviors of ED and MED when comparing with traditional eigenvalue detection of narrowband signals via Equations (3)–(6). This indicates that the empirical test statistics Equations (27) and (34) have more statistical power than Equations (26) and (33), which means that Equations (26) and (33) have margin for improvements in their definitions.

Still referring to

The major difference between the sample fusion and the eigenvalue fusion strategies is the amount of data sent to the FC. For the parameters used in the numerical results for the OFDMA signal, we had the following situation: The primary signal was made up with

A general analysis of the volume of data sent to the FC and the complexity tradeoff is made in the next section, also considering the sensing of general wideband signals.

In this section, we generalize the exemplifying analysis given in the previous subsection, concerning the tradeoff between the volume of data sent to the FC and the complexity related to the number of samples handled and to the computations of eigenvalues for all fusion methods under analysis. We consider a WiMAX system as a case study for providing numerical results as well.

Assume that the WiMAX channel has 2048 subcarriers. For spectral roll-off reasons, only 1, 680 subcarriers are utilized, leaving unused the subcarriers at the edge of the channel. The OFDMA subchannels are created by partitioning the

Let us consider first that detecting the

Consider now an eigenvalue fusion scheme. For a fair comparison, assume again that received sample matrices of order

The above analysis shows that the volume of data sent to the FC in the case of sample fusion (∝

In terms of complexity, in the case of eigenvalue and decision fusions, each CR must be capable of processing

Now, let us consider that detecting the unused subchannels of the OFDMA signal is the goal. Consider first the eigenvalue fusion scheme. The number of lines in the received sample matrix Equation (22) is equal to the number of subcarriers in a subchannel, which is

Let us now consider a sample fusion process, using the concatenation approach to form the received sample matrices, as determined from Equation (28). The choice for the concatenation approach is based on the fact that it produces better performance than MRC, also avoiding the need of knowing the channel gains used in the MRC. A number of

The analysis considering the detection of unused OFDMA subchannels shows that the volume of data sent to the FC in the case of decision fusion is mP bits. For the eigenvalue fusion this volume is

In terms of complexity, in the case of eigenvalue and decision fusions, each CR must be capable of processing

Let us make a last comparison between the eigenvalue fusion and the samples fusion by fixing the number of samples. Assume that each CR will take N samples per subcarrier. Therefore each CR will collect ^{2}^{2 }K

In this paper, a new eigenvalue-based fusion scheme has been proposed for sensing subcarriers or sub-bands of general wideband signals and for sensing subchannels of OFDMA signals, in the context of cognitive radio systems.

Simulations were performed, comparing our scheme with the fusion of samples collected by the cooperating CRs and with the fusion of CR decisions, considering the test statistics GLRT, MMED, MED, ED and their empirically-modified versions proposed here.

If the system parameters are chosen to build a fair comparison scenario, the eigenvalue strategy can provide better performance than all fusion schemes, for any test statistic and for any wideband signal. Moreover, the eigenvalue fusion can drastically reduce the amount of data sent to the fusion center when compared with the sample fusion method, reducing the volume of data in the corresponding control channel. If local decisions at the CRs are made from the eigenvalues computed, a decision fusion strategy can be adopted, which can further reduce the amount of data sent do the fusion center. The reduction in the volume of data produced by the eingenvalue and decision fusion, however, must be traded with the increased complexity of the cognitive radios, since they must be able to compute the eigenvalues of the received signal covariance matrices before forwarding them (or the decisions) to the fusion center. An analysis of this tradeoff was also presented in this paper.

Comparing the spectrum sensing of general wideband signals with that of OFDMA signals, one can notice that two major differences arise: the general wideband channel is partitioned according to the channelization chosen for sensing purposes, while the OFDMA channel is partitioned according to the sub-channel definition. As a consequence, the strategies for constructing the sample matrices are different from each other. Nevertheless, the approach for detecting OFDMA signals can be adapted to the detection of a general wideband signal by partitioning each sub-band or channel of the general wideband signal as follows: the number of sub-bands or channels of the wideband signal becomes the number

One can notice that if the sensing of subchannels in OFDMA systems can be coordinated under the information of unused subchannels in a given area, the data traffic in the control channel for the eigenvalue fusion can be further reduced, since some subchannels would not need to be sensed at all.

The performances of the decision fusion with OR logic and with majority-voting have shown to be close to the performances obtained with the eigenvalue fusion, for sensing subcarriers or sub-bands of general wideband signals, and for sensing subchannels of OFDMA signals, respectively. Since the volume of data sent to the FC is smaller than in other fusion schemes, our immediate conclusion is that these decision fusion strategies are preferred over the eigenvalue fusion. However, we conjecture that bit errors in the control channel can be more disastrous to the data representing CR decisions than to the data representing eigenvalues. This in turn would demand increased protection of the decisions data, reducing the difference in the volume of data in the cases of eigenvalue and decision fusion. This conjecture represents a good opportunity for further contributions. Nevertheless, this investigation could be complemented with an analysis of the influence of different system parameters in the spectrum sensing performance, which could help in constructing the conclusions concerning the influence of these differences on the ranking of the decision fusion combining rules.

It was verified that the wideband spectrum sensing approach proposed here can be applied to any wideband signal. Combined with the subcarrier nulling flexibility of OFDM signals, OFDM-based cognitive radios [

In [