Signal Classification based on Spectral Redundancy and ... - ISIP40

Signal Classification based on Spectral Redundancy and Neural Network Ensembles Luca Bixio, Marina Ottonello, Hany Sallam, Mirco Raffetto, Carlo S. Regazzoni Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, 16145 Genoa, Italy Email: {bixio, marina, sallam, raffetto, carlo}@dibe.unige.it Abstract—In the last couple of decades, the introduction of new wireless applications and services, which have to coexist with already deployed ones, is creating problems in the allocation of the unlicensed spectrum. In order to overcome such a problem, by exploiting efficiently the spectral resources, dynamic spectrum access has been proposed. In this context, cognitive radio represents one of the most promising technologies which allows an efficient use of the radio resource by collecting, processing and exploiting information regarding the spectrum utilization in a monitored area. To this end, in this paper the problem of classifying similar signals characterized by different spectral redundancies is addressed by using a neural network ensemble. A set of simulations have been carried out to prove the effectiveness of the considered algorithms and numerical results are reported.

I. I NTRODUCTION In the last few years, the growing success of wireless applications and services, and the consequent overcrowding of the licensed bands, have induced the governmental regulatory agencies to consider more flexible strategies for spectrum management. As a matter of fact, the Federal Communication Commission (FCC) has shown that a great part of the radio resource, although licensed, is underutilized [1]. It is clear that a dynamic and flexible management of the spectrum is necessary. In fact, “in many bands, spectrum access is a more significant problem than physical scarcity of spectrum, in large part due to legacy command-and-control regulation that limits the ability of potential spectrum users to obtain such access” [2]. In particular, Dynamic Spectrum Access (DSA) techniques [3] have been proposed in order to efficiently exploit the available radio resource. In this context, Cognitive Radio (CR) represents one of the most promising solutions to improve resource utilization by exploiting a dynamic allocation of free or underutilized radio resource [2]. To this end, one of the most challenging tasks which a CR terminal has to perform is a reliable classification of signals in the monitored area, in order to obtain information regarding spectrum occupancy (e.g. the number of active terminals, their related transmission standards, etc.). Signal classification has been treated in literature for both civilian and military passive applications. In spite of this, it remains a complex task especially if the terminals in the monitored area use spread spectrum transmission techniques [4]. Moreover, if a multipath and noisy channel is considered, signal classification can become even impossible

due to heavily corrupted received signals [5]. For these reasons a reliable signal classification is still an open research problem. Among the signal classification techniques which could be applied in the considered scenario, in this paper a feature detection strategy has been considered. In this context a feature can be defined as a characteristic of the signal which allows to detect and classify it [4]. In particular, modulated signals are said to be cyclostationary since their mean and autocorrelation exhibit redundancies which can be extracted and used as features by using the cyclic spectrum [4], recently proposed as an effective solution [3]. Such an approach provides significant benefits if compared with classical signal detection techniques (e.g. radiometers, matched filters) especially in multipath and noisy channels [4]. The feature detection techniques extract valuable information which need to be processed by a classifier whose output is the presence or the absence, at a certain time instant, of a given signal and its related characteristics. To this end, it is possible to borrow pattern classification techniques which, in the last few years, have turned out to be an important tool for many engineering applications [6]. The success of a CR system used as a spectral occupancy detector can be intimately related to the accuracy, robustness, and fast convergence of the selected classifier. Most state-ofthe-art pattern classifiers methods usually need long training time and large sample sizes to achieve good performances [7]. These requirements make the training process computationally expensive, an undesiderable feature in a CR system that can operate in an unknown environment and can perform an on– line training. In the family of Adaptive Resonance Theory (ART), a Simplified Fuzzy ARTMAP (SFAM) neural network is a robust model for classification, especially in real-world problems [8]. The SFAM strategy is characterized by a reduced computational overhead and an architectural redundancy [8]. Among the SFAM models intentionally developed to be faster and simpler variants of the original fuzzy ARTMAP, in this work the model presented in [9] is utilized, since it has a simpler architecture and is faster than other approaches [10]. Although it has been reported that SFAM and other fuzzy ARTMAP versions have accurate and fast learning in performing various classification tasks [7], their major drawback is that the network performances are affected by the ordering and by the sequence of training examples [8]. Moreover, in [7] has reported that SFAM networks are sensitive to statistical

overlapping between the classes. One of the proposed solutions to overcome these problems is to train ensembles of SFAM classifiers. Generally, an ensemble of classifiers has smaller error and variance as compared to a single network classifier. It is well known that bagging and boosting are the most suitable solutions to avoid the above mentioned drawbacks of SFAM [11]. In this paper a CR architecture for signal classification purposes in a DSA context will be provided. The signal classification is composed by two phases. Firstly the received signal is processed in order to extract spectrum redundancy. Secondly the spectrum redundancy is used as input to a classifier in order to identify the received signal. The paper is organized as follows: in Section II the architecture of the proposed CR system will be provided. In Section III the proposed approach for signal classification based on spectrum redundancy extraction and SFAM classification will be presented. Finally before concluding, in Section IV the simulation set up and numerical results for classification of similar signals in a DSA context will be discussed. II. P ROPOSED S YSTEM A RCHITECTURE Let us consider a CR wireless communication system, employed in a DSA context, able to gather information from the external environment by using a single antenna. The goal of the proposed system is to identify the presence of other transmitting terminals in the given frequency band (in order to find the so called “spectrum holes” [2], and so improving the spectrum utilization). Moreover, additional information regarding the transmission standards used by the transmitting terminals can be of great importance, as shown for example in [3], [4]. The proposed architecture for the CR system is shown in Fig. 1. Data collected from the environment by the antenna

Feature extractor

Signal Classifier

Spectrum manager

Parameter selector

Transmitted data

Fig. 1.

Proposed architecture for the cognitive radio system.

The antenna senses the radio environment collecting a raw signal, which is sampled and used as input to a feature extractor. The sampled signal is then processed to obtain useful features for identifying transmitted signals. This phase is of foundamental importance since it has to provide concise and precise information regarding the spectrum occupancy. In fact, classification performances are sensitive to input data dimension, which has to be kept as small as possible to reduce the amount of data that have to be processed during the next classification phase. It is important to note that clear features (i.e. features that permit to easily classify the signal present in the monitored environment) are difficult to be obtained, especially if the received signal is corrupted by multipath fading and noise. It is now clear that the feature extractor plays a critical role within the proposed architecture since it can affect the performance of the whole system. The extracted features are then used by a signal classifier which determines the presence or absence of terminals, as well as other additional information such as the number of active terminals, their transmission standards, their bandwidth, etc., in the monitored area and in the given frequency band. These precise information are used as input to a spectrum manager, whose task is to decide if the terminal can transmit, according to the available resources and the amount of data that have to be transmitted. Finally, the transmission parameters are adjusted accordingly with the information coming from spectrum manager. As an example, in this phase, the parameter selector will choose the carrier frequency, the transmission standard and the corresponding bandwidth, transmission power, etc. in order to exploit the spectrum hole, if any. Such operations can be performed by using techniques similar to Adaptive Modulation and Coding (AMC), shown in [12]. In the next Section the processing techniques used by the features extractor and the signal classifier will be analysed in details, while the development of the spectrum manager and the parameter selector will be addressed by future researches. III. P ROPOSED S IGNAL C LASSIFICATION

APPROACH

A. Signal processing for Spectrum Redundancy extraction In the proposed architecture the received signal is sampled and processed in order to extract useful information for the signal classification. In this work a feature extractor, shown in Fig. 2, based on cyclostationary analysis is used because of its good performances in low SNR environments and its capability to extract information regarding spectral redundancies of the signals under investigation [4]. In fact, cyclostationary signal analysis can extract periodicities of the statistical parameters of the second order that can arise during the modulation process of digital communication signals [3]. The Spectral Correlation Function (SCF), also known as cyclic spectrum [4], represents the tool employed to extract features from the signal of interest. Let the signal x(t) be “a cyclostationary random process, whose probabilistic or statistical parameters vary periodically with time, reflecting the characteristic property of regenerative periodicity” [4].

are well suited to detect signals even if low SNR environments are considered [4]. Such an approach allows not only to discriminate the presence or absence of a given signal in a given bandwidth, but also the signal classification [3] by determining key signal properties such as modulation type, carrier frequency and phase synchronization, etc. [3]. In the considered architecture the following discrete version of eq. (4) [3] is used as cyclic spectrum estimator:

Feature extractor

raw signal from antenna

Fig. 2.

Cyclic spectrum estimator

patterns

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to classifier

Proposed feature extractor for cognitive radio systems.

Generally speaking, x(t) is defined to be second order cyclostationary (in wide sense) if its autocorrelation function Rx (t, τ ) can be written as [3]: Rx (t, τ ) = E {x (t + τ /2) x (t − τ /2)}

(1)

which is a periodic function in t for each delay τ , and thus may be represented as a Fourier series: X Rx (t, τ ) = Rxα (τ ) ei2παt (2) α

where α represents the discrete cyclic frequency, and i = √ −1. The second order periodicities can be found by using the Fourier coefficients Rxα (τ ) that can be calculated by: Z 1 ∆t/2 Rxα (τ ) = lim Rx (t, τ ) e−i2παt dt (3) ∆t→∞ ∆t −∆t/2 Rxα

where ∆t is the measurement time interval. (τ ) is known as the cyclic autocorrelation function [4] and it corresponds to the autocorrelation function for α = 0. The Fourier transform of Rxα (t) gives the SCF [3], [4]: Z  α ∆f ∆t/2 X1/∆f t, f + lim ∆f →∞ ∆t→∞ ∆t −∆t/2 2   α ∗ ·X1/∆f dt (4) t, f − 2 where the complex envelope of the narrowband spectral component with center frequency v and bandwidth ∆f is given by Z Sxα (f ) =

lim

L−1 1 X Xl (k)Xl∗ (k − α)W (k), Sbxα (k) = L

where Xl (k) represents the discrete time Fourier transform of a chunk of length NSCF of the sampled received signal x(n), L is the number of processed block of dimension NSCF and W (k) is a smoothing spectral window. Since the dimension of data to be processed by the signal classifier can heavily affect the performance and elaboration time, the amount of data are reduced by evaluating the normalized profile of the SCF: maxk Sbxα (k) , α = 0, . . . , NSCF − 1, (7) P (α) = maxk Sbx0 (k) which represents the pattern used as input to the signal classifier. B. Signal Classification based on Simplified Fuzzy ARTMAP ensemble In the proposed architecture, shown in Fig. 3, the patterns received from the feature extractor are processed in order to classify signals by using a SFAM neural network ensemble. Such an approach allows to obtain satisfying performances, simple implementation and robustness in real-world problems [8]. Signal classifier M A X

t+1/2∆f

x (u) e−i2πuv du.

X1/∆f (t, v) =

(5)

t−1/2∆f

The SCF represents a measure of the correlation between the spectral components of the signal x(t) at the frequencies f + α2 and f − α2 and it reduces to the conventional power spectral density function for α = 0 [4]. The cyclic spectral analysis and the related SCF function have shown a lot of advantages [4] with respect to traditional approaches like energy detector [4] or matched filtering [4]. It is important to note that SCF extracts the periodicities of the modulated signals, allowing an easier separation of signals and noise in comparison with traditional detection techniques. As a matter of fact, the noise is a wide-sense stationary random process [4], with no spectral correlation, while the modulated signals are cyclostationary, with spectral correlation due to embedded periodicity of the carrier, as an example. For the above reasons, cyclostationary approaches

(6)

l=0

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Fig. 3.

Neural Networks Ensemble

V O T I N G

decisions to spectrum manager

Proposed signal classifier for cognitive radio systems.

Fuzzy ARTMAP (FAM) is an ART network for the association of analog patterns in a supervised mode. SFAM is a simplification of FAM since it has simpler architecture and faster training. A SFAM strategy can be described as a constructive “two layer” feedforward neural network since it allows the nodes to be added as necessary during the training process [13]. The learning algorithms of the ART networks are prototypebased methods. This type of learning strategy is based on the

construction of a nearest neighbor look-up table [10].A SFAm performes a classification of a pattern whose complement coded representation is denoted by I, by the following three steps: prototype choice, prototype match, and learning [7]. In the first step the algorithm searches for the nearest subclass prototype (winner) that “resonate” with the input pattern by calculating the choice function for input I and each prototype wj : kI ∧ wj k , (8) Tj = γ + kwj k where Tj is the output activation of the j th output node, γ is the tie-breaker, wj is the corresponding weight, and ∧ is the fuzzy AND operator defined by a∧b = min(a, b). The winner prototype J is the one which achieves the highest value of the choice function:   J = arg max(Tj ) . (9) j

The second step calculates the match function between the selected prototype J and the input I as follows: kI ∧ wj k . kIk

(10)

The match function tests the matching between the input I and the prototype wj : if the match value is greater than the vigilance parameter ρ ∈ [0, 1], this means that there is a resonance between the input I and the prototype wj . In this case, the prototype wj will be selected to represent the input I, otherwise the next winner is checked. The learning step starts when the winner class label matches the input class label and the prototype is updated as follows: (new)

wj

(old)

= β(I ∧ wj

(old)

) + (1 − β)wj

,

(11)

where β is the learning rate, 0 < β ≤ 1. If no winner has the same class label of the input, a new class is then created. Several researches have shown that an ensemble of classifiers has a generalization error usually smaller than that one obtained with a single network and, moreover, the variance of the ensemble is lower than the variance of a single network. It is important to underline that generalization is an important feature for learning algorithms since the target of learning is to predict hidden data [14]. Finally, the ensembles of neural networks exhibit some of the advantages of large networks, without their problems of long training time and overfitting risks. The design of the ensemble of classifiers requires to choose some parameters such as the method to design and train the member classifiers, the ensemble size, and the method of combining classifier output, that will have an impact on the performance of the whole ensemble [15]. There are many methods for creating ensembles such as, bagging, boosting [16], [17], negative correlation learning (NCL) [11], multiobjective learning [18], cooperative coevolution [15], etc.

Since SFAM methods are sensitive to the order of the training patterns [7], [8], our discussion will be limited to bagging and boosting. In fact, these methods rely on resampling techniques to obtain different training sets for each classifier to achieve diversity. Moreover, sampling methods have shown to be successful in improving the performance of different classifiers in artificial and real-world data sets [16], [17]. The bagging (after bootstrap aggregating) algorithm generates different bootstrap samples from the training set [11], [16], [17]. In this technique individuals of the ensemble are generated with different random samples of the training set. The training set of the classifier is generated by randomly drawing, with replacement, N patterns, where N is the size of the original training set. Among the other advantages, bagging generally produces more accurate ensembles with respect to single classifiers. In boosting technique the training set used for each individual classifier is chosen based on the performance of the earlier classifiers [11], [16], [17]. The main idea of boosting is to choose, for the training set, more often the examples incorrectly predicted by previous classifiers than the one correctly classified. Boosting produces dramatic reduction in error on some data sets and on other data sets increases the error over a single classifier [16]. Arcing and Ada-boosting are well known boosting methods: they select a training set of size N for the K + 1 classifier by a probabilistic selection, with replacement, of the examples from the original N training examples. Initially, the probability of selecting each pattern is set to 1/N and then they are updated as shown in [16]. Based on the results obtained in [16], the Ada-boosting method is used in order to train the SFAM ensemble. In the next section the obtained numerical results will be presented using either bagging or Ada-boosting methods for signal classification in the proposed architecture. IV. N UMERICAL

RESULTS AND SIMULATIONS

In order to verify the effectiveness of the proposed cognitive system, a set of simulations have been carried out. The reference scenario of the developed tests is represented by a DSA network, in which different cognitive radios can communicate by using IEEE 802.11a [19] and IEEE 802.16e [20] transmission standards. It is important to remark that the proposed scenario is challenging since both considered transmission standards use Orthogonal Frequency Division Multiplexing (OFDM) and IEEE 802.16e bandwidth is chosen to be approximately similar to the IEEE 802.11a one [20], [21] (about 20 MHz). Moreover, the transmitted signals are corrupted by multipath distorsions by using the COST 207 – Bad Urban channel model [22] and Additive White Gaussian Noise (AWGN). According to the considered architecture, the corrupted received baseband signal is sampled at fs = 40 MHz and it is processed by the feature extractor: it is composed by the cyclic spectrum estimator, whose dimension is set to NSCF = 160, and the profile evaluator as described in Section III. The normalized profile P (α), α = 0, . . . , 79, obtained form

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eq. (7), is shown in Fig. 4 and it is used as input to an ensemble composed by L ∈ {10, 15} SFAMs. It has to be noted that the normalized profile, shown in Fig. 4 for the two signals of interest, exhibits peaks due to the spectral redundancy (derived from the pilot carriers inserted, as indicated by the standards, in the transmitted signals for equalization purposes), which can be considered features of the considered signals.

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Fig. 4. Profile P (α) for the considered signals with Tobs = 5 [ms] and Eb /N0 = 5 dB.

In order to provide a general classifier, 500 normalized profiles for each of the three signals to identify (i.e. IEEE 802.16e, IEEE 802.16a, and noise), for each considered energy per bit to noise ratio Eb /N0 ∈ {−10, −5, 0, 5, 10, 15, 20} and for each used observation time Tobs ∈ {2, 3, 5, 10} [ms] has been generated and utilized to create an ensemble of SFAMs by using either bagging or Ada-boosting training methods. Finally, a majority voting is used to combine the outputs of the SFAMs in the ensemble. A signal classifier is created for each considered Tobs by training the ensemble of SFAMs with Mtrain = 5250 patterns. In particular, either bagging or Ada-boosting methods have been used for training ensembles composed by L SFAMs. In order to evaluate the classification rate, that is the probability of correct decision, the created ensembles for different L and Tobs are tested with Mtest = 5250 patterns. Table I summarizes the classification rate for the created ensembles. Tobs [ms] 2 3 5 10

Ada-boosting L = 10 L = 15 98.00% 98.27% 98.06% 98.34% 98.30% 98.78% 98.81% 99.10%

bagging L = 10 L = 15 96.38% 98.02% 96.11% 97.94% 97.28% 98.23% 98.06% 98.67%

TABLE I C LASSIFICATION RATE COMPARISON FOR DIFFERENT OBSERVATION TIMES Tobs AND SFAM S IN THE ENSEMBLE L

It is clear that the performances increase as the observation time Tobs or as the number of SFAMs in the ensemble L increase. In particular, an improvement in the performance can be obtained against an increment in complexity, a longer observation time and a higher received signal to noise ratio. In fact, the performance increases by augmenting the number of

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(c) (d) Fig. 5. Probability of false alarm and probability of missed detection for Tobs = 3 ms: (a) bagging, L = 10; (b) boosting, L = 10, (c) bagging, L = 15; (d) boosting, L = 15.

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(c) (d) Fig. 6. Probability of false alarm and probability of missed detection for Tobs = 5 ms: (a) bagging, L = 10; (b) boosting, L = 10, (c) bagging, L = 15; (d) boosting, L = 15.

the SFAMs in the ensemble, but the hardware cost increments as well. Moreover, a longer observation time is undesirable in practical DSA networks (it has to be kept in the order of milliseconds [23]). Furthermore, in a DSA network it is necessary to classify the signals of interest even at low SNR (e.g. at the edge of the covered area). It is possible to state that the proposed cognitive system architecture is well suited for a DSA network since it allows to obtain satisfactory classification rates even if short observation times, and low computational capacities are considered, as shown in Table I. Finally, the probability of false alarm Pf a and the probabil-

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(c) (d) Fig. 7. Probability of false alarm and probability of missed detection for Tobs = 10 ms: (a) bagging, L = 10; (b) boosting, L = 10, (c) bagging, L = 15; (d) boosting, L = 15.

ity of missed detection Pmd have been evaluated for different Eb /N0 , Tobs and L, as reported in Fig. 5, Fig. 6 and Fig. 7. It is easy to observe that the probability of false alarm and the probability of missed detection decrease as the observation time and the signal to noise ratio increase. Moreover, these results indicate that ensembles created by using the adaboosting training method provides better performance than ensembles created by using the bagging training method, especially if a short observation time and a low signal to noise ratio are considered. In particular, the ada-boosting training method allows to shorten the observation time, as it can be seen by comparing Fig. 5(d) and Fig. 6(c), guaranteeing similar performance to the one obtained with the bagging training method with 5 additional SFAMs. Finally, it is necessary to remark that both ensembles created by using either the bagging or the ada-boosting training method provide satisfactory results in signal classification even if a low SNR and a severe multipath channel are considered. V. C ONCLUSIONS In this paper a cognitive system composed by a feature extractor based on cyclic spectrum evaluation and a signal classifier based on ensemble of Simplified Fuzzy ARTMAP neural networks has been proposed. A set of simulations have been carried out in a DSA scenario where IEEE 802.16e and IEEE 802.11a can be adopted as transmission standards. This context is challenging since both transmission standards are based on the OFDM technique, with approximately the same bandwidth. Moreover, signals are transmitted within the same frequency band and are affected by multipath distorsions. Although the complexity of the considered scenario, the proposed algorithm exhibits satisfactory performances as obtained by comprehensive numerical simulations.

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