A New Approach to Signal Classification Using Spectral Correlation and Neural Networks A. Fehske, J. Gaeddert and J. H. Reed Virginia Polytechnic Institute and State University Mobile and Portable Radio Research Group 432 Durham Hall, Mail Stop 0350, Blacksburg, VA 24061, USA E-mail:
[email protected]
Abstract— Channel sensing and spectrum allocation has long been of interest as a prospective addition to cognitive radios for wireless communications systems occupying license-free bands. Conventional approaches to cyclic spectral analysis have been proposed as a method for classifying signals for applications where the carrier frequency and bandwidths are unknown, but is, however, computationally complex and requires a significant amount of observation time for adequate performance. Neural networks have been used for signal classification, but only for situations where the baseband signal is present. By combining these techniques a more efficient and reliable classifier can be developed where a significant amount of processing is performed offline, thus reducing online computation. In this paper we take a renewed look at signal classification using spectral coherence and neural networks, the performance of which is characterized by Monte Carlo simulations. Index Terms— signal classification, cognitive radio, spectral coherence, neural networks, wireless communications, channel sensing
I. I NTRODUCTION With the growing demand for spectrally efficient communications systems comes the need to quickly probe the channel to assess spectrum availability and link quality. First introduced by Joseph Mitola in [1] the term ‘cognitive radio’ (CR) has recently received a considerable amount of interest in the wireless radio engineering community. Looking for new methods to overcome spectrum access conflicts due to the virtual scarcity of free channels in unlicensed bands, the FCC has heralded interest in the CR concept for solving such issues. Perhaps the most appealing property of the CR is its ability to sense and characterize its RF environment and adapt accordingly. The adaption process thereby may be driven by some simple goals such as “maximize throughput” or “minimize interference” or may even be governed by a more complex decision-making process [2], [3]. With these capabilities a CR lends itself very well to detection of temporarily unused spectral resources and operation in licensed bands without interfering with licensed services. Consequently, spectrum sensing performed by CR cannot be restricted to simply monitor the power in some frequency bands of interest but must include detection and identification in order to avoid interference [4]. Recent research efforts exploit the cyclostationary features [5]–[7] of signals as a method for classification, which has been found to be superior to simple energy detection and
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matched filtering. Energy detection as a non-coherent method is easy to implement and does not require prior knowledge of signal parameters such as carrier frequency or signal bandwidth, but is highly susceptible to in-band interference and changing noise levels [8]. More importantly, an energy detector cannot differentiate between signal types, but can only determine whether or not one is present. Additionally, the energy detector, although principally able to detect spread spectrum signals, works poorly for classifying this type of interface [9]. Conventional signal classification approaches such as those in [10]–[13] usually exploit signal properties such as instantaneous frequency, amplitude, or phase information and generate distinct features for each modulation type by performing standard signal processing operations such as computing moments or by applying transformations. The generated features are then classified by a pattern classification algorithm, or a decision theory inspired approach is applied which leads to some kind of multiple hypothesis testing. In all cases, however, either a baseband representation or significant amounts of signal processing is required. In [14]–[16] Spooner and Brown present pioneering work in the field of automated radio signal detection. Their method exploits second as well as higher order time variant periodic cumulant functions which allows for classification of a large number of modulation types [17]. In this paper we take a renewed look at signal classification using the same framework from a spectral correlation standpoint. To circumvent issues with classification where the signal’s carrier and bandwidths are unknown, we propose using neural networks to do the classification after preprocessing. Neural networks have long been considered for pattern recognition and modulation classification [18] and have proven to be robust to a variety of conditions such as interfering signals and noise, as confirmed in our results. II. C YCLIC S PECTRAL C ORRELATION A. Overview Statistical spectral analysis can be described as the decomposition of a function into sinusoidal waveforms called spectral components; and to represent the function as a sum of weighted spectral components. Cyclic spectral analysis deals with second order transformations of a function and its spectral
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representation. A function x(t) is said to exhibit second order periodicity if spectral components of x(t) exhibit temporal correlation. Important parameters to measure the spectral correlation of a time-series x(t) is the spectral correlation density (SCD) and the spectral coherence function (SCF). The SCD of a function x(t) is defined in [5] as: α SX (f )∆t T
. 1 = ∆t
∆t/2 Z
α α ∗ ∗ 1 XT t, f − dt XT t, f + 2 2 T
−∆t/2
(1) with frequency components f + α/2, f + α/2, f , spectral location (center of shift), α spectral separation (amount of shift). The local spectra content of the function x(u) is defined as: t+T Z /2 . XT (t, v) = x(u)∗ e−i2vf u du (2) t−T /2 α SX (f )∆t T
is called the limit SCD. The SCF and lim lim T →∞ ∆t→∞ of a function x(t) is defined as: α SX (f ) α CX = 1/2 α ∗ 0 0 SX (f + 2 ) SX (f − α2 )
(3)
but no significant additional insights would have been gained. For the interested reader we refer to [21] and [22] where the spectral correlation densities of different signal types are presented. A key problem to address is the narrow signal features within the α-domain. That is, if a particular feature doesn’t lie exactly on a value of α for which the SCF has been computed, the feature won’t present in the SCF and a misclassification is likely to occur. Practically speaking a very high resolution in α is needed to detect all features with high probability. This in turn leads to a large amount of data to be processed by the neural network. Figure 6 illustrates the problem for a BPSK signal which the SCF has been computed for with different α resolutions. The features associated with the signal’s keying rate (see [22] for explanation) are not present in the SCF with the lower resolution. This SCF is identical to the one of an AM signal with the same carrier which leads to erroneous classification despite the obvious differences in the two signals. In order to reduce the large amount of data introduced by high α resolution only the highest value of the SCF for a given α was taken, viz. α prof ile(α) = max [CX (f )] f
The SCF has magnitude constrained to be within [0, 1] with 0 CX (f ) = 1 for all f . Low-pass frequency smoothing along the α domain distinguishes spectral features and is necessary for analysis. Examples of SCFs of typical digitally modulated signals can be found in figures 1-5. For a more detailed description of the methods of statistical spectral analysis and cyclic spectral analysis we refer to [19] and [20]. The following properties make cyclic spectral analysis a very useful tool for signal classification: • Different types of modulated signals (BPSK, AM, FSK, MSK, QAM, PAM) with overlapping power spectral densities have highly distinct SCDs/SCFs • Stationary noise exhibits no spectral correlation • The spectral correlation function contains phase and frequency information related to timing parameters in modulated signals (carrier frequencies, pulse rates, chipping rates in spread spectrum signaling, etc.). B. Cyclic Spectral Analysis for Different Signal Types The simulations were restricted to the following signal types: BPSK, QPSK, FSK, MSK, and AM, due to the following reasons: 1) Signal classes that are commonly used such as higher order QAM and higher order PSK don’t exhibit second order periodicity or exhibit the same features as QPSK. Therefore these signals cannot be distinguished from one another as they exhibit the same features as QPSK. For this reason higher order spectral analysis is required [19]. 2) The computation of various versions of the SCF is complex and time consuming, thus by analyzing another signal class (e.g. PAM) that is not commonly used in practice the simulation time would have increased,
(4)
Using this approach, the amount of data could be reduced by a factor equal to the number of points used in the spectral frequency domain. III. N EURAL N ETWORK S TRUCTURE A. Network Training Due to its simplicity, a multilayer linear perceptron network (MLPN) with 4 neurons in the hidden layer was used for each signal class, trained on a 199-point α-profile defined in (4). Each MLPN was trained with a back propagation algorithm [23] with an initial learning rate η = 0.05 decreasing with each epoch, a momentum constant α = 0.7, and an activation function tanh(x). The output of each MLPN is there a continuous value in the range (−1, 1). The MAXNET structure shown in figure 7 simply chooses the signal whose MLPN outputs the largest value. Signals of varying carrier frequency, symbol rate, SNR, and observed time were generated using a square-root raised cosine filter with an excess bandwidth constant of β = 0.5. Different training strategies were tested based on these limitations, the results of which can be seen in Figures 8 and 9. B. Estimator Confidence Besides being computationally efficient, a classifier must operate reliably. We therefore propose a simple self-confidence analysis for the classifiers which makes use of the continuous output of the MLPNs. The performance of the classifier can be separated into two hypotheses: H1 Signal is classified correctly H0 Signal is classified incorrectly One measure of performance is the ability for the network to classify a signal reliably given one of the two hypotheses
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(a) SCF
(a) SCF qpsk: Fc/Fs=0.25, Fd/Fs=0.1, f: 200 points, α: 200 points, SNR= 9.9682dB
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bpsk: Fc/Fs=0.25, Fd/Fs=0.1, f: 200 points, α: 200 points, SNR= 9.9946dB
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(b) α-profile Fig. 1.
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Fig. 2.
above. Because the MAXNET operates on a single decision statistic z = arg max [y]i (5) we can devise a reliability parameter, χ, defined as half the distance from the largest MLPN output, yi to its closest competitor, viz yi − arg max [yk ]k6=i
0.2
0.6 0.4 cycle frequency α/Fs
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1
(b) α-profile
Spectral coherence function and α profile for BPSK
χ=
0
(6) 2 Because the MLPN output is bounded by −1 and 1, the reliability is therefore at maximum 1 and at minimum 0. The situation where χ = 0 describes the case where the maximum value of the MAXNET is shared by two or more MLPNs. The classifier, therefore, is perfectly unreliable as either modulation type could be present. A perfectly reliable situation, χ = 1, happens only when the output of exactly one MLPN is +1 and the output of all other MLPNs is −1. Therefore χ determines the confidence of each signal classification. Figure 10 demonstrates how the confidence changes with each hypothesis and signal type. From Figure 10(a) it is apparent
Spectral coherence function and α profile for QPSK
that the reliability is generally low when the signal has been mis-classified and high for correct classification. Because of this strong correlation, the reliability factor is a good measure for confidence of correctly classifying a modulation type. If, for example, the confidence is low enough, the system may look for other methods (e.g. higher order cyclic spectral analysis) for classification. Furthermore, this structure allows larger networks to be instanced wherever necessary. For low SNR levels, the keying features of BPSK sink below the noise floor (especially when insufficient numbers of data symbols are observed) and looks similar to AM. It may therefore be necessary to increase the number of neurons in the BPSK and AM networks to extract these subtle differences. MLPN structure is independent of the MAXNET and thus lends itself well to optimizing network structure. IV. R ESULTS Training the networks with different realizations of the signal allowed them to abstract from the noise features and
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(a) SCF
(a) SCF msk: Fc/Fs=0.25, Fd/Fs=0.1, f: 200 points, α: 200 points, SNR= 9.9644dB
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fsk: Fc/Fs=0.25, Fd/Fs=0.1, f: 200 points, α: 200 points, SNR= 9.9232dB
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(b) α-profile Fig. 3.
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(b) α-profile
Spectral coherence function and α profile for FSK
Fig. 4.
pick out the carrier and keying-rate features of the signal. Time constraints limited the amount of data we were able to generate to test the MAXNET classifier, however considering its sufficient performance with a considerable observation window (on the order of 16,000 samples) we believe it is possible for this type of network to classify signals with low SNRs and fewer observed samples while preserving a performance and computational complexity similar to classifiers such as those presented in [18]. As demonstrated by Figure 9, when trained with a variety of signal realizations with different SNRs, the network performs exceptionally, even at low signal levels. This is significant for detection theory, and suggests that the network will be able to detect spread spectrum signals such as CDMA or Bluetooth. Two different scenarios were examined in our simulations. First we assumed the signal’s carrier and bandwidth to be known. For this case we used different SNRs varying between -9dB and 15dB. The result of these Monte Carlo simulations with 460 trails is shown in table IV. Because the peaks in the SCF, on which the classification approach is based, are more
Spectral coherence function and α profile for MSK
pronounced the longer a signal has been observed, we were interested primarily in the probability of classification given a certain number of observed symbols. The simulation results for a fixed SNR of 5dB and 1,000 trails are shown in figure 8. Figure 9 shows the dependency of the probability of detection upon SNR and demonstrates that training the network with signals of varying SNR levels yields better performance than training with a fixed SNR. This suggests that the network is forced to abstract from the effects of the noise and focus on the location and magnitude of the component features. As a second scenario we assumed no prior knowledge of the signal other than its presence. The result of Monte Carlo simulations is tabulated in Table IV. An SNR of 15dB was assumed and the network was trained with different versions of each modulation type, each with one of 23 combinations of carrier offset and bandwidth. For classification, a separate set of signals was used in order to demonstrate that the network was able to classify signal realizations for which it had not been trained.
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(a) SCF
(a) high α resolution
am: Fc/Fs=0.25, Fd/Fs=0.1, f: 200 points, α: 200 points, SNR= 10.0069dB
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α profile
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(b) low α resolution
Spectral coherence function and α profile for AM
Fig. 6.
The effect of α resolution on a SCF for BPSK.
Fig. 7.
MAXNET classifier structure.
TABLE I C LASSIFICATION OF S IGNALS : C ARRIER AND BANDWIDTH K NOWN .
BPSK QPSK FSK MSK AM
BPSK 292 0 0 0 2
QPSK 3 295 1 16 0
FSK 0 0 294 1 0
MSK 0 0 0 278 0
AM 0 0 0 0 293
TABLE II C LASSIFICATION OF S IGNALS : C ARRIER AND BANDWIDTH U NKNOWN .
BPSK QPSK FSK MSK AM
BPSK 453 0 4 2 0
QPSK 0 452 0 0 15
FSK 6 0 456 0 0
MSK 1 0 0 458 0
AM 0 8 0 0 445
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Probability of Classification, 5dB SNR
1 Probability Distributions for Confidence Levels
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Probability of Classification
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Fig. 8.
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Probability of classification vs. number of observed symbols. Probability of Classification vs. Training SNR
Probability Distributions for Confidence Levels
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Fig. 9. Network performance when training for different situations with a network structure of [4 1].
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(b) Reliability given modulation type Fig. 10. Cumulative distribution of confidence levels given (a) hypothesis (b) modulation type. Training sequence: 75 patterns. Testing sequence: 1,575 patterns.
V. C ONCLUSIONS In this paper we suggested a method for classification of communication signals based on cyclic spectral analysis and pattern recognition performed by a neural network. Two cases were studied: Classification with and without prior knowledge of carrier and bandwidth of the signal. Distinct features of each signal type were extracted using cyclic spectral analysis, and a neural network was designed to classify signals based on these features. Simulations demonstrated exceptional classification performance for both cases under various noise conditions. A performance analysis for several neural network architectures was presented. The set of signals was limited to BPSK, QPSK, FSK, MSK, AM the case of two or more signals present at a time was not considered. Further efforts should include classification of more signal types, especially more relevant digital modulation types such as higher order QAM and PSK. Higher order spectral analysis should be incorporated to extract features using higher order modulation types. Furthermore the classification of more than one signal at a time has to be addressed. Estimations of
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signal parameters such as carrier and bandwidth could be incorporated in the classification. Many of these research goals have been achieved in the past (e.g. [6] and [7]) without the use of a neural network. Further research should therefore address the question whether previous methods can be enhanced or simplified by using this or a similar neural network approach. Figures 8 and 9 show how classifier performance is affected by signal quality and observation interval. By training the network with signals of varying SNR levels at the receiver, classifier performance can be significantly improved. Additionally, the classifier can operate with only a few hundred symbols (Figure 8) rather than several thousand as shown in [6], however practical limitations of the number of modulation types analyzed in this paper makes comparisons difficult. Figure 10 demonstrates that the confidence measure described in (6) is a reliable metric for gauging classifier performance. In Figure 10(b) it is apparent that QPSK is the most unreliable in terms of MLPN output. This can be
explained by the low spectral features observable in secondorder cyclostationary analysis as seen in figure 2. For this reason, higher-order analysis is required, but only when the confidence level of the MAXNET is below a certain level. Furthermore for a correctly classified signal the probability of the confidence level being greater than 0.75 is approximately 80%, as seen in figure 10(a). Using the proposed approach, signal modulation types can be determined quickly and reliably as a first, but important step to dynamic spectrum access and interference mitigation techniques. Advantages of the proposed method include robustness to stationary noise, separating signals with overlapping power spectral densities, and keying component extraction; all inherent attributes to cyclostationary feature detection. Finally, using a neural network for classification constitutes a highly flexible method since the network can be retrained easily in order to incorporate new signal types. were generated
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VI. S PECIAL T HANKS We would like to thank Chad Spooner and Krishnan Ramu for their invaluable help with this project. R EFERENCES [1] J. Mitola, “Cognitive radio an integrated agent architecture for software defined radio,” Ph.D. dissertation, KTH Royal Institute of Technology Stockholm, Sweden, 2000. [2] T. Rondeau, B. Le, C. Rieser, and C. Bostian, “Cognitive radios with genetic algorithms: Intelligent control of software defined radios,” in Proceedings of the SDR Forum Conference 2004, 2004. [3] J. Polson, “Cognitive radio applications in software defined radio,” in Proceedings of the SDR Forum Conference 2004, 2004. [4] R. Brodersen, A. Wolisz, D. Cabric, S. Mishra, and D. Willkomm, “Corvus: A cognitive radio approach for usage of virtual unlicensed spectrum,” available at http://bwrc.eecs.berkeley.edu/Research/MCMA/. [5] W. Gardner, Statistical Spectral Analysis: A Nonprobabilistic Theory. New Jersey: Prentice Hall, 1987. [6] C. Spooner, “Automatic radio frequency environment analysis,” in Proceedings on the Thirty-Fourth Asilomar Conference, October 2000. [7] ——, “On the utility of sixth-order cyclic cumulants for rf signal classification,” in Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, vol. 1, November 2001, pp. 890–7. [8] D. Cabric, S. Mishra, and R. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Conference Record of the 38th Asilomar Conference Signals, Systems, and COmputers, 2004, pp. 772–776. [9] R. A. Dillar and G. M. Dillard, Detectability of spread-spectrum signals. Norwood, MA: Artech House, 1989. [10] E. Azzouz and A. K. Nandi, “Automatic identification of digital modulation types,” Signal Processing, vol. 47, pp. 55–69, November 1995. [11] Y. C. Huang and A. Polydoros, “Likelihood methods for mpsk modulation classification,” IEEE Transactions on Communications, vol. 43, 1995. [12] C. Schreyogg, “Modulation classification of qam schemes using the dft of phase histogramm combined with modulus information,” in MILCOM 97, November 1997. [13] Y. C. Lin and C. C. J. Kuo, “Modulation classification using wavelet transform,” SPIE 1995, pp. 492–503, July 1995. [14] C. M. Spooner, “Classification of cochannel communication signals using cyclic cumulants,” in Proc of the 29th Asilomar Conference on Signals, Systems, and Computers, 1995, pp. 531–536. [15] C. M. Spooner, W. A. Brown, and G. K. Yeung, “Automatic radiofrequency environment analysis,” in Proceedings of the 34th Asilomar Conference on Signals, Systems, and Computers, 2000, pp. 1181–1186. [16] C. M. Spooner, “On the utility of sixth-order cyclic cumulants for rf signal classification,” in Proceedings of the 35th Asilomar Conference on Signals, Systems, and Computers, 2001, pp. 890–897.
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