Automatic Modulation Classification for Rapid Radio Deployment

Transcription

1 Automatic Modulation Classification for Rapid Radio Deployment Adolfo Recio Department of Electrical and Computer Engineering Virginia Tech Blacksburg, VA 46 Jorge A. Surís Oak Ridge National Laboratory Oak Ridge, TN Peter Athanas Department of Electrical and Computer Engineering Virginia Tech Blacksburg, VA 46 Abstract Cognitive Radio and signal intelligence (SIGINT) applications require radios to perform situation-awareness functions, as spectrum sensing to detect the spectral occupation. In more advanced systems, for SIGINT and for interference cancellation purposes, a radio receiver may need to classify an otherwise unknown signal without prior information about its modulation type, and rapidly synthesize, prototype, and deploy a suitable demodulator. The Rapid Radio framework uses a signal analysis stage to obtain the parameters of the signal of interest, to quickly prototype a suitable radio demodulator using the reconfiguration features and processing capabilities of FPGAs. This paper presents the techniques devised to perform the Automatic Modulation Classification stage of the framework, considering its interaction with the parameter estimation and signal synchronization stages, and presents performance results obtained under simulation conditions as well as in over-the-air transmissions. I. INTRODUCTION Automatic Modulation Classification (AMC) is an important stage of the Rapid Radio prototyping framework, allowing a receiver to be constructed by analysis of an otherwise unknown signal. While traditional approaches for radio design are focused on area and power efficiency, in applications as SIGINT and Cognitive Radio, a tradeoff between efficiency and speed of development may be desired. Today s large FPGA platforms make this tradeoff worthy of consideration even for more traditional applications. While there are many proposed AMC techniques, few consider the problem of lack of synchronization at the symbol and the carrier levels, as well as the capability to classify an arbitrary set of modulation types. This paper focuses on the description of the AMC strategy adopted for the class of linear modulations, as well as its interactions with the synchronization stages and with the general flow of the prototyping system. This paper is organized as follows: Section II presents an overview of AMC techniques. The approach chosen for the modulation classification stage is explained in Section III. The parameter estimation and signal conditioning stage is presented in Section IV. Section VI shows the format of the XML constellation descriptors used to feed constellation types to the classifier. The classification features are explained in Section VII, while the Bayesian network classifier is discussed in Section VIII. Section IX is an introduction to the prototype construction. The results are presented in Section X. Finally, conclusions are drawn in Section XI. II. PREVIOUS WORK The literature about Automatic Modulation Classification (AMC) covers several techniques directed toward classifying a signal using diverse features or performing likelihood tests. Many of these techniques rely on assumptions about the stage of processing of the signal (i.e.: a baseband representation is available, or sampling is synchronous to the symbol epochs), or about the modulation being restricted to a limited set. A comprehensive summary of the literature in AMC can be found in []. The author classifies the algorithms as either likelihoodbased (LB) or Feature-based (FB). Likelihood-based algorithms perform hypotheses testing directly over a baseband representation of the signal. Simplifications of the exact likelihood function lead to the generalized likelihood ratio test (GLRT), the average likelihood ratio test (ALRT), and the hybrid likelihood ratio rest (HLRT). Detailed explanations of each of the methods can be found in []. The work [3] proposes the quasi-log-likelihood ratio qllr to approximate the likelihood function of BPSK/QPSK signals, assuming that the carrier frequency and symbol timing are known. [4] presents a suboptimal implementation of a HLRT that provides independence of the noise parameters for the M-PSK class of modulations. [5] develops asymptotic results on the performance of maximum likelihood classifiers in the I-Q domain for linear modulations. A drawback of this family of methods is their capability to differentiate only among a particular set of constellations, given that other constellations get nested, that is, when a set of constellations generate the same value of the test statistic. Most of the already mentioned authors use the quasibaseband signal obtained after downconversion, which is known the signal space approach. The signal space approach has the advantage that it is readily available as an intermediate signal in a receiver, after the symbol timing recovery. Alternative analysis of the constellation in the signal space using pattern recognition techniques such as clustering have

2 also been proposed in [6], and [7]. However, clustering introduces additional degrees of freedom to the problem, which are not required as linear digital modulation constellations have highly regular shapes. Modulation classification techniques based on fuzzy logic [8], and artificial neural networks [9], [], [] are also proposed in the literature. Feature based algorithms include the wide family of cyclostationarity based classifiers [], as those based in spectral coherence and spectral correlation [3], [4], [5], and [9]; cyclic cumulants [6], [7], [8]; and higher order statistics [9]. Other features explored in the literature are: moment matrices [], the standard deviation of the normalized-centered instantaneous amplitude and kurtosis [], and Hellinger distance []. Holistic approaches that acknowledge the requirement to gather the basic parameters of the signal and consider the interactions between modulation recognition and synchronization are presented in [3], [4], [5], [6], and [7]. Fig. : Signal parameter estimation and pre-conditioning Fig. : Symbol synchronizer architecture III. PROPOSED APPROACH The problem of developing a Rapid Radio receiver prototype fits the holistic models considering, first, that an important portion of the signal processing used for recognition purposes can be re-used in the implemented receiver and second, that the synchronization and re-sampling tasks must be solved before running the modulation classification algorithms. Only the family of linear modulations is considered at this time. The technique implemented for AMC is based in the analysis of four features: amplitude, differential phase, and I-Q plane histograms, as well as the symbol transition matrix. Symbol synchronization is a condition to obtain the amplitude and differential phase profiles. Carrier synchronization is required to obtain the I-Q plane histogram and the symbol transition matrix. The generation of a baseline probability density function (pdf) for histogram matching with each hypothesized constellation type requires accurate constellation descriptions. SNR estimates are also needed for the construction of the baseline pdfs. A Bayesian network is used for the integration of the metrics and for the calculation of total scores used to reach a classification result. IV. PARAMETER ESTIMATION AND SIGNAL CONDITIONING The first step for the classification of the signal is the isolation of the frequency band where the carrier of interest resides, the implementation of a downconverter, and the coarse estimation of the parameters of the signal, including carrier frequency offset (CFO), symbol rate, roll-off factor, and signal to noise ratio, as described in [8]. The complex baseband signal x(n) signal is conditioned according to the system presented Figure by using the estimates of the symbol rate and the roll-off factor to produce a matched filter followed by an arbitrary frequency re-sampler to obtain a filtered signal y(m) with a nominal sampling frequency of four samples per symbol, value assumed at the succeeding symbol synchronization stage [9]. V. SYNCHRONIZATION AND AMPLITUDE NORMALIZATION Symbol timing recovery is a baseband adaptation of the Godard synchronizer [3] at four samples per symbol, which uses a non-linearity to generate a spectral line at the symbol rate, aided by a half-symbol delay in one of its branches, as proposed in [3], followed by a PLL to filter out the phase noise. Figure presents a block diagram of the synchronizer. This symbol synchronization approach is constellation agnostic, and can be performed without any previous assumptions on the hypothesized constellation. The value of the signal s(k) at the optimum sampling instant is found using a Lagrange polynomial interpolator controlled by the PLL time base. A. Carrier Frequency Offset Synchronization Ambiguity Two of the modulation classification features presented below, the differential phase profile and the amplitude profile, can be applied to the signal without the need of carrier frequency offset (CFO) synchronization, and a low-tier classification can be performed using the symbol synchronizer and the aforementioned features. A high-tier classification system requires the implementation of a CFO synchronizer, which allows testing two additional features: the two dimensional probability density function (pdf) and the symbol differential matrix. The CFO synchronizer must be fed the parameters of the hypothesized constellation to obtain hard decisions used to measure the phase error, and therefore is not constellation agnostic. This approach produces constellation nesting. For instance, an 8-PSK CFO synchronizer applied to a QPSK signal may produce what looks like a 8-PSK constellation, by introducing an additional π/4 phase rotation between consecutive symbols. Similarly, a π/4-dqpsk modulated signal fed to a 8-PSK hypothesis will produce a valid two-dimensional pdf. The differential matrix comes handy at resolving the rotation

3 .5 Amplitude profile under 6QAM Band Edge Sync Hypothesized pdf.5 f(x).5 Fig. 3: XML description of a QPSK constellation ambiguities introduced by a CFO synchronizer running under different hypotheses. VI. CONSTELLATION XML DESCRIPTORS To avoid the burden of modifying the classification algorithms, the Rapid Radio framework uses a Plug-in approach: a new constellation can be added to the set of hypotheses just by creating an XML constellation description file and adding it to the working directory. Figure 3 presents a sample XML description file. In it, the Constellation element has associated a Name and BPS, attributes, used to identify the constellation type and to indicate the number of bits per symbol respectively, a child elements Factor, with a Value attribute containing a normalizing factor to obtain unit power, and Symbol elements with attributes I, Q, and Value, containing the coordinates and index for each point of the constellation which defines the modulation type. A. Amplitude Profile Test VII. CLASSIFICATION FEATURES If the channel noise is assumed to be AWGN, the theoretical amplitude probability density function at the proper sampling instants can be described as a mixture of Ricean-distributed random variables calculated according to (). f ap c (x) = N i= p i f(x, ν i ) () where the value ν i represents the magnitude of the i th element of the constellation under test, N is the number of elements in the constellation, and p i is the probability of a constellation element. All of these values are obtained from the XML constellation description assuming equiprobable symbols. The function f(x, ν) is the pdf of the Ricean distribution given by (). f(x, ν) = x ( x σ exp + ν ) ( xν ) σ I σ () where I (x) is a Bessel function of the first kind. To obtain the proper constellation points, the amplitude of the signal is normalized according to (3), in order to x Fig. 4: Amplitude profiles of a 6-QAM constellation with 8 db SNR achieve unit power. The parameter σ can then be calculated as according to (4). s(k) = s(k) P γ γ where P = E[s (k)] is the mean square value of the received symbol sequence s i assuming E[s(k)] =, and γ is the measured carrier plus noise to noise ratio obtained at the parameter estimator. σ = γ A histogram of the received signal amplitudes is obtained with L bins of size δ, chosen according to Scott s rule [3]. This histogram is scaled to form the empirical pdf of the received data set. A similarity metric between the hypothesized pdf and the empirical pdf is obtained using the Hellinger distance (5), presented in []. The factor δ/ is added to produce results in the interval [, ]. d H (f, f ) = δ L i= B. Differential Phase Profile Test (3) (4) ( f (x i ) ) f (x i ) (5) The amplitude profile test is useful to classify amplitudemodulated signals. However, it does not permit a classification among phase-modulated signals, such as BPSK, QPSK, 8- PSK, and π/4-dqpsk. The differential profile is obtained by forming the histogram of the phase difference between consecutive symbols. Contrary to the amplitude profile, it is not independent of the CFO: the obtained profile will be phase-shifted by an amount of π f T symb, where f is the CFO, and T symb is a symbol duration. The hypothesized phase profile is obtained as a mixture distribution from the XML constellation description and the estimated SNR value using

4 .8 Hellinger Distance of phase difference under QPSK Band Edge Sync Hypothesized pdf under QPSK Band Edge Sync Lag (bins).8.6 Hypothesized pdf Q I Hypothesized pdf under QPSK Band Edge Sync Q I.4 Q Q Differential angle I I Fig. 5: Differential phase profile under QPSK with db SNR Fig. 6: Two-dimensional pdf under QPSK with db SNR the expression for the pdf of the angle between two vectors contaminated by AWGN [33], presented in (6). π/ f(ψ) = exp ( ρ( cos ψ cos θ)) π ( + ρ + ρ cos ψ cos θ) cos θ dθ (6) where ρ = /σ, and ψ = θ(n) θ(n ) represents the phase difference between consecutive symbols. The integral is solved numerically for each angle under evaluation. In order to overcome the offset introduced by the CFO, an exhaustive search is performed over all the phase shifts allowed by the discrete histogram bins, looking for the smallest Hellinger distance. The minimum distance is used as the metric for this classification feature. An example differential phase profile is presented in Figure 5. The top part of the figure presents the results of the minimum search, while the bottom part presents the matched pdfs. C. Two-dimensional pdf Test The two-dimensional pdf is one of the features that can be obtained after the CFO tracking loop. As the CFO tracking system requires knowledge of the hypothesized constellation, this measurement is sometimes meaningless when used under incorrect hypotheses, being usually out-of-lock. However, under the correct hypothesis, the tracking loop will be locked, producing a small distance metric when the empirical and the hypothesized pfds are compared. The hypothesized pdfs are build as two-dimensional gaussian mixtures, with centers given by the constellation points, and variance σ obtained from the SNR estimate. An example for the case of QPSK modulation is presented in Figure 6. D. Transition matrix test The transition matrix test is added to solve constellation nesting problems presented in 8-PSK vs. π/4-dqpsk or QPSK vs. π/4-dqpsk. When a signal is demodulated under certain hypothesis, a transition matrix is calculated. This feature provides insight into the differential structure of the modulation scheme, allowing, for example, the classification of a π/4-dqpsk signal, that would obtain the same metric as 8-PSK under the two-dimensional pdf test, and the same metric as QPSK under the differential phase test. VIII. BAYESIAN NETWORK CLASSIFIER Several approaches to signal classification make use of decision trees and class spaces. To support the plug-in capabilities of the signal classifier, a Bayesian Network was chosen to form the classifier. The Bayesian approach offers several advantages, among them: ) Different sets of prior probabilities can be used according to the environment and previous experience. ) There is no need to revise a decision tree if a new constellation type is added to the set under consideration. 3) The classifications are soft: instead of a yes/no answer, the posterior probabilities can be sorted and used as a likelihood measurement. A human can then participate in a decision in the case of similarly-ranked top results. To apply a Bayesian approach to the metrics discussed above, the conditional probabilities of an empirical pdf given hypothesis h i is assigned according to (7). P (ap h i ) = d H (f ap, f ap ci ) P (pp h i ) = d H (f pp, f pp ci ) P (sd h i ) = d H (f sd, f sd ci ) Amplitude profile Differential phase profile -D distribution P (tm h i ) = d H (f tm, f tm ci ) Transition matrix (7) where the set of functions f x represent the empirical distribution for the feature x, and the functions f x ci represent the theoretical pdf of such feature given the hypothesized constellation c i. The posterior probabilities are calculated according to Bayes rule, as presented in (8). P (h i ap, pp, sd, tm) = P (ap, pp, sd, tm h i )P (h i ) N i= [P (ap, pp, sd, tm h i)p (h i )] (8)

5 TABLE I: Set of metrics for a BPSK signal BPSK 99.4% 99.59% 97.68%.% 66.6% QPSK 99.4% 69.6% 68.97% 5.76% 6.47% 8PSK 99.4% 48.7% 49.7% 8.7% 4.68% 6QAM 8.78% 46.7% 6.35% 8.57% 4.59% 64QAM 75.84% 44.9% 6.% 7.49% 3.83% 3QAM 7.43% 43.6% 49.7% 3.9% 3.% PI4DQPSK 99.4% 69.5% 49.7%.7%.63% 8QAM 4.% 48.7% 9.% 8.46%.36% STAR6 9.7% 48.7%.8% 4.9%.8% TABLE II: Set of metrics for a QPSK signal QPSK 99.6% 99.8% 96.95% 99.89% 48.4% BPSK 99.6% 7.9% 45.% 99.99% 5.9% 8PSK 99.6% 7.9% 68.94% 55.7% 3.68% 6QAM 78.7% 68.6% 68.43% 4.% 7.6% 64QAM 74.7% 64.4% 6.% 37.9% 5.56% 3QAM 68.7% 63.6% 54.9% 45.6% 5.38% PI4DQPSK 99.6% 99.6% 68.94% 4.73%.6% 8QAM 39.9% 7.9% 4.48% 66.84%.38% STAR6 6.8% 7.9% 3.4% 48.6%.6% where the set of prior probabilities P (h i ) can be chosen according to an experience-based criteria. Conditional independence is assumed for the set of conditional probabilities. Therefore: P (ap, pp, sd, tm h i ) = P (ap h i )P (pp h i )P (sd h i )P (tm h i ) (9) IX. RADIO PROTOTYPE CONSTRUCTION The results of the analysis stage are written into an XML platform-independent radio description file (RDF), which combined with a platform specific description file performs the tasks of generating the required modules using a creation script that automatically invokes Matlab and Coregen, in the case of Xilinx FPGAs, to generate modules that are instantiated in a platform specific top-level file [34]. A radio prototype can be created this way with minimum user intervention. The detailed flow of the radio creation process is presented in Figure 7. X. RESULTS The results of the AMC system implemented are affected doubly when the signal to noise radio is low. A low SNR affects the synchronization stages, specially for highly dense constellations, as 64-QAM. Therefore, the rate of correct classification is much lower to the one obtained under ideal synchronization conditions. Tables I to IX present results of the individual metrics and the Bayesian network output for the classification of signals of different modulation types under a SNR of 8 db. 496 symbols are used to obtain this result. An important aspect that requires further development is the fact that the transition matrix is only being helpful in the case of a QPSK constellation being masked as π/4-dqpsk. In other cases, as in 64-QAM, presented in Table IX, it even produces a classification error that could have been otherwise avoided by using only the remaining three features, which are clear winners against the set of false hypotheses. XI. CONCLUSION A system for rapid prototyping of radio receivers was presented, with an emphasis in the automatic modulation classification stage. The use of a holistic approach to modulation classification that considers the effect of symbol and TABLE III: Set of metrics for an 8-PSK signal 8PSK 99.6% 98.75% 95.7% 99.79% 33.% PI4DQPSK 99.6% 69.87% 95.7% 7.5% 6.76% QPSK 99.6% 69.89% 54.53% 99.93% 3.4% 6QAM 8.6% 85.68% 64.% 6.% 9.97% 3QAM 7.45% 86.64% 53.5% 68.6% 7.98% 64QAM 76.4% 86.66% 6.75% 48.93% 7.9% BPSK 99.6% 49.% 34.43% 99.98% 5.95% 8QAM 43.99% 98.75% 3.8% 99.84% 3.65% STAR6 33.3% 98.75% 7.73% 89.85%.85% TABLE IV: Set of metrics for a π/4-dqpsk signal PI4DQPSK 99.45% 99.5% 95.% 99.4% 4.68% 8PSK 99.45% 7.66% 95.% 75.5% 3.46% 6QAM 84.39% 7.44% 6.5% 5.8% 8.84% 3QAM 73.7% 66.37% 53.47% 55.94% 6.66% BPSK 99.45% 7.% 9.65%.% 6.8% 64QAM 77.88% 67.4% 63.3% 38.98% 5.9% 8QAM 45.69% 7.66% 4.4% 77.84%.8% QPSK 99.45% 98.9% 4.8% 99.97%.93% STAR6 35.9% 7.66% 8.56% 66.44%.45% TABLE V: Set of metrics for an 8-QAM signal 8QAM 99.35% 98.% 94.5% 99.83% 35.34% STAR % 98.% 8.4% 77.5%.66% 3QAM 88.66% 9.86% 73.3% 67.9% 5.63% 64QAM 84.96% 9.83% 7.7% 55.%.84% 6QAM 7.3% 9.63% 35.94% 84.86% 7.56% 8PSK 35.44% 98.% 8.65% 99.85% 3.83% PI4DQPSK 35.44% 69.6% 8.65% 7.63%.9% QPSK 35.44% 69.% 6.44% 99.96%.55% BPSK 35.44% 48.63% 9.8% 99.98%.65% carrier synchronization is presented. A set of extracted features conducts to successful classifications under non-ideal synchronization conditions. The symbol transition feature prevents the nesting of the

6 Fig. 7: System for rapid assembly of a prototype radio TABLE VI: Set of metrics for a 6-QAM signal 6QAM 99.64% 98.85% 9.4% 99.7% 7.45% 3QAM 88.73% 98.7% 7.4% 9.97% 7.6% 64QAM 9.6% 98.64% 77.38% 69.73% 5.8% STAR % 86.6% 5.56% 97.45%.4% 8PSK 73.9% 86.6% 53.% 99.63%.% 8QAM 7.9% 86.6% 34.6% 99.% 6.37% PI4DQPSK 73.9% 67.% 53.% 67.8% 5.36% QPSK 73.9% 67.3% 3.63% 99.9% 4.9% BPSK 73.9% 46.85% 6.%.%.76% TABLE VIII: Set of metrics for a 3-QAM signal 3QAM 99.74% 99.% 88.8% 96.53% 6.7% 64QAM 97.43% 99.% 84.55% 74.84% 8.96% 6QAM 88.4% 97.4% 59.87% 97.99% 5.6% STAR6 77.5% 86.76% 55.8% 99.%.54% 8QAM 86.47% 86.76% 45.6% 98.33%.45% 8PSK 63.89% 86.76% 44.6% 99.83% 7.67% PI4DQPSK 63.89% 6.48% 44.6% 7.% 3.93% QPSK 63.89% 6.48% 3.45% 99.97% 3.9% BPSK 63.89% 43.8%.49%.%.87% TABLE VII: Set of metrics for a STAR-6 signal STAR % 96.64% 9.77% 99.8% 37.4% 8QAM 9.59% 96.64% 54.4% 96.% 9.44% 3QAM 79.5% 95.5% 6.4% 84.8% 6.77% 6QAM 74.47% 93.6% 43.87% 93.75%.8% 64QAM 78.9% 95.7% 63.49% 58.66%.87% 8PSK.56% 96.64% 4.5% 99.87%.9% PI4DQPSK.56% 68.86% 4.5% 7.%.6% QPSK.56% 68.9% 8.9% 99.97%.5% BPSK.56% 47.9% 4.9%.%.% TABLE IX: Set of metrics for a 64-QAM signal 3QAM 96.% 99.5% 77.83% 96.6%.36% 64QAM 99.79% 99.7% 87.63% 76.73%.84% 6QAM 9.9% 97.59% 6.% 97.87% 6.33% STAR % 87.39% 53.87% 99.%.4% 8QAM 8.4% 87.39% 4.46% 98.66% 9.3% 8PSK 67.4% 87.39% 47.69% 99.79% 8.77% QPSK 67.4% 63.69% 34.33% 99.97% 4.6% PI4DQPSK 67.4% 63.69% 47.69% 69.7% 4.44% BPSK 67.4% 44.5% 4.65% 99.97%.3% π/4-dqpsk modulation for QPSK classification, but presents problems under other modulation types. Future work in this project can include the classification of single-carrier modulation families, as FSK and MSK, as well as multi-carrier modulations, along with their prototype generation flow. ACKNOWLEDGMENT The authors would like to thank the Harris Corporation, Government Communications Division, for supporting this research. REFERENCES [] O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, Survey of automatic modulation classification techniques: Classical approaches and new trends, Communications, IET, vol., no., pp , 7. [] P. Panagiotou, A. Anastasopoulos, and A. Polydoros, Likelihood ratio tests for modulation classification, in MILCOM. st Century Military Communications Conference Proceedings, A. Anastasopoulos, Ed., vol.,, pp vol.. [3] A. Polydoros and K. Kim, On the detection and classification of quadrature digital modulations in broad-band noise, IEEE Transactions on Communications, vol. 38, no. 8, pp. 99, 99. [4] A. A. Tadaion, M. Derakhtian, S. Gazor, and M. Aref, Likelihood ratio tests for PSK modulation classification in unknown noise environment,

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