NEW METHODS FOR CLASSIFICATION OF CPM AND SPREAD SPECTRUM COMMUNICATIONS SIGNALS VIS RAMAKONAR, DARYOUSH HABIBI, ABDESSELAM BOUZERDOUM School of Engineering and Mathematics Edith Cowan University 100 Joondalup Drive, Joondalup, W.A., 607 AUSTRALIA Abstract: - This paper introduces an algorithm that extends the capability of digital modulation classifiers to cope with continuous phase modulated (CPM) signals as well as spread spectrum (SS) signals. The algorithm employs the decision-theoretic approach where the identification of different signal types is performed by developing a set of decision criteria. Some new key features have been proposed and the performance of the classifier has been evaluated by simulating different types of bandlimited digital signals corrupted by Gaussian ise. It is shown that the overall success rate is nearly 100% for SS signals and > 95% for signals within the CPM signal class. Key-Words: - Modulation Classification, Spread Spectrum, CPM Signals, Decision Theoretic Approach. 1 Introduction Modulation identification plays an important part in both military and civilian operations. There are many applications that necessitate signal monitoring and identification. For military applications, signal identification is used for purposes such as surveillance, electronic warfare and threat analysis. For civilian purposes, some applications are signal confirmation, interference identification and spectrum management. The main aim of the surveillance system is to identify the signal characteristics of intercepted emitters against a catalogue of signal sorting parameters or reference characteristics. Signal modulation type is one of the important characteristics. There have been numerous publications concerning techniques for automatic modulation classification of digital signals. Significant contributions in the area of automatic modulation classification has been made by Nandi and Azzouz [1], [], and [3]. They propose a digital modulation recogniser that can classify ASK (amplitude shift keying), ASK4, PSK (phase shift keying), PSK4, FSK (frequency shift keying) and FSK4 signals. Modulation classification is based on the decision-theoretic approach. The same signals have been addressed by Ramakonar et al using a DT approach in [7], but new key features were proposed and the addition of an MSK signal gave rise to a different tree structure. In a military communication system, there may be a continuous wave (CW) jamming signal present. A modulation technique that can be used in aid of preventing interference such as jamming and multipath interference is kwn as spread spectrum (SS). This type of modulation has t been considered by other authors in regards to modulation recognition. There are two types of spread spectrum: 1. The first is kwn as direct-sequence spread spectrum (DS-SS).. The second is frequency-hopped spread spectrum (FH-SS). The signals considered by Nandi and Azzouz are also all memoryless meaning that there is dependence between signals transmitted in verlapping symbol intervals. However, signals with memory have t been considered. A class of signals that have memory incorporated in the modulation scheme is continuous phase modulated (CPM) signals. These signals have constant amplitude and the transmitted information is contained in the phase [4]. This paper evaluates the performance of the modulation recogniser in [7] with the addition of CPM signals and spread spectrum signals.
Signal Representation The CPM signal can be expressed as ξ s( t ) = cos[ πf c t + φ( t; Ι ) + φ o ] (1) T where ξ is the signal energy, f c is the carrier frequency, T is the symbol period, φ o is the initial phase of the carrier and φ(t;i) is the time varying phase of the carrier which is defined in [4]. Various pulse shapes g(t) are used in the modulation process. If g(t) = 0 for t > T, the CPM signal is called full response CPM. If g(t) 0 for t > T then the signal is called partial response CPM. The simplest form of DS spread spectrum uses BPSK as the spreading modulation. Ideal BPSK SS modulation can be mathematically represented as a multiplication of the carrier by a function c(t) which represents the spreading waveform and takes on values of ±1. The resulting transmitted waveform is [5]. s ( t ) = P c( t )cos ω t + θ ( t ) () t [ ] where P is the power of the signal, θ d (t) is the data phase modulation and ω o is the radian frequency. QPSK is used in spread spectrum applications due to the fact that it is less sensitive to some types of jamming and more difficult to detect using feature detectors in low probability of detection applications.the output of the QPSK SS modulator is s( t ) = Pc ( t )cos Pc ( t ) sin 1 o d [ ω ot + θ d ( t )] [ ω t + θ ( t )] o d (3) where c 1 (t) and c (t) are the in-phase and quadrature spreading waveforms which are assumed only to take on values of ±1. The frequency hopped SS (FH SS) signal is represented as: s( t ) = cos( πfθ t) (4) where n fθ = nrsm( t ) + nrsc( t ) Rs (5) where R s is the symbol rate, nr s is the width of the data modulation, m(t) is the data modulation and c(t) is the random frequency hop band sequence..1 Spreading Codes The waveform c(t) used to spread and despread the data-modulated carrier is usually generated using a shift register. This waveform c(t) is a pseudorandom code kwn as a PN sequence. This PN sequence is periodic with ise-like properties which makes the spread-spectrum signal hard to intercept. Each user in the CDMA system has a unique PN sequence assigned to them. Because users will be transmitting messages simultaneously, the PN code sequences must be mutually orthogonal so that interference from other users is avoided [6]. In this paper, Gold codes from a set of orthogonal Gold codes were used as the spreading sequence. These sequences were 7-bits in length and could accommodate up to 9 users in a CDMA scheme. The set of Gold codes is shown in Table 1 in [6]. 3 Classification Procedure The procedure for digital signal classification is based on the method outlined in []. The intercepted signal s(t) with length K seconds and sampled at sampling rate f s is divided into M successive frames. Each frame is N s samples long (N s = 048) which is equivalent to 1.76ms. This results in M (=Kf s /N) frames. A set of key features is extracted from each frame to decide the type of modulation. These key features are derived from the instantaneous amplitude A(t), the instantaneous phase φ(t) and the instantaneous frequency f(t) of the intercepted signal. The signals that have been added to the modulation classifier are: BPSK SS, QPSK SS, FH SS, and CPM. Within the CPM class of signals the pulse shapes that can be classified are LREC, LRC (raised cosine), HCS (half cycle sinusoid), and GMSK (Gaussian MSK). These signals are classified as full response, partial response or GMSK. 3.1 Key Feature Extraction The following key features were introduced to classify the spread spectrum signals and the CPM signal set as a whole: γ maxf is the maximum value (measured in db) of the power spectral density (PSD) of the rmalised instantaneous frequency of the intercepted signal and is defined as γ = 10log (max DFT( f ( i )) ) (6) max f 10 This key feature is used to distinguish between CPM signals and FSK4 signals. This is because the frequency components in CPM are smaller than in FSK4. For CPM signals, the transmitted information is contained in the phase, whereas in FSK the information is contained in the frequency. The threshold value to discriminate between these two types of signals is tγ maxf = 15.5. n
γ min is the minimum value (measured in db) of the smoothed PSD of the signal and is defined as: γ min = 10log10(min DFT( s( t )) ) (7) This key feature is used to differentiate between BPSK SS signals and PSK signals. By observing the smoothed power spectral densities of both signals, it is found that the power of the BPSK DS- SS signal is spread due to the addition of the spreading sequence. In contrast, the PSK signal has most of the power centred around the carrier frequency. For the PSK signal, the power drops off dramatically at frequencies further from the carrier frequency. However for the BPSK DS-SS signal, this degradation is t so steep because of the addition of more frequencies by the spreading sequence. The same key feature is used to distinguish between QPSK SS signals and PSK4 signals. The power of the QPSK DS-SS signal is spread due to the addition of the spreading sequence and for the PSK4 signal, most of the power is centered around the carrier frequency. Thus the PSK4 signal has a lower minimum PSD value compared to the QPSK DS-SS signal. FH-SS and CPM signals are also separated by the same key feature. By observing the smoothed power spectral densities of both signals, it is found that FH SS signals also have a greater power spread than CPM signals due to the addition of the spreading sequence. The following key features were used to separate partial response CPM, full response CPM and GMSK: σ da which is the standard deviation of the direct value of the instantaneous amplitude and is defined by: N 1 s N 1 s σ = da A ( i ) A( i s i= 1 ) (8) N N s i= 1 where A(i) is the value of the instantaneous amplitude at time instants t = i/f s (i = 1,3,,N s ) and f s is the sampling frequency. σ fn which is the standard deviation of the rmalised instantaneous frequency, evaluated over the n-weak segments of the intercepted signal and is defined by: 1 1 σ fn = f n ( i ) f n( i ) (9) C A > > n( i ) a C t An ( i ) at where f n is the rmalised instantaneous frequency defined by f n = f(i)/r s where R s is the symbol rate, C is the number of samples in {f n (i)} for which A n (i) > a t, A n (i) = A(i)/m a where m a is the average value of the instantaneous amplitude over one frame and a t is a threshold for A(t) below which the estimation of the instantaneous phase is very sensitive to ise. L diff is the PSD value of the signal at the corresponding frequency of 164kHz. By inspecting the spectral performance of full and partial response schemes in [8] it can be concluded that increasing the pulse duration L leads to a more compact PSD with side lobes that fall off more smoothly. The partial response schemes should have lower PSD values therefore this key feature named L diff can be used to separate partial response CPM from full response CPM. 3. Modulation Classification Method The CPM signals have similar characteristics due to the fact that they belong to the CPM signal type, it was necessary to use three conditions to distinguish the signals. This is because the signal statistics overlap frequently and cant be separated by just one decision. Therefore, one type of signal is distinguished by one criterion while ather type of signal is distinguished by ather criterion. The criteria were chosen to maximise the probability of a correct decision. The flowchart depicting the classification of CPM signals is shown in Figure 4. The highest occurrence from the three simultaneous decisions is chosen as the correct classification. For the spread spectrum signals, a flowchart depicting the classification procedure is shown in Figure 5. The incoming signal is categorised as one of two possible sets of signals by comparing a key feature value of the signal with a certain threshold. The thresholds are chosen so that the number of correct decisions made is optimal. The determination of the thresholds is outlined in section 3.3. Since it is possible to classify the M-segments as more than one type of signal, the classification with the largest number of repetitions is chosen. If there are two or more classifications with equal repetitions the method outlined in [] is used. 3.3 Threshold Determination The key feature thresholds for the spread spectrum signals are chosen so that the probability of a correct decision is obtained from 400 realisations of each modulation type at signal to ise ratios (SNR) of 10 and 0 db. A set of modulation types is separated
into two n-overlapping subsets (A and B) by a decision rule defined as: >A P( A / x ) P( B / x ) (10) <B where x represents the value of the chosen key feature, P(A/x) is the conditional probability of the correct decision being in subset A given the key feature value and P(B/x) is the conditional probability of the correct decision being in subset B given the key feature value. It can be shown that: P( A / x )P( x ) = P( x / A )P( A ) P( x / A )P( A ) P( A / x ) = P( x ) P( x / B )P( B ) P( B / x ) = P( x ) SNRs of 0dB, 15dB and 10dB. It can be deduced from the figure that for SNRs of 15dB and 0dB, the GMSK signal can be separated from the other CPM signals. Therefore the key feature σa is used to separate GMSK at SNR of 0dB and 15dB. However at the SNR of 10dB this is t possible. (11) >A P( B / x )P( B ) (1) <B where P(x/A) is the probability of the particular value (x) of the chosen key feature kwing that the signal belongs to the subset A and P(x/B) is the probability of that particular value of the chosen key feature kwing that the signal belongs to the subset B. P(A) and P(B) are the a prior probabilities of the subsets A and B respectively. We assume that P(A) = P(B) = 0.5. Therefore the key feature threshold is chosen such that P(x/A) = P(x/B). (13) The cumulative distribution functions (cdf) for groups A and B are plotted and the threshold is chosen where the two graphs intersect or in the centre of the two cdfs. P(A) is plotted against 1P(B). P( x / A )P( A ) Figure 1: Cumulative distribution functions for the key feature γmin, of PSK (subset A) and BPSK DSSS (subset B). For SNR of 10dB, it can be observed from Figure 3 that the values of σfn for GMSK (also represented by + ) lie between 0.5 and 0.6. Therefore this feature is used to separate GMSK at SNR of 10dB. The optimum thresholds tσa1, tσa, tσa3, tσa4, tσa5, tσa6, tσfn1, and tσfn and their corresponding values are 0.17, 0.15, 0.34, 0.45, 0.95, 0.17, 0.5, and 0.6 respectively. An example is shown to find the threshold value for the key feature γmin where the cdfs are plotted in Figure 1. It can been seen that the value -3 lies around the centre of the two cdfs. The optimum values for the key feature thresholds tγmaxf1, tγmaxf, tσdp, tσda, tσap, tσfn, tγmin1, tγmin, and tγmin3 are 0, 15.5, 0.7, 0.33, 0.5,1.63, -3, -5 and -17 respectively. These threshold values are used to discriminate between groups of signals as shown in Figure 5. The relevant thresholds for the CPM signals are determined graphically. An example for the GMSK signal is shown in Figure and Figure 3. The values of σa for the GMSK signal are represented by +. Figure contains plots for the GMSK signal at Figure. Plot of Values of the Key Feature σa for Different Types of CPM Signals
for SNR of 10dB are better than for higher SNR. This is because the correct classification is dependent on more than one key feature. So if one key feature is used for the SNR of 0dB and 15dB, ather key feature may be used for the SNR of 10dB because it gives better results than the previously mentioned key feature. L = 1 L = GMSK 0dB 93.58% 99.67% 100% 15dB 93.5% 97.33% 97.5% 10dB 94.08% 93% 91.5% Table. Overall Classification Success Rate for CPM Signals Figure 3. Plot of Values of the Key Feature σ fn for Different Types of CPM Signals 4 Simulation Results The performance results were derived from 400 realisations of each modulation type in the presence of AWGN. The carrier frequency, sampling rate and the symbol rate were given values of 150kHz, 100kHz and 1.5kHz respectively. The digital symbol sequence was randomly generated. Simulations in Matlab were carried out with four full response CPM signals (LREC, LRC, GMSK and HCS) and 3 partial response signals (LREC, LRC, HCS). For all signals h = ½ and M =. For the partial response signals, L=. BPSK SS, QPSK SS and FH SS signals were also simulated with the first 7-bit Gold code in Table 1 of [6] used as the spreading sequence. BPSK QPSK FH CPM 0dB 100% 100% 100% 100% 15dB 100% 100% 100% 100% 10dB 100% 100% 100% 100% 5dB 100% 100% 100% 99.5% Table 1. Classification Success Rate for SS and CPM Signals The performance results for the spread spectrum signals and the CPM signal type as a whole are shown in Table 1 for SNR of 0dB, 15dB, 10dB and 5dB. The results show that the performance does t degrade with decreasing SNR. Only the CPM signal group has a slight degradation at the SNR of 5dB. The overall results for the signals within the CPM type are shown in Table for SNR of 0dB, 15dB and 10dB. For the full response signals (L=1), the results 5 Conclusion This paper introduced an algorithm that extends the capability of digital modulation classifiers to cope with continuous phase modulated (CPM) signals as well as spread spectrum (SS) signals. The decision theoretic approach was used for classification and some key features and relevant threshold values were presented. Results indicate that the SS and CPM signal group can be classified with almost 100% accuracy even at the SNR of 5dB. For signals within the CPM signal class, the overall classification success rate is > 95%. References: [1].E.E Azzouz and A.K. Nandi, Automatic identification of digital modulations, Signal Processing, vol. 47, pp55-69, Nov 1995. [].E.E. Azzouz and A.K. Nandi. Automatic modulation Recognition of Communication Systems. Netherlands: Kluwer Academic Publishers, 1996. [3].E.E Azzouz and A.K. Nandi, Algorithms for automatic modulation recognition of communication signals, IEEE Trans. Commun, vol. 46, pp431-436, April 1998. [4].J.G. Proakis. Digital Communications. New York: McGraw Hill, 1995. [5].R.L Peterson, R.E Ziemer, D.E Borth. Introduction to Spread Spectrum Communications. New Jersey: Prentice-Hall, 1995. [6].V. Ramakonar. SIMULINK Implementation of a CDMA Transmitter. Hours thesis dissertation, Edith Cowan University, Perth, Western Australia, 1996. [7].V. Ramakonar, D. Habibi, A. Bouzerdoum, Automatic Recognition of Digitally Modulated
Communication Signals, Proceedings of Fifth International Symposium on Signal Processing and its Applications '99', Brisbane Australia, August 1999, pages 753-756. [8] J.B Anderson, T Aulin and C.E Sundberg. Digital Phase Modulation. New York: Plenum Press. 1986. CPM tσ a1 <σ a < tσ a or tσ a <σ a < tσ a3 or tσ a4 <σ a < tσ a5 L diff > t Ldiff tσ a6 <σ a < tσ a7 or σ fn <tσ fn Yes No Yes No Yes No L=a L=1a L=1b L=b GMSK L=1c Figure 4: Decision Tree for CPM Signals Digitally modulated signal γ maxf < t γ maxf1 γ min < t γ min3 σ ap > t σ ap σ dp > t σ dp σ fn > t σ fn FSK γ min < t γ min QPSK-SS σ da > t σ da γ maxf < t γ maxf PSK4 BPSK-SS γ min < t γ min1 ASK4 ASK PSK FH-SS FSK4 CPM Figure 5. Flowchart for identification of digital modulation schemes.