Automatic identification of digital modulation types

ELSEVIER Signal Processing 47 (1995) 55-69

SKNAL PROCESSING

Automatic identification of digital modulation types

E.E. Azzouz, AK. Nandi*

Department of Electronic and Electrical Engineering, University of Strathclyde, 204 George Street, Glasgow GI IXW, UK

Received 28 November 1994; revised 30 March 1995

Abstract

In both covert and overt operations, modulation identification plays an important role. In communication intelligence (COMINT) applications the main objective is the perfect monitoring of the intercepted signals and one of the parameters that affect the perfect monitoring is the modulation type of the intercepted signal. In this paper, a set of decision criteria for identifying different types of digital modulation is developed. Also, all the key features used in the identification algorithm are calculated using the conventional signal processing methods. Computer simulations for different types of band-limited digitally modulated signals corrupted by band-limited Gaussian noise have been carried out. Expressions for the instantaneous amplitude, and phase of different types of digitally modulated signals are derived. Also, two software solutions for estimating the instantaneous phase in the weak segments of a signal are introduced and analyzed. Finally, it is found that all modulation types of interest have been classified with success rate 290% at SNR = 10 dB.

Sowohl in verdecktem, als such in offenem Betrieb spielt die Identifikation von Modulationen eine wichtige Rolle. In Anwendungen der Kommunikationsiiberwachung (COMINT) besteht die Hauptaufgabe im perfekten Uberwachen der aufgefangenen Signale und einer der Parameter, die die perfekte tierwachung beeinflussen, ist der Modulationstyp des aufgefangenen Signals. In dieser Abreit wird ein Satz von Entscheidungskriterien zur Identifikation verschiedener digitaler Modulationstypen entwickelt. AuDerdem werden alle grundlegenden Eigenschaften, die im Identifikations- algorithmus benutzt werden, mit Hilfe von konventionellen Signalverarbeitungsmethoden berechnet. Rechner- simulationen mit verschiedenen Typen bandbegrenzter digitalmodulierter Signale, die durch bandbegrenztes GauBsches Rauschen gestijrt wurden, wurden durchgefiihrt. Ausdriicke fur die Momentan-amplitude und -phase verschiedener Typen digital modulierter Signale werden hergeleitet. Zusltzlich werden zwei Softwareliisungen fur die Schatzung der Momentanphase in abgeschw;ichten Signalsegmenten eingefiihrt und analysiert. Schlieglich wird gefunden, daI3 alle interessanten Modulationstypen mit einer Erfolgsrate 290% bei einem SNR = 10 dB klassifiziert wurden.

RCUld?

L’identification de modulation joue un role important aussi bien dans les operations secretes que les operations publiques. Dans les applications d’intelligence des communications (INTCOM), l’objectif principal est l’observation parfaite des signaux intercept& et l’un des parametres qui atTecte cette observation parfaite est le type de modulation du signal intercept&. Dans cet article, on developpe un ensemble de criteres de decision pour identifier differents types de modulation numerique. De plus, toutes les caracteristiques-cl&s utilisees dans l’algorithme sont calcuRes en utilisant des

*Corresponding author. Tel.: 141 552 4400. Fax: 141 552 2487.

0165-1684/95/%9.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0165-1684(95)00099-2

56 E.E. Azzouz, A.K. Nandi / SignaI Processing 47 (1995) 55-69

mkthodes de traitement du signal conventionnelles. Des simulations ont CtC faites g l’ordinateur pour diffkrents types de signaux modulks numkriquement et A bande limit&e, corrompus par du bruit blanc gaussien B bande limitke. On derive des expressions pour l’amplitude instantanke et la phase de diffkrents types de signaux modulks numkriquement. En outre, deux solutions logicielles pour l’estimation de la phase instantanke dans les segments faibles d’un signal sont introduites et analyskes. Enfin, on verra que tous les types de modulation qui sont intkressants ici ont Ctk classks avec un taux de succes 290% pour un SNR = 10 dB.

Keywords: Digital modulation; Modulation identification; Signal classification

1. Introduction

Signals travelling in space with different modulation types as well as different frequencies fall in a very wide band (HF-VHF). There are many applications that require signal identification and monitoring. Some of these applications are for mili- tary purposes such as surveillance, electronic war- fare and threat analysis. The others are for civilian purposes such as signal confirmation, interference identification and spectrum management. The first objective of a surveillance system is to identify the signal characteristics of intercepted emitters against a catalogue of reference characteristics or signal sorting parameters. One of the important characteristics is the signal modulation type.

In the past, COMINT systems have relied on the operator interpretations of measured parameters of the intercepted signal (manual modulation identification). Recently, several modulation identifiers that automatically identify the type of modulation in an incoming RF signal have been develoed [1,3-121. Automatic modulation identification is more valuable than manual modulation identification because by integrating the automatic modulation identifier into an electronic support measure- ment (ESM) receiver, including energy detector and direction finder units, will increase the efficiency and the ability of the operator to monitor the activities in the frequency band of interest.

In modern communication systems, the digital modulation techniques rather than the analogue ones are frequently used. So, the new trend is the digital modulation identifiers. Because of the classified nature of the problem, the open literature does not contain all the information on the subject of modulation identification. Until now, there are two main approaches for the modulation identification

process. The first is a decision theoretic approach, the other approach is the statistical pattern recognition. Also, there are five methods of modulation identification. They are: (1) spectral processing, (2) instantaneous amplitude, phase and frequency parameters, (3) instantaneous amplitude, phase and frequency histograms, (4) combination of the pre- vious three methods and (5) universal demodula- tors. In this paper, the first approach was carried out and the second method was used to develop the identification algorithm.

The following is an overview of some of the recently published algorithms. Liedtke [lo] used both the decision theoretic approach and the pattern recognition approach to discriminate between the digitally modulated signals. The hardware implementation of this identifier is excessively complex. He claimed that error-free modulation identification was achievable at SNR > 18 dB. Mammone et al. [11] follow the pattern recognition approach. Through simulations they demon- strate that the classifier performs well for SNR > 35 dB. Polydoros et al. [12] follow the decision theoretic approach to discriminate between PSK2 and PSK4 signals. Their classifier is less robust in the sense that signal parameters such as the initial phase and the symbol rate need to be available to the classifier. Huse et al. [7] follow the decision theoretic approach. Their identifier is used only for constant amplitude signals (CW, MPSK and MFSK). They claimed that successful modulation identification is valid for SNR > 15 dB. Dominguez et al. [4] follow the pattern recognition approach. This classifier is a general approach for both analogue and digital modulations. However, they claimed that this recognizer performed well at SNR > 40 dB. But at SNR = 10 dB the probability of correct modulation recognition is 0% for all

E.E. Azzouz, A.K. Nandi / Signal Processing 47 (199s) 55-69 51

digital modulation types except for PSK4 (= 7%) and at 15 dB the performance is still wanting especially for FSK4 (= 56%), FSK2 (=84%) and ASK4 (= 87%). However, it should be noted that the work in [4] attempts to identify digital as well as analogue modulations. Huse et al. [8] follow the decision theoretic approach to estimate the number of levels in MPSK signals. They claimed that the eighth moment is sufficient to classify PSK2 signals with reasonable performance. The pattern recognition usually required long signal duration and the processing time may be very long; this leads to the use of the pattern recognition algorithms in the off-line analysis. In [4], the number of samples per frame used in performance evaluation is 3000 samples and nothing is mentioned about the sampling rate. However, the number of samples used in the proposed algorithm here is 2048 (equivalent to 1.7066 ms) and this is likely to be suitable for the on-line analysis.

In the next section the proposed identification algorithm for digitally modulated signals along with the key features used in the algorithm are introduced. The details of computer simulations are presented in Section 3, while thresholds determination and performance evaluations are given in Section 4. Finally, the paper is concluded in Section 5.

2. Digitally modulated signals identification algorithm

In this paper an algorithm is developed to decide reliably the type of modulation of the intercepted signal - whether the intercepted signal contains the information in the instantaneous amplitude, in the instantaneous phase, in the instantaneous frequency, or in a combination of them. Additionally, a criterion is developed to judge the quality of different segments of a signal under consideration according to their suitability for modulation identification. The proposed global procedure for digital modulation identification comprises the following steps.

First, the intercepted signal with length K sec- onds and sampled at sampling rate& divided into M successive frames, each with length N samples,

results in M ( = KfJN) frames. In order to identify the intercepted signal according to its modulation type and to discriminate good frames from bad ones (a good frame is the frame that has the same decision as the global decision), it is suggested to proceed as follows.

(a) From every available frame decide about the type of modulation. The key features proposed for this identification algorithm are derived from the instantaneous amplitude A(t), the instantaneous phase 4(t) and the instantaneous frequencyf(t) of the signal under consideration (see Appendix A).

The first key feature, ymax, is defined by

ymax = max lDFT(&(i))12, (I)

where AC,,(i) is the value of the normalized-centered instantaneous amplitude at time instants t = i/fs (i = 1,2,..., N) and it is defined by

A,,(i) = =

where is average of instantaneous over frame;

ma = k i$, A(i). (3)

Normalization of the instantaneous amplitude is necessary in order to compensate the channel gain. Thus, yrnax represents the maximum value of the spectral power density of the normalized-centered instantaneous amplitude of the intercepted signal.

The second key feature, gap, is defined by

where cjNL(i) is the value of the non-linear component of the instantaneous phase at time instants t = i/h, C is the number of samples in { 4(i)) for which A,(i) > a,, and a, is a threshold for A(t) below which the estimation of the instantaneous phase is very sensitive to the noise. Instead of using a phase-locked loop (PLL) as a hardware solution for this problem Cl], there are two software solutions. Both of them start by localizing the weak signal samples by simply checking the inequality

58 E.E. Azzouz, A.K. Nandi / Signal Processing 47 (1995) 55-69

A,(i) < a, for every sample. The first solution is very simple and consists in assigning a constant phase (e.g. x/2) to these samples. The second solution is more sophisticated and needs to interpolate the phase in the localized weak intervals utilizing the estimated values for the instantaneous phase in the non-weak signal intervals. The interpolation technique used is illustrated in Appendix B. The first solution is adequate for every part of the identification algorithm except for the estimation of the number of levels for MFSK signals. Thus, the second solution is used to discriminate between the different types of M-ary FSK signals. Thus, uap is the standard deviation of the absolute value of the non-linear component of the instantaneous phase, evaluated over the non-weak segments of the intercepted signals.

The third key feature, o&,, is defined by

Thus, gdp is the standard deviation of the non- linear component of the direct (not absolute) instantaneous phase, evaluated over the non-weak segments of the signals.

The fourth key feature, craa, is defined by

Thus, eaa is the standard deviation of the absolute value of the normalized-centered instantaneous amplitude of the signal.

The fifth key feature, afa, is defined by

where

h’(i) =fc(ibb,

.I$) =f(i) - mf; (8)

mf = $ ,i f(i), l-1

where rb is the bit rate. Thus, bfa is the standard deviation of the absolute value of the normalized- centered instantaneous frequency, evaluated over the non-weak segments of the intercepted signal.

The choice of the yrnax, cap, cdp, aaa and ofa, as key features for the proposed algorithm is based on the following facts: - yrnax is used to discriminate between FSK2 and

FSK4 as one group and ASK2, ASK4, PSK2 and PSK4 as the second group. As the FSK2 and FSK4 signals have constant instantaneous amplitude, their normalized-centered instantaneous amplitude is zero. Thus, their spectral power densities are zero; i.e. they have no amplitude information ( y max < tyma,) by their nature. On the other hand, ASK2 and ASK4 signals possess amplitude information (ymax > ty,.J. Further- more, the PSK2 and PSK4 signals have amplitude information because the bandlimitation imposes amplitude information especially at the transition between successive symbols as will be explained later. So this key feature can be used to discriminate between the signals that have amplitude information (ASK2, ASK4, PSK2 and PSK4) and those that have no amplitude information (FSK2 and FSK4).

_ hap is used to discriminate between ASK2, ASK4 and PSK2 signals as one group and PSK4 signals as the second group. ASK2 and ASK4 signals have no absolute phase information (oap d t,,,) by their nature. Also, it is well known that the direct phase of PSK2 takes on values of 0 and R, so its absolute value after centering is constant (=x/2) such that it has no absolute phase information (a,, d t,,,). On the other hand, PSK4 has absolute and direct phase information (cap > t,,.,) by its nature. So, ~~~ can be used to discriminate between the types that have absolute phase information (PSK4) and those that have no absolute phase information (ASK2, ASK4 and PSK2).

- odp is used to discriminate between ASK2 and ASK4 signals as one group and PSK2 signals as the second group. ASK2 and ASK4 have no direct phase information (e.dp < t,,+) by their nature, but the PSK2 signal has direct phase information (cdp > t_) by its nature (the instantaneous phase takes on values of 0 and x).

E.E. Auouz, A.K. Nandi / Signal Processing 47 (1995) 55-69 59

so, gdp can be used to discriminate between the types that have direct phase information (PSK2) and those that have no direct phase information (ASK2 and ASK2). u,, is used to discriminate between ASK2 and ASK4 because the normalized-centered instantaneous amplitude of the ASK2 signal is changed between two levels (+ 1) so its absolute value is constant and it has no absolute amplitude information (CT,, < t,..). On the other hand, the ASK4 signal has absolute and direct amplitude information (a,, > t,,.) by its nature. So, CT,, can be used to discriminate between ASK2 and ASKA

- cfa is used to discriminate between FSK2 and FSK4 because the normalized instantaneous frequency of FSK2 is changed between two levels

( f 1) so its absolute value is constant and it has no absolute frequency information (afp < tO,,.)_ On the other hand, the FSK4 signal has absolute and direct frequency information (rrfa > t_) by its nature. So, crfa can be used to discriminate between FSK2 and FSKC

(b) As it is possible to obtain different decisions of these M-frames, the majority logic rule is applied; i.e. select the decision with the largest number of repetitions. If two or more classifications have equal maximum numbers of repetitions, they are regarded as candidates for the optimal decision. In this case it is necessary to continue as follows: 1. Group the frames corresponding to each of the

candidate decisions.

Fig. 1. Functional flowchart for automatic identification of digital modulations.

60 E.E. Azzozu. AK. Nan& / Signal Processing 47 (1995) 55-69

2. Within a group determine for every frame the number of samples of A(i) falling below the threshold a,. Evaluate the total numbers of these samples over the group.

3. Adopt the decision whose corresponding group has minimum number of samples falling below the threshold a,.

The discrimination between the different types of digital modulation is carried out according to the following rules: 1.

2.

3.

4.

5.

A

Comiare ymax, which is defined by (I), with a suitable threshold $,, such that

ASKZ, ASK4, PSKZ, and PSK4

Ymax >< L,

FSKZ, FSK4

(9)

Compare gap, defined by (4), with a suitable threshold toal such that

PSK4

gap 2 Lp ASKI. ASK4, PSK2

(10)

Compare cdp, which is defined by (5), with a suitable threshold t,_ such that

PSK2

gdp >< bd

ASKZ. ASK;

(11)

Compare o,, with a suitable threshold toan such that

ASK4

gas 3 to*. (12)

ASK2

Compare crfa with a suitable threshold t,,. such that

FSK4

@ra >< tc& (13) FSK2

detailed pictorial representation of the above

1200 kHz and 12.5 kHz, respectively. The modulating digital symbol sequence was derived from 2048 independent random numbers to increase the de- gree of realism. Thus, the generation of the modulating symbol sequence comprised the following steps:

The average value x,, of the random sequence {x(i) > was calculated. The number of samples per symbol duration, N, = 96, was determined from the assumed symbol and sampling rates. The simulated random sequence {x(i)} was divided into adjacent sets of N, = 96 samples. Then in every set when the number of samples exceeds a certain threshold, the set was represented by a certain level (e.g. for the binary case, if the number of samples exceeding the average value of the random sequence {x(i)} was larger than 47 samples, the set was represented by binary bit ‘l’, otherwise the set was represented by a binary ‘0’).

MASK, MPSK, and MFSK signals were derived from a general expression

se(i) = aOcos(y + 4.);

N,>i>l, fJ=O,l,..., M-l. (14)

The selections of the parameters uO,fO, and & used in order to simulate the above-mentioned digitally modulated signals (M = 2 and 4) are presented Table 1.

in

Table 1 Digitally modulated signals parameters selection

Modula- tion type M a0 .h W-W

procedure for digital modulation identification is shown in Fig. 1 in the form of a flowchart.

3. Computer simulations

The carrier frequencyf,, the sampling ratef,, and the symbol rate I, were assigned the values 150 kHz,

MASK 2 0.88 + 0.2 L 0 4 0.258 + 0.25 fC 0

MPSK 2 1 .L (1 - e)x 4 1 fc WQ)

MFSK 2 1 4r,e +f. - 2rb 0

h (8 - +

l)rb if 0 < 2

4 1 fc + (0 - 1)~ if e 2 2

0

E.E. Azzouz, A.K. Nandi / Signal Processing 47 (1995) 55-69 61

3.1. Band-limiting of simulated modulated signals

Every communication transmitter has a finite transmission bandwidth. Consequently, the trans- mitted signal is band-limited. Therefore, the simulated digitally modulated signals were band- limited to make them represent more realistic test signals for the proposed global procedure for modulation identification. The band-limitation of the simulated digitally modulated signals was carried out in accordance with the usual implementation in practice. Thus, the band-limitation of digitally modulated signals was exercised after generation. Note that digital modulation systems are usually implemented in practice as shift-keying systems and hence cannot be regarded as versions of analogue modulation systems. However, there are two ways of implementing band-limitation of digitally modulated signals. These are: (1) using smoothed square pulses such as raised-cosine square function or Gaussian signal instead of ideal square pulses [13]; such band-limitation might be similar to that exercised in analogue modulation systems and it is not often used in practice, and (2) shift-keying systems in which the band-limitation is applied on the modulated signal instead. In this case the simulated digitally modulated signals were band- imited to bandwidth containing 97.5% of the total average power according to the definition [13]

s

L + B2 G,(f)df= 0.975

l---82 s

co G,(f) df, (15)

-0D

where G,(f) is the power spectral density of the modulated signal s(t).

The analytic expressions of the 97.5% bandwidth are derived for different types of digital modulation in Appendix C. Finally, the theoretical expressions

Table 2 Bandwidths of digitally modulated signals

Modulated signal Modulation bandwidth (theoretical

type expression)

Modulated signal bandwidth (simulated value (kHz))

MASK MPSK MFSK

4r,

. . . . . J---l ..: I

500 1000 1500 2000 Time instants

I I 500 1000 1500 2000

Time Instants

Values of the key features for the ASK2 signal

Key feature Corresponding value at co SNR

YrnlX 248 530 % 0.028 udP 0.028 caa 0.000 cra 0.000

Fig. 2. Band-limited ASK2 modulation.

and the simulated values of the bandwidth of the simulated digitally modulated signals are presented in Table 2.

Typical examples of the modulating signal, modulated signal and all the aforementioned key features for each type of modulation based on 1.7066 ms duration signals (equivalent to 2048 samples) are shown in Figs. 2-7.

4. Thresholds determination and performance evaluations

4.1. Thresholds determination

The implementation of the proposed algorithm requires the determination of five thresholds. These

are t,,.., &a09 trTdDY t,_. and t,,.

62 E.E. Azzouz, AK. Nandi / Signal Processing 47 (1995) 55-69

I 500 1000 1500 2000

Time instants

I I 500 1000 1500 2000

Time instants

Values of the key features for the ASK4 signal


Ymsr 87 130

*w 0.029

% 0.029

o,, 0.324

%3 O.OC!O

Fig. 3. Band-limited ASK4 modulation.

A. Determination of tymx The dependence of ymax on the SNR was com-

puted for six digitally modulated signals - band- limited ASK2, band-limited ASK4, band-limited PSK2, band-limited PSK4, band-limited FSK2, and band-limited FSKA Of course only two of these six signals have no amplitude information and they are FSK2 and FSK4 signals. The results for one simulation of digitally modulated signals are presented in Fig. 8. From Fig. 8, it is clear that for SNR > 7 dB the curves corresponding to FSK2 and FSK4 signals fall below the threshold level 10000. Furthermore, for SNR > 7 dB the curves corresponding to band-limited ASK2, band-limited ASK4, band-limited PSK2 and band-limited PSK4 are above the threshold 10 000. Thus, it is clear that a good choice of tyma, is 10000.

J 500 1000 1500 2000

Time instants

500 1000 1500 2000 Time Instants

Values of the key features for the PSK2 signal


12596 0.040 1.570 0.000 0.101

Fig. 4. Band-limited PSK2 modulation.

B. Selection of the threshold t,,. If the non-linear phase component is uniformly

distributed between -b and + b, then its absolute value is uniformly distributed between 0 and b has

a standard deviation r~.~ = b/(2/$). Thus, the range of variation of the absolute non-linear phase component b may be estimated from oap as

2$% . Throughout the paper, to,. = x/6 and then

b=xj,/?. U sually the non-linear phase component of PSK2 is uniformly distributed between -n/2 and n/2. So its absolute value is uniformly distributed between 0 and 7t/2. Thus, cq,p = 0.4534, which is less than the chosen threshold, toap = z/6. Furthermore, the range of variations of the non- linear component of the instantaneous phase for ASK2 and ASK4 is very small; i.e. cap is very small

E.E. Azzouz, A.K. Nandi / Signal Processing 47 (199s) 55-69 63

J 500 1000 1500 2000

Time instants

500 1000 1500 2000 Time Instants

Values of the key features for the PSK4 signal Values of the key features for the FSK2 signal

Key feature Corresponding value at co SNR Key feature Corresponding value at co SNR

. :_

.$OJ. i. _: :.

&8. _.. .: . . . . . . . . . . ,.,., ,..:, .., ..!. s zJO.4.. .i . . . . . . .,.:. .._ I!

,...

IO.2. . . . . . . . . . . . -.

0 500 1000 1500 2000

Time instants

I 1

. I

1 !ml 1000 1500 2000

Time Instants

YllWl. 14021 Yma. 308.076 % 4.712 % 6.391 % 6.674 % 9.467 6,. 0.000 0.n 0.000 %, 0.131 Of. 0.061

Fig. 5. Band-limited PSK4 modulation. Fig. 6. Band-limited FSK2 modulation.

(ideally zero). Meanwhile, in PSK4 the range of variation of c,,, is larger than the other types. This argument motivated assigning the threshold tnap to the value n/t/6.

C. Selection of the threshold tudp ‘If the non-linear phase component is uniformly

distributed between - b and + b, then it has a stan-

dard deviation odp = b Jfi. Thus, the range of variation of the direct non-linear phase component

b may be estimated from edp as &&,. Through-

out this paper, t_, = 743 and then b = n/d.

D. Selection of the threshold teaa and t_ This is done in a similar way to that used in the

selection of to,*.

The chosen values of the thresholds tYr,, t,,, t,,&., and to,. are 10000, x/6, x/3, 0.25 and 0.35 respectively. It is worth noting that all these thresholds are chosen such that an optimal correct decision for all types of modulation can be obtained. Also, the values of these thresholds are determined from 400 realizations for each type of modulation of interest.

It is necessary to check the suitability of the pre-chosen thresholds. Fig. 9 presents the dependence of gap on the SNR for the ASK2, ASK4, PSK2 and PSK4 types. Fig. 10 presents the dependence of edp on the SNR for the ASK2, ASK4 and PSK2 types. Fig. 11 presents the dependence of cr,, on the SNR for the ASK2 and ASK4 types. Fig. 12 presents the dependence of of,, on the SNR for the FSK2 and FSK4 types. From the obtained simulation results it is observed that a correct decision can

64 E.E. Azzouz, A.K. Nandi J Signal Processing 47 (1995) 55-69

0' 1 500 1000 1500 2000

Time instants

I I 500 1000 1500 2000

Time Instants

Values of the key features for the FSK4 signal

Key feature Corresponding value at 00 SNR

Ymar 187.006

cal, 5.621

cdP 8.504

c,, 0.000

%a 0.479

Fig. 7. Band-limited FSK4 modulation.

be made using the decision rules (9)-(13) when the SNR 2 10 dB.

.4.2. Pe$ormance evaluations

The results of the performance evaluation of the proposed procedure for digitally modulated signals classification are derived from 400 realizations for each type of modulation, with a, = 1, and are presented, for two values of SNR (10 and 20 dB), in Tables 3 and 4. It is shown that six modulation types have been simulated and sample results at two different SNR corresponding to 10 and 20 dB are presented in Tables 3 and 4, respectively. Each of the modulation types at each SNR was simulated 400 times. Consider Table 3 for example; it can be observed that six modulation types have been correctly

10 15 20 SNR (de) ~-

Fig. 8. Dependence of y,,,.. on the SNR for (a) ASKZ, (b) ASK4, (c) PSK2, (d) PSK4, (e) FSK2 and (f) FSK4. The dashed line represents the chosen threshold.

class&d with more than 90% success rate except for the band-limited PSK4 with success rate 89.25%. Indeed, two of these six modulation types have suc- cessfully been classified every time (100% success rate). The results in Table 4 correspond to the SNR of 20 dB. It is clear that the success rate for correct identification has increased with increasing SNR, and now four of the six modulation types have been classified with 100% success rate and the other two types have been classified with success rate 295%.

5. Conclusions

The aim of this paper is to introduce a fast and reliable digitally modulated signals identifier. The

E.E. Azzouz, A.K. Nandi 1 Signal Processing 47 (1995) 55-69 65

I I I 2 , I I

Fig. 9. Dependence of oap on the SNR for (a) ASKZ, (b) ASK4, (c) PSK2 and (d) PSKA The dashed line represents the chosen threshold.

current approach has been to carry out this task using the decision theoretic approach. A number of parameters (key features) are proposed to fulfil the requirement of this algorithm. These key features are calculated using conventional signal processing methods. The most interesting observation is that these key features can be extended to larger number of levels (M > 4). Furthermore, the decision on the modulation type is achieved in a very short time due to the simplicity of key features extraction.

Extensive simulations of six digitally modulated signals have been carried out at different SNR. Sample results have been presented at the SNR of 10 and 20 dB only. It is found that the threshold SNR for successful modulation recognition (at

1.8 I .!. .;. .;. -I ,,6_. ............. ..).

j (c) ................ . .................. . .... ........... _

1.4

I

,...............: . . . . . . . .

i

1.2 c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .f ..,,., -I n i Thr ‘CI, _._._._._.;._._.__.-;-.-._.-._.;._ _.-__._. g , _.......... ..: . 1. . . I. ..,..,....,,.,_

+I

O.B_ . . . . . . . . . . . . . . . . . . . . . . . . . . ..,.......... ;. ..,,.,. ..,.,( _

o-e_ . . . . . . . . . . . . . ,. j .._..._. ,,,_

0.41.......... ..; I. . . . . . . . . . i .,..... . .._I

Fig. 10. Dependence of q,,, on the SNR for (a) ASKZ, (b) ASK4 and (c) PSKZ. The dashed line represents the chosen threshold.

a success rate of greater than 90%) is about 10 dB, which is an improvement in the SNR threshold. Currently, work is under way in implementing and testing these criteria for M > 4 as well as implementing and testing a number of ideas for modulation identification without knowing if the signal is analogue or digital.

Appendix A. Analytic expressions of the instantaneous amplitude and phase of digitally modulated signals

The OOK signal is represented by [2]

s(r) = m(t)cos(2xf,t), (A. 1)

66 E.E. Azzouz, AK. Nandi / Signal Processing 47 (1995) 55-69

0.51 I I I

0.M I . . . . . . . . . . . . . ...! . . . . . . . . . . . . . . . . . . . . j

0.4 ................ . ................. j.. .............. .

0.35

t ! ! ! ............

................ . ................. i.. .............. . ............

0.3 ..i . ..; ..!??... ..: .._. .,

a by-yy 0.25 --..._-_.-. - ..-..._. -._.+.__-__.-_-..~__,_._.

o.2t. .I. . .:. ,. .;

Fig. 11. Depcndene of uss on the SNR for (a) ASK2 and Fig. 12. Dependence of at. on the SNR for (a) FSK2 and (b) ASKA The dashed line represents the chosen threshold. (b) FSKI The dashed line represents the chosen threshold.

._

._

._

._

..- .._

._

,_

._

._

25

where

m(t) = 1 1 O<t<T,,

0 O<t<.T,, 64.2)

and Tb is the bit duration (= l/r,,). Consequently, by straightforward analysis, the

complex envelope is given by

q(t) = m(t). 64.3)

The instantaneous amplitude can be expressed as

A(t) = Im(t)l

i

0 if m(t) = 0,

= 1 if m(t) = 1, (A.4) s(t) = -m(t) sin(27cfc t), 64.7)

and the instantaneous phase is given by

&J(t) = 0. (A.3

Thus the instantaneous amplitude looks like the bit stream, while the instantaneous phase is always 0.

The PSK2 signal is represented by [2]

s(t) = cos(2nf,t + D,m(t)), (A4

where D, is the modulation index of the PSK signal and m(t) = f 1 instead of (0,l) in OOK. Thus, by straightforward analysis and by letting D, = n/2, which achieve the maximum power in the signal [13], s(t) can be re-expressed as

Thus, the complex envelope is given by

a(t) = j * m(t). 64.8)

E.E. Azzouz, AX. Nandi / Signal Processing 47 (1995) 55-69 67

Table 3 Confusion matrix for the digital modulation recognition procedure (based on 400 realizations) at SNR = 10 dB

Simulated modulation

type

Deduced modulation type

ASK2 ASK4 PSK2 PSK4 FSK2 FSK4


98.25% 1.75% 100% - - - -

90.75% 0.25% 9% - 89.25% 10.75% - - 91.25% 8.75% - 100%

Table 4 Confusion matrix for the digital modulation recognition procedure (based on 400 realizations) at SNR = 20 dB

Simulated modulation

type

Deduced modulation type



100% - - - - 100% - - - 96.25% 0.25% 3.5%

- 99% 1% - - 100%

- - - - 100%

Also, the instantaneous amplitude and phase are given by (A.9) and (A.lO) respectively.

A(t) = Im(t)l = 1, (A-9)

(A.lO)

The FSK2 signal is represented by [13]

s(t) = cos(2rtl.r + Dr jym nr(l)dI), (A.ll)

where Dr is the modulation index of the FSK2 signal. Also, (A.1 1) can be re-expressed as

s(t) = Re(a(t)ej”*‘), (A.12)

where

a(t) = ejb@). (A.13)

Thus, the instantaneous amplitude and given by (A.14) and (A.15), respectively:

A(t) = 1

and

’ 4(t) = Df m(l)dl. -a,

phase are

(A. 14)

(A.15)

Although m(t) is discontinuous at the bit transition, the instantaneous phase is continuous because 4(t) is proportional to the integral of m(t).

Appendix B. Interpolation techoique for the phase sequence

For the number of levels estimation in MFSK, the phase assignment is not sufficient. Thus, an

68 E.E. Azzouz, A.K. Nandi / Signal Processing 47 (1995) 55-69

interpolation technique is used to define the phase sequence in the weak segments of the signal. The interpolation technique used is illustrated as follows.

After calculating the complex envelope and nor- malizing its real and imaginary parts, we get

x,,,(t) = cos(4W))

= cos(at + b) (BeI)

and

Y,&) = sin(W))

= sin@ + b). (B.2)

Also,

In this case, there are three possible situations with respect to the interval of a signal in which this is applied: - If the interval is at the beginning of the frame, we

use the backward extrapolation only. _ If the interval is at the end of the frame, we use

the forward extrapolation only. _ If the interval is in the middle of the frame, we use

some weighting function to combine both the forward and backward together to form what is called interpolation.

Let the interval in which the extrapolation is applied be t1 < t < tZ; then the optimum and normalized real and imaginary parts of the complex envelope are given by (B.lO) and (B.ll), respectively:

x,2,&) + Ylt&) = 1.

At a time instant to,

xno*(to) = cos(atrJ + b)

and

(B.3)

(B.4)

x”or,op&) = XFE 5 + XBE

t - t1 - 2 t2 - t1’

t - t2 t - t1 Yn~r,opt = YFE t + YBE t,

1 2 2 1 (B.11)

ynor(to) = sin& + b). (B.5)

After some manipulations,

X,0&0 + A) = Cd&) - YL&J)l %Ior@cl - d 1

+ 2X,,*(tO)Yno,(tO)Ynor(to - 4% 03.6)

where XFE and YFE represent the forward extrapolation while XBE and YBE represent the backward extrapolation. After applying the interpolation techniques (forward and backward), and applying some weighting function, there may be a need for a smoothing function, and the simplest form is the use of the averaging as follows:

Ynor(h + A) = CY&&) - d&o)l Yn&o - A)

+ 2X,,,(t0)Ynor(tO)X,,,(tO - A)* (B.7)

4(i) = [4(i - 1) + 4(i) + @(i + 1)]/3. (B.12)

Eqs. (B.6) and (B.7) represent the forward extrapolation. Similarly,

XIX& - A) = C&ro) - Y,2,,@0hl&0 + A)

+ 2x,,*(to)Y,,,(to)Ynor(to + d ),

(B-8)

Appendix C. Bandwidths of digitally modulated signals

For the OOK signal, the spectral power density G,(j) is given by [13]

G,(f) = $ CW-fc) + W-+fc)l

Y,,&o - A) = CY,$&) - &&o)1 ~nor@o + A)

+ 2~,,,(to)~nor(to)~,,,(tO + A).

(B.9)

A2 sin27cTb(f--f,) + sin2nT,(f+f,)

+ 16 7?Tb(f-fJ2 [ x2 7W+fc)2 1 ’ (C.1)

Eqs. (B.8) and (B.9) represent the backware extra- where Tb is the bit duration and it is the inverse polation. of the bit rate (= l/+,). Substitution of (C.l) into

E.E. Azzouz, A.K. Nandi / Signal Processing 47 (1995) 55-69 69

(15) gives

A2 - 16 [ 1 *+; =0.975$, where

s

nTtJl2 sin2 x a=

-nTbB/2 --Ip- dx.

(C-2)

(C.3)

The solution of (C.2) is a = 0.95~ and it is sub- stituted in (C.3) which is numerically approximated to obtain B. Its solution is

B = 4rb. (C-4)

For the binary PSK2 signal, in a similar way to that used in OOK, the 97.5% bandwidth is given by

B = 6rb. (C.5)

By analogy to FM signals, the bandwidth of the binary FSK signal can be expressed as

(C.6)

where fA is half the difference between the mark and the space frequencies and fx is the maximum frequency of the random bit stream spectrum. The spectral power density of a random bit stream is easily deduced from (C.l) by substituting f, = 0. It can be shown in a similar way that fx = 2rb. Thus,

B = Ifmark -&aceI + 4&Y (C.7)

where fmark is the frequency corresponding to a binary ‘l‘, andf,,,,, is the frequency corresponding to a binary ‘0’.

Acknowledgements

The authors wish to thank anonymous re- viewers for helpful comments and suggestions

which have improved the presentation of the work.

References

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Automatic identification of digital modulation types