Automatic modulation recognition—I

J. Franklin Inst. Vol. 334B, No. 2, pp. 241 273~ 1997

~ ) Pergamon

PII:

S0016-0032(96)00069-5

Copyright © 1997 The Franklin Institute Published by Elsevier Science Ltd Printed in Great Britain 0016-0032/97 $17.00 + 0.00

Automatic Modulation Recognition--I by E. E. AZZOUZ* and A. K. NANDI Department o f Electronic and Electrical Engineering, University o f Strathclyde, 204 George Street, Glasgow G1 1 X W , U.K. (Received 3 April 1996; accepted 21 M a y 1996)

ABSTRACT: In this paper, a review of the more recent papers published in the area o f modulation recognition is introduced. Three alternative algorithms, representing modifications o f earlier works and based on the decision-theoretic approach, are presented. These appear to offer the best performance over a large number o f modulation types. For example, the average analogue modulations recognition success rate is ~99%o at l0 dB SNR, the average digital modulations recognition success rate is ~99% at the S N R o f l0 dB, and the average analogue and digital modulations recognition success rate is ~ 93% at 15 dB SNR. Copyright © 1997 Published by Elsevier Science

Ltd

L Introduction Communication signals travelling in space with different modulation types and different frequencies fall in a very wide band (HF and VHF). Usually, it is required to identify and monitor these signals for many applications. Some of these applications are for civilian purposes such as signal confirmation, interference identification and spectrum management. Civilian authorities may wish to monitor their transmissions in order to maintain control over these activities as well as detecting and monitoring nonlicensed transmitters. The other applications are for military purposes such as electronic warfare, surveillance and threat analysis. In electronic warfare applications, electronic support measures system plays an important role as a source of information required to conduct electronic counter measures, threat detection, warning, target acquisition and homing. Modulation recognition brings together many aspects of communication theory such as signal detection, parameter estimation, channel identification and tracking. Modulation recognition is important in many applications for several reasons. First, applying the signal to an improper demodulator may partially or completely damage the signal information content. It is worth noting that any partial damage of the signal information content considerably confuses the following deciphering process which converts the demodulated message from its non-intelligible (ciphered) form to the * Present address: Department of Electronic and Electrical Engineering, Military Technical College, Koubry Elkobba, Cairo, Egypt. 241

242

E. E. Azzouz and A. K. Nandi

A.

l

FM

]

demodulator J

From Rx. IF Output

ModulationType

demodulator J

_[

FSK

]

demodulator J FIG. 1. A modulation recogniser using a blank of demodulators and a set of decision algorithms. intelligible one (deciphered). Second, knowing the correct modulation type helps to recognise the threat and determine the suitable jamming waveform. Also, modulation recognition is important for national security. This paper is concerned with reviewing the most recent papers (since 1984) in the area of modulation recognition, in addition to introducing three new algorithms, based on the decision-theoretic approach. The available references (1-23) can be classified into three categories according to the interested modulation types for each of them. The first category is concerned with the recognition of analogue modulations only (4, 7, 15, 17, 20, 22). The second category is concerned with the recognition of digital modulations only (1, 6, 10, 11, 13, 14, 16, 18, 19, 21, 23). The third category is concerned with the recognition of both analogue and digital modulations without any prior information (2, 3, 5, 8, 9, 12). It is worth noting that in the first category, which is concerned with the analogue modulation recognition only, none of the available references considered the VSB, and the combined modulations except Ref. (22). Also, in the last category, which is concerned with both analogue and digital modulation recognition, not all the well known modulation types were considered in the available references but only subsets of these types. In these references, two philosophies for approaching the modulation recognition problems exist--a decision-theoretic approach and a statistical pattern recognition approach. The use of artificial neural networks (ANNs) for solving the modulation recognition problem will be considered in the forthcoming paper by the authors (Part II). Before the recent modulation recognisers are taken into consideration, the oldest version of modulation recognisers (2) used a bank of demodulators, each designed for only one type of modulation. An operator examining or listening to the demodulators output could decide about the modulation type of the received signal. This recogniser, however, requires long signal durations and highly skilled operators. The automation of this recogniser is achieved by introducing a set of intelligent decision algorithms at the demodulators output as shown in Fig. 1. However, the implementation of this

Automatic Modulation Recognition--I

243

recogniser is complex and requires excessive computer storage. Moreover, the number of modulation types that can be recognised is based on the number of demodulators used.

II.

AnalogueModulated Signals Recognition Algorithms

2.1. Review Fabrizi et al. (4) suggested a modulation recogniser for analogue modulations, based

on the variations of both the instantaneous amplitude and the instantaneous frequency. The key features used are the ratio of the envelope peak to its mean, and the mean of the absolute value of the instantaneous frequency. This recogniser is used to discriminate between some types of analogue modulation--CW, FM and DSB. This recogniser is tested by 24 realizations each with 250 ms length for each modulation type of interest. In Ref. (4), it is claimed that with these two key features the discrimination between the AM and the FM signals could be achieved at SNR ~> 35 dB. However, SSB could be separated from AM and FM signals at SNR/> 5 dB. Chan and Gadbois (7) proposed a modulation recogniser based on the envelope characteristics of the intercepted signal. This recogniser employs a technique in which the instantaneous amplitude of the intercepted signal is computed using a 31-coefficients Hilbert transformer. It uses the ratio R of the variance of the squared instantaneous amplitude to its mean square, as shown in Fig. 2, as a decision criterion to decide about the correct modulation type. This recogniser is used for the recognition of some analogue modulated signals--AM, FM, DSB and SSB. The choice for the ratio R to discriminate between these modulation types is based on the following fact: in noisefree signals, the ratio R ought to be zero for FM signals and close to unity for AM signals. Also, the ratio R for DSB signal ought to be 2 and it is equal to 1 for SSB signals. The simulation results for the developed recogniser were derived from 200

FromRx.IFOutput [

31 Coefficient Hilberttransform

Modulation Type

[

Decisioncircuit

~

FIG. 2. Simplified block scheme of the recogniser using the envelope characteristic only (7).

244

E. E. Azzouz and A. K. Nandi

realisations for each modulation type of interest, each with length 2048 samples (equivalent to 20 ms) introduced in Ref. (7), Table 3. In Ref. (7) it is claimed that at SNR = 7 dB, the probability of correct modulation recognition is 100% for F M signals, 90.5% for AM signals, 80% for SSB signals and 94% for DSB signals, but Azzouz in Ref. (24) numerically analysed the mathematical expressions of the ratio R for different modulation types in Ref. (7) and it was found that this recogniser requires SNR >~ 13.5 dB to distinguish between the amplitude signal and the non-amplitude signal with confidence levels not less than 89%. Furthermore, in Ref. (7) nothing is mentioned about the recognition of the VSB and the combined modulated signals. From the authors' point of view, this recogniser by its nature cannot recognise the signals that have both amplitude and phase information (combined modulated signals). Nagy (15) proposed a modulation recogniser for analogue radio signals only. In this recogniser, the Chan and Gadbois parameter (7), R, in addition to the variance of the instantaneous frequency normalised to the squared sample time are used as key features to discriminate between the different modulation type of interest. The modulation types that can be classified by this recogniser are AM, DSB, SSB, F M and CW. In Ref. (15), it is mentioned that the performance evaluation of this recogniser was derived from 500 realisations, each with 1024 samples (equivalent to 0.25 s), for each modulation type. In Ref. (15), it is claimed that the different modulation types have been classified with a success rate/> 90% at SNR = 15 dB except that the SSB was classified with a success rate 66%. So, Nagy suggested another key feature, which is the mean value of the instantaneous frequency. In this case the SSB has been classified with a success rate ~> 94% at SNR = 15 dB, and the other types have been classified with a success rate of 100%. Jovanovic et al. (17) introduced a modulation recogniser to discriminate between a low modulation depth AM and a pure carrier wave (CW) in a noisy environment. The key feature used is defined as the ratio of the variance of the in-phase component to that of the quadrature component of the complex envelope of a signal. The only thing mentioned about the performance evaluation is that the proposed key feature is a highly reliable tool for separating the AM signals with low modulation depth from the unmodulated carrier, even if the SNR is poor. A1-Jalili (20) proposed a modulation recogniser to discriminate between the USB and LSB signals. This recogniser is based on the fact that the instantaneous frequency of the USB signal has more negative frequency spikes than positive ones, and the opposite for the ISB signal. The key feature used in this recogniser is defined as the ratio, G, of the number of negative spikes to the number of positive ones of the instantaneous frequency. So, G > 1 for USB and G < 1 for LSB. In Ref. (20) the performance measure is derived from 10 realization, each with 128 ms for each modulation type and it is claimed that this recogniser performs well for SNR >/0. Nandi and Azzouz (22) introduced a modulation recogniser for the well-known analogue modulation types. This recogniser utilises the decision-theoretic approach. Four key features are used in this recogniser to discriminate between the AM, DSB, VSB, LSB, USB, FM and combined modulated signals. The key features used are: (1) the maximum value of the spectral power density of the normalised~:entred instantaneous amplitude; (2) the standard deviation of the absolute value of the centred nonlinear component of the instantaneous phase in the non-weak intervals of a signal

Automatic Modulation

Recognition--I

245

I Modulated Analogue signal

yes

yes

yes

no

yes

no

:s __iio ._Iii -

-

FM

._ r~

I,

',

DSB'

AM

,, VSB' .

.

,, L S B .

.

' •

,, U S B .

'

Combined '

.,

FIG. 3. Functional flowchart for Nandi and Azzouz algorithm (22).

segment; (3) the standard deviation of the direct (not absolute) value of the centred non-linear c o m p o n e n t of the instantaneous phase, and (4) the RF spectrum symmetry measure around the carrier frequency of the intercepted signal. In this recogniser the decision about the modulation type is carried out according to the decision rules shown in Fig. 3. In Ref. (22), all the modulation types of interest have been classified with

246

E. E. Azzouz and A. K. Nandi

success rates > 90% at the SNR of 10 dB. Excluding the VSB, LSB and USB, the success rate for all the other modulation types of interest is > 98%. 2.2. A modification Now an alternative decision flow for the algorithm presented in Ref. (22) is presented. This modulation recogniser comprises two main steps: (1) pre-processing, and (2) modulation classification. In the pre-processing stage, the main functions from the modulation recognition point of view are: the signal isolation and segmentation. For signal isolation, one signal only of all the activities in the frequency band of interest is required at a time for the modulation recognition process. In the signal segmentation, the choice of the segment length should have two requirements: (a) avoid the fading modulation effects, and (2) allow good features extraction from each segment. Let the intercepted signal frame with length K seconds be divided into M successive segments, each with length Ns = 2048 samples (equivalent to 1.707 ms), resulting in M( = Kfs/Ns) segments, wherefs (= 1200 kHz) is the sampling rate. 2.2.1. Proposed algorithm. In the modulation classification stage of the proposed algorithm, the decision about the modulation type is taken first from each available segment. Second, a global decision is determined from all the available M-segments of the intercepted signal frame by comparing the global decision with each segment decision. So, the proposed algorithm for analogue modulation recognition requires classification of each segment and classification of a signal frame. Classification of each segment. From every available segment, the suggested procedure to discriminate between the different types of analogue modulations comprises two steps: (A) key features extraction and (B) modulation classification. (A) Key features extraction In the proposed analogue modulation recognition algorithm, four key features are used to discriminate between the modulation types of interest and they are derived from the instantaneous amplitude a(t) and the instantaneous phase ~b(t) as well as the RF signal spectrum. The mathematical expressions of the instantaneous amplitude and phase for different types of analogue modulations are introduced in Appendix A of Ref. (22). In Ref. (22), the mathematical expressions of the RF signal spectrum for different types of analogue modulations are introduced. The first key feature, ~. . . . is defined by ~)max :

maxlDFT(acn(i))12/Ns

(1)

where a~n(i) is the value of the normalised-centred instantaneous amplitude at time instants t = ilia, (i = 1,2 . . . . . Ns), defined by ac.(i) = an(i)-- 1, where a.(i) -

a(0 , ma

(2)

where ma is the average value of the instantaneous amplitude over one frame; i.e. 1

~vs

ma = ~ i~ ' a(i).

(3)

Normalisation of the instantaneous amplitude is necessary to compensate the channel

Automatic Modulation Recognition--I

247

gain. Thus, ])maxrepresents the maximum value of the spectral power density of the normalised-centred instantaneous amplitude of the intercepted signal. The second key feature, aap, is defined by

O'.p =

¢i)~> ¢~NL(i) -- ~ an

at

/

Z

\~'~an(i)>a

I4NL(i) I

(4)

I

where qSNL(i) is the value of the centred non-linear component of the instantaneous phase at time instants t = i/fs, C is the number of samples in {qSNL(i)} for which an(i) > at and at is a threshold for {a(i)} below which the estimation of the instantaneous phase is very sensitive to the noise. Thus, flap is the standard deviation of the absolute value of the centred non-linear component of the instantaneous phase, evaluated over the non-weak intervals of a signal segment. The third key feature, ~rdp,is defined by

(5) Thus, fdp is the standard deviation of the centred non-linear component of the direct (not absolute) instantaneous phase, evaluated over the non-weak intervals of a signal segment. The fourth key feature is used for measuring the spectrum symmetry around the carrier frequency, and is based on the spectral powers for lower and upper sidebands. So, it is defined as: PL - Pu P - PL + P u '

(6)

where Ln

eL = 2 [ Xc(i)12,

(7)

i=t

Ln Pu = ~ [ Xc(i-[-fcn -[- l)[2,

(8)

i=1

and (Jcn -'[-1) is the sample number corresponding to the carrier frequency. In this paper, an algorithm, based on the aforementioned four key features, is considered further to measure its success rate. A detailed pictorial representation for key features extraction from a signal segment is shown in Fig. 4 in the form of a flowchart. (B) Modulation classification procedure Based on the aforementioned four key features, many algorithms can be developed according to the chosen decision flow. Only one algorithm is chosen to measure its performance. In this algorithm, the choice of ]).... lap, aap and the ratio P as key features for the proposed algorithm is based on the following facts: • ])maxis used to discriminate between FM signals as a subset and DSB, and combined

248

E. E. Azzouz and A. K. Nandi

Gaussian noise simulation

Modulated signal simulation x(t) = s(t) + R * n(t)

Ratio P, PL, PU

]

l+sig.
IZ(O Key feature (4) z (t) = x (t) + j

x (t)

Complex Envelope

I Instant. Phase Phase Unwrapping

Instant. amplitude

[

Linear Phase Component Removal

standared deviation of the

non-linear component of the abslute and direct instant, phase in the non-weak intervals

Spectral power density of the normalized-centered instantaneous amplitude

~ Key feuture (2) key feature (3)

Keyfeature ( 1 ) )

"~

FIG. 4. Flowchart for key features extraction in the analogue modulations recognition algorithm.

(AM FM) signals as the second subset. As the FM signals have constant instantaneous amplitude, their normalised-centred instantaneous amplitudes are zero. Thus, their spectral power densities are also zero; i.e. they have no amplitude information (Tmax < t~.m,x). On the other hand, DSB, and combined ( A M - F M ) signals possess amplitude information (~;max/> t~=,x)- SO this key feature can be used

Automatic Modulation Recognition--I

249

to discriminate between the signals that have amplitude information (DSB, and combined) and that do not have amplitude information (FM). • ~rap is used to discriminate between DSB signal as a subset and combined ( A M FM) signals as the second subset. From Appendix A in Ref. (22) it is clear that the direct phase of a DSB signal takes on values of 0 and rt, so its absolute value after centring is constant ( = g/2) such that it has no absolute phase information (trap < t~,~). On the other hand the combined modulated signals have absolute and direct phase information (aap ~ t,,,). SO, a.p can be used to discriminate between the types that have absolute phase information (combined) and those that have no absolute phase information (DSB). • Crdp is used to discriminate between AM and VSB signals as a subset and DSB, LSB, USB, F M and combined ( A M - F M ) signals as the second subset. AM and VSB have no direct phase information (adp < t~d~). On the other hand, the other types have direct phase information (adp ~> t~dp) by their natures. So, aap can be used to discriminate between the types that have direct phase information (DSB, LSB, USB, FM and combined) and those have no direct phase information (AM and VSB). • The ratio P is used to discriminate between the VSB and AM signals as well as to discriminate between the SSB (LSB and USB) as a subset and the DSB, F M and combined modulated signals as the second subset, since [ P[ at infinite SNR ought to be 1 for SSB signal ( + 1 for LSB and - 1 for USB), and 0 for AM, DSB, FM and combined modulated signals. It is well known that the VSB is an intermediate type between the AM and the SSB (USB) signals from the spectrum symmetry point of view. So, it is suggested that the threshold tp is chosen between 0 and 1. Thus, by using this rule, it is possible to discriminate the VSB signal from the AM one as well as to discriminate the SSB from the DSB, FM and combined ( A M FM) modulated signals. A detailed pictorial representation of the developed analogue modulations recognition procedure is shown in Fig. 5 in the form of a flowchart. Classification of a signalframe. As it is possible to obtain different classifications of the M segments (generated from a signal frame segmentation), the majority logic rule is applied; i.e. select the classification with largest number of repetitions. If two or more classifications have equal maximum numbers of repetitions, they are regarded as candidates of optimal decision. In this case, we continue as follows: (1) group the segments corresponding to each of the candidate decisions; (2) determine for every segment within a group the number of samples of the instantaneous amplitude falling below the certain threshold. Evaluate the total numbers of these samples over the group; and (3) adopt the decision whose corresponding group has a minimum number of samples falling below the threshold a,. 2.2.2. Computer simulations. Because of the classified nature of the problem, the authors found it is difficult to obtain real modulated signals. So, a software generation of different types of analogue modulated signals--AM [with amplitude modulation depth (Q = 60%)], AM (Q = 80%), DSB, VSB, LSB, USB, FM [with frequency modulation index (D = 5)], FM (D = 10), combined (Q = 60%, D = 5), combined

250

E. E. Azzouz and A. K. Nandi Analogue Modulated Signal

no

IPI

yes

yes

< I P

[ no

yes

cr

ap

<

t

o ap

1

S

IDSBI

ICombinedl~FMI

/LSB/

IUSBI

FIG. 5. Flowchart for the analogue modulations recognition algorithm. ( Q = 6 0 % , D = 10), combined ( Q = 8 0 % , D = 5 ) and combined ( Q = 8 0 % , D = 10)--with high degree of realism is introduced. In our simulations, the carrier frequency, fc, and the sampling rate, f~, were respectively chosen to be equal to 150 and 1200 kHz. In order to increase the degree of realism, a non-intelligible simulated speech signal is used as a modulating signal for all analogue modulation types of interest. The simulated modulated signals were band-limited in order to make them represent more

Automatic Modulation Recognition--I

251

TABLEI Bandwidths of analogue modulated signals Modulated signal bandwidth Modulation type

Theoretical expression

AM, DSB VSB SSB Combined

2f~ f,+~ f~ 2(D + 2)/~,

FM

2(D+l)f~

Simulated values (kHz) 16 10 8 112 if D = 5 192 if D = 10 96ifD = 5 176ifD = 10

realistic test signals for the proposed global procedure for analogue modulation recognition. The band-limitation of the simulated analogue modulated signals was carried out in accordance with the usual implementation in practice. Thus, in analogue modulated signals the band-limitation was exercised on the modulating signal (non-intelligible speech signal) as well as on the modulated signals. Finally, the bandwidths of the simulated analogue modulated signals are presented in Table I. 2.2.3. Performance :valuation. The implementation of the proposed algorithm introduced in Fig. 5, requires the determination of four key features thresholds: t;.m~,, t~ap, t~dp and tp in addition to the normalised amplitude threshold, at,,,, which is used in measuring the key features gap and ado- As a result of the signal segmentation in the pre-processing stage (the available signal frame is divided into M successive segments), the thresholds determination and the performance evaluation are derived from 400 realizations, each with 2048 samples (equivalent to 1.707 ms) for each modulation type of interest at SNR of 10 and 20 dB. From Fig. 5, it is clear that each decision rule is applied to a set of modulation types, G, separating it into two non-overlapping subsets (A and B) according to:

KF ~ ~ Xopt,

(9)

where KF is the measured value of the chosen key feature and Xopt is the corresponding optimum threshold value. The determination of the optimum key feature threshold, Xopt is as follows: Xopt = arg min, {K(x) },

(1 O)

where

K(x) -

P(A(x)/B) P(B(x)/A) + +] 1 - P ( A ( x ) / B ) - P(A(x)/A) ]. P(A(x)/A) P(B(x)/B)

(11)

The optimum key features threshold values, t~o,ax, t~,o, /"do and tp are chosen to be 6, re/4, n/6 and (0.6 for VSB) and (0.5 for SSB). Sample results at SNRs corresponding

E. E. Azzouz and A. K. Nandi

252

TABLE II

Confusion matrix for the presented analogue modulations recognition algorithm [based on 400 realizations] at SNR = l 0 dB Deduced modulation type Simulated modulation type AM DSB VSB LSB USB Com. FM

AM

DSB

VSB

100%

. 100% ---

. . 98.0% 0.2% 2.2% . .

-

-

----

.

LSB

USB

.

Com.

FM

---

----100%

.

.

.

. 2.0% -97.8%

-99.8%

.

.

100% --

--

TABLE III

Confusion matrix .for the presented analogue modulations recognition algorithm [based on 400 realizations] at SNR = 20 dB Deduced modulation type Simulated modulation type AM DSB VSB LSB USB Com. FM

AM

DSB

100%

. 100% ----

.

.

.

-

-

----.

t o 10 a n d 2 0 d B a r e p r e s e n t e d o v e r a l l s u c c e s s r a t e is 9 9 . 4 %

VSB

LSB

. . 100% 0.5% 1.2% --

USB

. .

. .

Com. .

.

. 99.5% ---

.

. .

-98.8% --

. --100%

.

in Tables II and Ill, r~spectively. It was found at the SNR

o f 10 d B , a n d 9 9 . 9 %

FM

at the SNR

---100%

that the

of 20 dB.

Recognition Algorithms

I l L Digitally Modulated Signals 3.1. Review

Liedtke was one of the first authors

to publish regarding

the modulation

recognition

process. He was also the first to present the concept of modulation recognition applied to digital modulations. L i e d t k e (1) i n t r o d u c e d a m o d u l a t i o n r e c o g n i s e r f o r s o m e t y p e s of digital modulations

ASK2,

utilises the universal

demodulator

FSK2,

PSK2,

technique.

PSK4, The

PSK8,

and CW. This recogniser

key features

used to discriminate

between these types are the amplitude histogram, the frequency histogram, the phase difference histogram, the amplitude variance and the frequency variance. The classi-

Automatic Modulation Recognition--I

253

o

FromIF

E

ModulationType ---,

L~

FIG. 6. Classification procedure for Liedtke modulation recogniser (1). fication procedure as shown in Fig. 6 comprises the following steps: (1) approximate signal bandwidth estimation; (2) signal demodulation and parameters extraction; (3) statistical computation; and (4) automation of modulation classification. In Ref. (1), it is clear that the hardware implementation of this recogniser is excessively complex. In Ref. (1), it is claimed that an error free signal, i.e. all the signal parameters are exactly known, can be recognised at SNR ~> 18 dB. In this recogniser, all the analogue modulated signals are classified as noise. In Ref. (6) DeSimio and Glenn introduced an adaptive technique for classifying some types of digital modulations--ASK2, PSK2, PSK4 and FSK2. In this recogniser a set of key features derived from the signal envelope, the signal spectra, the signal squared and the fourth power of the signal are used to decide about the modulation type of the intercepted signal. These key features are the mean and variance of the envelope, the location of the peaks in the signal spectrum, the location of the peaks around twice the carrier frequency of the spectrum of the signal square, and the location of the peaks around four times the carrier frequency of the spectrum of the signal raised to the fourth power. In Ref. (6), the classification procedure consists of the following steps: (1) feature vectors extraction; (2) weight vectors generation for each signal class; and (3) modulation classification. In Ref. (6), the decision functions used are generated using an adaptive technique based on the LMS algorithm. Furthermore, the decision rule used is similar to that applied in the pattern recognition algorithms. So, any intercepting signal is divided into two sets: a learning set, which is used to perform the weight vectors and a test set that is used in the decision about the modulation type using the weight vectors generated from the learning set. This classifier is trained using the values of the extracted key features at 20 dB SNR. The only thing mentioned about the performance evaluation of this recogniser is its ability to discriminate between PSK2 and PSK4 at the SNR of 5 dB. Polydoros and Kim (10) introduced a modulation recogniser, following the decisiontheoretic approach, to discriminate between PSK2 and PSK4. In Ref. (10), all signal

254

E. E. Azzouz and A. K. Nandi

parameters such as the carrier frequency, the initial phase, the symbol rate and the signal-to-noise ratio are assumed to be available. This recogniser uses the log-likelihood ratio to estimate the number of levels, M, of the MPSK signals. Also, a comparison between three classifiers for MPSK signals was introduced. These classifiers are: (1) phase-based classifier (PBC) that is based on the phase difference histogram; (2) squarelaw classifier (SLC) that is based on the fact that squaring of MPSK signal in MPSK with M/2 phase states; and (3) quasi-log-likelihood ratio (QLLR) classifier which uses the likelihood ratio estimation principles. In Ref. (10), it was proved analytically that the performance of the Q L L R classifier is significantly better than the PBC or the conventional SLC. Also, it is claimed that the proposed recogniser (QLLR) can be extended to address MPSK signals classification with M > 4. Hsue and Soliman (11) introduced a modulation recogniser based only on the zero-crossings characteristic of the intercepted signals. The modulation classification procedure comprises three steps: (1) extraction of the zero-crossing sequence, the zerocrossing interval sequence and the zero-crossing interval difference sequence; (2) intersymbol transition (IST) detection as well as carrier frequency estimation; and (3) decision about the modulation type. The phase and frequency information are derived from the zero-crossing sequence, the zero-crossing difference sequence and the zerocrossing interval difference sequence. The decision about the modulation type is based on the variance of the zero-crossing interval sequence, G, as well as the frequency and phase difference histograms. This recogniser can be implemented using a parallel processing technique to increase the speed of computations. Also, three processors are recommended, each processor associated with one of the three above mentioned sequences. However, this recogniser is used to report the modulation type of constant amplitude signals such as CW, MPSK, MFSK. In this recogniser, the classification strategy as shown in Fig. 7 comprises two main steps; first discrimination of singletone (CW and MPSK) from multi-tone (MFSK) signals, and secondly determination of the number of states (M). In Ref. (11), the discrimination between the single-tone A received

signal

of unknown

[

type

I

Obtain

[

of Freque~y

. . . .s t ~ t ~

I M I F S 1~

(x(i)

..

°rl

)

( y(J) ) ,

. . . r. .. o o" "r'r o

and

(z(i)

)

i

.... "

I

I

. . . .s l l ~ t e s

o f tdll~ p h ~

1

IMIPSI~

FIG. 7. Simplified block scheme of a recogniser based on the zero-crossing of a signal (11).

Automatic Modulation Recognition--I

255

and the multi-tone is based on comparing the variance of the zero-crossing difference sequence in the non-weak intervals of a signal with a suitable threshold. The determination of the number of states in single-tone signals is achieved by measuring the similarity of the normalised phase difference histogram. The determination of the number of states in multi-tone signals is based on the number of hills in the zerocrossing interval difference histogram. Finally, the performance of this recogniser was derived from 100 realizations for each modulation type of interest. From the simulation results it is claimed that a reasonably average probability of correct classification is achievable for SNR >/ 15 dB. Anyway, this recogniser cannot identify the analogue modulated signals, MASK and the signals having both amplitude and phase information. Also, Soliman and Hsue (13) introduced another modulation recogniser based on the statistical moments of the intercepted signal phase. In this recogniser, the even order moments of the signal phase are used to estimate the number of levels, M, in M P S K signals. The classification procedure comprises the following steps: (1) instantaneous phase extraction; (2) even order moments computation; (3) threshold comparison; and (4) decision about the modulation type. In Ref. (13), all the signal parameters are assumed to be exactly known. Under this assumption, it is claimed that the second order moment is sufficient to discriminate the CW from the M P S K signals and, the eighth order moment is adequate to classify BPSK signals with reasonable performance at low SNR. Also, it is claimed that the suggested classifier is better than the PBC and the SLC. Assaleh et al. (14) proposed a modulation recogniser for some types of digital modulations. The types that can be classified by this recogniser are: CW, PSK2, PSK4, FSK2 and FSK4. The key features used were derived from the averaged spectrum of the instantaneous frequency (average over M successive segments). These key features are the mean and the standard deviation of the averaged instantaneous frequency, and the height of the spikes in the differential instantaneous frequency. It is claimed that the performance evaluation of this recogniser is derived from 1000 realizations for each modulation type of interest. Also, it was found that the success rate of the modulation type of interest is >~ 99% at an SNR of 15 dB. As this recogniser uses the averaging over M successive segments, long signal duration is required and hence this recogniser is mainly suitable for the off-line analysis. Nagy (16) introduced a modulation classifier for multichannel systems. This classifier was accomplished by dividing the analysed signal into individual components and each signal component is classified using a single tone classifier. The types that have been classified by this recogniser are CW, ASK, PSK2, PSK4 and FSK2. The developed classifier comprises two steps. First, detection and filtering of each signal component in the estimated amplitude spectrum, e.g. the FSK2 is considered as two correlated ASK2 signals. Second, computation of the differential phase to discriminate between the different types of single harmonic signal. In Ref. (16) the performance of the developed recogniser was derived from 100 realizations for each modulation type of interest. Finally, it is claimed that all the single-tone types (CW, ASK2, PSK2 and PSK4) have been classified with a success rate of ~> 90% at 10 dB SNR except the ASK2 ( = 87%). Beidas and Weber (18) proposed a modulation recogniser for M F S K signals. This

256

E. E. Azzouz and A. K. Nandi

recogniser is based on the time-domain Higher-Order Correlations. This classifier is used to discriminate between the M F S K signals. This classifier comprises a bank of matched filter each of which is tuned to one of a prescribed frequency locations and a set of successive correlators. Also, it is based on comparing the log-likelihood function with a suitable threshold to decide about the number of levels of M F S K signals. In Ref. (18), it is claimed that this recogniser is immune to the imperfect knowledge of exact frequency locations. Huang and Polydoros (19) introduced an algorithm for classifying the M P S K signals based on the likelihood function of the instantaneous phase. This algorithm utilises the decision-theoretic approach as the likelihood function of the instantaneous phase is compared with a suitable threshold. This recogniser can be considered as a generalisation of the modulation recogniser introduced in Ref. (10) because it can be used for M > 4. The decision about the modulation type (estimating M for M P S K signals) is carried out according to the following rule MPSK LMPSK--LM,PS K ~<~ T h r e s h o l d , MPSK

(12)

where LMPSKis the log-likelihood function of the instantaneous phase of M P S K signals. Furthermore, the criterion used to decide about the modulation type is the maximum likelihood criterion. In Ref. (19) it is claimed that the best performance over all the known M P S K classifiers (PBC, SLC) can be obtained from this classifier. Yang and Soliman (21) modify the modulation recogniser, introduced in Ref. (13) which uses the statistical moments to estimate M in the MPSK signals. This modification is in the way of approximating the probability distribution function of the instantaneous phase. In Ref. (21), the Fourier series expansion is used for the exact phase distribution approximation instead of the Tikhonov probability density function used in Ref. (13). In Ref. (21) it is claimed that the developed algorithm offers improvement of 2 dB for 99% success rate and it offers simpler computation for the nth order moments than Ref. (13). In both Refs (13) and (21), nothing is mentioned about the performance evaluation of these two recognisers. Azzouz and Nandi (23) proposed a modulation recogniser for the digital modulation types up to 4-levels (ASK2, ASK4, PSK2, PSK4, FSK2 and FSK4). The key features used are derived from three important qualifying parameters the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the signal under consideration. These key features used are: (1) the maximum value of the spectral power density of the normalised-centred instantaneous amplitude; (2) the standard deviation of the absolute value of the centred non-linear component of the instantaneous phase in the non-weak intervals of a signal segment; (3) the standard deviation of the direct (not absolute) value of the centred non-linear component of the instantaneous phase; (4) the standard deviation of the absolute value of the normalisedcentred instantaneous amplitude; and (5) the standard deviation of the absolute value of the normalised instantaneous frequency. In this recogniser, the discrimination between the different digitally modulated signals is as shown in Fig. 8. In Ref. (23), all the digital modulation types of interest have been classified with success rate > 90% at an SNR of 10 dB except PSK4 (89.25% success rate). At the SNR of 20 dB all the modulation types of interest have been classified with a success rate of > 96%.

Automatic Modulation Recognition--I Digitally

257

signal modulated

yes

PSK4 •

.

.

.

' , .

.

•

PSK2 •

.

.

.

.

' .

•

,

ASK4 •

.

.

.

.

' .

•

,

ASK1 ,

.

.

.

.

' .

,

,

FSK4 •

.

.

.

.

' . .

,

FSK2 .

.

.

.

, .

-

FIG. 8. Flowchart for Azzouz and Nandi algorithm (23). 3.2. A modification 3.2.1. Proposed algorithm. In this paper an alternative decision flow for the algorithm presented in Ref. (23) is presented. Similar to the analogue modulation recognition algorithm introduced in Section II, instead of taking the decision about the modulation type from only one segment, the decision is derived from the available M segments of the intercepted signal frame. Thus, the proposed global procedure for digital modulations recognition comprises two main steps: (1) classification of each segment, in which the proposed key features are extracted and compared with suitable thresholds values; and (2) classification of a signal frame.

Classification of each segment. In the following digital modulation recognition algorithm (DMRA), the discrimination between the different types of digital modulations based on each segment requires key features extraction and modulation classification.

258

E. E. Azzouz and A. K. Nandi

(A) Key features extraction In the proposed digital modulation recognition algorithm, the key features used are derived from three important qualifying parameters--the instantaneous amplitude a(t), the instantaneous phase q~(t) and the instantaneous frequencyf(t) of the signal under consideration. The first key feature is 7.... which is defined by Eq. (1). The second key feature is ~ap, which is defined by Eq. (4). The third key feature is ~dp, which is defined by Eq. (5). The fourth key feature, O'a~,is defined by:

(~aa=~s(~la2n(i))--(~l]acn(i)])2" Ns

1 Ns

(13)

Thus a~a is the standard deviation of the absolute value of the normalised-centred instantaneous amplitude of a signal segment. The fifth key feature, a,f, is defined by:

1E

2

(14)

where 1 Ns

fN(i) = fm(i)/rs, fro(i) = f(i)--mr;

mf = ~ ~f(i),__l

(15)

and rs is the symbol rate (Baud rate in the binary digital modulations) of the digital symbol sequence (in binary modulations, the symbol rate is equal to the bit rate). Thus aaf is standard deviation of the absolute value of the normalised instantaneous frequency, evaluated over the non-weak intervals of a signal segment. A detailed pictorial representation for key features extraction from a signal segment is shown in Fig. 9 in the form of a flowchart. (B) Modulation classification procedure Based ~)n the above mentioned five key features, many algorithms can be developed according to the sequence of applying these key features in the classification algorithm. Only one algorithms is considered further to evaluate its performance. In this algorithm, the choice of the 7. . . . Gap, Gdp, O'aaand aaf, as key features for the proposed algorithm for digital modulation recognition is based on some facts similar to those explained in Ref. (23). A detailed pictorial representation of the proposed digital modulation classification procedure is shown in Fig. 10 in the form of a flowchart. Classification of a signal frame. Based on the obtained M decisions from the available M-segments and applying the same procedure used Section II, it is possible to obtain a global decision about the modulation type of a signal frame. 3.2.2. Computer simulations. In this section a software generation of different types of band-limited digitally modulated signals corrupted with band-limited Gaussian noise are introduced and analysed. The simulated band-limited digitally modulated signals and the band-limited Gaussian noise (23) are used in measuring the performance of

Automatic Modulation Recognition--I

259

R 1

Gaussian noise simulation

Modulated signal simulation -~

x(t) = s(t) + R * n(t)

~(O

^ z(t)=x(t) + j x (t)

/

Complex Envelope ]

I Instant. Phase Phase

Unwrapping

Key feature (2) key feature (3)

t Instant. amplitude

Linear Phase Component Removal

Instant. freq.

t Centering & Normalization [

I standard deviation of its absolute

f (

Key feature

(1)

standard deviation of its absolute

t ( keyfeature(5) )

J

(

)

FIG. 9. Flowchart for key features extraction in the digital modulations recognition algorithm. the developed DMRA. To increase the degree of realism of the simulated band-limited digitally modulated signals, random pattern sequences are used as modulating signals and the band limitation is carried out according to the usual implementation in practice. In our simulations, the carrier frequency, f~, the sampling rate, fs and the symbol rate rs, were assigned the values 150, 1200 and 12.5 kHz, respectively. The modulating

260

E. E. Azzouz and A. K. Nandi Digitally modulaled signal

yes

yes

~-

,

FSK4 ' ' FSK2 . . . . . . . . . . .

o

'

2

PSK4

'; ,'

PSK2

"

ASK4

"; ;

ASK2

";

FIG. 10. Flowchart for the digital modulations recognition algorithm. digital symbol sequence, as explained in Ref. (23), was derived from the modulating speech signal used in the analogue modulated signals simulations, in order to ensure that both analogue and digitally modulated generated realizations have almost the same quality with respect to the modulation recognition in the presence of a common noise sequence. It is well known that every communication system has a definite bandwidth. So, any transmitted signal should be band-limited to the pre-defined system bandwidth. Therefore, the simulated digitally modulated signals were band-limited in order to make them represent more realistic test signals for the proposed D M R A . The bandlimitation of the simulated 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. Furthermore, the digital modulation systems are usually implemented in practice as shift-keying systems and hence they cannot be

Automatic Modulation Recognition--I

261

TABLEIV

Bandwidths of digitally modulated signals" Modulation type MASK MPSK MFSK

Modulated signal bandwidth (Theoretical expression)

Modulated signal bandwidth (Simulated value (kHz))

4r~ 6r~

[IJm.~k

max--fsp . . . .

in l+4r~]

50 75 100 or 87.5

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. 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-limited to bandwidth containing 97.5% of the total average power according to the definition (25)

fJc+B/2 G~(f) d f = ,)fc- B/2

0.975

I= Gs(f) df, oc

(16)

where G~(f) is the power spectral density of the modulated signal So(t). The analytic expressions of the 97.5% bandwidth for different types of digital modulations are introduced by Azzouz and Nandi in Ref. (23). Furthermore, the theoretical expressions and the simulated values of the bandwidth of the simulated digitally modulated signals are presented in Table IV. In our simulations, the value of fmar k . . . . = f c + 2 r s for FSK2 as well as for FSK4 if the fourth level exit, otherwise fmark max = J'c + rs. Also, f s p . . . . . in =fc--2rs for FSK2 and for FSK4 if the first level exit, otherwise f s p . . . . . in =fc-rs. Note that the situation for M F S K signal, with fmark max = f c - [ - r s and f~p. . . . . in =fc--rs does not exist. 3.2.3. Performance evaluation. The implementation of the proposed algorithms for digital modulation recognition, requires the determination of five key features thresholds t;.max, t~ap, t~dp, t,,~ and t~.f in addition to the normalised-amplitude threshold atopt. Similar to the algorithm introduced in Section II, the optimum key features threshold values are derived from 400 realizations for each modulation type at the SNR of 10 and 20 dB. Applying the same procedure presented in Section II, the optimum values for the key features thresholds, tTm.~,t,,,, t ~ , taa" and t,a~ are chosen to be 4, n/5.5, n/5, 0.25 and 0.4, respectively. In Ref. (23), the success rate of M P S K is lower than the other types due to the inaccurate determination of the key features threshold. This is solved in the developed algorithm by applying the procedure for key features thresholds determination defined in Section II. The results of the performance are evaluated from 400 realizations for each type of modulation of interest at an SNR of 10 and 20 dB as shown in Tables V and VI, respectively. It was found that all the digital modulation types of interest have been

E. E. Azzouz and A. K. Nandi

262

TABLE V

Confusion matrix for the presented digital modulations recognition algorithm [based on 400 realizations] at SNR = 10 dB D e d u c e d m o d u l a t i o n type Simulated m o d u l a t i o n type ASK2 ASK4 PSK2 PSK4 FSK2 FSK4

ASK2

ASK4

PSK2

98.3%

1.7% 100% -----

. . 99.3% ----

-

-

-----

PSK4 . .

. .

FSK2

FSK4

0.7% 1.2% 99.5% 0.7%

---98.3%

. .

-98.8% 0.5% 1.0%

TABLE VI

Confusion matrix for the presented digital modulations recognition algorithm [based on 400 realizations] at SNR = 20 dB D e d u c e d m o d u l a t i o n type Simulated m o d u l a t i o n type

ASK2

ASK4

ASK2 ASK4 PSK2 PSK4 FSK2 FSK4

100% ---. .

. 1O0 % --.

. .

PSK2 .

PSK4 .

. 100% --

. .

classified with overall success rates ~99% o v e r a l l s u c c e s s r a t e is ~ 1 0 0 % .

.

FSK4

. .

-99.8%

. .

FSK2

.

. -0.2% 100%

--100%

a t a n S N R o f 10 d B , a n d a t 20 d B S N R t h e

IV. Recognisers used for both Analogue and Digital Modulations 4.1. Review I n R e f . (2) C a l l a g h a n et al. p r o p o s e d a m o d u l a t i o n r e c o g n i s e r u t i l i s i n g t h e e n v e l o p e and the zero-crossings characteristics of the intercepted signal. This recogniser uses a phase-locked loop (PLL) for carrier recovery in the weak intervals of the intercepted s i g n a l s e g m e n t . I t is w o r t h n o t i n g t h a t i n s o m e m o d u l a t i o n t y p e s s u c h a s D S B , M P S K and AM with high modulation depth, the carrier frequency may be severely suppressed o r a b s e n t . C a r r i e r r e c o v e r y d u r i n g t h e s u p p r e s s e d p o r t i o n s ( w e a k i n t e r v a l s ) is e q u i v a l e n t t o r e c e i v i n g a s i g n a l w i t h v e r y l o w S N R . So, u s i n g t h e P L L as a c a r r i e r r e c o v e r y (hardware solution) overcomes the problem of needing high SNR for accurate instant a n e o u s f r e q u e n c y e s t i m a t i o n f r o m t h e z e r o - c r o s s i n g s . A l s o , t h e a c c u r a c y o f t h i s rec-

Automatic Modulation Recognition--I

263

ogniser deteriorated rapidly if the receiver is not perfectly tuned to the centre frequency. The modulation types that can be recognised by this recogniser are CW, AM, FM, FSK2. In Ref. (2), it is claimed that this recogniser requires SNR/> 20 dB for the correct recognition of the different modulation types of interest. Furthermore, this recogniser cannot discriminate the MPSK and the DSB signals due to the incorrect estimate of the instantaneous frequency of the intercepted signal that result from the effect of the noise on the weak intervals of a signal segment. Jondral (3) proposed a modulation recogniser utilising the pattern recognition approach for the noise signal and two types of analogue modulated signals--AM and SSB--as well as for four types of digitally modulated signals ASK2, PSK2, FSK2 and FSK4. The key features used are derived from the instantaneous amplitude, phase and frequency. These key features are the instantaneous amplitude, phase difference and frequency histograms. In this classifier, the instantaneous amplitude histogram is computed for the normalised instantaneous amplitude. The normalisation is done with respect to the maximum values of the intercepted signal. As this classifier uses the pattern recognition approach, the received signal is divided into two adjacent sets: learning set and test set. The segment length used in this recogniser is 4096 samples for each modulation type. In ref. (3) real signals have been used and it is claimed that all the above mentioned modulation types have been classified with success rates/> 90% except the SSB ( = 83%) and FSK4 ( = 88%). Aisbett in Ref. (5) proposed a modulation recogniser, based on some key features derived from the instantaneous amplitude and instantaneous frequency of a signal. In Ref. (5), it was mentioned that the developed key features are noise resistant, and they are A 2, AA" and AO" where A is the signal envelope, A' is the signal envelope derivative and 0' is the instantaneous frequency. The estimation of these key features is derived from 10 realizations, each with 90 ms length, for each modulation type of interest. Also, another unbiased key feature is added by Aisbett in Ref. (5) and it is defined as the variance of the squared instantaneous amplitude minus its squared mean. The modulation types that can be classified by this recogniser are: AM, DSB, FM, ASK2, PSK2, FSK2 and CW signals. In Ref. (5), it is claimed that the success rate of the discrimination between the modulation types appears to be at least good on strong signals. Petrovic et al. (8) suggested a modulation recogniser based on the variations and zero-crossing rate of the AM detector output as well as the variations in the FM detector output. The modulation types that can be classified by this recogniser are AM, FM, SSB, CW, ASK2, FSK2. This modulation recogniser comprises three main steps as shown in Fig. 11. These are: (1) AM and FM demodulation; (2) key features extraction, in which three key features are derived from the AM detector output and they are: detect the presence of the signal, measure the amplitude variations and the instantaneous amplitude zero-crossing rate. Also, for the F M detector output a narrow band a wide band FM detection are performed; and (3) modulation classification. The only thing mentioned about the performance evaluation is that the results of the preliminary test with real signals show the success of this recogniser. Martin (9) proposed a modulation recogniser for some analogue and digital modulation types. These types are: AM, FM, SSB, CW, ASK2 and FSK2. The key features used are derived from the instantaneous amplitude, the IF signal spectrum and its

264

E. E. A z z o u z and A. K. Nandi

Y

••

ModulationType

- [ FM dele¢li0u I

FI6. 11. Simplifiedblock scheme of Petrovic modulation recogniser (8). derivative. These key features are: the amplitude histogram, the signal bandwidth and the relationship between the spectral components. In Ref. (9) real signals have been used and it is claimed that all the modulation types of interest have been classified with a success rate > 90% except the FM (= 80%). Dominguez et al. (12) introduced a modulation recogniser which is a general approach for both analogue and digital modulations. This recogniser is concerned with some types of analogue and digitally modulated signals. These types are AM, DSB, SSB, FM, CW, noise and digitally modulated signals up to 4-levels. This recogniser comprises three subsystems: (1) pre-analysis subsystem; (2) features extraction subsystem; and (3) classifier subsystem. The recognition algorithm is based on the histograms of the instantaneous amplitude, phase and frequency. In Ref. (12), it is claimed that this recogniser performed well and all types have been correctly classified at SNR ~> 40 dB. At an SNR of 10 dB the probability of correct modulation recognition is 0% for all digital modulation types except for PSK4 (7%) and at 15 dB SNR the performance is still wanting, especially for FSK4 (56%), FSK2 (84%) and ASK4 (87%). In Ref. (12) the number of samples per segment used in performance evaluations in 3000 samples. However, it should be noted that this work attempts to identify most of the well-known analogue and digital modulation types. Nandi and Azzouz (26) developed a modulation recogniser for both analogue and digital modulations without any a priori information about the nature of a signal. In this recogniser, the well known analogue modulation types (22) as well as all the digital modulations up to 4-levels (23) are considered. All the key features used in the proposed algorithm are derived from three important qualifying parameters, except the signal spectrum symmetry which is derived form the RF signal spectrum. These parameters are the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the intercepted signal. The four key features, used in Ref. (22), are also used for this recogniser Ref, (26); two of the key features used in Ref. (23)--~raa, and a , ~ are also used here in this algorithm, while three other key features are introduced,

Automatic Modulation Recognition--I

265

These three key features are: (1) the standard deviation of the normalised-centred instantaneous amplitude in the non-weak intervals of a signal segment; (2) the kurtosis of the normalised instantaneous amplitude; and (3) the kurtosis of the normalised instantaneous frequency. The discrimination between the different analogue and digital modulation types was carried out according to the procedure introduced in Fig. 12. In this recogniser, it was found that all the modulation types of interest have been classified with success rate ~> 90% except AM (= 88.8%), ASK4 (= 77.3%) and FSK4 (=88.0%). 4.2. A modification 4.2.1. Proposed algorithm. An alternative view for the decision flow algorithm introduced in Ref. (26) is introduced here and the decision is derived from all the available M segments of a signal frame. Thus, the proposed global procedure for both analogue and digital modulation recognition comprises two main steps: (1) classification of each segment; and (2) classification of a signal frame. Classification of each segment. From every available segment, the suggested procedure to discriminate between the different types of modulation requires key features extraction and modulation classification, which gives a decision about the modulation type present in each segment by comparing each key feature with a suitable threshold. (A) Key features extraction All the key features used in the proposed algorithm are derived from three important qualifying parameters, except the signal spectrum symmetry which is derived from the RF signal spectrum. These parameters are the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the intercepted signal. The four key features, used in Section II, are also used here in the developed algorithm for both analogue and digital modulation recognition, and they are 7 O'ap, O'dp and the ratio P. Two of the key features used in Section III are also used here in the developed algorithm, and they are aa, and O'af. For the completeness of the proposed global procedure for analogue and digital modulation recognition, three new key features are introduced. These are: ....

• the standard deviation of the normalised-centred instantaneous amplitude in the non-weak intervals of a signal segment, defined by ,.}~> a ~ , ( i ) -

O'a---an(

•

at

~,

ac.(i)

;

(17)

an(O>a t

the kurtosis of the normalised instantaneous amplitude, #]2, defined by

E{a4.(t)} It~42 -- {E{a~n(t)} } 2 ,

(18)

where acn(t) is the normalised-centred instantaneous amplitude as expressed by Eq. (2); • the kurtosis of the normalised instantaneous frequency,/~2, defined by

266

E. E. Azzouz and A. K. Nandi

i

DIitltal and AItalolgte ModalatedSlgsals

yes

no

I AM,MASK,VS8 ]

FM,MFSK,DSB, I LSB,USB, MPSK Combll~d

I FM,MFSK,I~B, I MPSK,Combined

ASK2& ASK4 J

ya yes

1

no

P~ ~4 on

y~ I FSK2 FSK4 J no

y~

;2;

FIG. 12. Flowchart for the analogue and digital modulation recognition algorithm (26).

Automatic Modulation Recognition--I

267

i~f42_ E{f~(t)} {E{fZ(t)}} 2'

(19)

wherefN(t) is the normalised instantaneous frequency, as defined by Eq. (15). A detailed pictorial representation for the key features extraction from an RF signal is shown in Fig. 13 in the form of a flowchart.

Modulated signal simulation

Gaussian noise simulation

x(t) = s(t) + R * n(t)

I (

Ratio P, PL, PU

l_

I xm

r ~

i÷sign,I,

z(f)

key featyre (4)

.... ^ =x(t) + j x (t)

Complex Envelope

[

I Instant. Phase Phase Unwrapping

(

Instant. amplitude

W

Linear Phase Component Removal

Centering & Normalization

I V

Key feature (2) key feature (3)

t ] kurtosis ]

(

I

Key feature (9)

Instant. freq.

kurtosis

t

standard deviation of its absolute

I

( ko,feat°re~6, ~

standard deviation of its absolute

(Keyreature(l) )

(

( ,ey,e.,ure,~, )

Key feature(8)

[

)

Remove the

--I w..'..m,'..

t ~ Keyfeatnre,7~ )

FIG. 13. Flowchart for key features extraction for the analogue modulation recognition

algorithm.

268

E. E. Azzouz and A. K. Nandi

(B) Modulation classification procedure Based on the aforementioned nine key features, many algorithms can be generated according to the sequence of applying these key features in the classification algorithm. Only one algorithm is considered for measuring its performance. In this algorithm, the choice of ? . . . . flap, fldp and the ratio P is based on some facts similar to those mentioned in Section lI. Also, the choice of Ga and traf is based on some facts similar to those discussed in Ref. (23). Furthermore, the choice of fla, fl,]2 and/~2 as key features for the proposed algorithm is based on the following facts: • fla is used to discriminate between the DSB and PSK2 signals as well as to discriminate between the combined (AM-FM) and PSK4. The PSK2 and PSK4 signals have no amplitude variations except at the transition between the successive symbols; i.e. the normalised-centred instantaneous amplitude is constant ( = 0 ) over the symbol duration (G < t,.). On the other hand, the DSB and the combined (AM-FM) signals have amplitude information (G > t,.). So, fla can be used to discriminate between the DSB and PSK2 as well as to discriminate between the combined (AM-FM) and PSK4 signals; • #]2 is used to discriminate between the AM signals as a subset and the MASK signals (ASK2 and ASK4) as the second subset. This key feature as defined by Eq. (18) is used to measure the 'compactness of the instantaneous amplitude distribution'. So it can be used to discriminate between the signals, in which the instantaneous amplitude has high compact distribution (/2]2 > t~42) such as the AM signals (related to the speech signal), and those in which the instantaneous amplitude have less compact distribution (~]2 < t~42) such as MASK (ASK2 and ASK4) signals (related to the symbol sequence); • /.1f2 is used to discriminate between the FM signals as a subset and the M F S K signals (FSK2 and FSK4) as the second subset. This key features as defined in Eq. (19) is used to measure the 'compactness of the instantaneous frequency distribution'. So, it can be used to discriminate between the FM signal, in which the instantaneous frequency (related to the speech signal) has high compact distribution (#~2 > tf42), and MFSK, in which the instantaneous frequency (related to the symbol sequence) has less compact distribution (#f2 < &2)A detailed pictorial representation for the developed algorithm for both analogue and digital modulation recognition is shown in Fig. 14 in the form of a flowchart.

Classification of a signal frame. Based on the obtained M decisions from the available M-segments and applying the same procedure used in the analogue modulation recognition algorithm (as in Section II), it is possible to obtain a global decision about the modulation type of a signal frame. It is worth noting that, the computer simulations for different types of analogue and digital modulation types of interest have been introduced in Refs (22) and (23), respectively. 4.2.2. Performance evaluation. The implementation of the above algorithm for both analogue and digital modulation recognition, requires the determination of nine important key features thresholds tTmax, t~,p, t%, tp, t~,, t~,,,~,tG2, t~,, and t~.~.The aforementioned key features thresholds have been determined based on 400 realizations for each modulation type of interest at an SNR of 15 and 20 dB. Applying the same procedure

Automatic Modulation Recognition--I

/

D/fftal and A~lope Modmlated sfgnmb

mo

yes

l

i

AM, MASK, I~B, LSB, USB, VSB, Combll~l, MPSK

AM, MASK, DSB,

]

I

I

LSB, USB, PSK4,

/\.

~"~,, !

i

AM.,~s,.

,.

I "°

\/

"

P

fATx~l

269

•

f,'

P

es

fASK+/

FIG. 14. Flowchart for the proposed analogue and digital modulation recognition algorithm.

E. E. Azzouz and A. K. Nandi

270

TABLEVII

Performance of the presented alyorithm for analogue and diyital modulations recognition at SNR = 15 dB Deduced modulation type Simulated types

AM

DSB

VSB

LSB

USB

Com.

FM

MASK PSK2 PSK4 MFSK

AM 88.8% . . . . . . DSB 100.0% . . . . . . . . . VSB --96.8% - 3.2% . . . . . . LSB --7.0% 93.0% . . . . . . . . USB --7.0% - - 93.0% . . . . . . Combined . . . . . 100.0% . . . . . FM . . . . . . 90.0% ---10.0% ASK2 4.7% . . . . . . 95.3% - --ASK4 22.7% . . . . . . 77.3% - --PSK2 . . . . . . . . 98.8% 1.2% -PSK4 . . . . . . 0.2% - --99.8% -FSK2 . . . . . . 8.0% ---92.0% FSK4 . . . . . . 12.0% ---88.0% 1

-

1

.

2

%

-

-

-

-

-

-

-

presented in Section II, the o p t i m u m values for these key features thresholds are chosen to be 2.5, ~z/5.5, ~z/6, 0.6, 0.25 (PSK2) a n d 0.15 (PSK4), 2.15, 2.03, 0.25 a n d 0.4, respectively. Sample results have been presented at S N R o f 15 a n d 20 dB only. The p e r f o r m a n c e e v a l u a t i o n s of the p r o p o s e d a l g o r i t h m for a n a l o g u e a n d digital m o d u l a t i o n recognition are derived from 400 realizations for the 12 a n a l o g u e m o d u lated signals (as in Section II) as well as the six digital m o d u l a t e d signals (as in Section III). F o r the p r o p o s e d a l g o r i t h m in this paper, the p e r f o r m a n c e results are s u m m a r i s e d in Tables V I I - X for two values o f S N R s (15 a n d 20 dB). F u r t h e r m o r e , the overall success rate is 93.3% at a n S N R of 15 dB, a n d it is 93.2% at 20 dB SNR.

V. Conclusions A n overview of m o s t o f the recent papers published in the area of m o d u l a t i o n r e c o g n i t i o n is introduced. Three modified a l g o r i t h m s - - o n e for a n a l o g u e m o d u l a t i o n s only, the second for digital m o d u l a t i o n s only, a n d the third for b o t h a n a l o g u e a n d digital m o d u l a t i o n s , w i t h o u t a n y a priori i n f o r m a t i o n a b o u t the n a t u r e o f a signal, are presented. Extensive s i m u l a t i o n s for 12 a n a l o g u e m o d u l a t e d signals a n d six digitally m o d u l a t e d ones have been carried out to m e a s u r e the p e r f o r m a n c e o f the presented algorithms. Sample results are i n t r o d u c e d at two S N R values (10 a n d 20 dB for b o t h a n a l o g u e only a n d digital only algorithms, a n d 15 a n d 20 dB for the recognition of b o t h a n a l o g u e a n d digital m o d u l a t i o n s w i t h o u t a n y a priori i n f o r m a t i o n ) . I n the N a n d i a n d A z z o u z a l g o r i t h m (22), the s e p a r a t i o n o f the VSB is achieved with 92.5% success rate, the U S B with 90.0% success rate, a n d the LSB with 91.0% success rate while the other types were separated with success rates ~> 98.0% at a n S N R of 10

Automatic Modulation Recognition--I

271

TABLE V I I I

PerJbrmance of the presented algorithm for analogue and digital modulations recognition at SNR = 2 0 dB Deduced

modulation

type

Simulated types

AM

AM

DSB

86.1%

VSB

.

.

LSB

.

100%

USB

- -

.

VSB

- -

LSB

--

--

7.5%

USB

- -

--

8.2%

Combined

.

.

.

.

0.5%

4.0%

.

19.7%

--

PSK2

.

PSK4

.

.

.

.

. .

.

. .

--

--

.

.

. .

.

. --

--

--

--

--

--

--

1.2%

--

--

90.0%

--

--

--

10.0%

96.0%

--

--

--

--

--

80.3%

--

--

--

96.3%

3.7%

--

. .

.

--

MFSK

--

.

---

PSK4

98.8%

.

.

FSK2 FSK4

.

91.8%

.

.

PSK2

--

--

ASK4

.

.

92.5%

FM ASK2

MASK 13.9%

.

99.5%

.

FM

.

DSB

.

Com.

.

. --

. --

--

TABLE

8.0%

--

12.0%

--

--

100.0%

--

--

92.0% 88.0%

I X

Performance of discriminating ASK2 and ASK4 SNR=

15dB

SNR=20dB

Type

ASK2

ASK4

ASK2

98.3%

1.7%

ASK4

0.2%

99.8%

ASK2

ASK4

100%

--

--

100%

TABLE X

Performance of discriminating FSK2 and FSK4 SNR=

dB. The and

LSB

classified

Type

FSK2

FSK2 FSK4

developed

recogniser

modulation

types,

with

rates

success

15dB

SNR=20dB

FSK4

FSK2

99.5%

0.5%

100%

--

0.5%

99.5%

--

100%

in this paper and

now

> 97%.

improved

all the

the success

modulation

In the Azzouz

and

FSK4

types

Nandi

rate

of the VSB,

of interest

algorithm

have

(23), there

USB been are

272

E. E. Azzouz and A. K. Nandi

two problems: (1) the separation between P S K 2 and P S K 4 as one group, and F S K 2 and F S K 4 as the second g r o u p and this is related to the choice o f t~.... ; (2) the separation between F S K 2 and F S K 4 and this is related to the choice o f t~ac These two problems are solved in the developed algorithm by applying the global procedure for key features threshold determination introduced in Section II and the alternative view for the decision flow used in Ref. (23).

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Automatic Modulation Recognition--I

273

(17) S. D. Jovanovic, M. I. Doroslovacki and M. V. Dragosevic, "Recognition of low modulation index AM signals in additive Gaussian noise", in "European Association for Signal Processing V Conference", Edinburgh, Scotland, pp. 1923-1926, 1994. (18) B. F. Beidas and C. L. Weber, "Higher-order correlation-based approach to modulation classification of digitally modulated signals", IEEE J. Selected Areas in Commun., Vol. 13. No. 1, 1995. (19) C. Y. Huang and A. Polydoros, "Likelihood method for MPSK modulation classification", IEEE Trans. Commun., Vol. 43, No. 3, pp. 1493-1504, 1995. (20) Y. O. Al-jalili, "Identification algorithm for upper sideband and lower sideband SSB signals", Signal Processing, Vol. 42, No. 2, pp. 207-213, 1995. (21) Y. Yang and S. S. Soliman, "An improved moment-based algorithm for signal classification", Signal Processing, Vol. 43, No. 3, pp. 231-244, 1995. (22) A. K. Nandi and E. E. Azzouz, "Recognition of analogue modulations", Signal Processing, Vol. 46, No. 2, pp. 211 222, 1995. (23) E. E. Azzouz and A. K. Nandi, "Automatic identification of digital modulations", Signal Processing, Vol. 47, No. 1, pp. 55~9, 1995. (24) E. E. Azzouz, "Signal intelligence processing: Modulation recognition", M.Sc. thesis, Military Technical College, Cairo, Egypt, February 1992. (25) K. S. Shanmugam, "Digital and analogue communication systems", John Wiley and Sons, Inc., NY, 1985. (26) A. K. Nandi and E. E. Azzouz, "Algorithms for modulation recognition of communication signals", Submitted to IEEE Trans. Commun.