A method of feature selection in the aspect of specific

BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 65, No. 1, 2017 DOI: 10.1515/bpasts-2017-0014

A method of feature selection in the aspect of specific identification of radar signals J. DUDCZYK* WB Electronics S.A., 129/133 Poznańska St., 05-850 Ożarów Mazowiecki, Poland Abstract. This article presents an important task of classification, i.e. mapping surfaces which separate patterns in feature space in the scope of radar emitter recognition (RER) and classification. Assigning a tested radar to a particular class is based on defining its location from the discriminating areas. In order to carry out the classification process, it is necessary to define metrics in the feature space as it is essential to estimate the distance of a classified radar from the centre of the class. The method presented in this article is based on extraction and selection of distinctive features, which can be received in the process of specific emitter identification (SEI) of radar signals, and on the minimum distance classification. The author suggests a RER system which consists of a few independent channels. The task of each channel is to calculate the distance of the tested radar from a given class and finally, set the correct identification coefficient for each recognized radar. Thus, a multichannel system with independent distance measurement is obtained, which makes it possible to recognize particular radar copies. This system is implemented in electronic intelligence (ELINT) system and tested in real battlefield conditions. Key words: radar emitter recognition (RER), specific emitter identification (SEI), minimum distance classification, ELINT system.

1. Introduction In the theory of radar signals recognition and their emission sources, the main task is to set distinctive patterns of such signals and work out methods for their distinguishing [1, 2]. In the literature, terms such as source emission patterns separating surfaces in the measurable features space are widely used to describe pattern recognition and pattern classification [3, 4, 5]. Taking into account the fact above, radar emitter recognition and classification is based on defining the location of the emission source from the above separating surfaces. Here, it is essential to indicate a very significant fact, namely, in order to set a distinctive radar signal pattern, radar metrics needs to be defined in the measurable feature space of this signal; only after that the pattern vector of such a signal in the database can be designed [1, 6, 7]. However, what needs to be taken into account is the specificity of such a database for ELINT systems and electronic warfare (EW), [8, 9, 10]. The specificity of such a database is not the subject of the content of this article. Radar metrics is based on a distinctive radar signal pattern used to calculate the distance of this pattern from the centre of the class. Classification in this case is based on calculation of the distance of the recognized radar pattern from the centre of the class and classifying it to the class with the smallest distance. In order for this problem of radar signal classification to be solvable, it is necessary to define the class of a radar. Defining classes is not only setting the expected average values of basic measurable parameters of a radar signal, i.e., radio frequency (RF), pulse width (PW) and pulse repetition interval (PRI). This process also requires defining variance and correlation of these features [11]. The second significant element of the classification pro*e-mail: [email protected]

cedure is the problem to define how to estimate the distance of a tested radar emitter signal from the centre of the class taking into consideration variance and correlation of vector’s features. The RER method also provides a solution when the features of radar patterns are not linearly separable. RER method bases on the analysis of basic measurable parameters of the radar signal (such as RF, PW, PRI) as result of which it is possible to extract additional distinctive features. The RER process is called specific emitter identification (SEI). Additionally extracted distinctive features, which are received in the process of RER, may be a product of out-of-band radiation of radar devices [12]. These features may be of fractal type, which is presented in the works [13, 14, 15]. The received features may also be a product of inter-pulse modulation [16] and intrapulse analysis of a radar signal [17]. Of course, there are more complicated approaches, which offer effective methods for solving the classification task (i.e. mapping separating surfaces). These are based on solving the linear approximation task recurrently, using gradient methods and nonlinear approximation [18], nonlinear approximation of random function [19] and other methods for adaptive regression splines, classification and approximation [20, 21]. This is a typical solution for identification systems such as perceptrons or artificial neural network (ANN), e.g., support vector machine networks (SVM) [22] using Widrow-Hoff learning algorithms, Adaline ANN or the method based on back-propagating errors and neural network classifier with low discrepancy optimization [23, 24]. Also, the Fourier transform has been widely used in radar signal and image processing. Another work [25] presents joint time-frequency (JTF) domain analysis as a useful tool for improving radar signal and image processing for time-and frequency-varying cases. In [26], quadratic time-frequency analysis and sequential recognition for SEI is presented. Another approach based on three-dimensional distribution feature is

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As a result of the procedure above, the Lestimation transform of the estimated difference, according to (7). measurement distance received from channels is the B  feature from G class of the distance   of VBvector measurement the distance channels is the Afrom significant problem value “significant the centre recognition. d w (u ) (umin destimated (V ), d as (V ). received Vfrom B point” to problem 1 B A dbase )for  min dof (V da 2Bdistance (2distance V tT2tr1Tnext y1   V , the measurement of12),the fromaschannels is the is the difference ry2V r  step is to define K11 B B 2 ).isreceived w The radar recognized belonging base for recognition. The radar is recognized as belonging B B Taking into consideration the fact that for (7) y Tr    of i-class. As a method result ofabove the procedure above, , the next the stepbase is to define Kwhich comes out in the method concerns the as rule of the V B  VB   T   base for recognition. Theabove radar is recognized belonging which comes out in the concerns the rule ofif to is the difference r... to a particular class with index,  w y ... t r 2 estimation of the distance of vector feature from G class L transform of the estimated difference, according to (7). V 2  to aa particular adecision, particular class with index, if measurement of the distance received from channels is the  w   B hoosing which is based on defining values of class which with w index, dwon (u) = min y estimated  T  (7) according to (7). {d1(V (7)   Trdifference, B1), d2(V choosing a decision, is based defining values ofB2)}. L transform of the significant problem d ))  d d 2The (V ). if A  B , the next B1 ), base for  as belonging 2 ). is Arecognized significant problem is the difference r  V rstep recognition. dww ((u uA significant  min min d11 ((V V VBBradar    is to define Ktn ...  yBn... V problem B1 ), d 2 (which 2 comes out in the method above T    tocomes a the particular class above withconcerns index, if which the of w to (7). rulethe of method choosing a decision, which based y n  difference, whichconcerns comes out out in in the method above concerns theisrule rule of on L transform of the estimated  t n raccording  significant d w (ua)  min  dof (VB(V ). 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In order to solve The decorrelation ofthe the normalization vector’s features’ co-ordiordinates according toprocess (8) and process of The decorrelation process of the vector’s features’ cochoosing a decision, which is based on defining values of this problem it is assumed that VBk is a random variable which nates according to (8) and the normalization process of disperdispersion co-ordinates’ values to (9) results ordinatesof according to (8) and the according normalization process of defines features’ values of elements of a radar class with k2index sion of co-ordinates’ values according to (9) results in a corcorrelation matrix equal tovalues an identity matrix according 2 in adispersion of co-ordinates’ according to (9) results and Edj(VBk) is an expected value of the distance dj for the radar relation matrix equal to an identity matrix according to (10). to in (10). a correlation matrix equal to an identity matrix according class with k index. to (10). 22 E(yy T )  E[Tr ][Tr ]T  TE(rrT )TT  TRT T  2 E(yy T )  E[Tr ][ Tr ]T T TE(rrT )TT  TRT T  3. Defining the distance t1T  t 1  on impartiality condition  Tt1T   Tt1T  t2   t 2    TR[t , t ,..., t ]    T   [Rt , Rt ,..., Rt ]  n 1 2 t To start with, a particular class G of radars is chosen for which ... 2  R[t , t ,..., t ]  ... t 2   [Rt1 , Rt2 ,..., Rtn ]  – n 1 2 1 2 n  T ...   T...  the centre of the class VB = E(VB) is defined and covariance t n T  tn T  matrix of the vector featuresVB from G class, according to (2), (8)  (8) tTn  t n  where T is a sign of matrix transposition. 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T n   y  1   T 1t n tT1 T 2 t n Tt 2 ..T  n t nTt n   11  011 ... 0 01 ...  0     2 of specific n n  signals ... 0   identification t n  of feature selection in theaspect 1t2nttn1t 2 2..t n t 2n t..n t n n tAnmethod    yT1 0 of radar Eyk2 1 1tn tdiag 1 2   y    E yk (12) (1 , 2 ,..., n )  Λ  z1   1   n 0 ... 0    T  0E  T2 0 ......2 ...   y...  ...y  (12) (12) , 2 ,..., (1, n 2) ,...,  diag(1diag  Λn )  Λ  z   y 2   E y  E y    k 1  k k 1  k  ... 1    ...  ... ... ... ...   ...  ... z   2    2  The    0 (9) 01  ...it possible   analysis above makes   1 n  to use the definition  y1   ...      0 0 0 ... 0  ...   with analysis makes it }possible to nchannel n   2 The    di(V  indexabove i 2 {1, 2, …, L  y1  y1     ...  of distance n B) 2for the n –Ey k y  z k of distance for the cha d ( V 1 2 2 2 2     y z n n n n n  1     n  according  where value of i G Bi)features’  EV  nexpected yktoE(13), yE yBik is the  – – T k yk   z1   z11  y 21         n  n E E   kwhile k 1 1 classvector, ) is the covari i = E(V kR k Bi ¡ V to (13), where i Bi {1)(V ,2,..., L}Biaccording Bi ¡ V  zz    z2z y  y 2 (9)  n  ancek matrix 1  k k k11 k k k 1  k 2  of Gi class. It is also necessary to mention that (9)  2 2 value of Gi features’di class    2  z   z  ... (9) (9)  z1 z1Thez1 zanalysis ... z z  functionals, which are defined by (14), where V is a random above makes it possible to use the definition 2 1 2 2 n Bi  ...   ...  ...  The analysis The analysis above makes above itdefines possible itthe possible tovalues use the to use definition the definition (makes variable which of G class elements, fulfill R  E ( V V )( V V )T is the co i    zn ...   y... of distance for the channel with  d V ) z z z z z z ... Bi Bi B index Bi i i  2 1 2 2 2 n i B n  )condition of distance for the for channel the with with index index E(zz' ) ofE  distance thedimpartiality Ed1(Vchannel  z n  z nyn  y n  i (VB ) di (V B1) = Ed2(VB2). Itis the is expected also necessary to G  ... i { B according to (13), where 1 , 2 ,..., L } ... ... ... V i class.  B i    n  according to (13),towhere (13),–where is the expected i {1,2i,..., {1 L,}2,..., L} according VB i is the VB i expected  – n n T ¡1    functionals, which are defined by (14 features’ vector, while z z ..of z ndzin(V GBi ) = (V )class Ri (V 1value  z n zvalue B ¡ V Bivector, B ¡ V Bi)(13) value ofn 2 G ofi features’ class class vector, while while Gi features’  z1 z1 z1 z 2 ... z1 z n   z1 z1 zz11zz21 ...z1 z 2z1 z... random variable which defines the v n  z1 z n  yBn )(VTB  VBT )T is the yR  y1 y1 covariance matrix of 1 yi 2 E(VB i y1V z 2 z n   z z zzz2 zzz1 z...z2 zz2 z z...  i V ) i V ) i ... R  E ( R V   E V ( V )( V  V  )( V is the is covariance the covariance matrix matrix of of the   i B iB i Bi Bi BiB i Bi iBi elements, fulfill impart E(zz ') 2 1E  22 21 2 2 2 ... n  z2 zn       1 E(zz' )  E(Ezz' )  E ...  ...    1, 2, …, L (14) It Ed also necessaryEdto({V mention that 1 i 2class. 1isin(V } G di ... ...  Bi) = n       i 2  . )  E d ( V ) class. class. It is It also is necessary also necessary to mention to mention that that d d G G  ...  ...   ... ...... ...... ...  1 B1 B2 i i i2 ywhich yfunctionals,  y2 y2i 2 y n  are defined by (14), where V 2 y2 is a  z n z1 z n z 2 ..  z n z n  ... which Bi a functionals, functionals, which are defined are defined by (14), by where (14), where is a is  V V   (10) diversity, the values In spite of R of Bi B i the distance i parameter 2  z n z1 zznnzz21 ..z n z 2z n z..n  z n z n   E 2 1   2 n  whichto defines random variable the of estimated according (13) can comparable are the y1 yn  randomrandom variable variable which which defines defines the values thebe values ofvalues Gi ofclass dGiand (iVGBclass )i class (VBbase  VBi )T Ri1 (V 4. The process of learning ... ... ...  ...   y1 y1  y1yy1 1y1 y2 yy11yy22 y... 1 y n  y1 y n  to define the class the recognized radar emitter signal. ...     fulfill the impartiality condition y2 (10) yelements, yfulfill  ynelements,  ofoflearning      4.fulfill process ofnearest learning elements, the impartiality impartiality condition condition n y 2 The ny nthe 4. process ... 1 12 1 n .. The . d ( V )  E d ( V ) 4. The process of learning  Ed (VEE   1  y y112 y y12 1n  y1yn  presented is supposed to i {1 1( )2n.(2VB2B)2. radar recognition process )n  (12V EBd1B2)The VE 1 B 2d Edi (VB i )  n 2 n   n 1 1 B1d  y2 y2  2y2 y2 2 y2 y22 y22 y... 2 yn  y2 yn  The presented radar recognition process is supposed to aims The presented radar recognition process isprocess supposed to be preceded by the process of learning. This ... ...  (10)    diag(10) 2 4. The process ofthe learning  E  E2 E1 2 2 112 (1,1,...,1) be preceded 22 The presented radar recognition process isof supposed toaims n (10)    by the process of learning. This process aims 2 be preceded by the process of learning. This process T 1  at estimation of expected value class patterns 2 n n     T  1 values R of the distance estimated a d(iVof (V (V (B)Vthe )The (VofBV Bclass V) Bof (13) ... ... di (V )Bthe )(15), Vof BR Vi1BV (i V )BTBilearning. R value (iV be process of This process aims i ) patterns (13)matrix at preceded estimation ... ... ... ...  ... ...  B ) diby BBthe Bi expected iV Biof B) value at estimation expected class patterns  ...   ...... ... i (13) according to estimation covariance ofcan be The presented radar recognition process is supposed to be prey y y y y y spite of parameter diversity, R   i at estimation of expected of class patterns of VB vector from G isthe defined  yn y2  nyn y2 n2 y2 ynn..y22 yThe  y(nnVyBnn) distance  according to class (15), estimation of value covariance matrix of of the n..y n d according to (15), estimation of covariance matrix of classes’ patterns according to (16) for each .. ceded by the process of learning. This process aims atclass estima    n 1  n 2 according    (11), where according the base to define the the neare T to (15), estimation of covariance matrix ofof the classes’ patterns according to (16) for each of the   nn to (14) E d ( V )  n i  { 1 , 2 ,..., L } functional defines the classes’ patterns according to (16) for each of d ( V ) n (14) (14)   collections class patterns and defining eigenvalues of E d ( V E ) d  ( n V )  n i  { 1 , 2 ,..., i  { L 1 } , 2 ,..., L } 1 1 2 2 n n n n i B G i B tion i of B     the value of class patterns according to (15), The analy iexpected Bii i T emitter signal. classes’ patterns according to (16) for each of the collections class patterns and defining eigenvalues of Gi of G collections class patterns defining eigenvalues ofThe re estimation covariance matrix ofand classes’ patterns according distance from VB features’ vector of a tested radar toRthe i recognitio  diag(1diag ,1diag ,...,(11)(,11,,..., 1,...,11)) a covariance matrix and belonging to them, orthogonal re i p collections class patterns andGaccording defining eigenvalues of G covariance matrix and belonging to them, orthogonal R i distance T The values of the distance estimated according to (13) in The d(V ) distance of V vector from G class is defined to (16) for each of the collections class patterns and defining The values The values of the distance of the estimated estimated according to (13) to in (13) in i B B i presented covariance matrix and belonging to them, orthogonal R recogn t 1 r  i to (17) and (18). p eigenvectors according 2 2 T V n to (11), n where 2covariance 2 matrix T parameter 2 Mahalanobis Tas a n the n ofspite neigenvalues centre distance. n nd(V nr n ) )functional defines distance of covariance matrix Ri comparable and belonging to are them, presen and to them, orthogonal R spite of(R diversity, can be and yk2 vector (tG R eigenvectors according to (17) and (18). BG spite parameter of diversity, diversity, bebelonging can comparable be comparable and areand are V(according R 2 of T) distance i can y t r kBfrom i) parameter y ( t r ) The class defined i i V 2 T – distance of of vector vector from from class is defined is defined 2 T eigenvectors according to (17) and (18). d (The VBtBdT)r(distance d V ) V V k k k k zB Bz   1according to (17, 18). d (VBradar )  z to z the    eigenvectors dV( z kof VBz)kBzz vector BB  VzBk centre as orthogonal  T2T from  B features’ 1class V  to xinearest i recognized {1 ,2,..., L } (15) eigenvectors according and a tested the base define the the radar (15) Tr (7) 2k 2 T k  the  base the tobase define totokdefine the class the ofBclass nearest of1(17) the nearest recognized radar radar n1 n1  k(11), kn1 (7) kV ithe   V  xof (18). {1,recognized 2,..., L} according to (11), where functional defines the 1 1 1 k  k  k  d ( )    tt1Tt... ording according to (11), to where where functional functional defines defines the the 1 1 1 k  k  k  k y ( t r ) d ( V ) d ( V ) k k r r r  B i V 2 T G BB k distance. k B 11 a Mahalanobis (15) x  G  x i  { 1 , 2 ,..., L } i 22 nnn signal. TTT 222 d (V z  z 1  Gi1i xG i  n B nnn emitter nnn emitter emitter nfrom BTT)T Tzfrom nT k yyk2ysignal. ((t(tsignal. G 2the 22 Tradar T T the (15) kk ktkr kr)r)) (15) V  x i  { 1 , 2 ,..., L } 1 distance features’ vector of a tested radar to 1 ance distance from features’ features’ vector vector of a tested of a radar to to the   x  G V V V T i T T i  T T B t t t r r r 1 1 1 k  k  k  (VV )ztzz)zzz  i  t2(2n2rnrt k2) Bn (t kBr(TrB) t2 ) n k (t rn)  2 k ddd(n(V       BB) B()r ( t zrzkz)kk Gi xGi  Tr) k nnn(7) k nnn y222 Tr Tr rn 2 nnn (7) (7) ((1tttTkTkTTkkrrrr))))2222k  k kkk11k1 kkk111kkk kkk111 kkk 1 y k  k k (1tTTkT kn 22 y y y ( ( t k   2 2 k  k k k 1 k 1 z    ... ... ... d z ( V ) z z      T T B)1centre   k 1 d d d z z z ( ( V ( V V ) ) ) z z z z z z                   B k V VB (kBcentre centre as(at aMahalanobis distance. distance.  distance.  BB kkk  as (16) ras rMahalanobis (xB )(V T VB i )i T {1,2i,...,  {1L,}2,..., (16) L} )1k   Tnnn tkka) BMahalanobis R i R i  T1 (x V x Bi )( Vx k 1 k )  10 T1 TTT 1 11 ... kkkk 11 11  kk1      Bi ) kk t kkkk1 kkTT  11  i T TTT1 T 0 1 1 1 1 k k     k k k k      G    0 ... 0 t 1 1  0 ... 0 t vector’s features’ co3 (16) kthe t1ttrr ’ofcoG R  ( x  V )( x  V ) i  { 1 , 2 ,..., L } (16) k r x  G ( ( r ( r r t t t ) ) ) ( ( t ( t t r r ) r ) )       i 1 1   1 1 i x  G  i i B B 1 n n n   i   nnnn kkk T i  1 1 Gi (xx  kTkk kkk  0  t1TT  (16) R i 0  t T  i  {1,2,..., L} 1 T the Gi VB i )( x  VB i ) 111 kkk T 0 T of 1process nd normalization 1 1 1  ... ess of T T T T T T T  0 ... 2 2 t2   t kr )r[t ,t   0 0 2t1 r...T 0  (11) 2 GiTT2TxrGi ((0t((tttkkkkrrrrt))))...  1((rt((rrrnr]ttTttktok[kk))t1))1(9) ,..., t nr] 1 2 (11) ] (11) 111  values results esults n... ( i ()i ) ( i ) ( i ) ( i ) )   ...T r [t1 , t 2,..., ,ktkkk2 ,...,    1 co   0 0 0 ... ... ... 0 0 0 t11 R i t(i(k)iR ... ... ... tt1...     of of ofthe the theaccording vector’s vector’s vector’s features’ features’ features’ cocokkkk1 11 i t t) k k t k k  {1,k2,..., n,}2,..., n} (17) (17)  {1 1 1 1 ... ... ... ... ... ... ... ... ... k(i)k (i  0 ... 0 t T identity matrix ( i )       k 2  (i ) (i ) 2 2 R t  =  λ    to an according {1, 2, …, n }(17) rding             1  T i (17) 1  T     k R i tkk tk  111  TT T  t k  { 1,2,..., n} r [ t , t ,..., t ] 1of 01 ... T r0  t 1of 1of TTT1  (11) nd the the normalization normalization normalization process process process    --dnd k k 1  T the 0 ... 0 t T 1 2 n  ... ... 000ttt2t22 R t (i )  (i ) t (i ) 0 1 ... 01111... ... 00 tt1t1n11 t n  0000  1 0...n ... ...... 0TTT 0t...nr00r...  ... 2022 ... ... (11) (17) k  { 1 , 2 ,..., n } n n        ,...,ttntn]n]] rrri k (11) k k (11) (11) (9) to(9) 2,..., values values according (9) results 1 according T results results  0 11111  ...  T  0r[[t[t1t1,1,tTtT,tTT2t2,..., to ffvalues ...... ... T T 1 t 2 0 (V according 0to (t1( i ) )T(t( i ) )T  3... ...... ......... ............ 1 T T 3... ... 2 V ... 122 ... T0 T  22   0 0 ... ... 0 0 0 t t t    T 3 22     ) T Λ T ( V V )    T T T 2 2 1 0 0 ...  t          lsto to toan an anidentity identity identity matrix matrix matrix according according according r  ( V V ) T Λ T ( V V )     B B B B     ( (11) ( V V ) T Λ T ( V V )     ,..., r   (11) rrrr T[[t[[t1tt1,11,t,,ttt2222,..., (11) B B n  BB TTT B  B  ( i ) T(t(1i )i ) )TT ,..., ,...,  (11) s...TE(rr 111  ...Tttttnnnn]B]]] ... ...n  ... rrBr 00(11) ... ... T )T ...TT ...     ... ... TRT 1  0 0 0 0 ... ... ...    t t t          ... ... ... ... ... ... ... ... ... ... ... ... ... ... 1  VT ) 1 (t(t21( i))()tT2( i )) T i 2  VB  VB )) T RT(V (V  ((V V gg  BB)BRVB()VB  VB) (V1B TV T nnnnnnTi  T B )T R 1(VB  VB ) i  {{11, 2, …, L ,2i ,..., B T( Λ } L} (18) (18)(18) VV    1 B  B B  {1L,}2,..., 1 1 1    T T T T i ...( i)(Tt2 )  Fig. 1. A Fs 1 1 1 T T T T T T    ... (n(V B)B))TTTΛΛΛ TTT BBttttnV 0t1  0 ...T n1  t n  0000 0000 ... ...... V V ( ( V ( V V V V V ) ) )           T  i  { 1 , 2 ,..., L} ... n(nnV nnnV     (18) B B B B B B B B t ( ) i 2 transform.F   TTV T T)TT R ( V TTT V ) ( V     T EE(B(rr BT  B 1 tr 1E  i  {1,2,..., L}  TRT (rr )BT rr))T T )averaging TRT TRT Ti (t (ni ) )T ( i... (18) 111 TTT  T TT T TTT T out 111Tthe ) T result of received functional ΛaT T (V V t T2T (VV V V ) Λ ( V V ) As    As a result of averaging out the received functional   result of averaging out the received functional B Ba   Fig. 1.tr ( ( V ( V V V V V ) ) ) R R R ( ( V ( V V V V V ) ) ) ( ( V ( V V V ) ) ) T T T Λ Λ Λ T T T ( ( V ( V V V V V ) ) )                    B B B B    t ( ) ...   BBB ,...,BB B BBB BBB BBB BBB BBB BBB n   ( i ) T [ , ]   Rt Rt Rt TTT 1(11),2 Ed (un) value is received according to 1ording (tn )assumption (tV transfo  ( i )to 11 t1... t11 Vto according to (11), according is received toT R(11), value is functional received toThe Ed (u) value analysisaccording requires the that covariance Ed (u)according assumption ) (V ((VV ((VV VBBBBaveraging VV VBBBB))T))TTR RR11out ((V VBBBBthe VV VBBBB)received )))  V  V analysisrequires requires that covariance maTheThe analysis the assumption that covariance (t n )T  the ).aTTTBTresult  B(of 5. Calc matrices might be nonsingular. Sometimes tests show, that (12). (12). The analysis requires the assumption that covariance As As Asout aaa result result result of of of averaging averaging averaging out out the the received received received functional functional functional to (11), is received according to (u)]]value As,..., aEd result of averaging the received functionalout ac-the trices might be nonsingular. Sometimes tests show that cova-that 5 ttt2t2n2[[Rt matrices might be nonsingular. Sometimes tests show, [ , , , ,..., ,..., ] ording Rt Rt Rt Rt Rt Rt Rt Rt    covariance matrix can be singular. As a result, it is not The analysis requires the assumption that covariance 1 1 1 2 2 2 n n n (8) value resu5 (8) matrices might be nonsingular. Sometimes tests show, that ... As according according according to to to (11), (11), (11), value value value is is is received received received according according according to to to Ed Ed Ed (u (u (u ) ) ) cording to (11), Ed(u) is received according to (12). riance matrix can be singular. As a result, it is not possible to eraging out the received functional ...As a result of averaging out the received functional covariance matrix can be singular. As a result, it is not ).... T result result of of averaging averaging out out out the thereceived received received functional functional functional 1 the possible coordinates of according K-L 1 might T matrices be nonsingular. Sometimes tests show, that t n aaaEdresult  tAs As V)B)Tvalue V (isVBreceived ) of E[(averaging 1d(according 1 value covariance matrix can becoordinates singular. Asof a transform result, it is not 5. C VB  V R V (VB B) V (VtoB normalize  BE)][(to  normalize coordinates of K–L transform to (8). Thus, B V(is VBV)BT )] RE V EVdEd (V(u ER[((12). Breceived to TTnT )according according to Ed (12). (12). to (11), is received B ) possible B )]normalize Ed (u ) B Bis to K-L transform according according according to to to (11), (11), (11), value value value is received received according according according to to  Ed Ed (u (u ) ) ) ttnt(u    T according to (8). Thus, there is a need to normalize There d covariance matrix can be singular. As of a result, it istransform not 11 T possible to normalize coordinates of K-L nnnt2 t n   E[r T TT Λ 1Tr ] (8) is a need normalize coordinates K–L transform acTthere T(8) EV to to (8). Thus, there isto a(19). need to normalize (12). VE Λ 1 y ]toof normalize Ed (VB )  E[(VBE[r(8) (yV]]B E[ yaccording TB[T)yTΛRΛ1Tr [ yBT)]Λ1Ey[]rT TT Λ 1Tr ]  possible coordinates K-L transform according (12). (12). (12). T TT coordinates of K-L transform channels to (19). according to Thus, there is a need to normalize TTTcording .)  tt1t1t1tntnn ddd((V VV V RR R11(1(V EEE (VV EE [([([(VVV (VV )])]K-L VVV (8). of according to (19). 11 ) nnn... BB)B))E BBB BB) B))coordinates BBBto B B)] B 1 yk transform r T TTΛ c T10Λ1 y according (8). Thus, there is a need to normalize    Th 0 ...   y Tr E [ ] E [ ]      TT T   coordinates of K-L transform according to (19).    0 ... 0 and mod 1  0 ... 0 if k  0 111 T 1 c 1 . t2ttntBnnn VB)T RE1d(V  T TT 111 111 TTT)]TT T 1  TTT   V )]   Ennnt[(ntt2tT2nV y   V V V R V V ( ) E [( ) (      (19)    1 B B to (19).  ΛΛΛ Tr VVBBBB0V VVBBBB1))) R RR ((V EEEdd0d(1(V (VVBBBB)))EEE... [([([(V (VVBBBB  r[BrBrBB)])] T)] TT Tr Tr]1]]Ecoordinates E [V [V EE [[y[yyΛΛΛ yy]y]]ofzK-L EEV k yk according a k  transform base for c chann  if  0    T  0 ... 0 k 2  0 ... 0 k  y2 T 1  (12) 11 T0 T ...  T  2 a T  T1 0  .TΛΛ ...1...Tr ... ]  y  (19) y  E if  0  z (19)  (12)       1 1 1 1 1 1 T T T T T T T T T   (12)   y E  k  y y y Λ  y y E [ ] E    0 if  0  class. In k    b 1 1 1 TΛ Λ...Tr Tr... Λ yyyy]]]] E[[r[[rrr TTT E[[[[yyyy Λ EEE EEE    000 ......... 000  k k z k k  if     ΛΛ Tr ΛΛ ]]]] (19)and bm Tr k  0 11 ... ... ...    0 k if ...0  ... ... ...   1... 0 ...21  ...  T  ...  ttTtTtTttn(12) method   0 (19)    z     1nnnnnnnn This causes that distance of the vector from G k d ( V ) V    1 (12)       1 1 1 1 y  k baseccf 1 B k 0 B0 1  0000 1 TTT 0000  01 0  ...E y 00  0111...  if  0 ... ... ... ... 0 0     k  0 0 0 ... ... ...  2 2 2  0 ... n [7,12,13,1         0 ... 1 1 1     ... ... ... ...  n   (12) (12) (12) n    yThis yycauses ΛΛΛ y1  1     This thatthat the G class.m kmodified  0ofofthe VB(11), )if distance Vvector class, defined according to is toVBthe formfrom offrom causes 11    EEEyyy ......... ......... ......  dd0(d(V B vector m distance G (CIC) 1 1    B) This causes that distance of the vector from G is[7 ( V ) V 0 ... 0 2 1 ... ... ... ...     0 0 0 ... ... ... 0 0 0 2 0yEn  0  2 ... n 0y T B B  2 2 2 2 2    n n y (12) defined n TT0 TE (20),class, where pthat is the number of(11), non-zero eigenvalues ofform yyyy  ynk ...yk 222(12) metho (12) y y E kE  n  y E class, defined according to is modified to the form of     (12) (12)  according to (11), is modified to the of  This causes distance of the vector from G [7    d ( V ) V  y y y E E   k k k   ...  n... ... ...n   E class,  111 defined according B B  ... 1  ... ...E...    n toof(11), is modified to theofform ofof[7,12, correc (C  ...   where 000000 ...... kn1 E ... ... ... ...... ... ...... ... ......   n(20), nn  p is the number non-zero eigenvalues co 2 2  ...    R covariance matrix, is Moore-Penrose inverse of (20), where p is the number of non-zero eigenvalues of  (C kn1  yy1y121   k k defined according (11), is modified to the form of of k 1 k 1 k k class, ykk1 k k 1 k 1111  y1 (20), where p is thetonumber of non-zero eigenvalues  E pattern v  T    (CIC) o 222 nnn 222  n 0 0 ...  0  ...En k   n n n    0(9)    0 0 0 0 0 0 ... ... ... n    T MT covariance according theMoore-Penrose relation Reigenvalues yykykk yykykk (20), EEE nnn wherematrix, p ismatrix, the number non-zero of of Rtoisof covariance inverse o k1  k (9) 1121 k 1  k EEE  ,where nnn covariance R(21). matrix, is Moore-Penrose inverse ofof copo     2 analysis 2above makes number e it possible to the definition n 2 2 ituse n n M is the matrix with  T The analysis above makes it possible to use the definition 2 2 2 2 2 2 The analysis above makes possible to use the definition n n n n n n ykyy... EyBull. Eyyyykkkk matrix, is Moore-Penrose k R  Tof kkk 111 covariance matrix, R according to the relationinverse p yyyykkkkthe E E E 2y22  kkk kkk111 kkk covariance T MT Tech. 65(1) 2017  din(Pol. collection Ac.:  nnnndistance E distance for channel with index VB) MT covariance matrix, according to the relation R  T T115 V   EEE   of for the channel with index of distance for the channel with index d ( V ) d ( ) y      patter n i B i B n  (9) (9) (9)111 to , where matrix, M is theaccording matrix with (21). ekanalysis itkkpossible use the definition 22k1 kabove makes Unauthenticated R2  T MT covariance to pthe kk kkkk1 n 2relation p p kkkkto 1 111 kkkk , where M isexpected the matrix with (21). according (13), where is the expected {distance 1,22 ,..., L}i  V yDate (t Tk r3:42 ) PM according to (13), where is the 2 i  1 , 2 ,..., L } according to (13), where is the expected T B{ ianalysis { 1 , 2 ,..., L } V k The The The analysis analysis above above above makes makes makes it it it possible possible possible to to to use use use the the the definition definition definition V Download | 3/7/17 for the channel with index d ( V ) numbcc B i B i ... ... ...    , where Md (isVthe with z k (21). z z i B )) n  B ) matrix ue class vector, while Gi features’ 2 of of of distance distance distance for forwhile the the the channel channel channel with with with index index index T p k 1  k p k 1 2  k p ddvector, (V (V VB)B)) for yyy n The value class vector, while k 1 makes it Lpossible to use value of G collec Gdefinition The of above makes possible to use the definition id i(idefinition to the (13), where the expected }analysis i Bfeatures’ VB i is class i features’ The The analysis analysis analysis above makes makes makes ititit itpossible possible possible to to toof use use use the the the definition definition p y k2 p 2 T z{11n,n2 z,..., ...according z1 z nabove above y  p ((ttkTrr)) 2  1 z2 z 2 p d ( V )  z Tz  T i

i

k (19) (19) z  z   k base base classification forother classification of of the radar tested radar an toworks an appropriate method with other methods described inappropriate works k  k of the with methods described in basefor for classification ofthe thetested tested radartoto an appropriate his causes causes that that dzdk (k(V distance vector from from G G(19) method his of the VVBBvector VBB)) distance k    0 if 0 if  0  0 class. In class. order In to order compare to compare the received the received results results of of RER  [7,12,13,15,16,17,32], Correct Identification Coefficient [7,12,13,15,16,17,32], Correct Identification Coefficient k k  to  if isis  0 (11), class. In order to compare the received results of RER RER k  0 ass, defined defined according according to (11), modified to the the form form of of ass, modified to method method with with other other methods methods described described in works in (CIC) set according according to (22), (22), where ndescribed the number number (CIC) isis set to where nBBPP isis the This causes Thisppcauses that distance of vector from from G dd(that (Vof V VB vector method with other methods in worksworks B This causes that distance ofthe the of vector from 0), where the number of) non-zero non-zero eigenvalues of GG (V VBB))ddistance VBBthe 0), where isis the number eigenvalues of [7,12,13,15,16,17,32], [7,12,13,15,16,17,32], Correct Correct Identification Identification Coefficient Coefficient [7,12,13,15,16,17,32], Identification Coefficient J. ofDudczyk correct comparisons comparisons of ofCorrect basic features’ features’ vectors to of correct basic vectors VBB to V  to (11),tois(11), class, class, defined according is modified to to the form of class,defined defined according (11), ismodified modified tothe theform form of ovariance matrix, Moore-Penrose inverse ofof RRaccording variance matrix, isis toMoore-Penrose inverse of (CIC) is (CIC) set according is set according toto(22), towhere (22), where is the number nnBP isis nBthe P number (CIC) is set according (22), where the number (20), where (20), where p is the p number is the number of non-zero of non-zero eigenvalues eigenvalues of of BP pattern vectors vectors V in aa particular particular class, class, where where is the the VPP in  NN is (20), where p isaccording the number ofrelation non-zeroReigenvalues MT of pattern ovariance matrix, according to the the  TTTTMT variance matrix, of correct of correct comparisons comparisons of basic of features’ basic features’ vectors vectors VVB totoVB to  to  relation R of correct comparisons of basic features’ vectors + R R covariance covariance matrix, matrix, is Moore-Penrose is Moore-Penrose inverse inverse of of B number of all allofcomparisons comparisons dividedofby by thefeatures’ numbervectors of test test of divided the number of RR (21). covariance is Moore-Penrose inverse of number where M is is the thematrix, matrix with (21). where M matrix with variance matrix, is Moore-Penrose inverse of covariance number correct comparisons basic VB pattern pattern vectors vectors ininV aaPparticular in a particular class, where class, where V T T NN isis the N is the + T  P pattern vectors particular class, where the V T collections. collections. R  T R MT  T MT covariance covariance matrix, matrix, according according to the relation to the relation matrix, according to the relation R  = T MT, where M is the to pattern vectors V in a particular class, and N is the number P P covariance matrix, according to the relation R  T MT number number of of alldivided comparisons divided divided by number the number of matrix with of all comparisons number of by test collections. , ,where ,M where M matrix is(21). the pmatrix p pwith (21). nnby pp pwith number ofall allcomparisons comparisons divided bythe the number oftest testof test B P B Pthe where Misisthe the with yyk2k2 (21). ((ttTkTkrr))22 (22) (22) CIC  T CIC  22 (21). Tmatrix collections. collections. VBB))  zz zz   dd((V zzkk        collections. NN kk11p kk11 p 2 T nnB P nB P p kk 2 kk1p1 p 2kkT p2 2 2 T p p p y y ( t r ) ( t r ) (22) B P CIC CIC 2y T T 2 k k k (tk r ) (22) (22) CIC 2 Tz) z z  k k      dpdp((VVBTT)) d(zV z     k NN (22) N   zk k  z11B z TT    B    The number of correct comparisons is set according The number of correct comparisons is set according n   ( r t ) ( t r ) nBBPP  (r t kk)  (t kkkrk)11 kkk111 k k k k1k11 k kkk1 k kk11 p p kk to (23), where function assigns assigns to to aa pair pair of of vectors vectors to (23), where i ij j function p 11T T 1 T TT The number The number of of correct correct comparisons comparisons is set according is set according t 11)Tr ) (t r )  n n  (r(rTTt ) ( r ( t The number of n correct comparisons is set according to B¡P B  P B  P k k k k     i t k )11(t k r )00 ... j j number of nBP correct comparisons is set according ... 00 tt11   the value value which which equals ‘1’ or the the ivalue j the equals ‘1’ ifif iiof == vectors j,j, or value  VBiBThe V(23),  V ,,V PP  where γ j function k 1 k 1  k assigns to a pair (V , V ) the j j    B P   kk  i k 1 toto (23), towhere (23), where assigns assigns toto aa pair to aof vectors of vectors  j function  function (23), where assigns pair ofpair vectors 00 11 ... 00 ttTpTpT which equals ‘0’ ≠function The received received CIC values are which equals ‘0’ ififi iii ≠‘1’ j.j.ifi The CIC values are T ... 1 value which equals i = j, or the value which equals ‘0’ if T      (20) i j i j (20) ...ttpp... ...ttnn]] 111 pp 0 r  t t ... 0 0 ... 0 rrTT[[tt11... r  1  1  1 the value value which equals ‘1’ oror i =the j,4. value or the value VVBBi 6i, ,V=VP j.PinjVinThe  4.the , Vreceived BTable P value ... CIC values areequals presented the which equals ‘1’ififi‘1’ i==inj,if j,Table the value presented Table 4. which presented ...tT1  T  (20) ... 1 ... ... 01... ... ... ...1 0... ... T0 0 1 ...0 ... t t 0     which equals ‘0’ j.j. The iThe ≠ j.received The received CIC CIC values are p   p   p 0t00]p p... whichwhich equalsequals ‘0’ ifif i‘0’ i ≠≠ if received CIC values values are are rrTT[[tt1... ...trtpT... [tt1n...]00t]p ... r  (20) ... ...00 0ttTnTnt prr (20) n (20)  1 p ...t n  ... I J presented presented in Table in 4. Table 4. I J ... ... ... ... ... ... ... ... ...  presented in Table 4. ... ... ...   j  (... ...V (23) (23) nnBBPP   i i j (23)  T  T   VBB V VBB))TTTTTTMT MT ( V V )  V ) ((V   B B B B T i 11 j  j 11 i 00 000 ......0 00...ttn n0 t n  I J I J I J i j VBB V VBB))TTR RTT((V  VBTB)) ((V TVBB  TV (23) ihundreds j nnB  P to naBafew   i j of During the the test, test, the the total total comes comes to of radar radar During hundreds TMT Pfew ( V V ( V ) T V ) T ( V MT V ( V ) V )        (23) (23)  B B B B B B B B  BP  (VB  VB ) T MT (VB  VB )  i j i j  1  1  1  1 During thein test, the total comes to a few hundreds of radar signals recorded in collections with the length of 5000 signals recorded collections with the length of 5000 i 1 j 1 T  T  TRV( V ((VVB V(VV signals recorded intotal collections length of 5000 pulses.of radar B )B)  B )B)  VB ) During During the test, the the test, thecomes totalwith comes totoaathe few to hundreds ahundreds few hundreds of R B()VBBRV(VV B B B During the test, the total comes few ofradar radar A superheterodyne ELINT receiver was used in the measuring signals signals recorded recorded in collections in collections with the with length the length of 5000 of 5000 signals recorded in collections with the length of of5000 procedure. This receiver makes it possible to define value RF 1 1 with measurement accuracy 0.5 MHz and value of PRI in the 0 ... 0    1 scope from 2 µs to 20 ms, with measurement accuracy 0.05 µs. 0  p ... 0  osed to (21) The recordings came from a dozen or so radars of the same type. M (21) 44  ... ... ... ... s aims Three copies were chosen to further analysis and their measurable   atterns parameters were as follows: RF = 1415 MHz, PW = 11.2 µs 0 ... 0   0 44 4 rix of and the following PRI values i.e. PRImin = 1400.96 µs, of the PRIave = 1745.93 µs and PRImax = 2090.91 µs. The pulse rep-

ues of ogonal

The analysis above makes it possible to create a scheme of The analysis above makes it possible to create a scheme etition interval value (measured between the arrival times of withthe theuse useofofK–L K-Ltransform, transform,which which ofrecognition recognition system system with is is two consecutive pulses on the level of the detection threshold) presented Fig. presented in in Fig. 1. 1. changes sequentially every pair of pulses, taking seven different

(15)

(16) (17)

(18)

ariance w, that is not nsform malize (19)

rom G orm of ues of se of TT MT

Fig.1.1.AA scheme scheme of of aa triple-channel triple-channel RER RER system system based based on on K-L K–L Fig. transform transform.

Calculation results received 5. 5.Calculation results andand received RERRER results results

The defined distance di(VB) for particular recognition channels with a coefficient to (13) and modifi{1, 2, …, L The definedi 2  distance di (}Vaccording B ) for particular recognition cation of this distance according to (20), is a base for classificachannels with a coefficient i {1,2,..., according to (13) L}In tion of the tested radar to an appropriate class. order to comandthe modification of this distance according to methods (20), is a pare received results of RER method with other base for classification of the tested radar to an appropriate described in works [7, 12, 13, 15‒17, 32], correct identification class. In (CIC) order istoset compare thetoreceived results RER coefficient according (22), where nB¡P of is the

method with other methods described in works [7,12,13,15,16,17,32], Correct Identification Coefficient 116 (CIC) is set according to (22), where nBP is the number of correct comparisons of basic features’ vectors VB to pattern vectors VP in a particular class, where N is the number of all comparisons divided by the number of test

PRI values. The complete cycle of value changes of PRI was as follows: PRI1 = 2091 µs, PRI2 = 1738 µs, PRI3 = 1575 µs, PRI4 = 1491 µs, PRI5 = 1447 µs, PRI6 = 1420 µs and PRI7 = 1401 µs. This is a complete cycle of value changes of the PRI in a measurement sample. The method by which it was possible to receive a complete cycle of changes of PRI values is described in the works [12, 28]. As a result of initial measurement data processing, VB vectors are received according to (1). On the basis of the received VB vectors, pattern vectors VP are also received. The method which is also used in this process is called the Holdout method. This method divides the available collection into two disjoint sets i.e. a set which is used to learn the classificator and a set to test the classificator. The usual division of the available data collection is as follows: 2/3 of available data is in the learning set and 1/3 is in the test set [12]. The identification process is carried out on the basis of the distance measurement with the use of the minimum-distance classification, according to the presented method. In order to assess the quality of the classification process the CIC index is defined. In the final process of identification, fast-decision identification algorithm (FDIA) of radar emission source is used in relational ELINT database (DB). The FDIA algorithm mentioned above is a three-stage parametrized by implementation of three different ways to define the similarity degree of the signal vector to the pattern in the database and by the possibility to define three-stage value of decision function. As a result this algorithm working in the classification process Bull. Pol. Ac.: Tech. 65(1) 2017 Unauthenticated Download Date | 3/7/17 3:42 PM

A method of feature selection in the aspect of specific identification of radar signals

of radar types, the following CIC values are received i.e.: 88% and 92% for three different values of decision function. In case of identification of copies, the following CIC values are received: 26%, 47% and 63%. The mechanism of FDIA algorithm and the received identification results are described in [7] in detail. The received estimation results are presented in Tables 1‒3 and illustrated in Figs. 2‒4. Appropriately crossed columns and lines of each VB vector and radar patterns in the form of VP vectors, present the degree of their similarity defined by the distance value. The less value of this distance means the bigger similarity of VB vector to the pattern. Also, in Figs. 2‒4 there are minimum values of the distance di(VB) marked with a red dotted ellipse in each Gi class. The received minimum Table 1 The results of distance calculations for a radar copy No. 1 in L1 channel for 16 comparisons in G1 class d1(VB – VP)

VP (for G1 class)

VB (for G1 class) 10,714

11,647

4,302

3,374

11,821

10,798

3,567

6,995

13,267

13,414

0,516

4,273

15,278

16,728

4,178

0,612

Fig. 3. 3D graphic illustration of the received distance values in L2 channel for 16 comparisons of the radar copy No. 2 in G2 class Table 3 The results of distance calculations for a radar copy No. 3 in L3 channel for 16 comparisons in G3 class d3(VB – VP)

VP (for G3 class)

VB (for G3 class) 10,349

11,105

15,705

13,401

11,258

10,217

32,061

12,715

15,804

32,012

10,249

17,058

13,432

12,617

16,994

10,315

Fig. 2. 3D graphic illustration of the received values of distances in L1 channel for 16 comparisons of the radar copy No. 1 in G1 class Table 2 The results of distance calculations for a radar copy No. 2 in L2 channel for 16 comparisons in G2 class d2(VB – VP)

VP (for G2 class)

VB (for G2 class)

Fig. 4. 3D Graphic illustration of the received distance values in L3 channel for 16 comparisons of the radar copy No. 3 in G3 class Table 4 CIC values of RER method for three recognized radar copies in G1÷ G3 classes

0,001

14,717

12,391

3,793

4,732

10,022

11,207

2,721

CICRER

G1 class

G2 class

G3 class

2,389

11,197

10,01

6,322

VB

0,234

0,194

0,264

4,796

12,717

16,329

0,008

VP

0,534

0,614

0,498

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J. Dudczyk

Fig. 5. Graphic illustration of CIC calculations for three radar copies in given classes G1÷G3 of triple-channel RER system

distances show at the same time the number of correct comparisons of basic features’ vectors to pattern vectors in the class. In each class (G1÷ G3) 16 comparisons of these vectors are carried out and CIC is calculated. The results are presented in Table 4 and illustrated graphically in Fig. 5. According to the SEI methods listed in this section, the received RER results are as follows: the use of out-of-band radiation described in the work [12] the CIC value for RER is about 90%. The method based on fractal features described in the work [15] the CIC value is 91.6% for Mahalanobis metric and 96.7% for Euclidean and Hamming metrics. Very similar RER results are received in the work [13], where RER also bases on the analysis of fractal features. The method based on inter-pulse analysis described in the work [16] increases the CIC coefficient up to 70%, and the method based on intrapulse analysis described in the work [17] makes it possible to receive RER results reaching 90% level. Data modeling applied to RER and identification is presented in the work [32]. In this work the value of CIC equals 98%. In the work [7], the fast identification algorithm for RER is presented. This algorithm is parametrized in three stages by implementation of three different ways to define the similarity degree of the signal vector to the pattern in the database. Based on this algorithm, the CIC value is 63%.

In order to depict it clearly, CIC values received in other RER methods which appeared in this section are presented in Fig. 6. It needs to be emphasized with full conviction that referring to the works above, during the RER procedure, the same recordings of a few hundred radar signals coming from the same type of radars are used. Only by this approach it is possible to compare the received results. It needs to be emphasized that the methods listed above, differ from each other as concerns the test procedure, the compilation level, calculation time and algorithm complexity. However, the main difference is that in the process of generating distinctive features, it is possible to achieve different distinctive features from a radar signal. In that way, a quasi-optimum radar signal pattern appeared.

6. Conclusion The received measurement data have a significant influence on the specific identification process of radar, in which it is aimed to receive very high level of radar emitter signal identification. Ultimately, signal source identification which is 100%, should be characterized by the maximization of explicitness of RER procedure. It is not a trivial matter to achieve such a result. It is also known that stochastic context-free grammars (SCFG) appear promising for the recognition and threat assessment of complex radar emitters in radar systems, but the computational requirements for learning their production rule probabilities can be very onerous [33]. As shown in [34], a self-organizing map and the maximum likelihood gamma mixture model classifier and adopted Bayesian formalism are too complicated for direct analytical use in automatic radar recognition. The presented RER method is realized on the basis of MatLab software package and received vectors are recorded in a dedicated database for ELINT system. The received CIC value indicates that there has been a noticeable rise in the radar signal correct identification. Comparing the received results of the identification process with other methods, it may be admitted that

Fig. 6. Graphic illustration of CIC values for other RER methods

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A method of feature selection in the aspect of specific identification of radar signals

the presented RER method based on multi-channel recognition system makes it possible to receive the CIC coefficient which equals 61.4%. In order to increase the CIC coefficient value, in further works on RER use in SEI process, a common similarity matrix will be defined. This matrix will include the complexity of algorithms which are used in the RER method, estimation time, the requirements of the equipment platform and other requirements, which are significant in the process of quality estimation of a particular method. Thus, it will be possible to count automatically the similarities between vectors of basic measurable parameters for different radar copies of the same type. For ELINT systems working in real conditions, on a contemporary battlefield the automation of RER process and explicit identification of every single emitter in real time (with minimum time burden) are currently primary challenges for ELINT specialists.

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