Sidelobe-Suppression Technique Applied To Binary Phase Barker Codes

Transcription

1 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN Sidelobe-Suppreion Tehnique Applied To Binary Phae Barker Code Aitant Profeor Dr. Imail M. Jaber Al-Mutaniriya Univerity College of Engineering Eletrial Eng. Dep. Abtrat Thi paper preent binary phae Barker ode and orreponding deoding filter. Thee filter are optimal in the ene that they produe no idelobe and they maximize the ignal-to noie ratio. Here, the input ode i ampled at a rate of N. Key Word: binary phae Barker ode, mathed filter, mimathed filter (idelobe-free deoding filter). الخالصة يقدم هذا البحث شفرات باركر ثنائية األطوار و مرشحات حل الشفرة المطابقة. هذه المرشحات مثالية بمعنى أنها ال تنتج قمم جانبية و هي تزيد نسبة اإلشارة إلى الضوضاء. هنا, شفرة اإلدخال مأخوذة العينة بمعدل.N Introdution Phae modulation i a priniple, whih divide the radar pule into a et of ub-pule of equal duration, and the phae of eah ub-pule i fixed. When two phae value with a phae differene of 180 i ued, the modulation i a binary ode. Biphae modulation of a radar tranmiion i a well-known method for inreaing radar tranmiion power, while till maintaining a good range reolution. Mathed filter i a filter, whih reate unwanted idelobe at the output of the reeiver. Thee idelobe an be eliminated by uing a mimathed filter. However, there i an aoiated lo in ignal-to-noie ratio (). In [1], Damtie, B, et. al., preented long optimal binary phae ode-mimathed filter pair that may be ued in everal appliation inluding ionopheri radar meaurement. Thi wa done by invetigating 1.04e 09 number of binary phae ode. Rohling and Plagg in 1989 have publihed a deferent approah of eliminating the idelobe in periodial binary phae ode by uing mimathed filter []. Exhautive earh for optimal aperiodi binary phae ode and mimathed filter pair up to length of 5 ha been arried out (by Lehtinen, et al., in 004) [3]. Coding Filter: [3] Aume that a ode oniting of N pule (an N-bit ode) uh that the pule length Tp i a multiple of the ampling interval T, i.e., TP=NT, where N i an integer indiating the 330

2 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN number of ample per bit. Thi mean that the poibility of over-ampling i taken into aount. Thu, by hooing T a the time unit, an elementary pule an be written a: N 1 i0 P( ( j, n=-,., (1) where δ i the direte time-impule (unit ample; not to be onfued with the delta funtio given a: ( 1 0 when; n 0 when; n 0 () Aordingly, the impule repone of a oding filter of an N-bit binary ode an be written a: N 1 j0 h ( a( j) ( n jn ), n=-,., (3) Where a(j) = ± 1 when j=0, 1,..., N-l. The equene of number a(j) define the binary ode. Note that h( i zero when n < 0 or n > N (N-l). General Tranmiion Code: [3, 4] A ode with length L an be deribed a an infinite length equene with a finite number of nonzero pule with phae and amplitude defined by parameter Фk and ak. Thee parameter obtain value Фk [0,π] and ak[amin,amax], where k [l,...,l]. In the ae of binary phae ode, the number of phae ha been retrited Фk work, the amplitude have been et to 1. The tranmiion ode i obtained by mean of a onvolution a: [0,π] and in mot traditional j) h j ( n j ( h ( p( p ( ), n=-,., (4) where * denote the onvolution. Note that ε( i zero when n < 0 or n >NS(N-1) Standard Mathed Filter: [3] The impule repone of the tandard mathed filter i a mirror image of the ode: ( ( h ( p(, n=-,., (5) The output of the tandard mathed filter, or weight funtion, i given a: 331

3 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN w ( ( ( h ( p( h ( p(, n=-,., (6) m Sidelobe-Free Deoding Filter [3] a: For deigning a idelobe-free deoding filter, firt the impule repone an be defined j h ( b( j) ( n jn ) (7) d where the equene of real number b(j) will be hoen to deode h( in Eq. (3). In addition, an impule repone q( i needed for filtering the elementary pule p(. Thu, the omplete truture of the idelobe-free deoding filter for proeing the ehoe i given by: j) h j d ( n j ( hd ( q( q ( ), n=-,., (8) The deoding of a binary phae oded ignal an be arried out by mean of a deoding filter uh that the onvolution of the deoding filter hd(, the filter mathed to the elementary pule q( and the ode ε( i a funtion with a deired hape. Thi hape define the range reolution. Mathematially, thi mean that: ( ( w( (9) The reult of the onvolution w( i a weight funtion, or the output of the mimathed filter, whih determine the range reolution and the range ambiguity funtion. Fourier tranform of onvolution are produt of the Fourier tranform of the onvoluted equene and thu the Fourier tranform of the weight funtion w( i given by: w( } hd ( } q( } ( } h ( } F[{ h ( )} q( } p( }] (10) d If hd( i hoen to make hd(} h(} = 1, then: 1 1 hd ( F { } (11) h ( } The invere Fourier tranform of Eq. (10) give: w q( p( (1) Thu, the impule repone defined by Eq. (11) make a idelobe-free deoding filter produing exatly the ame weight funtion to what would reult from uing no oding at all, 33

4 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN jut the elementary pule p( and a filter q( mathed to it. In partiular, no idelobe are produed. By ombining Eq. (8), (10), (1) in a proper manner, the mathematial expreion for the tranfer funtion of the omplete idelobe-free deoding filter that give w( with a deired hape an be eaily obtained and it i given by: Where Q( w) ( w) ( } (13) H ( w) jnw ( w) q( n e (14) n Q ) And jnw ( w) q( n e (15) n H ) Finally, the impule repone of the idelobe-free deoding filter i obtained by mean of the invere Fourier tranform, whih i: 1 Q( w) jnw ( ( w)} e dw (16) w H( w 0 ) Performane of a Deoding Filter: [3] There i a dereae in when one applie a idelobe-free ompreion filter intead of the tandard mathed filter. In thi etion, the performane of idelobe-free deoding of different Barker ode i invetigated by omparing it with that of the orreponding mathed filter. If the power petral denity of white noie entering a filter with a tranfer funtion H(v) i S(v)=Sn, the total output noie power i: n Sn H( v) dv Sn h ( t) P dt (17) Hene, the given by the mathed filter i: m S P wm n n ( (18) where wm i the peak value of the weight funtion wm( of the mathed filter and P i a aling oeffiient defining the reeived power. In a imilar manner, the value at the output of the idelobe-free deoding filter i: S P w n n ( (19) 333

5 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN where w i the peak value of the weight funtion w( of the idelobe-free deoding filter. The noie performane of different idelobe-free filter an be ompared with that of the mathed filter by alulating the ratio of the two ignal-to-noie ratio. Sine the idelobe-free deoding filter i deigned to give (thi i illutrated in Fig. 3 and 4), thi parameter i: R m n n ( ( (0) The value of µ( and λ ( n ) needed in Eq. (0) are obtained from Eq. (5) and Eq.(16), repetively. A uffiient auray for omparion purpoe i obtained by trunating λ at the point where it abolute value are below Reult Sine the data analyi i baed on direte ample, and the theory i preented in term of direte ignal. Thi lead to reult, whih an be ued in MATLAB programming language. Table 1 give the value of R for Barker ode of different length. They illutrate the fat that idelobe-free deoding of Barker ode degrade the by about (5%-30%) relative to tandard deoding. However, the degradation i mallet for the 5-bit and 13-bit Barker ode whih are often ued in inoherent atter radar meaurement. In the ae of the 13-bit ode, the lo i only about 5%. Hene, in thi repet the 13-bit ode i the optimal Barker ode. Figure (1) indiate that, the oeffiient of the idelobe-free ompreion filter, applied to the 13-bit Barker ode ampled at a rate, are 10-baed logarithm of the abolute value of the their normalized oeffiient. While the Figure () and (3) indiate the output of the orreponding mathed filter and mimathed filter, repetively. Table (1): of the idelobe-free deoding filter relative to that of mathed filter for Barker ode of different length. Length in Bit Binary Barker Code R (N =3) It i well-known that, the performane of mathed-filter deoding of Barker ode i better than deoding without idelobe. In the ae of the 7-bit Barker ode, it i hown that, the given by idelobe-free deoding i nearly 30% wore than that of tandard deoding, but for the 13-bit ode idelobe-free deoding i only about 5% wore. The deterioration of hould be evaluated againt the benefit gained in dipoing of the idelobe, whih, even for the 13-bit ode, ontribute by 7.1% to the total ignal power from a homogeneou target. A pratial example i hown where idelobe mak a weak ignal when the tandard mathed filter i ued in the analyi. An improvement i ahieved when idelobe-free filtering i arried out. 334

6 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN Figure (1): The 10-baed logarithm of the abolute value of the oeffiient of the idelobefree ompreion filter applied to the 13-bit Barker ode ampled at a rate of 3 ample per bit. Figure (): The mathed filter output when the input i the 13-bit Barker ode ampled at a rate of 3 ample per bit 335

7 Journal of Engineering and Development, Vol. 16, No.4, De. 01 ISSN Figure (3): The weight funtion (The mimathed filter output) when the input i the 13-bit Barker ode ampled at a rate of 3 ample per bit Referene [1]. Damtie, B., Lehtinen, M., Oripaa, M. and Vierinen, J., "Optimal long binary phae ode-mimathed filter pair with appliation to ionopheri radar", Bull. Atr. So. India 35, pp , 007. []. Rohling, H., and Plagge, W., "Mimathed-Filter Deign for Periodi Binary Phaed Signal", IEEE Tranation on Aeropae and Eletroni Sytem, Vol. AES-5, No.6, pp , November [3]. Lehtinen, MS., Damtie, B., & Nygren T., "Optimal binary phae ode and idelobe-free deoding filter with appliation to inoherent atter radar", Annale Geophyiae,, pp ,8 April 004. [4]. Damtie, B., Lehtinen, M., Oripaa, M. and Vierinen, J., "General radar tranmiion ode that minimize meaurement error of a tati target", IEEE Tranation on Information Theory, Vol. 1, No. 11, November