Rejection of PSK Interference in DS-SS/PSK System Using Adaptive Transversal Filter with Conditional Response Recalculation

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1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol., No., November 23, 3-9 Rejecton of PSK Interference n DS-SS/PSK System Usng Adaptve Transversal Flter wth Condtonal Response Recalculaton Zorca Nkolć, Bojan Dmtrjevć, Nenad loševć Abstract: PSK nterference rejecton usng complex adaptve flter wth condtonal response recalculaton n DS-SS/PSK system s consdered n ths paper. New adaptve flter decreases error probablty for several orders of magntude when compared to the standard adaptve transversal flter. Keywords: PSK nterference rejecton, Adaptve flter. Introducton Spread spectrum, by ts very nature, s an nterference-tolerant modulaton. However, there are stuatons where the processng gan s nsuffcent and adaptve flters must be employed [, 2]. The nfluence of non-lnear correlaton recever on the rejecton of non-gaussan and mpulse nterferences s analysed n paper [3]. Rejecton of PSK nterference n DS-SS system usng modfed complex adaptve flter s consdered n [4-8]. Performance of DS-SS system that uses adaptve transversal flter wth condtonal response recalculaton (CRR-ATF) s consdered n ths paper. The use of CRR- ATF sgnfcantly decreases the error probablty n case of nterference power domnance. 2 System model Block dagram of the DS-SS recever s shown n Fg.. There s addtve Gaussan nose (n(t)) and PSK nterference (j PSK (t)) besdes the DS-SS/PSK sgnal at the nput of recever. The nput sgnal s s () t = s() t + j () t + n() t, () n PSK s t) = m ( t, Q) e ( t, )cos( ω ), (2) ( ct where m( t, Q) s bpolar rectangular data bts havng perod T; e( t, ) s bnary pseudo random pulses havng duraton seconds; ω c s the carrer frequency of the DS-SS sgnal. Rato Q=T/ s the processng gan of the system. Faculty of Electronc Engneerng of N{, Beogradska 4, 8 N{, Serba and ontenegro E-mal: 3

2 Z. Nkolć, B. Dmtrjevć, N. loševć j () t = Ap(, t T )cos( ωt+ θ ), (3) PSK h where p ( t, T h ) s pseudo random varable whch determnes the sequence of the nterference bts; ω I s the carrer frequency of the nterference, A s ampltude of the nterference and T h s duraton of each PSK nterference bt. Input sgnal s multpled by a carrer, fltered and sampled. It can be expressed, at the nput of the adaptve flter, as x(k)=s (k)+j PSK (k)+n (k), (4) where J = A p ( k, T ) e PSK h j( ω k+ θ), (5) ω = ω ω, t = k and A= c J/ S 2. (6) Desred sgnal s ( k, Q) e ( ) s k) = m,. (7) ( k Nose s referred to as N (k): σ σ N k Na k j Nb k 2 2 ' ' ( ) = ( ) + ( ), (8) where N k N k are Gaussan random varables whch varances are equal to. The adaptve flter model s shown n Fg. 2. Two flters are consdered n ths paper (ATF or CRR-ATF). a ' ( )and ( ) b ' Fg. - System model. In case of PSK nterference, absolute values of adaptve flter complex weghts decrease from the reference sgnal to the flter end. Therefore classcal adaptve flter lmts 4

3 Rejecton of PSK Interference n DS-SS/PSK System... the nfluence of partal errors that are contaned n ths dstant flter branches. Ths effect s more emphaszed f the PSK nterference has wder bandwdth. If we take a look at the quares of partal errors absolute value we can conclude that t s convenent to use just some of the partal errors at a tme, n order to mnmze flter response. Therefore we made a modfcaton of ATF. The modfed flter s based on the classcal ATF whch response s modfed usng a certan condton. The modfed response s calculated usng weghts, whch are normalzed over modulo n order to avod partal errors rejecton from certan flter branches. Now, a set of partal errors, whch wll nfluence the response, s determned. They are determned on the bass of the followng condton: square of partal error modules has to be less than the average value of the sum of all partal errors modules. Fg. 2 - CRR-ATF model. Condtonal response recalculaton s defned by: X ( ) W 2 W C = X k, for < <,, (9) C = C, () 2 = y = X W W X, C C, for < <,, (), C > C, C C n =, for < <, (2), C > C 5

4 Z. Nkolć, B. Dmtrjevć, N. loševć and n = n (3) = y = y, (4) n( k) = where W (k) are ATF complex weghts, and y(k) s the CRR-ATF output. The ATF and CRR-ATF use the same standard LS algorthm 3 System Performances Snce we consder the transmsson of the PSK sgnal, bt error probablty wll be defned for the n-phase sgnal and the quadrature sgnal s not consdered. The error probablty s Pe = n n aa aa l = n= Pe ( nq) where n aa represents the number of ensemble members, and, (5) ( ) SNR ( ) ( nq) Pe l nq = erfc. (6) 2 2 where n =,..., and s the number of bts n the consdered member of the ensemble. Index l represents the ordnal number of ensemble member wth respect to the whole statstcal ensemble. Ordnal number of bt whch error probablty s beng computed s referred to as n. Value SNR (l) (nq) represents sgnal to nose rato of n-th bt of the PSK sgnal n the l-th member of ensemble: and SNR ( l ) ( nq) = SNR' Q (7) Q DS = ( ) Q k SNR' nq = (8) 2 ( n+ ) Q Q 2 ( DS ) DS Q k= nq Q k= 2 6

5 Rejecton of PSK Interference n DS-SS/PSK System... There s parameter (l) DS n (8) whch s determned as follows DS { y } sgn[ Re{ s }] = Re, (9) where y(k) s adaptve flter output sgnal at the moments k. 4 Numercal Results System performances are analysed by a quas-smulaton technque. The error probablty at the output of recever s calculated based on formula havng sgnal to nose rato (SNR) as a parameter and t s obtaned by smulaton and computed before the decson s made. Fg. 3 shows the error probablty as a functon of flter length, for dfferent nterference bt rates x -4 Pe x Fg. 3 - Error probablty as a functon of CRR-ATF length,. The result stands for PSK nterference, sgnal to nose rato s SNR = db and o ω = 2. It can be noted that hgh bt rate nterference s rejected more effcently 7

6 Z. Nkolć, B. Dmtrjevć, N. loševć wth a short flter, whle n case of narrowband nterference t s desrable to have flters wth greater length. Error probablty as a functon of the nterference power at the nput of the recever s shown n Fg. 4. The result stands for PSK nterference, sgnal to nose rato s SNR = o db and ω = 2. On the bass of Fg. 4 one can conclude that performances of CRR-ATF are sgnfcantly better than ATF, both for T h = 2 and T h = 4. It s very mportant to notce that the error probablty for CRR-ATF does not ncrease when nterference power ncreases, and the system based on ATF can not operate for hgher nterference power (for example J/S=3dB, Pe. 5 ) x -4 Pe x J/S (db) Fg. 4 - Error probablty as a functon of the nterference power, One can also note the mprovement of ATF performances because the nterference has narrower spectrum. 8

7 Rejecton of PSK Interference n DS-SS/PSK System... 5 Concluson Interference rejecton usng complex adaptve flter wth condtonal response recalculaton n DS-SS/PSK system s consdered n ths paper. Ths paper also consders the nfluence of flter length on the system performance. It was shown that wdeband nterference s best rejected wth short flter, and longer flters are the most approprate for narrowband nterferences. CRR-ATF has much better performances than ATF, especally n case of hgh nterference power. Performances of CRR-ATF are also better n case of wdeband nterference. References [] L L.., lsten L. B.: Rejecton of narrow-band nterference n PN spread-spectrum systems usng transversal flters, IEEE Trans. on Commun., vol. CO -3, pp , ay 982. [2] Ansar A.: Performance study of maxmum lkelhood recevers and transversal flters for the detecton of drect-sequence spread-spectrum sgnal n narrow-band nterference, IEEE Trans. on Commun., vol. 42, No 2/3/4, pp , Feb/ arch/ Aprl 994. [3] L L.., lsten L. B.: Rejecton of pulsed cw nterference n PN spread spectrum sgnals usng complex adaptve flters, IEEE Trans. on Commun., vol. CO - 3, pp. - 2, January 983. [4] S. Glsć, Z. Nkolć, D. Pokrajac, P. Leppanen: Performance Enhancement of DS Spread Spectrum Systems: Two Dmensonal Interference Suppresson, IEEE Trans. Commun., October 999, No., pp [5] S. Glsć, Z. Nkolć, B. Dmtrjevć, G. Woodward: ultlayer LS Interference Suppresson Algorthms for CDA Wreless Networks, IEEE Trans. Commun., Vol. 48, No. 8, August 2, pp [6] Z. Nkolć, B. Dmtrjevć, N. losevć: Rejecton of PSK nterference n DS-SS/ QPSK system usng complex adaptve flter and non-lnear correlaton recever, Electroncs Letters, vol. 33, No 7, arch 997. [7] Z. Nkolć, B. Dmtrjevć, N. losevć, \. Paunovć: Constant odulus Interference Rejecton at DSSS/QPSK Transmsson System, Electroncs Letters, vol. 33, No 7, arch 2. [8] S. Glšć, Z. Nkolć, B. Dmtrjevć: Adaptve Self Reconfgurable Interference Suppresson Schemes for CDA Wreless Networks, IEEE Trans. Commun., Vol. 47, No. 4, Aprl 999, pp

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