Journal of Asian Scientific Research CONTROLLING THE PERFORMANCE OF MDPSK IN BAD SCATTERING CHANNELS

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Journal of Asian Sintifi Rsarh journal hompag: http://assb.om/journal-dtail.php?

MDPSK shm. This mthod rdus th numbr of phass hih improvs th prforman of th systm by applying a mathmatial mthod from th ombinatorial thory alld Baland Inomplt Blok Dsign BIB-dsign.

1 Journal of Asian Sintifi Rsarh journal hompag: CONTROLLING THE PERFORMANCE OF MDPSK IN BAD SCATTERING CHANNELS Arafat Zaidan 1 Basim Alsayid 2 ABSTRACT This papr dsribs a modifiation of th onvntional M-ary Diffrntial Phas Shift Kying MDPSK shm. This mthod rdus th numbr of phass hih improvs th prforman of th systm by applying a mathmatial mthod from th ombinatorial thory alld Baland Inomplt Blok Dsign BIB-dsign. It is a oding modulation thniqu in hih th signal is rprsntd by a st of phass sltd and ontrolld by th nodr. Eah blok is transmittd srially or in paralll ith qual nrgy. Ky Words: MDBSK; Nakagami-m; Bad sattring hannls; BIB-dsign. INTRODUCTION Physial limitations on irlss hannls prsnt a fundamntal thnial hallng to rliabl ommuniations. Bandidth limitations, propagation loss, nois, intrfrn, and multi-path fading mak th irlss hannl a narro pip that dos not radily aommodat rapid flo of data. Transmit divrsity shms us prossing at th transmittr to sprad information aross th antnnas. BIB dsign is a olltion of b bloks, formd by th arrangmnt of v distint lmnts, satisfying th folloing onditions (Bos and Manvl, 1986): ah blok ontains lmnts, ah lmnt ours in r bloks and ah pair of lmnts ours togthr in λ bloks. This arrangmnt of lmnt is alld a BIB dsign ith paramtrs (v, b, r,, λ). Thr ar to basi rlations among ths paramtrs, b vr (1) 1 Collg of Enginring and Thnology Palstin Thnial Univrsity, Palstin 2 Collg of Enginring and Thnology Palstin Thnial Univrsity, Palstin 759

2 v 1 r 1 (2) Th numbr of bloks and th numbr of rptitions of a partiular lmnt ar givn by v v 1 b (3) 1 v 1 r (4) 1 A spial as of BIB dsign hn λ = 1, it is alld Stinr systms, v k S,, hr k is th numbr of bits pr symbol. Only som valus of v and ar possibl to insur intgr numbrs of b and r hr v must b v mod 1 (5) Th BIB-MDPSK is an arrangmnt of v phass into b avforms, ah avform ontains distint phass. Evry singl phas in a avform an b usd in th transmission of r diffrnt avforms, and vry pair of phass ours in λ avforms. (Bos and Manvl, 1984), Tabl 1 shos th admissibl valus of v for diffrnt, rquird to rprsnt M= 2 k avforms for BIB- MDPSK. A omparison btn ths valus to ths rquird by onvntional MDPSK modulation is illustratd. (Mobbaidn, 2000) From this tabl, it is lar that BIB-MDPSK hav som advantags rathr than MDPSK suh as th lor numbr of phass v than M hih ill improv th BER. Also, inrasing th distan btn th lmnts ill also mak good improvmnts. Tabl - 1. Th valus of v for =3, 4, 5 to rprsnt M = 2 k. 3 v k S 4 v, k S v, k S, 5 MDPSK k v b v b v b M This papr studis th prforman and dtrmin th advantags and limitations of divrsity applid to a modulation/oding shm using MDPSK signals. This modulation/oding shm is rfrrd to as BIB-MDPSK, and is implmntd basd on baland inomplt blok dsign (BIBdsign) from ombinatorial thory. It is ptd to gain por ffiiny hn omparing th BIB-MDPSK to th onvntional MDPSK ithout inrasing th omplity of th systm. Th 760

3 papr is organizd as follos: in Stion 2, prsnt th systm modl. Th probability of rror is introdud in Stion 3, and th hannl modl is prsntd in Stion 4, thn th numrial rsults ar ompard ith onvntional MDPSK and prsntd in Stion 5. Finally, Stion 6 prsnts th onlusions of our study. SYSTEM MODEL Figur- 1. Blok diagram of BIB-MDPSK transmittr Data Blok B i i t Sltor S v, k v-dpsk Figur 1 shos th transmittr blok diagram. Th transmittr slts, aording to th input data, a S v, k. Thn, th v-dpsk modulator divids qually its nrgy into blok of lmnts from th th signal orrsponding to th lmnts forming th sltd blok, transmitting a signal onsists of phass, ah of thm orrsponds to a rtain lmnt of th input blok. (Atkin and Corrals, 1989) Th transmittd output signal i t is i t ui t kt hr: Th signal k k1 j2ft (6) Ts - T (7) - is th numbr of phass to rprsnt th i th signal. - f is th arrir frquny - u is th k th phas transmittd in th i th signal i k i t is to b snd ovr multi-path frquny non-sltiv Nakagami-m fading hannls ith impuls rspons. j (8) Th rivd signal for th L hannl is r l t ui t kt hr i k l k k1 j l j2ft l zi k, l (9) z, is th AWGN assoiatd ith th k th phas on th i th signal ovr th l th hannl. Th rivr ill onsist of L branhs, ah of thm onsists of a mathd filtr (mathd to f ) and a diffrntial dttor. Aftr that, all th branhs ar summd, bfor insrtd to a phas dttor to gt th stimatd transmittd blok Bˆ i thn, th blok dsign dodr rovrs th data 761

4 j ft 2 j ft T 2 j ft T 2 stram bak. Th blok diagram of th transmittd MDPSK basd on BIB dsign rivr is shon in Fig. 2 Figur -2. Blok diagram of BIB-MDPSK rivr Corrlator T. 0 dt T T T s Data Corrlator2 Phas BIB CorrlatorL PROBABILITY OF EROR Probability of rror alulations To insur that th signal is orrt, all th phass in th blok must b orrt, so, (Papoulis, 2002) P P i orrt isorrt isorrt (10) i1 s i2 i Th probability that is orrt is: P is orrt P is transmitt d (11) substituting quation (11) in quation (10), hav P P i1 i1 i1 i2 i2 i2 i i i (12) baus all th disions ar indpndnt, an rit quation (12) as: i1 i1 i1 P P (13) Th probability of rror is Th probability that on hip of th blok is in rror an b tratd as th ordinary probability of rror alulation for th onvntional MDPSK givn in quation (14) P v r, b Pr i Ri o (14) W K i1 762

5 FADING CHANNEL MODEL Whn transmit a signal ovr a radio hannl, it travls ovr multi-path hannls. Eah path is a tim varying random pross. Th larg numbr of paths mak it possibl to rprsnt th hannl impuls rspons as a ompl valud Gaussian random pross aording to th ntral limit thorm. If th impuls rspons has zro man, th nvlop of th hannl rspons at any tim has a Rayligh probability dnsity funtion (PDF) and a uniformly distributd phas ovr th intrval 0,2 (Proakis, 1995). But if th impuls rspons in no longr ith zro man, Nakagami-m distribution is prsntd as a statistial modl for th nvlop of th hannl rspons. Th PDF of Nakagami-m is (Proakis, 1995). 2 2 / 2 1 m f m, 0 (15) m hr: is th absolut valu of th impuls rspons. is th man squar of. is th gamma funtion m 0.5 is th fading paramtr Nakagami-m distribution is th most gnral as that fits th pratial masurmnts of th nvlop of th hannl impuls rspons. Spial ass of Nakagami-m distribution is hn m = 0.5 and m = 1 hih rprsnt a on-sidd Gaussian distribution and Rayligh distribution rsptivly. Also, undr rtain onditions, Riian and log-normal distributions may b obtaind from Nakagami-m distribution. RESULT AND DISCUSSION Figur 2 shos th mirostrutur of SS440C stl in (a) as-rivd and (b) as-qunhd stl. Th as-rivd sampl had bn tratd through th annaling pross at 1040 o C. This tratmnt rsults in th formation of frrit matri and arbid partils. In this stion, W ll sho that BIBvDPSK has som improvmnts ompard ith th onvntional MDPSK. Whn using K s = 10, hav 1024 phass pr symbol in onvntional MDPSK and 79, 112 and 145 phass in BIB-MDPSK for = 3, 4 and 5 rsptivly. So, pt improvmnt baus thr ar rdution in phas numbrs. Thr ar many fators that afft th prforman of th systm hn transmitting in a irlss hannl. In as of Nakagami-m hannl, th fading fator m is on of th most fftiv fators. In Fig. 3, a omparison btn MDPSk and BIB-vDPSK has bn shon for diffrnt valus of fading paramtr. It is lar that all of th BIB dsign ass ar muh bttr than MDPSK spially hn = 3. This is baus th systm ill trat th BIB dsign modl as a 79-DPSK instad of 1024-DPSK. 763

6 Figur- 3. BIB-vDPSK vs. MDPSK for diffrnt fadings. In Fig. 4, did th sam plotting but for diffrnt divrsity lvls of th multi-path hannl. W tstd th systm for a singl bath and 3 paths. It has bn shon th divrsity gav nhanmnt in th bhavior, and BIB-vDPSK still bttr that MDPSK. Figur -4. BIB-vDPSK vs. MDPSK for diffrnt divrsitis Th sam thing is don in Fig. 5, but for diffrnt orrlation valus. Corrlation fator givs an ida about th multi-path hannls to kno ho muh th diffrnt paths ar orrlatd to ah othr. Corrlation valus ar th lmnt for th ovarian matri of th hannl. Figur- 5. BIB-vDPSK vs. MDPSK for diffrnt orrlations. 764

7 CONCLUSION Baland inomplt blok dsign is studid and applid to th MDPSK modulation to form an important modulation/oding thniqu, hih improv th prforman of th MDPSK modulation by rduing th bit rror rat by rduing th numbr of transmittd phass. This modulation/oding thniqu hav bn studid ovr Nakagami-m fading hannls, and its prforman is bttr than th onvntional MDPSK ith lss omplity. ACKNOLEDGMENT Authors ould lik to thank Palstin Thnial Univrsity for sponsoring this ork. REFERENCES Atkin, G. and H. Corrals, An ffiint modulation/oding shm for mfsk systm on bandidth onstraind hannls. IEEE J. on Sltd Aras in Comm., 17(9). Bos, R. and B. Manvl, Combinatorial thory. N York: John Willy and Sons. Bos, R. and B. Manvl, Introdution to ombinatorial thory. N York: John Willy and Sons. Mobbaidn, A., Combind oding modulation shm for multipl arrir phas shift kying signals: Prforman valuation and appliations. Jordan Univ. for Sin and Th. Papoulis, A., Probability, random variabls and stohasti prosss. Mgra hill. 4 Edn. Proakis, J., Digital ommuniations. Mgra hill. 3 Edn. 765

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