Correlation effects of frequency hopping diversity systems in indoor mobile communications environments

CORRELATION EFFECTS OF FREQUENCY HOPPING DIVERSITY SYSTEMS IN INDOOR MOBILE COMMUNICATIONS ENVIRONMENTS R.AGUSTI and P.DIAZ Depa men o Signal Theo y and Communica ions Uni e si a Poli&nica de Ca alunya Absuac - F equency-Hopping (FH) echniques in conjunc ion wi h coding ha e been p oposed o indoo adio sys ems based on he ac ha FH beha es as an in insic equency di e si y echnique. In his pape we assess he pe o mance o a FH-BPSK o o he si ua ions no p e iously conside ed in he li e a u e. In pa icula , he e ec s o ha ing a non-null co ela ion coe iiien in unc ion o he equency sepa a ion as well as he p esence o coding schemes ha e been conside ed. 1. INTRODUCTION The pe o mance o an indoo mobile adio sys em ope a ing in he UHF band is se e ely a ec ed by he mul ipa h p opaga ion medium. To coun e ac he e ec s o he ading one can eso o coding, di e si y o combined coding/di e si y schemes. The mo e ecen s anda d sys ems o mobile communica ions use in some ex en combined coding/di e si y schemes by means o he F equency Hopping (FH) echniques in o de o ake ad an age o he in insic equency di e si y ha he FH enable. In his pape , we analyze he pe o mance o a speci ically FH o ien ed sys em p oposed o be used in indoo communica ions. In pa icula , we ha e analyzed he sensibili y o his sys em wi h espec o he hopping equency sepa a ion. SI. The men ioned scheme is a TDMA cyclical slow FH sys em p opxed in [l] o indoo applica ions and simila o he GSM scheme. To ake ull ad an age o i s in insic equency di e si y, FH has o be used in conjunc ion wi h coding and in e lea ing echniques. In his sense besides he Reed-Solomon (6.2) coding e ained in [I] a Repe i ion coding wi h he same edundancy has also been in oduced. In o de o assess he pe o mance o his scheme we ha e conside ed a disc e e model wi h a Powe Delay P o ile modeled as a double Poisson P ocess [2] ha allows us o analyze any ansmission a e. 2. SIGNALING FORMAT In o de o ob ain some ep esen a i e esul s o he e ccLq o bo h he hopping equency sepa a ion and he coding u.scd in he sys em pe o mance, a signaling o ma as p oposed in [ 11 has been e ained. Fo his pu pose da a packe s a e o med acco ding o he ollowing s eps: 1- Da a en e ing a 64 Kb/s a e collec ed as a 384 bi block 6 ms. long 118 shown in Table 1. Table 1. 2- A a e 1/3: R46.2) o Repe i ion code is o med gi ing a 384 symbol block 6 ns. long. 3- Ihe symbols a e s o ed in o a bu e in succesi e columns and ead ou in ows as shown in Table 2. Table 2. 4- P eamble, sync wo d and spa e ime a e added o each ow gi ing a slo 1 ms. long as shown in Table 3. To make use o he FH in insic di e si y in he sense ha some equency channels a e be= han o he s in e ms o he ecei ed powe and/o dis o ion. he 6 o med slo s a e inally modula ed acco ding o 6 assigned hopping eouencies. 192 8 I Table 3. 5- The ml TDMA FH o ma esul s om sha ing each 1 ms. ame du a ion among n use s. The esul ing ai bi a e is hen Rkn.256 KWs. 3. SYSTEM ANALYSIS Each onc o he 6 ca ie s abo e men ioned is used o CH29645/91/0000-0712$01.00 01991 IEEE 712 pe o m a BPSK modula ion. Then, wi h espec o he ansmission poin o iew, he base band model sys em is simply o mcd by a cascade o a ansmi lc il e , he mobile channel and hc ccci c ille , so ha , he o e all impulse esponse complex en elope in absence o channel dis o ion is a aisedcosine wi h a 0.5 Roll-o pa ame e equally spli ed be ween ansmi e and ecei e . The complex en elope o he channel impulse esponse, hN( ). is modcled acco ding o 121 as whc c bk,, and Elk,, a e Rayleigh and uni o mly dis ibu ed espec i ely. Fu he mo e, in his model he ecei ed signal ays a i e in clus e s, so ha , he a i al imes o he ays wi hin he clus e , Tk,i, and he clus e s hemsel es, Ti,a e bo h dis ibu ed acco ding wo Poisson a i al p ocesses wi h pa ame e s h and A espec i ely. The modcl pa ame c s a e =6om. y=2(k s 1 1 1 Mean Time Bnween Rays:-=Sns (2) Mean lime Be ween C1u e s:- =3QQm In he abo e FH-BPSK sys em he hopping- equency sepa a jon be ween he di e en ca ie s dc c mine he deg ee o co ela ion ha he six coded symbols cn e ing he decode p esen . Fu hc mo e, he symbol e o p obabili y a he inpu o he decode is posi ion dependen due o he ac ha each g oup o h ee bi s ha make up a symbol is ansmi ed h ough a di c cn i- h equency channel cha ac e ized by a di e en complex en elope impulse csponse h,( )=hl( )el p02x i S,O (3) whe e h,( ) is a sample o h( ), S, is he hopping- cquency sepa a ion and i a ies om 1 o 6. To obuin hc BER a he ou pu o he decode , he Bl:R ;i dic ou pu o hc BPSK dc cc o is li s cqui c l. Fo Ihis pu posc a combina ion o analy ical and Mon e Ca lo simula ion echniques ha c bccn cn isagcd acco ding o he ollowing wo s eps p ocedu e: 1. A sample o h( ), deno ed h,( ), is gene a ed acco ding o i s s a is ical p ope ies. Only ays wi h ampli udes g ea e han 0.01 mul iplied by he ampli ude co esponding o he i s ay a e aken in o accoun . Conside ing ays wi h g ea e ampli udes hey do no1 change he esul s signi ican ly. A squa ing iming loop is used o clock cco c y. The sampling ins an is [3] (4) A loop ha elimina es he c oss- alk is adop ed o ca ie eco e y. Then [4] A as bi e o a e, deno ed he e ~b,~,~. compu a ion me hod is hen used o each i- h equency channel. In he simple case ha la ading had been assumed, ha is 11 R =-e- ’ Tb OS whe e R, deno es he da a bi a e. The bi e o a e co esponding o he i- h equency channcl o he m- h impulse esponse sample would hen be (7) 713 2-The bi e o a e,pb,m, a he decode ou pii , co esponding o he m- h sample, is calcula ed om he symbol e o p obabili y a he decode inpu gi cn by This is shown in he ollowing o bo h Reed-Solomon coding and Repe i ion coding. 3.1. REED-SOLOMON CODING The em p obabili y o he decoded symbols o a gi en h,( ) sample is 6 6 6 6 (9 ) I.1 66 I k I4 The pb,,, can be ob ained as [SI 1 -Pe,mn iPb, P,, 2 I In o de o ob ain nume ical esul s, he uppe bound o he h,,, has been e ained. 3.2. REPETITION CODING Inpu X,,X2 Le he inpu and he ou pu o he decode be ou p~~:~,,~.x,~,,~,x~ Then, we ha e pb=,pEm 1 3- The inal BER esul s om a e aging Pb,,, o a g ea numbe o h,,,( ) samples. In he abo e calcula ions he signal o noise a io in he ecei e inpu depends on he m- h channel impulse esponse pa ame e s. Tha is, gi en he complex en elope o he ansmi ed signal as whe e cn=+l o -1 and hd ) is he ansmi e impulse esponse, i can be shown ha equal o m Mhz., 10 MHz.,~ MHz. and 2.5 Mb. ha e been conside ed. The co esponding BER o hese cases a e displayed in Figu es 1,2,3,4 espec i ely. I can be no iced ha no signi ican a ia ions appea when compa ing SF- and S,=lO MHz. So inc easing S, beyond 10 MHz. i is no con enien . Ano he conclusion ha could be also ex ac ed om he obse a ion o he Figu es 2,3 and 4 is ha Reed-Solomon coding ou pe o ms he Repe i ion coding o S,Ds g ea e han 0.05 app oxima ely. Rb alues o 2.56 Mb/s, 5.12 Mb/s and 10.24 Mb/s ha e been also conside ed and simila igu es o hose shown o he 256Kb/s case ha e been ob ained. S, alues g ea e han 10 Mhz a e no conside ed because he changes a e no signi ican . Fo he obse a ion o he esul s ob ained i can be concluded, o all Rb alues, ha Reed-Solomon coding ou pe o ms he Repe i ion coding o S,Ds g ea e han 0.05 app oxima ely. Wha e e Rb is conside ed, S,.Ds g ea e han abou 0.1 and 0.2 o he R- S and Repe i ion codes espec i ely does no imp o e he sys em pe o mance signi ican ly. This can be be e app ecia ed in Figu es 5 and 6 o 256 Kb/s and 5.12 Mb/s espec i ely. This di e en beha io o bo h codes could be explained because he R-S ecei ed symbols p esen a g ea e co ela ion han he co esponding epe i ion symbols in ol ed in he in e lea ing p ocess. Finally a igu e o me i o he sys em could be gi en by saying ha Ou age Ra es lowe han 0.01 o BER=10-3 seems possible o Rb=5.12h4b/s. In pa icula , in he case o using Repe i ion Coding, i is in e es ing o poin ou ha he ecei e could be implemen ed wi h low powe consump ion echnologies as needed o ealis ic po able ope a ion. AGREEMENTS TIC880543. (14) This wo k has been inanced by Spain CICYT REFERENCES [l] A.A.M. Saleh, A.J.Rus ako, J ., L.J.Cimuni, J ., "A TDMA indoo adio communica ions sys em using cyclical slow equency hopping and coding-expe imen al esul s and implemen a ion issues", Globecom 88. [2] A.A.M. Saleh, R.A. Valenzuela, "A s a is ical modcl o indoo mul ipa h p opaga ion", IEEE SAC, Feb ua y whc c E, is he bi enc gy a he ecei ed inpu and U( ) is he s ep unc ion. The ou age p obabili y o g ea in e es in quasi-s a ic indoo en i onmen s is also e alua ed o he wo coding schemes. I is gi en by Ou age P ob&li y=P ob.[BER BER J (15) whe e BER, is a h eshold bi e o a e. 4. RESULTS Some esul s ha e been ob ained in o de o de ine a p ope design alue o S, as well as o assess he coding sys em pe o mance o inc easing Rb alues, in he p esence o bo h R-S(6,2) and Repe i ion coding. A i s , Rb=256 Kb/s has been e ained and S, alues 1987. [3] J.C-I Chuang, " he e ec s o mul ipa h delay sp ead on iming eco e y", IEEE T ans. on Vehicula Technology, Augus 1987. [4] S.Mo idi, H.Sa i, "Analysis o decision- eedback ca ie eco e y loops wi h applica ion o 16 QAM digi al adio sys ems", ICC 1983. [5] D. To ie i, "The in o ma ion bi a e. o block codes", IEEE T ans. on Comm.. Ap il 1984. 714 I I4 n I1 m EblNa Figu e 1. BER o Rb=256Kb/s and S~2.5Mhz Rb=5.12Hbps Eb/No=lSdB In-' L , - -.- -. ' .-:_ - ' :. .. : . .- '._ .. I lg-l -. .. .:*. ......... .A.. _.A.. ...... .:. ........ ......... .'"'... ............ w b- U 0: B 6 ; m Eblk Figu e 2. BER o Rb=256Kb/s and S,=5Mhz Eblk Figu e 3. BER o Rb=256Kb/s and S,=lOMhz 71 5 .. :....:..:. ..... : ....... : 3 : 'p --no * ... -- qdi i code 0 5 10 .i @i-"[& j I **. .. i ' . .;F . 'A' ' '"A' ' * l . EblNa Figu e 4. BER o Rb=256Kb/s and S in ini y E, m Figu e 5. BER e sus no malized FH sepa a ion o Rb=256Kbls w 6 LI a 0 CL LI w .... ....... S O5 Figu e 6. BER e sus no malized FH sepa a ion o Rb=5.12Mb/s