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BPSK and QPSK Modulation Techniques with Optimum Tree Based Interleaver in Iterative IDMA Systems

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In Interleave-Division Multiple-Access (IDMA) scheme, user specific interleavers are employed as the only means for user separation. It is well established fact that these interleavers must have property of orthogonality amongst each other. The
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  BPSK and QPSK Modulation Techniques with Optimum Tree Based Interleaver inIterative IDMA Systems Sanjiv Mishra Research Scholor Mawar UniversiryChittorgarh, India sanjivpbh@rediffmail.com  .S. !ripathi "ept. of #lectronics $ Comm. #ngg.M.%.%.I.!.&llahabad, Indiavst@mnnit.ac.in  M. Sh'(la, MI###, MIS### "ept. of #lectronics #ngg.).*. !ech. Istit'te+anp'r, Indiamanoj(rsh'(la@ieee.org  Abstract   In Interleave!Division Multiple!Access "IDMA#scheme$ user speci%ic interleavers are employed as the onlymeans %or user separation& It is well esta'lished %act that theseinterleavers must have property o% ortho(onality amon(st eachother& The interleavers are$ there%ore$ re%erred has the heart o% IDMA system& The researchers have proposed various non!ortho(onal interleavers in the literature which are easy to(enerate and have near!)ero collision property& The Tree BasedInterleaver "TBI# is one o% those non!ortho(onal interleaverswhich not only reduces the 'andwidth requirement incomparison to that required in case o% *andom Interleavers"*I# 'ut also reduces computational comple+ity drasticallywhen compared with that o% master random interleavers& Thememory requirement at receiver end and its cost pro'lem arealso solved 'y tree 'ased interleaver with %urther reduction o% the amount o% in%ormation e+chan(e 'etween mo'ile stationsand 'ase stations required to speci%y the user!speci%icinterleavers& In this paper$ the per%ormance analysis o% iterative IDMA receivers have 'een evaluated with BPSK ,QPSK modulation techniques employin( tree 'asedinterleavers and random interleavers$ as representative o% non!ortho(onal interleaver$ in uncoded and rate - covolutionallycoded conditions with Additive .hite /aussian 0oise "A./0#channel& In the simulation results$ the IDMA system withQPSK modulation techniques employin( TBI outper%orms the*andom Interleavers optimally&  Keywords-Tree Based interleaver; Random Interleaver; Multiuser Detection, AWG !"annel, IDMA receiver; B#R;modulation tec"ni$ues% I. I  %!R"UC!I%  In -/, the researchers have demonstrated that Interleaversmay be employed as the only means for 'ser separation initerative interleave0division m'ltiple0access 1I"M&2systems. I"M& system inherits many advantages fromC"M& systems, incl'ding diversity against fading andmitigation of the worst0 case other0 cell 'ser interference problem. 3'rthermore, it allows a very simple chip by chipiterative MU" strategy. !he normali4ed M'lti0'ser "etection 1MU"2 cost 1per 'ser2 is independent of then'mber of 'sers while in case of C"M& systems, the MU"cost is solely dependent on 'ser co'nt. n the other hand, the power cons'mption of C"M& systems is also 'ser dependent. In -/, researchers have presented an I"M& systemwhich employs randomly and independently generatedinterleavers. 5ith randomly generated interleavers, theI"M& system in -/ performs similarly and even better thana comparable C"M& system. If this is the case, the basestation 1*S2 has to 'se a considerable amo'nt of memory tostore these interleavers, which may ca'se serio's concern incase of large 'ser co'nt. &lso, d'ring the initial lin( setting0'p phase d'ring start of transmission, there sho'ld bemessages passing between the *S and mobile stations 1MSs2to inform each other abo't their interleavers. If theinterleavers 'sed by the *S and MSs are long and randomlygenerated, e6tra bandwidth reso'rce will be cons'med for this p'rpose.!he researchers have s'ggested sol'tion of high memoryre7'irement in -8/. In this paper, the 'ser specificinterleavers are generated by master random interleaver method, b't the comp'tational comple6ity re7'ired togenerate the interleaving se7'ence is increased e6tensively,and it is 'ser dependent in spite of adopting some specialarrangements -8/. &t the receiver section, fre7'entinterleaving and deinterleaving is re7'ired d'ring the processof iterative decoding in t'rbo processor. !herefore, largeamo'nt of calc'lations are re7'ired in receiver section andhence, the comp'tational comple6ity is increased drasticallywith high 'ser co'nt. In -9/, M. Sh'(la et al proposed !ree *ased Interleaver 1!*I2 to alleviate the concerns related to bandwidth andmemory re7'irements in addition to problem of comp'tational comple6ity optimally. !he !*I re7'irese6tremely less bandwidth and memory devices whencompared with power interleaver -8/ and cons'mesmarginally higher bandwidth to that of random interleavers.n the other hand, it merits very less comp'tationalcomple6ity when compared to power interleavers.!he paper is organi4ed as follows. Section II presents anintrod'ction of the iterative I"M& comm'nication system.Section III contains importance of digital mod'lationschemes with special foc's on :;S+ scheme. Section I presents sim'lation res'lts of I"M& systems with the !ree  *ased Interleaver 1!*I2 and random interleaver 1RI2 'sing*;S+ and :;S+ signaling. Section  concl'des the paper.II.I !#R&!I#  I"M& S <S!#M &n iterative I"M& system -/, is shown in 3ig're , for +    sim'ltaneo's 'sers with a single path channel. !he 'pper  part in the fig'reshows the transmitter, with %0length   inp'tdata se7'ence   from 'ser ( is d  (  = -d (   12, >>>, d  (   1i2 , >d (   1%2 / !  and is encoded 'sing low rate code C   into c (  = -c  (  12, >>>, c  (   1j2 , > c (   1?2 / !  , where ? is denoted as theChip length and coded bits are chips following theconvention of C"M& systems. In encoder0spreader bloc(, the code C is constr'cted byserially concatenating a forward error correction 13#C2 codeand repletion code of length0  sl  . !he 3#C code 'sed here ismemory08 rate08 convol'tional coder and repetition codewith spread length of A. 3'rther, the chips c (   are interleaved by a chip levelinterleaver B (  D, prod'cing a transmitted chip se7'ence as6 (  = -6  (   12, >>,6 (   1j2 , > 6 (   1?2 / !  . &fter transmittingthro'gh the &5E% channel, the bits are observed at thereceiver side as r = -r   ( 12> r (   1j2 > r   (   1?2 / ! . !he Channelopted for sim'lation p'rpose may be changed depending onthe environment. In the iterative receiver section, after chip matchedfiltering, the received signal form the  K 'sers can be writtenas . 1 2 1 2 1 2,  K k k k  r j h x j n j = = + ∑  j = , 8> ? >>... 12where k  h  is the channel coefficient for 'ser0( and Fn 1j2G aresamples of an &5E% process with 4ero mean and variance, 8H  @8  N  σ    = . &ss'ming that the channel coefficient F  k  h Gare (nown a priori at the receiver.  3ig're . !ransmitter and Receiver str'ct'res of I"M& scheme with  K  sim'ltaneo's 'sers !he receiver consisting of the primary signal estimator 1;S#2 and + single 'ser a posteriori probability 1&;;2decoders 1"#Cs2, the data is iterated for pre0decided n'mber iterations before finally ta(ing hard decision on it. !hemod'lation techni7'es 'sed for sim'lation are binary phaseshift (eying 1*;S+2 and 7'adrat're phase shift (eying1:;S+2 signaling. !he o'tp'ts of the ;S# and "#Cs aree6trinsic log0li(elihood ratios 1Rs2 abo't F6 (  G defined as ( )  1 J 1 22 .1 2 log , ,1 J 1 22 . k k k   p y x je x j K j p y x j   = += ∀ ÷= −   >>>>.. 182!hose Rs are f'rther disting'ished by s'bscripts, i.e., ( ) 1 2  PSE k  e x j  and  ( ) 1 2  DEC k  e x j , depending on whether they are generated by the ;S# or "#Cs. 3or the ;S# section,  y in 182 denotes the received channel o'tp't while for the"#Cs,  y in 182 is formed by the deinterleaved version of theo'tp'ts of the primary signal estimator 1;S#2 bloc(. & globalt'rbo type iterative process is then applied to process theRs generated by the ;S# and "#Cs bloc(s -/.   "'e to the 'se of random interleaver F  k  π  G, the ;S#operation can be carried o't in a chip0by0chip manner, withonly one sample ( ) r j  'sed at a time. 1 2 1 2 1 2 k k k  r j h x j j ξ  = +  >>>>>>>>> 1925here 1 2 k   j ξ   is the distortion 1incl'ding interference0 pl's0noise2 in ( ) r j  with respect to 'ser0(. 3rom the centrallimit theorem, K (  1j2 can be appro6imated as a Ea'ssianvariable, and r(j) can be characteri4ed by a conditionalEa'ssian probability density f'nction.III.M "U&!I%  ! #C)%I:U#S   I%  I"M& S <S!#MS 5e define mod'lation scheme -L/ as an operator on the baseband signal. Mod'lation is one of the most importantsignal processing operations that ta(es place in acomm'nication system. It can be effectively employed tomatch a signal with the channel characteristics, to minimi4ethe effects of channel noise, and to provide the capability tom'ltiple6 many signals, practicability of antennas.In any mod'lation scheme, specific parameter is varied inaccordance with the carrier signal. &lso, the selection of the partic'lar mod'lation method 'sed is determined by theapplication intended as well as by the channel characteristicss'ch as available bandwidth and s'sceptibility of channel tofading. !he researchers have gone thro'gh large variety of mod'lation techni7'es for 'se in mobile radioComm'nications systems with endless efforts.&ccording to norms of IM! 8HHH, the prime objective of f't're re7'irements of wireless comm'nication is to providehigh data rate and high spectral efficiency with optim'm*#R at those channels which are s'bjected to M'ltipathRayleigh 3ading and &dditive 5hite Ea'ssian %oise1&5E%2 depending on environment. In this paper, I"M& system with coherent *;S+ $:;S+ mod'lation schemes has been st'died. In *;S+ scheme, the binary symbols $ H differ only in a relative phase shift of H degrees. Coherent *;S+ system istherefore characteri4ed by having a signal space that is onedimensional, with a signal constellation consisting of twomessage points.  In :;S+ scheme, the fo'r symbols are generated for every co'ple of inp't bits hence it is (nown as bandwidth0conserving mod'lation scheme. Similar to *;S+ scheme,the :;S+ scheme also carries information in terms of the phase variations. In partic'lar, the phase ta(es on one of fo'r e7'ally spaced val'es s'ch as NL, 9NL, ONL, PNL, whereeach val'e of phase corresponds to a 'ni7'e pair of message bits. &ccordingly, a :;S+ signal, has two0dimensionalsignal constellation and fo'r message points, M=L, whose phase angles increase in co'ntercloc(wise direction.If special characteristics of :;S+ are to be mentioned,we 7'ote that for the same #b%o, a :;S+ system transmitsthe information at twice the bit rate of *;S+ for the samechannel bandwidth, and :;S+ provides twice the spectralefficiency, compared to that of *;S+ with the same energyefficiency. In other words for a prescribed performance,:;S+ 'ses channel bandwidth better than *;S+, 3or thesame bit rate :;S+ 'ses only half the channel bandwidth,for the same bit rate, #b%o and channel bandwidth, the performance is based on *it #rror Rate of :;S+$ *;S+ system 'sing M&!&* P. sim'lation 'nder &5E%channel.!he mapping r'le for :;S+ 'sed   in the sim'lations isgiven as followsQ1 H2 = 10j21H H2 = 100j21H 2 = 10j21 2 = 1j2I.% UM#RIC&  R  #SU!S "'ring sim'lation, some ass'mptions have been made. Itis ass'med that every 'ser is having same dat length andsimilar coding scheme. &ss'ming I"M& system with *;S+ $ :;S+ signaling schemes in single path &5E% channels,with 'ne7'al power allocation scheme -P,/, we employRandom Interleaver 1RI2 and !ree *ased Interleaver 1!*I2mechanisms for 'ser separation p'rpose d'ring sim'lation.!he reason for selection of RI mechanism lies with the factrelated to better probability of orthogonality amongst 'ser specific interleavers -/.!he !*I mechanism cons'mes e6tremely less memoryfor storing 'ser0specific interleavers when compared to that pf RI mechanism, however Master Random Interleaver 1MRI2 mechanism -8/ re7'ires similar memory re7'irement.In fig're 8, the memory re7'irement has been sim'lated for HH 'ser co'nt with all the three interleavers and sim'lationres'lts confirm the optimality of !*I mechanism -O/.&t first, the 'ncoded I"M& has been consideredemploying tree based interleavers. Sim'lation has been performed ta(ing parameters as data length O8, spreading asrepetition code of length A, iteration n'mbers O. 3romfig're 9, it is evident that :;S+ techni7'e has better *#R  performance as compared to that of *;S+ techni7'e for vario's n'mber of 'sers n=,L,,A,98,AL. It is also observedthat above 98 n'mber of 'sers :;S+ and *;S+ has almostsame *#R performance, with difference that :;S+ improves its *#R performance at lower #b%o. 010203040506070809010000.511.522.533.544.55x 10 6 User Number  M e m o r y R e q u i r e m e n t o f I n t e r l e a v e r ( N o . o f b i t s r e q u i r e d / u s e r )  With Random InterleaverWith Master Random InterleaverWith Tree Based Interleaver 3ig're 8. Comparison of RI, MRI, and !*I for memory re7'irement -O/ 4 6 8 1010 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Eb/No  B i t E r r o r R a t e  QPSKQPSK BPSK 3ig're 9. Sim'lation of 'ncoded I"M& 'sing !*I with *;S+ $ :;S+ for variation in 'ser co'nt. .C %CUSI%S In this paper, the I"M& system has been eval'ated on the basis of bit error rate 1*#R2 with *;S+ $ :;S+ Tmod'lation techni7'es with random interleaver and tree based interleaver in 'ncoded and rate  convol'tionallycoded environments. !he sim'lation res'lts have beencompared with variation in 'ser co'nt, variation in datalength and for different val'es of #b%o. 3rom thesim'lations, it can be concl'ded that 'ncoded and codedI"M& system with random interleaver and tree based  interleaver has better *#R performance with :;S+ mod'lation in comparison to that of I"M& with *;S+ mod'lation.It is also demonstrated that tree based interleaver hasalmost similar *#R performance as of random interleaver,however tree based interleaver o'tperforms the randominterleavers in terms of memory and bandwidth re7'irement problems -9/. !he tree based interleaver is also reported to perform better than master random interleaver in terms of comp'tational comple6ity -9/. !herefore it can be concl'dedthat tree based interleaver 'sing :;S+ mod'lation canreplace random interleaver 'sing *;S+ or :;S+ mod'lation.It has also been observed that for larger n'mber of 'sers1more than LH2 :;S+ mod'lation has same *#R  performance as that of *;S+ mod'lation scheme however on the front of bandwidth conservation, :;S+ schemealways demonstrate its 'pper edge on *;S+ schemeregardless of the m'ltiple access scheme employed for the p'rpose of comm'nication.R  #3#R#%C#S-/i ping, ihai i', +eying 5' and 5. +. e'ng, VInterleave0"ivisionM'ltiple0&ccess,W I### !rans. 5ireless Comm'n., vol. O, pp. 90LP, &pril 8HHA. -8/ ). 5', . ;ing and &. ;erotti, VUser0specific chip0level interleaver design for I"M& systems,W I### #lec. ett., vol. L8, no. L, 3eb.8HHA. -9/M. Sh'(la, .+. Srivastava, S. !iwari 1 &nalysis and "esign of !ree*ased Interleaver for M'lti'ser Receivers in I"M& Scheme $2 A th I### International Conference on %etwor(s VIC% 8HHW, "elhi,India, pp. 0L, "ec. 90L, 8HH. -L/!heodore S. Rappaport, V5ireless Comm'nicationW, ;)I, pp. 8O0LH,LLP0LAH, 8HHP. -O/M. Sh'(la, .+. Srivastava, S. !iwari, V&nalysis and "esign of ptim'm Interleaver for Iterative Receivers in I"M& SchemeW,5iley ?o'rnal of 5ireless Comm'nication and Mobile Comp'ting,ol.  1H2, pp. 9809P, 8HH.-A/M. Sh'(la, .+. Srivastava, S. !iwari  1 Interleave "ivision M'ltiple&ccess for 5ireless Comm'nication $2  XInternational Conference on %e6t Eeneration Comm'nication SystemsQ & ;erspectiveD,VIC%E#%CM HA 2 , ?.+. Instit'te, &llahabad, India, pp. OH0OL $ "ec 0, 8HHA.-P/M. Sh'(la, R.C.S. Cha'han, R'chir E'pta, .+. Srivastava, S. !iwari 1 ;erformance &nalysis of !ree *ased Interleaver with IterativeI"M& Receivers 'sing ptim'm ;ower &llocation &lgorithm $2  3irstU+0India I### International 5or(shop on Cognitive 5irelessSystems held in II!, "elhi, India, "ec. 08, 8HH.-/M. Sh'(la, .+. Srivastava, S. !iwari V;erformance &nalysis of !ree*ased Interleaver with I"M& Systems 'sing ptim'm ;ower &llocation &lgorithm,W 8nd I### International Conference on#merging !rends in #ngineering $ !echnology VIC#!#!0HW, %agp'r, India, "ec. A0, 8HH.-/M. Sh'(la, &asheesh Sh'(la,, .+. Srivastava, S. !iwari  1 "ifferent"esigning 3actors for I"M& Systems,W  S!  International Conferenceon Comp'ter, Comm'nication, and Control and Information!echnology VC9 I! 8HHW in &cademy of !echnology, Calc'tta, India, pp. PL0POA, 3eb. A0P, 8HH.
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