Drect Sequence Spread Spectrum (DSSS) DS-SS DS-SS uses sequences for spectrum spreadng and phase modulaton Modulaton s bnary SK (BSK) or quaternary SK (QSK) Message BSK - - - - QSK BSK Bt hase Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 8 QSK Bts hase - - - 9-8 7
DS-SS Transmtter Dgtal nformaton m(t) X m(t) c(t) Balanced Modulator m(t) c(t) p(t) c(t) Sequence generator Carrer p(t) m(t) c(t) p(t) X [m(t) c(t) p(t) ]c(t) Low-pass IF Flter Demodulator Informaton detected c(t) Sequence generator ecever Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Carrer p(t) DS-SS eceved sgnal: (T s the propagaton delay between transmtter and recever) s t T m t T c t T eceved sgnal after compresson g t T m t T c t T p t T p t T c t T Snce c(t) s a polar sgnal then c(t) c(t)=+ for any sequence c(t) and any tme hence we obtan g t T m t T pt T At the demodulator output we obtan the message m(t-t) Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons
DS-SS BSK Transmtter Dgtal nformaton m(t) code c(t) m(t) c(t) T b sequence T c sequence c(t) ecever ecovered nformaton g(t) T b dt m(nt) Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons DS-SS BSK Transmtter Dgtal nformaton m(t) m(t) c(t) T b sequence T c T c / Synchronzaton problem n recever sequence c(t) ecever ecovered nformaton g(t) T b dt m(nt) Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 3
DS-SS Informaton Spread spectrum sgnal Interference or jammng eceved sgnal Channel ose ecovered sgnal Interference Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons ose ose nterferers and jammng sgnals are spread snce they do not contan the sequence therefore all of these sgnals are consdered nose rocessng an The processng gan s defned as p B F where s the nformaton bt rate. e can obtan an expresson of S/ at the nput of the system as a functon of the rato of the bt energy and the power spectral densty of the nose E b / as follows S E b E b. B F p Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons The S/ at the nput and output are related by the processng gan.e. S S p. Therefore we can wrte the followng E b S S p. 4
CDMA System erformance FDMA and TDMA are known as dmenson-lmted systems. The dmenson s determned by the number of ndependent avalable channels. If all the channels are busy then no user wll get servce and the system wll be lmted Spread spectrum systems can tolerate some degree of nterference. hen a new user s accepted the nterference n the base staton s ncreased accordng to the receved sgnal power. A CDMA system s lmted by the nterference (nose) that can be tolerated. The nterference can be dmnshed wth codng technques and thus capacty ncreased. Dgtal modulaton schemes have expressons for the Bt Error ate (BE) as a functon of E b /. If the performance of the codng s known one can defne a mnmum rato E b / for approprate functonng of the system. The relaton between the number of moble users M the processng gan and E b / s p M E b / Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sequences 5
Sequences ropertes of sequences eneraton of sequences alsh Functons Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sequences Use of sequences Spectrum spreadng Sgnal dentfcaton of a user to make t dfferent from the others usng the same F bandwdth by means of multple access sequence propertes Determnstc and perodc elatve frequency of zeros and ones s / (Balance) For zeros or ones / of the bursts have length ; /4 of the bursts have length ; /8 have length 3... n general / n of the bursts have length n. (Burst length) Any shftng of a sequence has the same number of agreements and dsagreements wth the orgnal sequence. (Delay and sum) eneraton of sequences s through shft regsters Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 6
Sequences There are several codes that can produce a sequence one s the maxmum length code better known as m-sequence ropertes of m-sequences Determnstc and perodc wth perod m - where m s and nteger Autocorrelaton s bvalued.e. at the orgn and -/( m -) for the remanng. ood property for synchronzaton They have the same burst length dstrbuton.e. bursts wth length between and m- appear for zeros and ones wth two exceptons: there s no burst of zeros wth length m-and there s no burst of ones wth length m- They have m- - zeros and m- ones per perod (Balance) Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons m-sequences Corrmento shft Shft X X X 3 X 4 3 4 5 6 7 8 9 3 4 5 6 Clock Intal state X X X 3 X 4 m=4 then perod s 4 -=5 From the output we have seven zeros and eght ones (Balance) these numbers dffer by one. B urst L en gth O nes Z eros C hp coun t 4 4 3 3 4 4 Modulo- Adder Output sequence: tme Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 7
Autocorrelaton The autocorrelaton s a measure of the smlarty of a sgnal wth copes of tself shfted Contnuous sgnals g(t) Adjustable delay X Integrator g() g(t ) g () g(t) g(t ) dt. Dscrete sgnals Consderng the sequence as polar nfnte and perodc wth perod chps we can represent t as b b b b b b b b where Ebn and Eb n n Consderng that b n =b n+ the autocorrelaton s calculated as follows b (k) b n b n k k n Snce the sequence has n general a perod much larger than the message duraton we use the partal autocorrelaton gven by Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons M M (k) b n b n k M k n Autocorrelaton E M (k) Consder the partal autocorrelaton M (k) b n b n k M k n Assumng ndependence of each chp n the sequence we obtan M Eb n b n k n M M Eb n M k n M Eb n Eb n k k n The mean value of the partal autocorrelaton s zero when the sequences are not algned n tme and t has a maxmum value of M when they are algned. Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 8
Autocorrelaton 5 (k)=5 k= 5 3... Tme algned ormalzng 5 (k)= k= 5 3... Orgnal sequence --- - - - - M=5 chps One chp shft 5 (k)= - k 5 3... Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons ormalzng 5 (k)= -/5 k 5 3... Autocorrelaton. Example wth m=4.8 Bvalued autocorrelaton wth and -/5 Autocorrelacón.6.4. - - 3 4 5 6 7 8 9 3 4 5 6 7 8 9 -. C o rrm en t o en ch p s Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 9
m- Sequence enerator rmtve polynomals generate the m-sequences. A prmtve polynomal (generator) g(x) of degree n contans at least two terms.e. g(x)=x n + s the polynomal wth the mnmum number of terms. Example: Defne g(x)= X 6 + X 4 + where X k s the output of the k-th element of memory of the shft regster hence m=6 and the sequence s Stages=m=6 3 4 5 6 erod= 6 -=63 chps CK If the clock has a frequency of MHz each chp has a duraton of T c = -7 sec. th m=4 stages the perod s = 4 -=.99x chps.e. seg T c.99 5 seg=.545 días Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons roblems Lmted umber of Sequences The number of sequences s lmted by the number of prmtve polynomals that exst. For an m- sequence the generator has degree m. The number of polynomals s p ( m) m m k p p where p s the prme decomposton of m - Correlacón Cruzada..8.6.4. -. -.4 -.6 -.8-9 -8-7 -6-5 -4-3 - - 3 4 5 6 7 8 9 Corrmento en chps Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons m L e n g th u m b e r o f S e q u e n c e s 3 3 7 4 5 5 3 6 6 6 3 6 7 7 8 8 5 5 6 9 5 4 8 3 6 4 7 7 6 4 9 5 9 6 3 8 9 6 3 4 6 3 8 3 7 5 6 5 3 7 6 7 8 6 6 5 5 3 5 4 8 4 8 5 7 5 9 3 7 3 7 4 8 3 8 8 6 3 5 8 4 3 9 3 6 9 3 9 5 3 8 7 5 6 9 7 6 9 6 Cross Correlaton The cross correlaton of two m-sequences s multvalued and t does not have small values. For ths reason m-sequences are not good for user dentfcaton n a CDMA system. The example shows the cross correlaton of two sequences wth m=3. They are: () and ()
old Codes m-sequence 3 m old code 3 m Clock m-sequence The sequence obtaned has a perod of m -. The old codes good propertes of cross correlaton snce t takes three values f the generator sequences are selected correctly (roblem: how to select them) Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sequences roblem: The cross correlaton of m-sequences and the selecton of them to generate old codes make them unsutable for user dentfcaton. Soluton: Orthogonal sequences. Two contnuous functons f (t) y f (t) are orthogonal f they satsfy T f (t) f (t) dt. Two dscrete functons f (n) y f (n) of length are orthogonal f they satsfy f (n) f (n). n Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons
Orthogonal Sequences There are sets of orthogonal bnary functons alsh functons form one of those sets. A alsh functon of length = k where k s an nteger has an equal number of ones and zeros.e. there are k - ones and k - zeros n every orthogonal sequence. The allzeros sequence s ncluded. + - + - + - = 3 =8 chps (n) (n) 3 (n) alsh functons satsfy the orthogonalty property.e. ( n ) ( n) ( n ) 3 ( n) ( n ) 3 ( n). n n n Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Orthogonal Sequences eneraton s by the Hadamard matrces H H H H H H H 4 H H H H In general we have H k H k H k H k H k where the length of the alsh sequence obtaned wth the matrx H k s =k CDMA IS-95 uses the alsh functons generated by H 64.e. 64 chps n length. Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons
alsh Functons Consder the alsh sequences of 8 chps generated by H 8 H 4 H 4 H 4 H 4 Assume that four statons A B C and D are transmttng wth the followng assgned alsh functons Staton alsh Sequence olar Sequence A - + - + - + - + B - - + + - - + + C - + + - - + + - D - - - - + + + + Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons alsh Functons Assume the followng scenaros Informaton Tx. Staton(s) Tx Sequence eceved - - - C S =(- + + - - + + -) - - C+D S =(- - + + ) tme - A+B+C S 3 =(-3 + + + -3 + + +) - - A+B S 4 =(- + - +) - A+B+C S 5 =(- - - +3 - - - +3) Assume that we should receve the nformaton from staton C.e. ( - ) for ths we obtan the nner product of the receved sequences and the alsh functon of staton.e. (- + + - - + + -) and normalzng we get S C 8 S C S 3 C 8 8 S 4 C S 5 C. 8 8 Hence we can recover the nformaton and dentfy our user wth alsh functons roblem: alsh functons do not provde a good spreadng of the spectrum. Soluton: Combne sequences and alsh functons Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 3
Spreadng The spreadng propertes are mproved modulatng the message wth the same sequence as shown User sequence p(t) User (t) (t) Spread sgnal user Spread sgnal user Assume that both users transmt and that we need to recover the nformaton from user then n the recever we need to perform the followng T T T p(t) (t) p(t) (t) p(t) (t)dt p (t) (t) (t)dt (t) (t)dt Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons T (t) (t) dt roblem: Orthogonalty s based when the alsh functons arrve at the same tme Soluton: Synchronze wth sequence Assumptons Uplnk of CDMA Chp rate s fxed for all users s the total bandwdth User can have dfferent transmt power rate and SI requrement User has a QoS requrement E b ath gan for user s Background addtve whte aussan nose wth one sded power spectral densty η Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 4
5 Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sngle Cell Case Sngle Cell Case Assume that users are n a cell At the optmal soluton all QoS constrants are met wth equalty.e. the optmal power vector can be obtaned by solvng the lnear QoS equatons I C j j j Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sngle Cell Case Sngle Cell Case ' ' j j j j j j
6 Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sngle Cell Case Sngle Cell Case A 3 ' 3 ' 3 3 3 ' 3 ' ' Let * be the optmal power vector that solves the matrx equaton Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Sngle Cell Case Sngle Cell Case Subtracton of equaton from equaton - we get The soluton of ths system of equatons s of the form K K K ' where. postve constant. real s some where c K m Cynara u and Dmtr. Bertsekas Dstrbuted ower Control Algorthms for reless etworks IEEE Transactons on Vehcular Technology vol. 5 o. pp. 54 54 March.
Synchronzaton Synchronzaton CDMA synchronzaton s obtaned from one of three means: lobal postonng System (S) Intermedate Frequency (IF) broadcastng system S Internal oscllator f=.57 Hz IF transmtter f=khz CDMA BS Local IF S Oscllator recever recever Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons CDMA BS IF recever S recever Local Oscllator 7
Synchronzaton S: conssts of 4 satelltes 6 orbtal planes equally spaced n the Equator orbtal perods of hours tlt of 55 Km of alttude wth 4 hour avalablty 365 days per year 5 to 9 satelltes are vsble at every nstant S provdes poston speed and tme Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons Synchronzaton by IF Frst de-spread and then demodulate Local oscllator sequence 9 MHz IF sgnal 7 MHz f f Carrer recovery 7 MHz f Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons f 8
Sequence Synchronzaton IF sgnal BF ( ) Correlator >? Yes o sequence / chp adjustment One perod eceved sequence sequence generated at the recever sequence generated at the recever / chp sequence generated at the recever Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons sequence generated at the recever arallel Synchronzaton BF ( ) Correlator BF ( ) Correlator BF ( ) Correlator BF ( ) Correlator Maxmum Lkelhood sequence / chp delay unts Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons 9
ake ecever C B A The ake recever combnes the multpath sgnals and delvers the one wth hghest qualty IF sgnal BF ( ) Correlator BF ( ) Correlator BF ( ) Correlator Maxmum lkelhood A B C sequence generator sequence generator sequence generator Multpath synchronzaton Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons CDMA Benefts 6 6 6 6 6 6 6 4 AMS channels AMS: assume that each cell n a seven-cell cluster has 6 channels of 3 KHz ths s equvalent to havng an avalable bandwdth of.6 MHz for the cluster.e. equvalent to the 4 channels. The capacty of ths system s 4 smultaneous users CDMA: uses.5 MHz of bandwdth and each cell uses the same bandwdth. If we want to transmt nformaton at 96 bps wth a Qualty of Servce (QoS) of E b / =6 db we get the followng number of users per cell 33 33 33 33 33 33 33 M p.5 6 / 9.6 3 33 usuaros por celd E b / 3.98 The ncrease n capacty s of 5.5 tmes over that of AMS Dr. Cesar Vargas osales Center for Electroncs and Telecommuncatons