Spread Spectrum Signal for Digital Communications

Transcription

1 Wireless Iformatio Trasmissio System Lab. Spread Spectrum Sigal for Digital Commuicatios Istitute of Commuicatios Egieerig Natioal Su Yat-se Uiversity

2 Spread Spectrum Commuicatios Defiitio: The trasmitted sigal must occupy a badwidth which is large tha the iformatio bit rate ad which is idepedet of the iformatio bit rate. Characteristics of Spread Spectrum Commuicatios Demodulatio must be accomplished, i part, by correlatio of the received sigal with a replica of the sigal used i the trasmitter to spread the iformatio sigal. Possess pseudo-radomess, which makes the sigals appear similar to radom oise & difficult to demodulate by receivers other tha the iteded oes. 2

3 Spread Spectrum Commuicatios Advatages Jam resistace Low probability of itercept Resistace to multi-path fadig Frequecy sharig Chael sharig, soft capacity, soft blockig Soft hadoff Disadvatages Self-jammig Near-far problem Implemetatio is more complex 3

4 Techiques for Spread Spectrum - Direct Sequece Spread Spectrum (DSSS) A carrier is modulated by a digital code i which the code bit rate is much larger tha the iformatio sigal bit rate. These systems are also called pseudo-oise systems. 4

5 Techiques for Spread Spectrum - 2 Time-hopped Spread Spectrum (THSS) The trasmissio time is divided ito itervals called frames. Each frame is divided ito time slots. Durig each frame, oe ad oly oe time slot is modulated with a message. 5

6 Techiques for Spread Spectrum - 3 Frequecy Hoppig Spread Spectrum (FHSS) The carrier frequecy is shift i discrete icremets i a patter geerated by a code sequece. Fast-hop: frequecy hoppig occurs at a rate that is greater tha the message bit rate. Slow-hop: the hop rate is less tha the message bit rate. 6

7 Idealized Model of Basebad Spread- Spectrum System (DSSS System) Trasmitter Chael 7 Receiver

8 Waveforms i the Trasmitter of DSSS 8

9 DSSS Techique i the Passbad - Coheret Biary Phase-Shift Keyig Trasmitter 9

10 DSSS Techique i the Passbad - Coheret Biary Phase-Shift Keyig Receiver 0

11 Power Spectral Desity

12 Power Spectral Desity Relative to Narrow Bad Iterferece (NBI) 2

13 Power Spectral Desity After Despreadig 3

14 Sychroizatio For proper operatio, a spread-spectrum commuicatio system requires that the locally geerated PN sequece used i the receiver to despread the received sigal be sychroized to the PN sequece used to spread the trasmitted sigal i the trasmitter. A solutio to the sychroizatio problem cosists of two parts: acquisitio ad trackig. I acquisitio, or coarse sychroizatio, the two PN codes are aliged to withi a fractio of the chip i as short a time as possible. Oce the icomig PN code has bee acquired, trackig, or fie sychroizatio, takes place. 4

15 Sychroizatio Typically, PN acquisitio proceeds i two steps: The received sigal is multiplied by a locally geerated PN code to produce a measure of correlatio betwee it ad the PH code used i the trasmitter. A appropriate decisio-rule ad search strategy is used to process the measure of correlatio so obtaied to determie whether the two codes are i sychroism ad what to do if they are ot. For trackig, it is accomplished usig phase-lock techiques, similar to those used for the local geeratio of coheret carrier refereces. 5

16 Wireless Iformatio Trasmissio System Lab. Orthogoal Codes: Hadamard Codes Istitute of Commuicatios Egieerig Natioal Su Yat-se Uiversity

17 7 Hadamard Codes Hadamard code is obtaied by selectig the rows of a Hadamard matrix. A Hadamard matrix M is a x matrix that ay row differs from ay other row i exactly /2 positios. = = = M M M M M M M ad form a liear biary code of block legth. M M mi We ca geerate Hadamard codes with block legth 2, ad 2, 2 where is a positive iteger. m m d m = = =

18 Example of Hadamard Codes Hadamard Code of Legth 8 8

19 Correlatio of Orthogoal Codes Correlatio properties of orthogoal codes are very sesitive to sychroizatio. Orthogoality of OVSF codes (or Hadamard codes) is achieved whe codes are sychroized. Orthogoality of OVSF codes (or Hadamard codes) may ot be maitaied whe codes are ot sychroized. 9

20 Orthogoality is achieved whe sychroizatio is maitaied

21 Orthogoality is maitaied whe codes are ot sychroized

22 Orthogoality is't maitaied whe codes are ot sychroized

23 Wireless Iformatio Trasmissio System Lab. Geeratio of Pseudo-Noise (PN) Sequeces Istitute of Commuicatios Egieerig Natioal Su Yat-se Uiversity

24 Pseudo-Noise Sequeces A pseudo-oise (PN) sequece is a periodic biary sequece with a oiselike waveform that is usually geerated by meas of a feedback shift register. 24

25 Pseudo-Noise Sequeces A feedback shift register cosists of a ordiary shift register made up of m flip-flop (two-state memory stages) ad a logic circuit that are itercoected to form a feedback circuit. With a total umber of m flip-flops, the umber of possible state of the shift register is at most 2 m. A feedback shift register is said to be liear whe the feedback logic cosists etirely of modulo-2 adders. The all-zero state is ot permitted. As a result, the period of a PN sequece produced by a liear feedback shift register with m flip-flops ca t exceed 2 m -. Whe the period is exactly 2 m -, the PN sequece is called a maximal-legth-sequece or simply m-sequece. 25

26 Properties of Maximal-Legth Sequeces I each period of a maximal-legth sequece, the umber of s is always oe more tha the umber of 0s. Amog the rus of s ad of 0s i each period of a maximallegth sequece, oe-half the rus of each kid are of legth oe, oe-fourth are of legth two, oe-eighth are of legth three, ad so o as log as these fractios represet meaigful umbers of rus. This property is called the ru property. By a ru, we mea a subsequece of idetical symbols (s or 0s) withi oe period of the sequece. Autocorrelatio property: the autocorrelatio fuctio of a maximum-legth sequece is periodic ad biary-valued. 26

27 Properties of Maximal-Legth Sequeces Covert 0 ad -. Let c(t) deote the resultig waveform of the maximal-legth sequece. The period of the waveform c(t) is: T b =NT c, where T c is the duratio assiged to symbol or 0 ad N=2 m -. The autocorrelatio fuctio of a periodic sigal c(t) of period b T /2 T b is: ( τ) () ( τ) Rc = c t c t dt T Tb /2 b 27

28 Properties of Maximal-Legth Sequeces The autocorrelatio fuctio of the maximal-legth sequece is: R c τ ( ) N + τ NTc = N τ T c otherwise 28

29 Properties of Maximal-Legth Sequeces Periodicity i the time domai is trasformed ito uiform samplig i the frequecy domai. + N ( ) ( ) 2 Sc f = δ f + sic δ f 2 2 N N = N NTc 0 29

30 Example of Maximum-Legth Shift- Register Codes Systematic Code 30

31 Maximum-Legth Shift Register 3

32 Maximal Legth Shift Register (m=5) 32

33 Maximal Legth Shift Register (m=5) 33

34 Maximal-Legth Sequeces of Shift- Register Legths (2-8) 34

35 Maximal-Legth Sequeces of Shift- Register Legths (2-34) Maximum-legth shift-register codes exist for ay positive value of m. 35

36 Problems with m-sequece Problems : jammer ca determie the feedback coectios by observig oly 2m- chips from the PN sequece. Solutio : Output sequeces from several stages of the shift register or the outputs from several distict m-sequeces are combied i a oliear sequece that is cosiderably more difficult for the jammer to lear. Solutio 2: Frequetly chagig the feedback coectios ad/or the umber of stages i the shift registers. 36

37 Problems with m-sequece Problem 2: periodic cross correlatio fuctio betwee ay pair of m-sequeces of the same period ca have relatively large peaks. Although it is possible to select a small subset of m sequeces that have relatively smaller cross correlatio peak values, the umber of sequeces i the set is usually too small for CDMA applicatios. 37

38 Correlatio Properties of PN sequeces Cosider two PN sequeces of period 2 7 -=27, oe feedback shift register has the feedback taps [7,] ad the other oe has the feedback taps [7,6,5,4]. Both sequeces have the same autocorrelatio fuctio. 38

39 Peak Cross Correlatio of m Sequeces ad Gold Sequeces 39

40 Gold s theorem: Preferred Sequeces Gold ad Kasami proved that certai pairs of m sequeces of legth (e.g. g (X) ad g 2 (X) ) exhibit a three-valued cross correlatio fuctio with values { -, -t(m), t(m)-2} where: tm ( ) ( m+ )/2 2 + odd m = ( m+ 2)/2 2 + eve m Two m sequeces of legth with a periodic cross correlatio fuctio that takes o the possible values { -, - t(m), t(m)-2} are called preferred sequeces. The shift register correspodig to the product polyomial g (X) g 2 (X) will geerate 2 m + differet sequeces, with each sequece havig a period of 2 m -. 40

41 Golde Sequeces From a pair of preferred sequeces, say a=[ a a 2 a 3 a ] ad b=[ b b 2 b 3 b ], we costruct a set of sequeces of legth by takig the modulo-2 sum of a with the cyclicly shifted versios of b or vice versa. Thus, we obtai ew periodic sequeces with period =2 m -. Together with the origial sequeces a ad b, we have a total of +2 sequeces, which are called Gold sequeces. With the exceptio of the sequeces a ad b, the set of Gold sequeces is ot comprised of maximum-legth shift-register sequeces of legth. The cross correlatio fuctio for ay pair of sequeces from the set of +2 Gold sequeces is three-valued with possible values { -, -t(m), t(m)-2}. The off-peak autocorrelatio fuctio for a Gold sequece takes o values from the set { -, -t(m), t(m)-2}. 4

42 Geerator for a Gold Sequece of Period 27 42

43 Cross-Correlatio Fuctio Cross-correlatio fuctio of a pair of Gold sequeces based o the two PN sequeces [7,4] ad [7,6,5,4]. 43

44 Wireless Iformatio Trasmissio System Lab. Elemetary Codes i WCDMA Istitute of Commuicatios Egieerig Natioal Su Yat-se Uiversity

45 Elemetary Codes i WCDMA Scramblig codes Uplik log scramblig codes Uplik short scramblig codes Dowlik scramblig codes Chaelizatio Codes Sychroizatio codes Dowlik Sychroizatio Chael Uplik PRACH Preamble Referece: 3GPP TS 25.2 &

46 Scramblig Codes Scramblig codes are used to scramble the spread sequeces Multiply the spread chip rate More radom ad orthogoal Uplik Log scramblig codes Short scramblig codes Possibility of multi-user detectio at base statios Dowlik Log scramblig codes 46

47 Spreadig for Uplik DPCCH ad DPDCHs c d, β d DPDCH DPDCH 3 c d,3 β d Σ I c d,5 β d DPDCH 5 S dpch, I+ jq c d,2 β d S DPDCH 2 c d,4 β d DPDCH 4 DPDCH 6 c d,6 β d Σ Q c c β c j DPCCH 47

48 Uplik Modulatio The modulatio chip rate is 3.84 Mcps. The complex-valued chip sequece geerated by the spreadig process is QPSK modulated. cos(ωt) Complex-valued chip sequece from spreadig operatios S Split real & imag. parts Re{S} Im{S} Pulseshapig Pulseshapig -si(ωt) 48

49 Cofiguratio of Uplik Scramblig Sequece Geerator MSB LSB x c log,, y c log,2, 49

50 Uplik Short Scramblig Sequece Geerator for 255 Chip Sequece d(i) mod mod additio multiplicatio mod 2 0 b(i) mod 4 + z (i) Mapper c short,, (i) c short,2, (i) a(i) mod

51 Spreadig for All Dowlik Physical Chaels Except Sychroizatio Chael (SCH) I Ay dowlik physical chael except SCH S C ch,sf,m I+jQ S dl, S P Q j 5

52 Spreadig ad Modulatio for SCH ad P- CCPCH Differet dowlik Physical chaels (poit S i Figure of previous page.) G G 2 Σ P-SCH Σ T G P S-SCH G S 52

53 Dowlik Modulatio I the dowlik, the complex-valued chip sequece geerated by the spreadig process is QPSK modulated: cos(ωt) Complex-valued chip sequece from summig operatios T Split real & imag. parts Re{T} Im{T} Pulseshapig Pulseshapig -si(ωt) 53

54 Cofiguratio of Dowlik Scramblig Code Geerator I Q

55 Chaelizatio Codes Each CDMA chael is distiguished via a uique spreadig code. These spreadig codes should have low crosscorrelatio values. I 3GPP W-CDMA, Orthogoal Variable SF (OVSF) codes are used. Preserve the orthogoality betwee a user s differet physical chaels. Scramblig is used o top of spreadig. 55

56 Code-tree for Geeratio of Orthogoal Variable Spreadig Factor (OVSF) Codes C ch,4,0 =(,,,) C ch,2,0 = (,) C ch,4, = (,,-,-) C ch,,0 = () C ch,4,2 = (,-,,-) C ch,2, = (,-) C ch,4,3 = (,-,-,) SF = SF = 2 SF = 4 The chaelizatio codes are uiquely described as C ch,sf,k, where SF is the spreadig factor of the code ad k is the code umber, 0 k SF-. 56

57 Chaelizatio Codes As the chip rate is already achieved i the spreadig by the chaelizatio codes, the symbol rate is ot affected by the scramblig. Aother physical chael may use a certai code i the tree if o other physical chael to be trasmitted usig the same code three is usig a code that is o a uderlyig brach, i.e. usig a higher spreadig factor code geerated from the iteded spreadig code to be used. Neither ca a smaller spreadig factor code o the path to the root of the tree be used. 57

58 Chaelizatio Codes The dowlik orthogoal codes withi each base statio are maaged by the radio etwork cotroller (RNC) i the etwork. The defiitio for the same code tree meas that for trasmissio from a sigle source, from either a termial or a base statio. Oe code tree is used with oe scramblig code o top of the tree. Differet termials ad differet base statios may operate their code trees idepedetly of each other. 58

59 59 Geeratio of Chaelizatio Codes C ch,,0 = = =,,0,,0,,0,,0,2,,2,0 ch ch ch ch ch ch C C C C C C ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = ,2,2,2,2,2,2,2,2,,2,,2,,2,,2,0,2,0,2,0,2,0,2,2,2 2,2,2,3,2,2,2,,2,0,2 : : : ch ch ch ch ch ch ch ch ch ch ch ch ch ch ch ch ch ch C C C C C C C C C C C C C C C C C C