Principles of Spread Spectrum and CDMA

Transcription

1 Separaton of Overlappng Sgnals Prncples of Spread Spectrum and CDMA Dr Bhasar Ramamurth Professor Department of Electrcal Engneerng Indan Insttute of echnology Madras. Frequency Dvson Multplexng sgnals non-overlappng n frequency sgnals overlap n tme separaton acheved by flterng - wndow n f-doman - convoluton wth flter mpulse response n t-doman f H 1 ( f ) h 1 ( t ) flters out sgnal n [f 1, f ] desred_sgnal = sum _ sgnal( )h ( t ) d 1 sldng correlaton wth h 1 (-t) f r e q f f 1 t m e Dr Bhasar Ramamurth CDMA_Wreless_Course 1 Dr Bhasar Ramamurth CDMA_Wreless_Course Separaton (contd ) Orthogonalty and Separaton of Sgnals me Dvson Multplexng n FDM, sgnals are orthogonal n frequency sgnals non-overlappng n tme freq Sgnal_1(f). Sgnal_(f) = sgnals overlap n frequency n DM, sgnal are orthogonal n tme separaton acheved by wndowng multplcaton n t-doman t 1 t tme t N sgnal_1(t). sgnal_(t) = sgnals can be contnuous-tme or dscrete-tme convoluton n f-doman f u(t; t 1, t ) s non-zero n [t 1, t ] desred_sgnal = sum_sgnal. u(t; t 1, t ) however n DM, sgnal s usual a d-t dgtal sgnal or dgtally-modulated c-t sgnal Is any other form of orthogonalty possble? Dr Bhasar Ramamurth CDMA_Wreless_Course 3 Dr Bhasar Ramamurth CDMA_Wreless_Course 4

2 Orthogonalty: Any Other Way? Yes, f we consder only dscrete-tme sgnals Let c 1 (t) and c (t) both of duraton be such that ther cross-correlaton = when tme-algned 1 c ( t )c ( t )dt = Let sgnal _ 1 be x 1 and sgnal _ be x n [,] Consder sum_sgnal(t)= x 1 c 1 (t)+ x c (t) x can be extracted by correlatng wth c (t) sum _ sgnal( t ).c ( t )dt = x [ c (t )dt] Orthogonalty (contd..) How many orthogonal functons c (t) can we get? Landau-Polla heorem: N W where W s the bandwdth avalable gven symbol duraton, N W / (1/) bandwdth expanson factor c (t) have to be tme-algned,.e. synchronous sgnals overlap n tme and frequency code tme freq Dr Bhasar Ramamurth CDMA_Wreless_Course 5 Dr Bhasar Ramamurth CDMA_Wreless_Course 6 Orthogonal Drect-Sequence Code Dvson Multplexng c (t) are bnary-valued sequences such that.e., c (t) = ( c 1 ) h( t c ) where = {,1}, and c s the chp perod = /L c equvalently j c ( t )c ( t )dt = L c 1 = L c 1 = c XOR c { c } are called codes, hence the terms CDMA and synchronous CDM j = L c c Orthogonal CDM (contd ) Example : Walsh codes 1 H used n IS-95 H 6 n-1 n-1 H H H H n-1 H n-1 H n Dr Bhasar Ramamurth CDMA_Wreless_Course 7 Dr Bhasar Ramamurth CDMA_Wreless_Course 8

3 Asynchronous CDMA n orthogonal CDM, codes are synchronsed dffcult to ensure between ndependent transmtters at varable dstances from recever (.e, multple access) synchronous orthogonal codes can have large correlaton when not synchronsed not used n CDMA employ pseudo-random or pseudo-nose (PN) sequences x 1 1 x 1 typcally, low but non-zero correlaton between any two sequences quas-orthogonal codes x 1 x Asynchronous CDMA (contd..) even chp algnment wll not be there f {b } and {c } are two truly-random bnary sequences L c 1 of length L c, and cross-correlaton β = ( b 1)( c 1 E[β] = and E[β ] = L c = ) nterference power from (N-1) sgnals (N-1) For the sgnal we desre to extract, L 1 desred_sgnal power = [ c ( c 1)( c 1)] = L c = undesred per-user nterference suppressed by factor 1/L c on the average for large N, varaton around average wll be less L c Dr Bhasar Ramamurth CDMA_Wreless_Course 9 Dr Bhasar Ramamurth CDMA_Wreless_Course 1 Sgnallng over Fadng Channels A fadng channel has deep nulls n ts frequency response Imp. Imp. multple paths taen by sgnals from x to Rx t t Freq. Freq. 1/ f 1/ f destructve nterference Only a small part of a wdeband sgnal s spectrum s severely dstorted by the nulls n FDM or OFDM, a (narrowband) sgnal located around f= 1/ wll be lost multpath leads to Inter Symbol Interference f ~ (symbol duraton) n DM, s small tolerable delay spread s less Dr Bhasar Ramamurth CDMA_Wreless_Course 11 Spread Spectrum Sgnallng and Fadng c(t) spreads a narrowband sgnal unformly over a band / c larger C(f) must be flat and wde R cc () must be mpulse le multpath sgnal α 1 x 1 c(t) + α x 1 c(t- ) correlated wth c(t) α 1 x 1 R cc () + α x 1 R cc () α 1 x 1 R cc () f > c delayed sgnal s suppressed for delay > c for slow frequency hoppng, some bursts of symbols fallng n spectral nulls are affected employ codng across bursts to overcome ths Dr Bhasar Ramamurth CDMA_Wreless_Course 1 C(f) convoluton s unform wdeband f

4 Spread Spectrum Dversty estmate path delays greater than c n a multpath channel mplement one correlator for every sgnfcant path : RAKE recever SS Dversty (contd ) each fnger wll gve α R cc () x 1 combne to get better decson on x 1 c 1 (t) c 1 (t- 1 ) c 1 (t- ) combne path gans ISI has been resolved and converted to dversty gan f path gans [α ] are also estmated, can weght each fnger proportonately maxmal rato combnng RAKE RECEIVER else equal gan combnng Dr Bhasar Ramamurth CDMA_Wreless_Course 13 Dr Bhasar Ramamurth CDMA_Wreless_Course 14 Mult-ranscever (Macro) SS Dversty multple transmssons on same carrer wth dfferent codes can be combned α 1 x 1 c (t)+ α x 1 b(t - ) b(t) c(t) sgnals from two base statons can be combned durng handoff + combner Macro Dversty (contd ) he fngers of a RAKE recever need not be fed by same RF front-end dfferent transcevers at same base staton (e.g., adjacent sectors) dfferent base statons! RF RF c(t) c(t-) + combner Dr Bhasar Ramamurth CDMA_Wreless_Course 15 Dr Bhasar Ramamurth CDMA_Wreless_Course 16

5 Mult-Access Interference n CDMA codes employed have low autocorrelaton sdelobes, and typcally low cross correlaton also assume all sgnals arrve wth equal power perfect power control at x to counteract path loss and fadng desred _ sgnal energy at each RAKE fnger L c sum of undesred - sgnal (nterference) energes at each RAKE fnger NL c f MAI s approxmated as Gaussan for large N, varance of MAI = NL c Carrer-to-Interference Rato (CIR) = L c / N Dr Bhasar Ramamurth CDMA_Wreless_Course 17 Refnement of MAI Computaton effect of bandpass transmsson - snce each nterferer wll have a random phase offset (actually, small frequency offset), MAI wll be less E[cos ϕ] =.5 for unformly dstrbuted ϕ effect of chp ms-algnment f nterference s y 1 for left algnment and y 1 y for rght algnment, actual nterference α y 1 + (1- α) y where α s unformly dstrbuted n [,1] E{[α y 1 + (1- α)y ]} = (1/3) [Ey 1 + Ey ] = L c /3 Net effect : CIR ncreases by a factor of 3 For large cells, thermal nose adds to MAI near cell boundares : CINR drops Dr Bhasar Ramamurth CDMA_Wreless_Course 18 y Sectorng Reduces MAI BS employ sectoral antenna downln adjacent cell nterference reduced upln uncontrolled nterference from adjacent cells reduced capacty mprovement factor vs-à-vs crcular cell = η 36 o / sectoral angle (η =.8 (4.5) for 3 (6) sectors) sectoral gan mproves ln budget n nose-lmted stuaton no mpact n nterference-lmted case uncontrolled adjacent sector nterference reduces capacty by.6 ~.6 x 6 x η (~35 η) users per cell wth varable rate codng Power Control n CDMA f an nterferer s power s hgher by, say, 1 tmes equvalent to 1 nterferers of equal power CIR drops dramatcally need to control power of each user to ±.5dB, - use combnaton of open-loop and closed-loop control path loss due to shadowng smlar on up and down lns even f frequences are dfferent open-loop control of x power based on local Rx sgnal strength Dr Bhasar Ramamurth CDMA_Wreless_Course 19 Dr Bhasar Ramamurth CDMA_Wreless_Course

6 Power Control n CDMA (contd ) fadng wll be dfferent n up and down ln (dfferent frequences) closed-loop control of x power based on feedbac from far-end Rx - usually a low btrate bnary sgnal :1/ up/down by.5 db Open loop Closed loop Statstcal Multplexng n CDMA ndvdual sgnal s bursty wth actvty factor γ bursts occur randomly for large N, total traffc at any tme t s equvalent to γ N non-bursty sgnals n CDMA, MAI from M bursty sgnals s not NP X /L c, but γ NP X /L c for large N f varable rate voce coder employed t x x x γ.4, N -3 suffcently large Rx duplexer control Rx Dplx Dplx Rx feedbac for IP pacets, γ.1 or less, but N has to be much larger due to long-taled dstrbutons of ON/OFF perods Dr Bhasar Ramamurth CDMA_Wreless_Course 1 Dr Bhasar Ramamurth CDMA_Wreless_Course Pros and Cons of CDMA spread spectrum dversty - multpath, macro statstcal multplexng easly exploted - large number of quas-orthogonal codes large number of bursty users easy to support a varety of bt-rates e.g; f chp rate s.48 Mbps servce at n bps, has a spreadng factor of 48/n n can be any power of strct power control requred - combnaton of open and closed loop control dffcult to hand over from one carrer to another - seamless handoff not possble between carrers, smlar to FDM Dr Bhasar Ramamurth CDMA_Wreless_Course 3