Comparison of Downlink Transmit Diversity Schemes for RAKE and SINR Maximizing Receivers

Transcription

1 Comparison of Downlink Transmit Diversity Scemes for RAKE and SINR Maximizing Receivers Massimiliano enardi, Abdelkader Medles and Dirk TM Slock Mobile Communications Department - Institut Eurécom 2229 Route des Crêtes, BP 93, F-694 Sopia Antipolis Cedex, FRANCE Tel: , Fax: flenardi,medles,slockg@eurecomfr Abstract In DS-CDMA communications, te conventional receiver is te RAKE receiver In te downlink (base station to mobile) signalling wit celldependent scrambling, ortogonal codes and a common cannel for all te users, tis receiver does not maximize te Signal-to-Interference-plus-Noise Ratio (SINR) at its output Anoter receiver, wit te same structure as te RAKE receiver, is suitable for downlink DS-CDMA communications; te one in wic te cannel matced filter gets replaced by a filter tat is designed to maximize te SINR at te receiver output In tis paper, we analyze te use of tree different Transmission Diversity (TD) tecniques, namely Space-Time TD (STTD), Ortogonal TD (OTD) and Delay TD (DTD) All of tem are compared for te two receiver structures: RAKE and max-sinr receivers Te max-sinr receiver structures proposed ere for te tree TD modes are new and are sown to usually significantly outperform te RAKE scemes We also discuss te relative performance merits of te tree TD scemes for one or te oter receiver structure I INTRODUCTION 3rd generation systems for wireless communications will require iger data rates and better BER Te multiple access interference being te major impairment for tese systems, its cancellation is a must for te receivers to reac suc performances In Direct Sequence Code Division Multiple Access (DS-CDMA) scemes, te uplink and te downlink interference is asymmetric due to te fact tat te uplink signalling is asyncronous, wile te downlink (intracell) signalling is syncronous Tis situation in te downlink makes wortwile te use of ortogonal codes wic, in te absence of multipat propagation, allow te cancellation of te multiple access interference by a simple correlator, maximizing te output SNR if te noise is wite Wen delay spread and multipat propagation are present, a RAKE receiver will treat te different contributions in a maximum ratio combining fasion, maximizing te SNR but destroying te ortogonality between intracell user codes, leading to intracell interference at its output In [], a cannel equalization approac as been studied, focusing on te intracell interference rater ten on noise and intercell interference cancellation Due to oversampling wrt to cip rate (or multiple antennas), some of te intercell interference can be also cancelled by using te excess bandwidt Since te ortogonality is restored by an equalizer, a simple correlator gets rid of te intracell interference Tis approac as te disadvantage to enance te noise muc more ten te RAKE approac, so tat, between te two structures, one is better tan te oter depending on weter te intracell interference is iger or lower tan te intercell interference plus noise In [2], a solution to improve te RAKE and te equalizer approaces is proposed and a new class of linear receivers is introduced Tese receivers ave te same structure as a RAKE receiver, were te cannel macted filter gets replaced by an equalizer filter designed to maximize te SINR at te receiver output Te idea beind tis ap- Eurécom s researc is partially supported by its industrial partners: Ascom, Swisscom, Tomson- CSF, IBM France, CEGETE, Motorola, France Télécom, itaci Europe and Texas Instruments Te work leading to tis paper was also partially supported by te Frenc RNRT (National Network for Telecommunications Researc) project AUBE Te researc of A Medles was also sponsored by te researc contract Multisensor Antennas of te Credits Incitatifs programme of te Groupe des Ecoles de Telecommunications (GET), France proac is tat wen a cell-dependent scrambler is superposed to te periodic spreading codes, te received signal is stationary if sampled at cip rate; terefore, a time-invariant MMSE design is feasible for te equalizer and it turns out to lead to te max-sinr receiver Te filter adaptation can be done at symbol or cip rate Multiple transmitting antennas at te base station can improve performances due to increase in diversity and some scemes ave been proposed for open loop systems (no knowledge of te downlink cannel at te transmitter) Basically, 4 kinds of Transmission Diversity (TD) scemes ave been proposed for a base station: Ortogonal TD (OTD, see [3]), Space-Time TD (STTD, see [4]), Time-Switced TD (TSTD, see [3]) and Delay TD (DTD, see []) Te UMTS norm for 3rd generation wireless systems specifies, for te FDD downlink, tat te use of Trasmission Diversity tecniques is optional at te base station, wile it is mandatory for te mobile station In tis paper, we analyze te use of tree TD tecniques, namely STTD, OTD and DTD All of tem are compared for te two receiver structures, RAKE and max-sinr receivers II BS TRANSMISSION DIVERSITY SCEMES Fig sows te downlink signal model in baseband Te K users are assumed to transmit linearly modulated signals over te same linear multipat cannels wit additive noise and intercell interference, by using two antennas j = ; 2 at te base station Te two signals are generated following different rules given by te Transmission Diversity Scemes described later in II-A to II-C Te symbol and cip periods T and T c are related troug te spreading factor : T = T c, wic is assumed ere to be common for all te users Te total cip sequences b l and b 2 l are te sum of te cip sequences of all te users over te respective antenna and 2 Every user cip sequence is given by te product between te nt symbol of te kt user and an aperiodic spreading sequence w k;l wic is itself te product of a periodic Wals-adamard (wit unit energy) spreading sequence c k =[ck; c k; c k;,] T, and a base-station specific unit magnitude complex scrambling sequence s l wit variance, w k;l = ck;l modsl: b j l = K X k= X b j K k;l = a j k;b l j =; 2 : () cwk;l k= Te scrambling operation is a multiplication of cip rate sequences Te spreading operation is represented by a filtering of an upsampled symbol sequence wit te spreading sequence as impulse response Te cip sequence b ;2 l get transformed into a continuous-time signals by filtering tem wit te pulse sape p(t) and ten pass troug te multipat propagation cannels (t) and 2 (t) (from antenna and from antenna 2 to te mobile station respectively) to yield te total received signal y(t) Te receiver samples M times per cip te lowpass filtered received signal Stacking te M samples per cip

2 a ;n a K ;n a 2 ;n c c K c 2 s l x b l s 2 l p(t) (t) v(t) y(t) PF M Tc a delay of D cip periods on te transmission on te second antenna So it works as if tere is just one antenna, but te cannel is te sum of (t) and 2 (t, D Tc): a k;n = a2 k;n = ak;n ;b l = b2 l = bl (z) = (z) z,d 2 (z) were (z) represent te cannel in te z-domain (6) a 2 K 2;n = T Tc c 2 K 2 x b 2 l p(t) b l b 2 l l 2 l 2 (t) v l Fig Downlink signal model period in vectors, we get for te sampled received signal = y l y2 l vl; yj l = K X k= were y j l = y j ;l y j M;l 3 7 ; j l = N X, i= j ;l j M;l j i bj k;l,i j =; 2 (2) ; vl = 4 v ;l v M;l 3 7 : (3) ere j l represents te vectorized samples of te overall cannel j (t), including pulse sape, propagation cannel and receiver filter Te overall cannels j (t) are assumed to ave te same delay spread of N cips If we model te scrambling sequence and te symbol sequences as independent iid sequences, ten te cip sequences b ;2 l are sums of K independent wite noises (cip rate iid sequences, ence stationary) Te intracell contribution to ten is a stationary (vector) process (te continuous-time counterpart is cyclostationary wit cip period) Te intercell interference is a sum of contributions tat are of te same form as te intracell contribution Te remaining noise is assumed to be wite stationary noise ence te sum of intercell interference and noise, v l, is stationary A OTD SCEME For eac user k, tis TD sceme generates, from a couple of symbols to transmit a k;2p and a k;2p, were2p stays for even symbol periods, te two pairs of symbols to be sent troug te two antennas as following: B STTD SCEME a k;2p = a k;2p a k;2p = a k;2p a 2 k;2p = a k;2p a 2 (4) k;2p =,a k;2p Similarly to OTD, tis tecnique produces two pairs of symbols, but now a k;2p = a k;2p a k;2p = a k;2p a 2 k;2p =,a k;2p a 2 k;2p = a k;2p were denotes te complex conjugate operation C DTD SCEME Tis sceme operates differently from te previous two, because it sends te same symbol sequenceon te two antennas, but it introduces () III RECEIVER STRUCTURES FOR BS TRANSMISSION DIVERSITY Fig 2 sows te receiver structure in case of no Transmission Diversity; it is similar to a RAKE receiver in wic te cannel matced filter is replaced by a general causal cip rate filter f l of te same lengt (in cip periods) of te cannel N, so tat te output estimate is delayed by a certain number of symbols l As in te RAKE, te filter f l is followed by a descrambler (delayed by some cips d = l l 2 = N,, l = b d c, l2 = d mod, and by a decorrelator for te user of interest (assumed ere te user ) Descrambling and despreading can be considered as a unique filtering wit input at cip rate (^b l,d) and output at symbol rate (te output estimate) s l,d ^b l,d f x z,l 2 l S/P X l Xn c ^b l,d c d ^a S ;n,l, n Fig 2 Te downlink receiver structure d ^a ;n,l, Te receiver outputs d ba ;n,l, = c X n (7) were X n is a vector of descrambled filter outputs, X n = S n,l,z n ; Zn = T (f )Y n ; (8) Z n is a vector of filter outputs, S n = diag fsn;,;::: ;s n;;s n;g is a diagonal matrix of scrambling code coefficients s n;l = s nl, T (f ) is te block Toeplitz filtering matrix wit f = f f N, (padded wit zeros) as first block row, and Y n = Y T n;l 2 Y T n, Y T n,l 3 Y T n,l 3,;l 4 i T were N,,l2 = l 3l 4, Y n = y T n;, y T n; T, Y n;l = y T n;l, yt n; T, Y n;l = y T n;, y T n;,l T,andyn;l = y nl Te structure of te vector Y n of received data tat contribute to te estimate ba ;n,l, is Y n = T ( )Sn K X k= C ka k;n V n (9) were T ( ) is again a block Toeplitz filtering matrix wit te zero padded = [ N,] as first block row, S n = blockdiag S n;l2 ;S n,;::: ;S n,l ; S n,l,;l 6 is te scrambling matrix, C k = blockdiag fck;l2 ; c k;::: ;ck; ck;l6 g (l c k s), A k;n = [ak;n ak;n,l,] T, V n is defined like Y n,ands n;l, S n;l, c k;l and c k;l are defined similarly to Y n;l and Y n;l except tat S n;l and S n;l are diagonal matrices, and 2N,2,l 2 = l l 6 We ave for te filter-cannel cascade T (f )T () =T () =T ( d)t (d) ()

3 were =[ 2N,2] ; d =[ d ] d =[ d, d 2N,2] : () In te noiseless case (and no intercell interference), te use of a ZF equalizer leads to d =[] and ba ;n,l, = a ;n,l, ( d = ) A RAKE receiver corresponds to f =, d = kk 2,were =[ T N, T ] T In [2] is presented te general expression for te SINR at te output of a receiver wen no BS Transmission Diversity is used, namely,= 2 j d j2 MSE or 2 2 j dj,= faf (2), tot 2 jdj2 Y 2P Y 2P f f c S 2P c S 2P c S 2P c S 2P - Fig 3 Te downlink receiver OTD structure z =2 d ^a 2P z 2 =2 22 d ^a 2P were A = R VV 2 tot T ( )T ( ), R VV = E VnV P n and tot 2 = K k= 2 k Te filter f tat maximizes te receiver output SINR is unique up to a scale factor and comes from te following problem f MAX = arg max, = arg min faf : (3) f :f= f :f= Te solution is ( d =) f MAX = A,, A, and te maximum SINR becomes ( MAX d =),MAX = (4) 2, A,,, 2 tot () A turns out to be te covariance matrix of te received signal, wile f MAX to be te unbiased MMSE receiver Te max-sinr receiver is terefore a cascade of an (unbiased if d = ) MMSE receiver for te desired user s cip sequence, followed by a descrambler and a correlator In te noiseless case, te MMSE receiver f MAX becomes a ZF equalizer A ECEIVER Te structure in Fig 2 is valid also in te case of Delay Transmission Diversity Eq (7) to Eq () are also applicable for tis TD sceme, wen te cannel is as in te Eq (6) Te same results and conclusions are ten valid, in particular, in te noiseless case, te max-sinr receiver becomes te ZF equalizer B ECEIVER Wen oter scemes of Transmission Diversity are used, oter structures are needed Te received signal in tis case can be expressed as Y n = Y n Y 2 n V n (6) were P Y n = T ( )S K n k= CkA k;n P Y 2 n = T ( 2 )S K (7) n k= CkA2 k;n were notations are te same as above but wit superscripts,2 Fig 3 sows te linear processing needed in an OTD receiver, wic distinguises even (2P ) and odd (2P ) symbol periods witin te received signal Y n Te receiver processes te two signals separetely wit two cip rate filters f and, wose outputs are ten despreaded, by applying a (total) despreader similarly to wat is sown in Fig2 Wen tis sceme is implemented, te two softoutputs (at alf of te symbol rate) are te estimators for even symbol period (z ) and odd symbol period (z 2 )were j j d is defined as in Eq () and Eq () for filter f j and cannel j : We can write te two softoutputs z j as j j d = f j j : (8) z = c S 2P T (f )Y 2P c S 2P T (f )Y 2P z 2 = c S 2P T ( )Y 2P, c S 2P T ( )Y 2P (9) Wen a RAKE implementation is wanted, ten f = and = 2, d = k k 2 and 22 d = k2 k 2 Te SINR for te softoutput z j is,j = 2 j jj d j2 2 f j A f (2) were j A = R VV 2 tot [T ( )T ( )T ( 2 )T ( 2 ),, 2 2 ] (2) From te OTD receiver structure is clear tat te maximization of, and, 2 is independent (z depends only on f and z 2 only on ) Te expression for te filters turns out to be te solution of f j;max = arg max,j = arg min f f j :2f j = f j :2f j j j A f j = tat is f j;max = (22) j A, j, j A, : (23) In tis case te maximum SINR for softoutput z j becomes,j;max =2 2 j A, j : (24), ;MAX and, 2;MAX are not equal so te transmission quality of te two equivalent cannels is different Te total SINR for OTD, is ten defined as,max;ot D =2, ;MAX, wic 2;MAX corresponds to take te MSE as te average of te MSEs for te two softouputs C ECEIVER Fig 4 sows te STTD receiver structure; now eac of te two softoutput depends on bot f j and te two input signals Y 2P and Y 2P are complex conjugated before being filtered by We can write te two STTD softoutputs z j as z = c S 2P T (f )Y 2P ct S T 2P T ( )Y 2P z 2 = c S 2P T (f )Y 2P, ct S T 2P T ( )Y 2P (2)

4 Y 2P Y 2P f c T ST 2P f c S 2P c S 2P c T ST 2P Fig 4 Te downlink receiver STTD structure z 2 - By defining F = [f ; ], = T ; 2i T and 2 =, 2T ; i T and by taking te expectation over te despreading/descrambling, we can restate te two softoutputs estimates z and z as z = F ^a 2P F2^a 2P z 2 = F ^a 2P, F 2^a (26) 2P and te SINR for te z j sofoutput becomes,j = 2,jF j 2 jf 2 2j F AF (27) R j A were A = A and A is defined in Eq (2) Te term R j in te denumerator depends mainly on te used spreading codes (so te mobile receiver sould know tem), but we will see in section IV tat it is negligible wit respect to te oter term, so tat, from Eq (27),, =, 2 and,sttd = 2 z, jfj 2 jf 2j 2 F AF (28) Sincewewantz to be te estimator for a 2P and z 2 te one for a 2P, te filter F MAX tat maximize,sttd comes from te problem arg max,sttd = arg min F AF (29) tat is F : F = F 2 = F : F = F 2 = F MAX = A,, A, : (3) In tis case te maximum SINR becomes,max;st T D = 2 A, 2 A, 2 : (3) i ; 2T, Wen a RAKE receiver is implemented, ten F = F =, k k 2 k 2 k 2 and F 2 = IV NUMERICA EXAMPES Fig to Fig 9 present some of te simulations tat we ave performed to evaluate te various scemes and receivers In te legends of tese figures, R and MS refer to RAKE and max-sinr receiver respectively Te K users are considered syncronous, wit te same spreading factor =32and using te same downlink cannels and 2 wic are FIR filters, convolution of a sparse Veicular A UMTS cannel and a pulse sape (root-raised cosine wit roll-off factor of :22) Te cannel(s) lengt is N =9cips, due to te UMTS cip rate of 384 Mcips/sec An oversampling factor of M =2is assumed Two possible user power distributions are simulated: all interferers ave te same power and te user of interest as eiter te same power also or db less power (near-far situation) Te performances of te different receiver instances are sown in terms of te output SINR versus te SNR at te receiver Te lengt of all te filters in te simulations is equal for all te TD scemes and is eiter te cannel lengt N or te cannel lengt of te DTD cannel (N D) Due to te interference between te two cannels (see Eq (2)) and to te presence of te te scrambler, it is clear tat a ZF equalization for OTD and STTD can not exist; tis is confirmed by te simulations in Fig to Fig 8, were tere is always SINR saturation for OTD and STTD structures, wile DTD is saturating for sorter FIR filters because teir lengt does not permit zero forcing In tis set of figures te delay D for DTD is equal to te cannel lengt N We can notice ow te DTD max-sinr receiver performs muc better tan te oter structures for bot user power distributions wen te filter lengts coincide wit te DTD cannel lengt (2N); see Fig and Fig 6 Te AKE implementation is also te best one in tese cases Wen, instead, te filter lengts are taken equal to te cannel lengt N, but maintaining D = N, te DTD receivers clearly suffer In tis case STTD performs better in te RAKE implementation (see Fig 7 and Fig 8) and besides te DTD complexity is ere alf of te STTD complexity Teir max-sinr performances are similar Fig 9 sows te case wen te delay D is taken as alf te cannel lengt N and te filter lengts are equal to N D (so te complexity is reduced by one quarter) Te performances are very similar to tose in Fig Te last figure, Fig, is sown to confirm tat te terms R j in Eq (27) are negligible We can see tat wen tey are taken into account (x s and sparse dots), te performance/results are identical, on te average, to te case wen tey are dropped (dased and solid lines respectively) V CONCUSIONS Te RAKE performs best wit te DTD sceme, regardless of ow muc delay is introduced between te two cannels (ence even if only partial diversity) Neverteless, lesser temporal overlap between te two cannels in DTD leads to better performance Wen a max-sinr receiver is employed, performance still gets improved significantly for DTD, compared to a RAKE receiver Te good performance of te DTD sceme can be explained by te fact tat it is te only TD sceme tat allows zero-forcing equalization STTD scemes often perform significantly worse tan DTD scemes, toug tey may occasionally outperform DTD scemes a bit We can also conclude tat te OTD sceme leads to te worst performance in all receiver cases REFERENCES [] I Gauri and D T M Slock, inear receivers for te DS-CDMA downlink exploiting ortogonality of spreading sequences, in Proc 32nd Asilomar Conf on Signals, Systems & Computers, (Pacific Grove, CA), November 998 [2] M enardi and D T M Slock, A RAKE Receiver wit Intracell Interference Cancellation for a DS-CDMA Syncronous Downlink wit Ortogonal Codes, in Proc VTC 2, (Tokyo, Japan), May 2 [3] Space Time Block Coded Transmit Antenna Diversity for WCDMA, tec rep, Texas Instruments, November 998 Contribution to 3GPP standardization [4] S M Alamouti, A simple transmit diversity tecnique for wireless communications, IEEE JSAC, vol 6, pp 4 48, October 998 [] A Wittneben, A new bandwidt efficient transmit antenna modulation diversity sceme for linear digital modulation, in Proc IEEE International Conf Communications (ICC 93), (Atlanta, GA), pp , May 993

5 SIRJ = db engts of te filters = 38 cips 4 6 SIRJ = db engts of te filters = 9 cips Fig Teoretical outputsinr versus SNR, % loaded system, spreading factor 32 and 8 Fig 8 Teoreticaloutput SINR versus SNR, % loaded system, spreading factor 32 and near-far situation SIRJ = db engts of te filters = 29 cips SIRJ = db engts of te filters = 38 cips 2 Fig 6 Teoretical outputsinr versus SNR, % loaded system, spreading factor 32 and near-far situation Fig 9 Teoreticaloutput SINR versus SNR, % loaded system, spreading factor 32 and all all SIRJ = db SIRJ = db engts of te filters = 9 cips engts of te filters = 9 cips Fig 7 Teoretical outputsinr versus SNR, % loaded system, spreading factor 32 and Fig Teoretical output SINR versus SNR, % loaded system, spreading factor 32 and, STTD case only