Near-Far Resistance of MC-DS-CDMA Communication Systems


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In this paper, the near-far resistance of the minimum
mean square error (MMSE) detector is derived for the
multicarrier direct sequence code division multiple access
(MC-DS-CDMA) communication systems. It is shown that
MC-DS-CDMA has better performance on near-far resistance
than that of DS-CDMA.

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Near-Far Resistance of MC-DS-CDMA Communication Systems

  1. 1. ACEEE Int. J. on Communications, Vol. 03, No. 01, March 2012 Near-Far Resistance of MC-DS-CDMA Communication Systems Xiaodong Yue1, Xuefu Zhou2, and Songlin Tian1 1 University of Central Missouri Department of Mathematics and Computer Science Warrensburg, MO USA Email: {yue, tian} 2 University of Cincinnati School of Electronics and Computing Systems Cincinnati, OH USA Email: {xuefu.zhou}@uc.eduAbstract—In this paper, the near-far resistance of the minimum on near-far resistance or not. It is worth mentioning that near-mean square error (MMSE) detector is derived for the far resistance also depends on the type of the receivermulticarrier direct sequence code division multiple access detector. In this paper, the near-far resistance of the widely(MC-DS-CDMA) communication systems. It is shown that used MMSE detector is derived for the MC-DS-CDMAMC-DS-CDMA has better performance on near-far resistancethan that of DS-CDMA. systems. It is shown that MC-DS-CDMA has better performance on near-far resistance than that of DS-CDMAIndex Terms—Code division multiaccess, Near-far resistance, systems.wireless communication II. SYSTEM MODEL I. INTRODUCTION Consider an asynchronous MC-DS-CDMA systems with Multicarrier CDMA, which combines the Orthogonal Nc subcarriers and J active users in a multipath fadingFrequency Division Multiplexing (OFDM) based multicarrier channel. Spreading codes of length Lc are used to distinguishtransmissions and CDMA based multiuser access, is a different users.promising technique for future 4G broadband multiuser It is shown in [4][5] that MC-DS-CDMA and DS-CDMAcommunication systems. The application of OFDM greatly have the similar baseband MIMO system model. The totalresolves the difficulty raised by multipath fading that is received signal vector χ M ( n) observed in additive whiteespecially severe for broadband communication systems. On Gaussian noise w(n) can be expressed as [4][5].the other hand, the application of CDMA greatly simplifiesthe multi-access and synchronization design. χ N ( n)  Ηs ( n )  w ( n ) (1) There have been many different types of multicarrier Where N is the smoothing factor, H is the signature matrixCDMA systems proposed [1][2]. One of them is MC-DS- and s(n) is the transmitted information symbol vector. ACDMA [3], where each OFDM block (after IFFT and cyclic smoothing factor N is indispensable to capture a completeprefix) is block-wise spreaded, i.e., the OFDM block is desired user symbol since the detector does not know thespreaded into multiple OFDM blocks, each multiplied with staring time of each desired user symbol.different chip of the spreading code. A major feature of MC- Since the channel effect on received energy can alwaysDS-CDMA communication system is that each OFDM be incorporated into a diagonal amplitude matrix A, withoutsubcarrier works like DS-CDMA. Specifically, if there is only loss of generality, we assume that the columns of the channelone subcarrier, then the MC-DS-CDMA reduces to a matrix H are all normalized in the following sections. Then (1)conventional DS-CDMA. One of the major advantages of can be rewritten asMC-DS-CDMA is that each DS-CDMA signal (in eachsubcarrier) of a user can be maintained orthogonal to that of χ N ( n)  ΗAs ( n)  w ( n) (2)all the other users, when orthogonal spreading codes areused. As a result, multi-access interference (MAI) is mostly III. NEAR-FAR RESISTANCE OF MMSE RECEIVER FOR MC-DS-CDMAavoided, which may greatly enhance the performance over SYSTEMSconventional DS-CDMA. The following assumptions will be made throughout this However, the well-known near-far problem in a multiuser paper. AS1: The symbols in s(n) are independently andsetting still places fundamental limitations on the performance identically distributed (i.i.d), with variance 1 (since symbolof MC-DS-CDMA communication systems. Therefore, near- energy can also be absorbed into the diagonal matrix A). AS2:far resistance remains one of the most important performance The noise is zero mean white Gaussian. AS3: The signaturemeasures for MC-DS-CDMA systems. Furthermore, it would matrix H is of full column rank (known as the identifiabilitybe interesting to explore whether the multicarrier has benefits© 2012 ACEEE 53DOI: 01.IJCOM.3.1.3
  2. 2. ACEEE Int. J. on Communications, Vol. 03, No. 01, March 2012condition in the blind multiuser detection literatures). Note H H  H d [00100] , where 1 is in the dth position. Note theAS3 is a reasonable assumption in practice considering the first and last equalities are based on the assumption of fullrandomness of the multipath channels [6]. column rank of the channel matrix H. From (3), it is seen that Without loss of generality, we assume that the dth symbol the AME does not depend on the interfering signal ampli-in s(n) is the desired transmitted symbol of the desired userand simply denote it by sd(n) (note the subscript d of sd(n) tudes. Thus, it is equal to the near-far resistance  d [7]. Itonly represents its position in s(n)). Therefore, the MMSE 1detector weight vector is given by fmmse=R-1Hd [6] , where R  d  d  1 then follows that ( H H H )( d , d )is the autocorrelation matrix of the received signal χ M ( n)and Hd is the dth column in corresponding to the desired Proposition 1 can be carried one step further to reach antransmitted symbol sd(n). It is also well known that when expression that facilitates comparison of near-far resistancenoise approaches zero, the zero forcing (ZF) detector is between multicarrier and single carrier DS-CDMA systems.proportional to the MMSE detector [6], fzf = αfmmse, where α is Before proceeding further, however, we need to define somea constant. Therefore, both detectors share the same near- useful matrices. Let I denote the subspace spanned by inter-far resistance. We have the following Proposition on near-far ference signature vectors Hi, i  d where Hi denotes the ithresistance of MC-DS-CDMA systems.  column in the signature matrix H. H is the matrix obtained byA. Proposition 1 deleting the dth column Hd from H. It is easy to show that  C ( H )  , where C ( ) represents the column space. Denote Proposition 1 The near-far resistance of the MMSE 1   M H H H , R d H H H and r d  H H H d is a vector resulting from   d 1detector for the MC-DS-CDMA system (2) is ( H H H ) ( d ,d ) deleting the dth entry from the dth column of M. Note Rd is non-singular due to AS3. We have the following proposition., where the subscript (d, d) denotes choosing the element atthe dth row and dth column. B. Proposition 2 Proposition 2 The near-far resistance in Proposition 1Proof: By applying the zero forcing detector to the received can be rewritten assignal vector, the output contains only the useful signal andambient Gaussian noise. The amplitude of the useful signal 1 H   d 1r d R d 1r dat the output is f H H d Ad s d ( n ) . Therefore, the energy of the zf 1 ( H H H ) ( d ,d ) (4)useful signal at the output isE s  E [f H H d A d s d ( n ) s* ( n ) Ad H d f zf ] Ad f H H d H H f zf . zf d H 2 zf d T he Proof: Equation (3) can be r ewritten asvariance of the noise is E n  2f H f zf where  2 is the power 1 det( M ) zf  d 1  d d ( H H H ) ( d ,d ) ( 1) det( R d ) , where det( ) represents thespectral density of white Gaussian noise. Using the definitionin [7], the asymptotic multiuser efficiency (AME) for the determinant of a matrix. To compute det(M), let i = d and dodesired transmitted symbol is show below the following row and column operations on M: 1) exchange the ith row column with the (i+1)th column; 2) exchange the  2[Q1( Pd ( ))] 2  2 Es E  2 A2 f zf Hd Hd f zf d H H ith row with the (i+1)th row and set i = i + 1. If i ‘“ col(H), where n d  lim 2  lim 2  lim 2 col(H) denotes the number of columns of H, go to step 1; else  0 Ad  0 Ad  0  2f H f zf A zf d terminate the row and column operations. We finally obtain H H H  H  f H H f H ( H 2 H  2I ) Hd Hd ( HA2 HH  2I ) Hd  lim mmseH d d mmse  lim d A H   0 f mmsef mmse  0 H 2 H 2  2 H 2  R d r d  Hd ( H A H  I ) ( HA H  I ) Hd M  H rd 1  . Since from M to M only even number of    HH HH A2 H Hd Hd HH A2H Hd H  d   (3) exchange operations are executed, as a result we have HH HH A2 H HH A2 H Hd d A4 1 H adj det( M )det( M ) det( R d )r d R d r d , where adj represents d   2 1 2   1 H Hd HH A ( HHH) A H Hd ( HHH)( d ,d ) adjoint of a matrix and the second equality is resulted from a standard matrix equality [8] (pp. 50). Therefore, Es ) H adjwhere P d ( ) Q ( , Q is the complementary Gaussian det( M ) det( R d )r d R d r d H  En  1r d R d 1r d . det( R d ) det( R d )cumulative distribution function, “+” representspseudoinverse. In (3), we have used the facts that  H 1 H( H A 2 H H )  ( H  ) A 2 H  , ( H H H )  H  ( H  ) as well as© 2012 ACEEE 54DOI: 01.IJCOM.3.1. 3
  3. 3. ACEEE Int. J. on Communications, Vol. 03, No. 01, March 2012 IV. COMPARISON OF NEAR-FAR RESISTANCE OF MMSE DETECTOR A. Proposition 3 BETWEEN MULTICARRIER AND SINGLE CARRIER DS-CDMA COMMUNICATION SYSTEMS Proposition 3 Denote  1 as the expectation of the near- d It is interesting to investigate how does the multicarrier far resistance of the MMSE detector in DS-CDMA and  2 as dscheme affect the near-far resistance in DS-CDMA systems. the expectation of the near-far resistance of the MMSETo this end, we analyze the near-far resistance of the MMSE detector in MC-DS-CDMA. Then under AS3, AS4, and AS5,detector for 1). DS-CDMA and 2). MC-DS-CDMA. In order to facilitate fair comparison between different 1  d  d 2 . Proof: under AS3, starting from (4), the conditionalscenarios, we make the following assumption. AS4: the expectation of  id ,conditioning on the interference subspaceprocessing gain Lc, the system load J, the smoothing factor I, is given byN, the distributions of multipath delay spread andasynchronous user delay are the same under different 1 1scenarios. Since the dimension of the signature matrix will E [ id |I ]1 E[r iH ( R i ) r id | I ]1 E[tr{r id r iH ( Rid ) }|I ] d d dprove to be useful for our following derivations, we now 1 1 E[tr{HiH Hid H iH Hi ( R id ) }| I ]  d specify those parameters. Let H1 denote the signature matrix 1 1 E[tr{Hid HiH Hi ( R id ) HiH }| I ]   dof the DS-CDMA system and H2 denote the signature matrix i iH | I ]  ( i ) 1  H } 1tr{E[ H d H d Hi R d Hiof MC-DS-CDMA systems. Under AS4, the dimensions of 1 1 1  iH Hi ( R id ) } tr{H the signature matrix H1 and H2 are N L c J ( L h CDMA  N 1) and DS row( H i ) 1 1 (7)N L c N c J N c ( L Mc  DS  CDMA N 1) h respectively [5][9], where Lh 1 tr{R id ( R i ) } d row( H i )(non-negative integer) is related to the maximum multipath col ( Hi )1 1delay spread and the maximum asynchronous user delay, and row( H i )is defined in [5][9] as follows.  L c  L g 1 d j   where tr ( ) represents the trace of a matrix, Hi , r id and R id areL DS CDMA  max  h  (5) j  Lc  defined similar as in section 3 for the ith scenario. The sixth equality is based on the property of conditional expectation  N cL  L g 1 d j L MC  DS CDMA  max  h c  (6) and seventh equality is based on the fact that j  N cL c   1 E[ H id H iH |I ] E[ Hid HiH ] Iwhere Lg denotes the maximum multipath delay spread and dj d d row( H i ) due to AS5. Based on (5)denotes the jth user’s asynchronous user delay. (6) and AS4, it is straightforward to show that Next we will compare the near-far resistance of MMSEdetector under different scenarios. The value of the near-far J ( L h CDMA N 1) 1 DS E[ 1 |I ]1 d (8)resistance derived in Proposition 1 clearly depends on the N Lcmultipath channels and asynchronous transmission delays.Since these parameters are random in nature, it is more 2 J N c ( L h  DS CDMA N 1) 1 MC E[ d | I ]  1  (9)meaningful to compare the statistical average of the near-far N Lc N cresistance rather than a particular random realization. To thisend, we need an additional assumption. AS5: Under the ith Subtracting (8) from (9), we havescenario, assume H id (the vector in Hi which is correspondingto the desired transmitted symbol of the desired user) is a 2 1random vector with a probability density function E[ d | I ]  E[ d | I ] 1 J ( LDS CDMA N 1)1 J N c( Lh DS CDMA N 1)1 h MC c (0 row ( H i ), I row( H i ) ) and is statistically independent   row ( Hi ) N Lc N Lc N c (10)of the interference subspace I (since it won’t affect the J N c( Lh CDMALh DS CDMA)1 N c DS MCderivation, here I is a general expression which includes all  N Lc N cscenarios), where  c represents the complex normal Under AS4, J, N and Lc are the same under different scenariosdistribution, row( H i ) denotes the number of rows in Hi, x  x 0 row ( H i ) represents the row ( H i )1 zero vector, and for each realization of I. It is also easy to show that       a   ab I row( H i ) represents the row ( H i )row( Hi ) identity matrix. The when x > a and b > 1. In other word, L DS CDMA  L h  DS CDMA . h MCfact that the variance is 1 row( Hi ) is because H id is normalized.We then have the following proposition. Based on (10), we have E[ 1 |I ] E[ 2 |I ] for each realization d d of I.© 2012 ACEEE 55DOI: 01.IJCOM.3.1.3
  4. 4. ACEEE Int. J. on Communications, Vol. 03, No. 01, March 2012Since  id  E I [ E[ id | I ]] , i = 1, 2, the claims in Proposition 3 are REFERENCESproven. Note when Nc = 1, MC-DS-CDMA reduces to a [1] S. Hara and P. Prasad, “Overview of Multi-Carrier CDMA,”conventional DS-CDMA and thus has the same near-far IEEE Communications Magazine, vol. 14, pp. 126-133,resistance as DS-CDMA. December 1997. [2] Z. Wang and G. Giannakis, “Wireless Multicarrier Communications,” IEEE Signal Processing Magazine, pp. 29- CONCLUSIONS 48, May 2000. The well-known near-far problem in a multiuser setting [3] V. DaSilva and E. Sousa, “Performance of Orthogonal CDMAstill places fundamental limitations on the performance of Codes for Quasi-synchronous Communication Systems,” Proc. of IEEE ICUPC’93, pp. 995-999, Ottawa, Canada,CDMA communication systems. In this paper, the near-far October 1993.resistance of the MMSE detector is derived for the MC-DS- [4] F. Ng and X. Li, “CFO-resistant Receiver for AsynchronousCDMA systems and compared with DS-CDMA. It is shown MC-DS-CDMA Systems,” Proc. of IEEE Internationalthat MC-DS-CDMA has better performance on near-far Conference on Acoustics, Speech and Signal Processing, pp.resistance than that of DS-CDMA. 253-256, Honolulu, HI, April 2007. [5] Q. Qin, Linear Prediction Approach for Blind Multiuser Detection in Multicarrier CDMA Systems, Master Thesis, University of Cincinnati, 2002. [6] H. Liu, Signal Processing Applications in CDMA Communications, Artech House, 2000. [7] S. Verdu, Multiuser Detection, Cambridge University Press, 1998. [8] H. Lutkepohl, Handbook of Matrices, John Wiley and Sons, 1996. [9] X. Li and H. Fan, “Direct Blind Multiuser Detection for CDMA in Multipath without Channel Estimation,” IEEE Trans. Signal processing, vol. 49, pp. 63-73, January 2001.© 2012 ACEEE 56DOI: 01.IJCOM.3.1. 3