Receiver Design for Downlink MIMO MC-CDMA in Cognitive Radio Systems
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1 1st Annual IEEE International Syposiu on Personal, Indoor and Mobile Radio Counications Receiver Design for Downlink MIMO MC-CDMA in Cognitive Radio Systes M. Raabzadeh 1, and. hoshbin 1 1 Electrical Engineering Departent, Ferdowsi University of Mashhad, Mashhad, Iran Razavi ouse of Elites, Mashhad, Iran Abstract Multiuser interference (MUI) and co-space interference (CSI) are two challenging issues in design of ulticarrier code-division ultiple-access (MC-CDMA) systes when ultiple antennas are used at both the transitter and receiver sides (MIMO transission). On the other hand, in cognitive radio (CR) syste, the secondary users that use MC- MCDA technique ust deactivate the subcarriers used by the priary users. his leads to loss of orthogonality of the conventional spreading codes such as adaard Walsh codes. In this paper, we have odified two recently proposed linear receivers to be deployed in MIMO MC-CDMA based CR downlink transission where soe of the subcarriers are turned off. o solve the resultant non-orthogonality proble, the coplex carrier interferoetry (CI) codes are utilized that exist for any length. he first ethod, called total interference cancellation (CI-IC), is able to copletely eliinate the CSI and the MUI. he other ethod is called CI sybol-chip level iniu ean square error (CI-SC-MMSE) that shows superior bit error perforance with respect to CI-IC. For different scenarios, siulation results show that the proposed CI based receivers are able to effectively itigate the MUI and the CSI in coparison with the case where adaard Walsh codes are utilized. Index ers cognitive radio, downlink MC-CDMA, MIMO, SVD, space-frequency spreading, MMSE. I. INRODUCION Cognitive radio is a novel approach for iproving the utilization of the scarce radio spectru by aking it possible for a group of secondary users (SU) to access the frequency bands which are not used by the priary users (PU). As the unused spectrus ay be non-contiguously available for the secondary users, ulticarrier techniques such as OFDM and ulticarrier code division ultiple access (MC-CDMA) are good candidates to efficiently utilize these spectru holes[1]. MC-CDMA syste is able to itigate the intersybol interference (ISI) and the ultiuser interference (MUI) in the frequency selective channels because of cobining orthogonal frequency division ultiplexing (OFDM) technique and orthogonal spreading codes. Benefitting the transission through ultiple antennas, ultiple-input ultiple-output (MIMO) MC-CDMA systes have attracted any attentions for being deployed in broadband wireless counications for attaining ore capacity[]. owever, the arising co-space interference (CSI) due to MIMO transission ruins the orthogonality of the spreading codes that causes ultiuser interference (MUI). o address these challenging issues, a ultiple of effective linear [,3] and nonlinear [4] receivers have been proposed. he chip level ordered successive spatial and ultiuser interference cancellation (OSSMIC) receiver [4] is a odified V-BAS based receiver to reect the spatial and ultiuser interference ointly. he linear total interference cancellation (IC) receiver, proposed in [3], is based on the singular value decoposition (SVD) of the channel atix. he IC copletely eliinates the CSI and MUI by using orthogonal Walsh spreading codes, however, its perforance suffers fro the sall singular values of the channel. So another linear SVD based receiver has been proposed that is naed as sybol chip level MMSE (SC-MMSE) [3] which solves this proble by iniizing the MSE criterion. It also relys on orthogonal spreading codes. o use MC-CDMA in cognitive radio transission, the SU base station can only deploy the non-contiguous spectru holes by turning off the subcarriers that are within the spectru used by the PUs. Such syste is called noncotiguous (NC) MC-CDMA [5,6]. In this case, the nuber of available subcarriers could be any integer values. he conventional orthogonal adaard-walsh (W) codes only exist when their length is ultiple of four. So these codes cannot provide the desired orthogonality in CR environent. In NC-MIMO MC-CDMA systes, the deactivation of soe of the subcarriers causes the spreading codes to be nonorthogonal and hence the challenginig issue of the oint presence of MUI and CSI is severed. Carrier interferoetry (CI) codes [7] are coplex orthogonal spreading codes that can be generated with any integer valued lengths. he utilization of the CI codes is investigated in [5] for the NC single-input single-output MC-CDMA systes. In this paper, we odel the downlink NC-MIMO MC- CDMA syste to be deployed in CR transission. he two linear SVD based receivers, IC and SC-MMSE are odified to be applicable to non-contiguous transission when soe of the subcarriers are deactivated. Also, the CI codes are deployed to solve the non-orthogonality of the conventional adaard-walsh codes. So we call these new receivers as CI- IC and CI-SC-MMSE. It is shown, by siulations, that the proposed NC CI-IC and CI-SC-MMSE keep their interference itigating perforance when the nuber of /10/$ IEEE 785
2 deactivated subcarriers is increased. So they are very good choices for any CR based reconfigurable ulti-user broadband systes. he paper is organized as follows. After introduction, downlink MIMO MC-CDMA syste odel based on spacefrequency spreading code and the SVD is introduced in Section II. he CI-IC ethod is developed in Section III. he SVD-based sybol-chip level MMSE ethod is derived in Section IV. Perforance evaluations and coparisons are considered in Section V by coputer siulations and the paper is concluded in Section VI. II. SYSEM MODE A downlink MIMO MC-CDMA syste with users and subcarriers is considered where the base station uses N transit antennas and each of the users eploy M receive antennas. It is assued that M N []. In this section, without taking into account the CR transission, we briefly introduce the downlink MIMO MC-CDMA odel based on the linear IC receiver[3]. After odulating the data bits, the data vector of the th user at the base station is fored as d [,1,,,...,, ] = d d d J where J nuber of substreas, J {1,.., N }. We assue that data sybols of different streas of different users are i.i.d with noralized power, so we have E[ ddk ] = I Jδ ( k) for k, {1,.., } where I J identity atrix with the size J J. In conventional MC- CDMA systes, each of the data sybols is spreaded in the frequency doain (i.e., on subcarriers). owever the spreading can be perfored ointly on space and frequency to benefit fro spatial diversity and design the ISI reecting receivers for MIMO MC-CDMA. he space-frequency (SF) spreading code atrix is C = [ c,1, c,,..., c, J] with the size of J that consists of J different spreading orthogonal code vectors and we have CCk = γi Jδ( k) for k, {1,,, } where γ = processing gain. he sybols of all the users are spreaded on spacefrequency subchannels and after adding theses spreaded data, the following data vector is sent by the base station: x = C d (1) k k At the receiver of the th user, the signal vector at the output of the fast Fourier transfor (FF) block becoes y = C d + ζ () k k Where y M 1 received signal vector and ζ additive white Gaussian noise vector with zero ean and covariance atrix Rζ = σζ I M. Also M block-diagonal space-frequency channel atrix between the base station and the th user. o highlight the oint presence of the CSI and MUI, y, can be rewritten as desired signal + CSI MUI noise y = C d + C d + ζ k k k A powerful tool for itigating CSI use of SVD based beaforing. he singular value decoposition of the block diagonal channel atrix,, is as follows = UΛV (4) In which U and V are M and block unitary atrices and Λ diagonal atrix. In the SVD based receiver IC, it is sufficient to deploy the beaforing and equalization atrices at the receiver and there is no need to deploy the atrix V as the transit beaforing atrix for the th user. So we have 1 1 = = k k + y Λ U y V C d Λ U ζ (5) o finalize the oint CSI-MUI reection, we deploy the despreading atrix at the receiver that satisfies the following relation G = CV (6) where the size of G is J. After despreading, we have ˆ 1 d = Gy = d + η (7) 1 where η = G ΛUζ J 1 noise vector at the output of the despreader. As it can be seen in (7), both CSI and MUI are copletely itigated and total interference becoes zero; consequently, the proposed ethod is called total interference cancellation (IC). III. CI-IC RECEIVER FOR NC-MIMO MC-CDMA In cognitive radio systes, the secondary users should use the part of the spectru that is not used by the priary user. Consider the case where P subcarriers out of total subcarriers are occupied by the priary user. For the secondary MC-CDMA users, these subcarriers are turned off to avoid the interference and the base station should spread the users data sybols on only I=-P subcarriers. In NC-MIMO MC-CDMA, the data sybols of each user are spreaded on NI space-frequency subchannels that could be any integer value and therefore allowing axiu full load = I distinct users. he orthogonality of the conventional spreading codes is applicable only when their length has a specific value. he well-known adaard-walsh codes only exist when I is a ultiple of 4. o solve this challenging issue, we deploy the coplex carrier interferoetry code set that its orthogonality property is independent of the codes length. et the CI spreading code atrix of the kth user be (3) 786
3 C k = [ c k,1, c k,,..., c k, J] with the size of NI J. he th colun of C is defined as 0 θk, ( NI 1) θk, k, = [ e, e,..., e ] c (8) where the phase of the code vector is set as follows π θ k, = k, NI 0 k NI 1 (9) where k = ( k 1) J +, 1 k I, 1 J (10) index of the substrea. It can be seen that the code length is NI. he CI codes are orthogonal, so we have C C k = γi Jδ( k) (11) for k, {1,,, } and γ = NI new processing gain. By spreading the data vector of all users, the SF data vector of the active subcarriers becoes (1) () ( I) k k,,..., x = C d = x x x (1) () where the size of x is NI 1 and x i represents the spatial N 1data vector on the ith active subcarrier. o deploy -point IDF at the transitter, he NI 1 data vector, x, is apped to active subcarriers of the 1 data vector, x = Map( x ). et the subset deterining the indexes of the available subcarriers to be F = { f1, f,... fi } where fi { 1,..., }. By deploying MAAB M syntax for referring to the rows and colun of the atrices, we have x ( nfi,1) = x ( ni,1), fi F for n { 1,..., N} (13) x ( ng,1) = 0 if g F he data vector x can also be written as x = x, x,..., x (14) in which x () represents the spatial N 1 data vector on the (1) () ( ) l lth subcarrier. o transit x, the subcarriers of each antenna branch is selected by the selection atrix P where for exaple P is defined as l = 1 l= l= n = P = n = So the tie-doain (D) data vector can be written as (15) [1] [] [ N] xd = WBD Px = D, D,..., D I x x x (16) where WBD block diagonal DF atrix as follows WBD= blockdiag ( W,..., W ) (17) and W FF atrix that its ( i, ) th eleent is ( i 1)( 1) 1 π 1 [ W ] i, = e. In (16), the coefficient is I used to allocate the available power to the active subcarriers. After adding cyclic prefix (CP) and upconversion, x D, is transitted by N antennas. At the receiver, after reoving CP and DF and discarding the turned-off subcarriers, the NI 1 space-frequency data vector for the active subchannels becoes y = C d + ζ (18) k k where MI NI space-frequency block diagonal channel atrix that is attained by discarding the subchannel atrices of the turned off subcarriers in. Siilar to (4), the SVD of can be obtained as follows = U Λ V (19) In which U and V are MI NI and NI NI block unitary atrices and diagonal NI NI atrix. Deploying the beaforer, equalizer and despreading atrices respectively, we have ˆ d = G U y = d + G U ζ (0) he despreading atrix, G, is calculated as G = C V (1) Note that in (0), the despreading coefficient is 1, because the available power is only allocated to the active subcarriers, as can be seen in (16). Although soe of the subcarriers are deactivated, by deploying the orthogonal coplex CI codes that exist for any integer-valued length, the ability of CI-IC to copletely eliinating CSI and MUI is retained. As it can be seen in (0), the SF noise at the input of the slicer is ultiplied with the inverse of related singular values of the channel atrix at that subchannel. So sall singular values degrade the perforance of the CI-IC ethod. In the next section, we develop another ethod based on MMSE criterion to address this challenging issue that can also be applicable in CR scenario. IV. CI SYMBO-CIP EVE MMSE MEOD Consider the received SF data vector in (18), in this ethod, 787
4 firstly the beaforing atrix, U, is utilized as follows y = U y () o avoid the noise aplification due to sall singular 1 values of, the NI NI diagonal equalization atrices are separately deployed for each substrea. So the th received datastrea after despreading becoes ˆ d, = g, F, y (3) In order to calculate the equalizer coefficients, we rewrite (3) by swapping the depsreader and the equalizer as ˆ d, = f, G, y = f, G, V C d + f G V C d + f G (4) U ζ,, k k,, k In the above relation, the first ter represents the desired sybol of the th user, the second and the third ters are CSI and MUI respectively and the last ter represents the noise part. o copute the equalization vector, f, that is utilized at the chip level, the MMSE criterion is eployed after despreading process at the sybol level. So, we call this ethod as sybol-chip level MMSE. he ean square error at sybol-level is defined as follows ε = E d ˆ, d, (5) By iniizing ε with respect to f, and after doing soe anipulations, we have ( ) 1 f = A + B a (6),,,, where A,, B, and a, are defined as A, = G, V C k C k V G, (7) B, = σ ζ G, G, (8) a = G V c (9),,, he NC-CI-SC-MMSE receiver eliinates the deteriorating effect of sall singular values of the channel atrix. herefore, coparing equations (4) for SC-MMSE with (0) for the IC, it can be seen that the orthogonality property is not preserved and thus the MUI is not copletely eliinated in the sybol-chip MMSE ethod. owever, the effect of interference plus noise on detection at the sybol level is iniized, resulting in superior perforance. V. SIMUAIONS AND COMPARISONS A MIMO MC-CDMA syste for downlink counication is considered in siulations when J = M = N = and the nuber of subcarriers is = 3. A sequence of independent, identically distributed signal vector with 16QAM odulation schee is sent fro transitter antenna arrays. Each frequency selective MIMO channel between the base station and each user has been realized based on an exponential power delay profile with c =8 resolvable paths where the exponential decay factor is assued to be β = 0.1. he proposed NC-CI receivers, naely CI-IC and CI-SC- MMSE, are copared with the case where the adaard- Walsh (W) codes are deployed instead of CI codes that we call the as W-IC and W-SC-MMSE. Since theses codes don t exist when the code length is not a ultiple of four, the adaard Walsh codes are generated whose lengths are the sallest ultiple of four that is larger than the required length and then they are cut off to the desired length. he perforance evaluation is done based on attained in different CR scenarios and single-user perforance is also included as the benchark. In Fig.1, the bit error rate perforances of the four ethods are copared when P=8 subcarriers are utilized by the priary users. So the nuber of active subcarriers is I=- P=4 and hence in the full-loaded case we can have =I=4 active users. It can be seen that the IC and SC-MMSE receivers can be utilized in the non-contiguous MIMO MC- CDMA where soe of the subcarriers are deactivated. he IC receivers copletely eliinate ultiuser interference however suffer perforance degradation due to sall singular values of the channel. he SC-MMSE receiver solves this drawback and shows superior perforance both in the single user and full-loaded scenarios, since the SC-MMSE 1 doesn t deploy Λ as the equalization atrix. In this scenario, as the codes length, NI=48, is ultiple of four, the W codes are orthogonal with no perforance loss. he CI receivers show the sae perforance of the W receivers proving the applicability of the coplex CI codes instead of the orthogonal antipodal W codes for downlink MIMO MC- CDMA transission. In Fig. we have considered the case where P=9 subcarriers are turned-off. Since NI= 46 is not ultiple of four, the W codes aren t orthogonal and significant error floor appears at =10 for W-IC. On the other hand, the CI-IC ability to MUI reection is aintained because of using the CI codes. For the SC-MMSE receivers, it can be seen that in the single user case, the perforance of both the receivers sae but in the fully loaded environent, SC-MMSE with W codes shows 5 db perforance loss due to MAI arising to the syste at =10 with respect to CI-SC-MMSE receiver. owever W-SC-MMSE doesn t experience any error floor coparing to W-IC. It shows that the SC- MMSE is uch stronger than the IC receiver to cope with the interferences even when the codes are not orthogonal. he perforance of the proposed receivers is depicted in Fig.3, when the nuber of deactivated subcarriers is increased to P=1, so only I=11 subcarriers are available. In this case the codes length NI= is not ultiple of 4. Coparing Figs. and 3, it can be seen that the perforance of the CI-IC receiver is slightly degraded in high SNRs only. Because with 788
5 less available subcarriers, the diversity order is decreased. owever, roughly speaking, the CI-IC perforance doesn t depend on the nuber of active subcarriers. But the perforance of both SC-MMSE receivers depends on the nuber of active subcarriers. he perforance of CI-SC- MMSE and W-SC-MMSE receivers is degraded about 5 db 4 at =10 in the full-loaded scenario. CI-IC, =1:4 W-IC, =1:4 CI-SCMMSE, =1 CI-SCMMSE, =4 W-SCMMSE, =1 W-SCMMSE, =4 VI. CONCUSIONS 10 - he Multiuser interference, co-space interference and the loss of spreading codes orthogonality due to deactivation of soe of the subcarriers are the challenging issues ahead of MIMO MC-CDMA systes for being utilized by the secondary users in downlink CR transission. In this paper, two SVD based linear receivers are developed for CR transission that deploy carrier interferoetry spreading codes to cope with the deactivation of the subcarriers. he first ethod, CI-IC is able to itigate the MUI and the CSI alost independently of nuber of available subcarriers. It is shown that when the IC is developed by using adaard Walsh codes, there will occur error floor in its perforance in the fully loaded case. Although the CI-IC copletely eliinates CSI and MUI, it aplifies the noise power. So the CI-SC-MMSE is also developed by considering both the interference and noise as well as the deactivation of the subcarriers. he CI-SC-MMSE ethod shows better perforance in coparison with the CI- IC due to using MMSE criterion to design equalizer weights. owever, in contrast to CI-IC, its perforance is degraded when the nuber of deactivated subarriers is increased. REFERENCES [1]. Weiss and F. Jondral, "Spectru pooling: an innovative strategy for the enhanceent of spectru efficiency," IEEE Coun. Mag., vol. 4, pp. 8-14, March 004. [] M. Vehkapera, D. ukovic, Z. i and M. Juntti, "Receiver design for spatially layered downlink MC-CDMA syste, " IEEE rans. Vehic. echnol., vol. 54, No. 3, pp , May 005. [3]. Zairi-Jafarian, M. Raabzadeh, SVD-based receiver for downlink MIMO MC-CDMA systes, IEEE ICC, June 009, pp [4] A. Phasouliotis and D..C. So, "A novel OSSMIC receiver for downlink MIMO MC-CDMA systes,", in Proc. IEEE VC, May 008, pp [5] Z. Wu, P. Ratazzi, V. D. Chakravarthy and ang ong, "Perforance evaluation of adaptive non-contiguous MC-CDMA and non-contiguous CI/MC-CDMA for dynaic spectru access", IEEE CrownCo, May 008, pp.1-6 [6] R. Rabanshi, et al., Quantitative coparison of agile odulation techniques for cognitive radio transceivers, IEEE CCNC, Jan. 007, pp [7] B. Nataraan, C. R. Nassar, M. Michelini, and Z. Wu, ighperforance MC-CDMA via carrier interferoetry codes, IEEE rans. Veh. echnol., vol. 50, no. 6, pp , Nov ACNOWEDGMEN his work was supported in part by Iran eleco Research Center (IRC) Fig.1. versus SNR for the IC and the SCMMSE ethods when I= CI-IC, =1:3 W-IC, =1 W-IC, =3 CI-SCMMSE, =1 CI-SCMMSE, =3 W-SCMMSE, =1 W-SCMMSE, = Fig.. versus SNR for the IC and the SCMMSE ethods when I= CI-IC, =1:11 CI-SCMMSE, =1 CI-SCMMSE, =11 W-SCMMSE, =1 W-SCMMSE, = Fig.3. versus SNR for the CI-IC and the SCMMSE ethods when I=
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