This paper studies a new robust constrained minimum output energy (CMOE)-based blind detector for multicarrier code division multiple access (MC-CDMA) systems. The proposed receiver intends to minimize the receiver's output energy while preserving the components of the desired user. By imposing quadratic weight constraints, the CMOE detector is made more robust against signal modeling errors, and a better performance over the standard CMOE detector is obtained. Steady-state signal-to-interference-plus-noise ratio (SINR) analysis of the blind CMOE detector and the minimum mean-squared error (MMSE) method with training sequences is presented. Numerical results show that the performance of the new robust detector is comparable to subspace-based method using exact singular value decomposition (SVD).published_or_final_versio

Chan, SC

Cheng, H

HKU Scholars Hub

Title THE performance and robust implementation of a blind CMOEreceiver for MC-CDMA systemsAuthor(s) Cheng, H; Chan, SCCitation Proceedings - Ieee International Symposium On Circuits AndSystems, 2004, v. 3, p. III377-III380Issued Date 2004URL http://hdl.handle.net/10722/46431Rights Creative Commons: Attribution 3.0 Hong Kong LicenseTHE PERFORMANCE AND ROBUST IMPLEMENTATION OF  A BLIND CMOE RECEIVER FOR MC-CDMA SYSTEMS H. Cheng and S. C. Chan Dept. of Electrical & Electronic Engineering The University of Hong Kong, Pokfulam Road, Hong Kong ABSTRACTThis paper studies a new robust constrained minimum output energy (CMOE)-based blind detector for multicarrier code division multiple access (MC-CDMA) systems. The proposed receiver intends to minimize the receiver’s output energy while preserving the components of the desired user. By imposing quadratic weight constraints, the CMOE detector is made more robust against signal modeling errors, and a better performance over the standard CMOE detector is obtained. Steady-state signal-to-interference-plus-noise ratio (SINR) analysis of the blind CMOE detector and the minimum mean-squared error (MMSE) method with training sequences is presented. Numerical results show that the performance of the new robust detector is comparable to subspace-based method using exact singular value decomposition (SVD).  1. INTRODUCTION MC-CDMA was recently proposed as an efficient multicarrier transmission scheme for supporting multiple access commu-nications [1]. It combines CDMA and orthogonal frequency division multiplexing (OFDM) techniques. It has received considerable attention because of its advantages in frequency diversity, multipath fading resilience and etc [2]. Similar to conventional CDMA systems, MC-CDMA is an interference-limited system. It is rather sensitive to multiple access interference (MAI), which arises from the other users signals transmitted using the same frequency band. In [3], Honig et al proposed a blind linear MMSE receiver, called the CMOE detector, for MAI suppression in CDMA systems. The CMOE detector minimizes the receiver’s output energy while preserving the components of the desired user in the received signal. Under ideal conditions, it has a performance close to the exact MMSE solution [4]. Also, it can be conveniently implemented using the standard RLS algorithm of )( 2MO  computational complexity ( M  is the length of the spreading code).  However, it is found that the performance of the CMOE detector will considerably degrade due to channel estimation error and other possible types of signal mismatch [5] [6]. In this paper, a robust CMOE detector with quadratic weight constraint is proposed for MC-CDMA systems. This technique is a simple and effective method for improving the robustness of the detector with respect to signal modeling errors. A CMOE-based channel estimator is also presented, where the channel can be estimated blindly by solving the minimum eigenvector of a matrix. Subspace-based blind MMSE receivers [7] are also investigated to compare the performance of the CMOE-based and subspace-based methods. The performances of the subspace-based MMSE detector using the exact SVD and the robust CMOE detector are found to be comparable.The rest of the paper is organized as follows: Section 2 describes the principle of MC-CDMA systems. Section 3 is devoted to the robust CMOE receiver, while SINR analysis is presented in Section 4. Section 5 gives the numerical examples, and finally, conclusion is drawn in Section 6.2. SYSTEM MODEL We consider a MC-CDMA system for uplink transmission from the terminal users to the base station. Fig. 1 shows the structure of an MC-CDMA transmitter. The original data stream of the kth  user is first converted into P  parallel data sequences. Eachserial/ parallel (S/P) converted output spreads with a spreading sequence of length M . The data chips after spreading are S/P converted into M  parallel subcarriers. The total PMN   chips are modulated by the IDFT and converted back into serial data. The cyclic prefix is inserted between symbols to avoid inter-symbol interference caused by multipath fading. Let T  be the symbol duration of the original data stream, and sT  be the one at the subcarrier, then it has TPTs  . The frequency separation between the successive subcarriers is sTf /1 ' . The complex equivalent transmitted signal of user k  can be written as tfpPmjPpMmsimkipkiikk eiTtcbPts'  f ¦ ¦ ¦ )(21010)(,)(,)()( S\ , (1)where kP  is the chip energy, )(,ipkb  is the transmitted thi  data bit in the thp  data stream, )(,imkc  is the thm  chip of the given spreading sequence, and )(t\  represents the rectangular pulse waveform. Note that there are P  data streams for the kth  user, and the data bits on different streams use the same spreading sequence. In order to achieve the maximum frequency diversity, the subcarrier separation for )(,npkb  is sTPf /'  ' . The kth  user’s signal )(tsk  propagates through a frequency-selective Rayleigh fading channel with L  received paths. The channel is represented by a time-variant impulse response  ¦   Lllklkk tttg1,, )()()( WGD , (2),,,;,((( ,6&$6where k  is the user index, )(, tlkD is the lth  path gain which is independent zero mean, complex Gaussian random process, and lk ,W  is the propagation delay for the lth  path, respectively.  In MC-CDMA systems, because of the large symbol duration, each subcarrier approximately experiences flat fading. Assume that there are K  simultaneous users in the system, all using the same selection of P  and M . At the receiver, the signal is sampled at a rate sTN / , the samples corresponding to the cyclic prefix are discarded, and a DFT of size N  is performed. For simplicity, we will consider a synchronous model, where all the users arrive at the same time. The received signal TpMPpp iyiyi )](,),([)( )1(  y after DFT operation with respect to the data symbol )(,ipkb  can be given as )()()(10)(,)(,10)(,)(,ibPibPiKk kipkipkkKkipkipkkkpndnhCy ¦  ¦    , (3)where (for convenience, the subscript i  is omitted) pkb ,  is the data symbol corresponding to the pth  data stream; kP  is the chip energy; pk ,h  denotes channel frequency response, whose element is 1,,0),(1)(210,,  ¦   MmeNh NpPmljLllkpPmk SD ;  kC]}1[,],1[],0[{ Mcccdiag kkk   is the code matrix; ,[ ,0, pkkpkhc dTpMPkMk hc ], )1(,1  represents the effective signature; and TpMPpPp ],,,[ )1(  KKK n  denotes complex additive white Gaussian with zero mean and variance 2vV .kc1TPTS  12P)2cos( 1tf PS)2cos( 1)1( tf MP Skc2kMc)2cos( 1tfS¦s (t)IDFTother usersS/P)(TDataFig. 1. Transmitter structure for MC-CDMA. 3. ROBUST CMOE DETECTION In practical applications, the estimated effective signature wave-form 0~d  generally contains errors. In addition, the covariance matrix is estimated from a finite number of the observed data. The performance of the standard CMOE detector will degrade greatly due to these two advert factors [3] [5]. Robust CMOE detectors are thus desirable to overcome the signal modeling errors. One simple and efficient method is to impose quadratic constraints on the norm of the weight vector )(nw . Without loss of generality, the subscript p will be omitted from Eq. (3), and user 1 is the desired user. The CMOE detector with quadratic constraints then can be formulated as follows 0021,1)(..,)()(min Tntsin HHHniin d ¦ wwdwywwO , (4)where 10  O  is the forgetting factor, and 0d  is the effective signature waveform of the desired user. To meet 1)( 0  dw nH , a vector qw  is defined as 1000)(  dddw Hq . A reasonable constraint value is 20 2 qT w . The solution to the constrained optimization problem in Eq. (4) is given by ].)(/[])[()(])([011100111011010dRRǿddRRǿdǿRdǿRdwyyyyyy  EEEEHH(5)Inspired by the approach in [9], we propose an algorithm to compute the diagonal loading E  given a quadratic constraint 0T ,and to implement RLS updating for Eq. (5). For small E , the term 11)(  yRǿ E  can be approximated using the first two terms of its Taylor series expansion, i.e., 111)(  | yy RǿRǿ EE . With this approximation, Eq. (5) becomes    )/()( 011001001101dRRddRddRRdRw yyyyyy | HH EE . (6)Let 010dRd y Hr , wRdRRv yyy~1011    r , and r/~ 01dRw y .We get )~~1/()~( wwvww Hr | EE . When w~  does not satisfy the norm constraint, we can solve the following equality for E ,   020    cbaTH EEww , (7)where2420~vw  rTa , ]~~([2 20 wvw rTebH  , and 20~w Tc . The solution of the diagonal loading E  should be real, non-negative value. More details of choosing the value of E  from Eq. (7) are presented in [9]. An appropriate solution of Eq. (7) is )2/()4(( 2 aacbeb  E .A RLS algorithm for updating the weight vector )(nw  in Eq. (5) can be summarized as follows: ]).[][1/(])[][(][,2/)]4([,][],][][][([2,][][],[][][),][(,][,][,)(][,][)][(][]},1[][*][]1[{1][,][]1[][][]1[][:;]0[,)0(:220202420000220100001001nnrnnnaacbebnTcnrTnnebnnrTannrnnrTnifnTnnnnnnnnnnnnnnnUpdateInitiationHHHqHqHHHMMwwvwwwwvwvwwPvdPdwwdddwdPdPdwPyKPPyPyyPKǿP0w       !       uEEEOOGNext, we consider a CMOE-based channel estimator. For a standard CMOE detector, the ideal solution is give by [3]  011010)())(( dRdRdw nn yyHo . (8) The resulting minimum output variance of the CMOE detector is ,,,1010min))(()(   dRdwRw nnP yHoyHo . (9)We can minimize the reciprocal of Eq. (9) with respect to 0d  to maximize the signal components at the receiver output,  0100)(minargˆ0dRdddnyH  . (10)Consider a channel with L  multipaths, and 0g  is the channel impulse response. It has 00 gFh m , where LMmuCF  is a DFT matrix. We then have 000 gˆFCd m , where 0C  is the code matrix of the desire user, and 0gˆ  denotes the estimation of 0g .Therefore, minimizing Eq. (10) with respect to 0g  yields 00100ˆ0 ])([minargˆ10gFCRCFggȍy   	 mHHmHCgnL u .(11)It can be seen that the channel estimate 0gˆ  is the eigenvector associated with the smallest eigenvalue of the matrix ȍ .4. SINR ANALYSIS  In this section, the steady-state SINR of blind CMOE and training MMSE detectors both with RLS adaptation rule will be presented. Assume that the transmitting symbols among the users are zero mean and i.i.d. sequences. Consequently, we have insnKkHkkkHH PPE RRǿddddyyRy  ¦   )(}{ 211000 V . The output SINR is defined as )/()( wRwwRw inHsHSINR  . Under ideal conditions, the CMOE detector maximizes the output SINR, that is, )( 0100 dRd inHopt PSINR .Steady-state SINR for RLS adaptive blind CMOE detector:The mean value )}()({ nnE sHwRw  is given as 0002000 })1({})()1({ PnEPnbPnEHH    dwdw . (12)Let the optimal weight vector be ow , and onn wwȗ  )()( .Therefore, )}()({)( nnEn yHwRw K  is given by )},1({2)]1([)]}1()[()()]1({[)(  nEntrnnnnEn HHHȗRwKRȗwyyȗwyyKK(13)where )/11(0 optH SINRP   wRw yK . Since 0)}({ onE ȗ  as fon , we have )()( nn exKKK | . In [10], it derives KOKOOK )1()1()]1(])1([)]1([)( 222   Mnntrn exex KRy ,where M  is the length of w . Since 1)1( 22  OO  for 10 dd O , )(nexK  converges, that is, KQK   ffo)]([lim)( ntrnex KRy , where )2/()1)(1( OOQ  M . The steady-state SINR of the RLS adaptive CMOE detector can be obtained as ])1/[( optoptmoe SINRSINRSINR  f QQ . (14)Steady-state SINR for RLS adaptive MMSE detector:In this case, the exponentially windowed RLS algorithm chooses )(nw  to minimize the cost function ¦  niHin inibP1200 |)()()(| ywO . (15) As fon , )(nw  converges to the optimal solution  w010 dR yP . Let wwȗ  )()( nn . Then )}()({ nnE sHs wRw K  is)},1({2)]1([)]}1([)]1({[000  nEntrnPnEsHssHHHHsȗRwKRwRwȗwddȗwK(16) where 201000 )( dRdwRw y HsH PP , and 0)}({ onE ȗ as fon .The weight error correlation matrix )(nK  is given as [10]  HOO 122 )1()1()}()({)( | yRKȗȗK nnnEnH . (17) where H  is the MSE of the optimum filter w , given by  optinHHSINRPPPbPE    1)(1}|{| 001000200dRdywH .Premultiplying both sides of Eq. (17) by sR , then taking the trace, it yields HOO )()1()]1([)]([ 010022dRdKRKR y| Hss Pntrntr .Hence, )]([ ntr sKR  converges for 10 dd O , and it has  f)(exK20 )1(11)]([limoptoptsn SINRSINRPntr fo OOKR . In practical applica-tions, O  is around 0.9. Therefore, with reasonably high SNR, it has 0)( ofexK , and )}()({ nnE sHwRw  can be approximated by 20 )1()}()({optoptsHsHSINRSINRPnnE | wRwwRw . (18) It is shown that [8] })()1({)}()({)(2nnEnnEn HyHywwRw   K)1/()(0 optopt SINRSINRP  Q . Therefore, the output SINR of the RLS adaptive MMSE detector is given by ]/)1/[( optoptmmse SINRSINRSINR QQ  f . (19) The steady-state output SINR given in Eq. (14) and (19) is consistent to the formulations in [9], where the SINR is defined as )]}()1(/{var[)]}()1([{lim 2 nnnnESINR HHnywyw  fof .5. NUMERICAL RESULTS Numerical simulations have been implemented to illustrate the performance of the proposed robust CMOE detector. We consider a synchronous MC-CDMA system in uplink channels with random spreading sequence. The quadratic constraint is set as 20 5.1 qT w . SNR is defined as the average transmitted bit energy to noise ratio 2/ vkP V . The multiple access interferers (MAI’s) are 10-dB, i.e., 10/ 0  PPk . The scalar ambiguity of the blind channel estimator is compensated with a complex constant, which makes the first element of the estimation p,0hˆ  and that of the true channel vector p,0h  identical.,,,First, the steady-state performance of the detectors is investigated. We set 32 M  and 3 P . A multipath channel with six paths is considered. The channel coefficients are randomly generated complex values. The simulation results are averaged over 200 Monte-Carlo trials. Fig. 2 shows the channel estimation error of the CMOE-based and subspace-based channel estimators. The normalized channel estimation error is measured by 2,02,0,0 /ˆppp hhh  . To recursively implement the subspace-based channel estimation, QR inverse iteration noise subspace tracking algorithm [11] is adopted. It shows that, at high SNR, the CMOE-based channel estimator has a similar performance to the subspace-based method. Fig. 3 illustrates the output SINR of the different linear MMSE detectors versus input SNR. It can be seen that the SINR performance of the proposed robust CMOE detector is much better than the CMOE, and it is comparable to that of the subspace-based blind MMSE detector. Next, a slowly time-varying channel with 6 L  Rayleigh fading paths in indoor environments is considered, where the multipath intensity profile decays exponentially. The maximum Doppler frequency ( Df ) is 52 Hz corresponding to a terminal speed smv /3  with a carrier frequency of 5.2 GHz. The subcarrier spacing ( f' ) is 312.5 KHz, and the time duration at the subcarrier is sTs P2.3 . Hence, the normalized fading rate is 410664.1 u sDTf . We average simulation results over 500 Monte-Carlo trials. Fig. 4 depicts the BER comparison for the CMOE detectors and the subspace-based receiver. To save simulation time, we set 16 M  and 8 P . Again, it can be seen that the robust CMOE detector performs much better than the CMOE detector and the performance is comparable to the subspace-based method.  6. CONCLUSIONS In this paper, a robust CMOE blind detector for MC-CDMA systems is proposed. By imposing quadratic weight constraints, the CMOE detector is made more robust against signal modeling errors, and a better performance over the standard CMOE detector is obtained. A convenient adaptive implementation of the robust CMOE detector is presented. Steady-state SINR performance of the blind CMOE detector and the training MMSE method is also presented.  10 15 20 2510-310-210-1100SNR(dB)BERCMOERobust CMOESub MMSEFig. 4. BER comparison when 16 M , 8 P , 7 K , six 10-dB MAI’s in the channel, 96.0 O , and 1.0 G .REFERENCES [1] N. Yee, J.P. Linnartz, and G. Fettweis, “Multicarrier CDMA in indoor wireless radio networks”, PIMRC, pp. 109-133, vol. 1, 1993.[2] S. Hara and R. Prasad, “Overview of multicarrier CDMA”, IEEE Commun. Magazine, vol. 35, pp. 126-133, Dec. 1997.[3] M. Honig, U. Madhow and S. Verdu, “Blind multiuser detection”, IEEE Trans. Inform. Theory, vol. 41, pp. 944-960, July 1995.[4] M. K. Tsatsanis and Z.Y. Xu, “Performance analysis of minimum variance CDMA receivers”, IEEE Trans. Signal Processing, Vol. 46, No. 11, Nov. 1998. [5] H. Cox, R. Zeskind, and M. Owen, “Robust adaptive beamforming”, IEEE Trans. ASSP, vol. 35, pp. 1365-1376, 1987. [6] Z. Tian, K. L. Bell, and H.L. Van Trees, “Robust constrained linear receivers for CDMA wireless systems”, IEEE Trans. Commun., vol. 49, pp. 1510-1522, July 2001. [7] J. Namgoong, T.F. Wong and J.S. Lehnert, “Subspace MMSE receiver for multicarrier CDMA”, IEEE WCNC '99, pp. 90-94, New Orleans, LA, 1999. [8] Z. Tian, K. L. Bell, and H.L. Van Trees, “A recursive least squares implementation for LCMP beamforming under quadratic constraint”, IEEE Trans. Signal Processing, vol. 49, pp. 1138-11145, June 2001. [9] H.V. Poor and X.D. Wang, “Code-aided interference suppression for DS/CDMA communications-part II: parallel blind adaptive implementations”, IEEE Trans. Commun., Vol. 45, No. 9, 1997. [10] E. Eleftheriou and D. D. Falconer, “Tracking properties and steady-state performance of RLS adaptive filter algorithms”, IEEE Trans. ASSP, vol. 34, pp. 1097-1109, Oct. 1986. [11] P. Strobach, “Square-root QR inverse iteration for tracking the minor subsapce”, IEEE Trans. Signal Processing, vol. 48, pp. 2994-2999, Nov. 2000. 500 1000 1500 2000 250000.020.040.060.080.10.120.140.16Number of samplesChannel estimation error CMOE(10 users)Subspace(10 users)CMOE(5 users)Subspace(5 users)(SNR = 20 dB) Fig. 2. Channel estimation error for the CMOE-based and subspace-based approaches. dBSNR 20 , 995.0 O , and 1.0 G .10 15 20 25 3051015202530SNR(dB)Average SINR(dB)Training MMSESubspace MMSERobust CMOECMOE(nine 10-dB MAI's in the channel) Fig. 3. Output SINR for the blind MMSE detectors and training MMSE versus SNR. 10 K , 995.0 O , and 1.0 G .,,,

THE performance and robust implementation of a blind CMOE receiver for MC-CDMA systems

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THE performance and robust implementation of a blind CMOE receiver for MC-CDMA systems

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