A particular property of the cellebrated MDIR receiver is introduced in this communication, namely, the fact that full exploitation of the diversity is obtained with multiple beamformers when the channel is spatially and timely dispersive. Therefore a new structure is developped which provides better performance. The hardware need for this new receiver may be obtained through reconfigurability of the RAKE architectures available at the base station. It will be tested in the FDD mode of UTRA.Peer ReviewedPostprint (published version

Agustin, Adrian

Cabrera-Bean, Margarita

Lagunas Hernandez, Miguel A.

Vidal Manzano, José

English

A particular property of the cellebrated MDIR receiver is introduced in this communication, namely, the fact that full exploitation of the diversity is obtained with multiple beamformers when the channel is spatially and timely dispersive. Therefore a new structure is developped which provides better performance. The hardware need for this new receiver may be obtained through reconfigurability of the RAKE architectures available at the base station. It will be tested in the FDD mode of UTRA.Peer Reviewe

UPCommons

Diversity mdir receiver for space-time dispersive channels

UPCommons. Portal del coneixement obert de la UPC

Diversity MDIR Receiver for Space-Time DispersiveChannelsJosep Vidal, Margarita Cabrera, Adrian Agustín, Miguel A. LagunasUniversitat Politècnica de Catalunya, Barcelona, {pepe,marga}@gps.tsc.upc.esAbstract1: A particular property of the cellebrated MDIR receiver is introduced in this communication,namely, the fact that full exploitation of the diversity is obtained with multiple beamformers when the channelis spatially and timely dispersive. Therefore a new structure is developped which provides betterperformance. The hardware need for this new receiver may be obtained through reconfigurability of theRAKE architectures available at the base station. It will be tested in the FDD mode of UTRA.I. IntroductionThe advent of the 3rd generation of mobile communications systems has been accompanied by therecognition of the large increase in system capacity that can be obtained from the use of adaptiveantenna arrays. Care has been taken in the definition of the standard to include capabilities for space-time processing of the signals incoming and radiated from the base stations. Therefore, a panoplia ofreceivers have arosen which improve the performance of the single sensor receiver without conveyingthe complexity of the optimum multiuser receiver [Jung][Vidal][Rüpf]. One of the most succesfulreceivers in this trading is the MDIR [Lagunas] whose capabilities for reconfigurability and use inboth TDD and FDD modes have been demonstrated [Mestre]. Some unpublished properties of thisreceiver are reported here, which allow further exploitation of the diversity present in the dispersivemobile channel. Section II shows two possiblities for spatial front-ends: a reduced complexityweighted V-RAKE receiver and the proposed Extended MDIR (E-MDIR). Similarities and differencesbetween are shown and performances compared in terms of BER equations in section III. Simulationsin section IV will demonstrate the superiority of the E-MDIR receiver in realistic conditions. Resultsshow a significant improvement in the probability of error with respect to conventional approaches,that is, only spatial beamforming or only VRAKE combiningII. Spatial front-endsA. Noise-plus-interference matrix inversion (NIMI) receiverThis receiver is a simplified version of the Weighted V-RAKE, that is, a Vector-RAKE with spatialpre-whitening matrix. The pre-whitening operation can be seen as a bank of beamformers bj which aregiven by the eigenvectors of the spatial correlation matrix (see figure 1)[Vidal]. The optimumcombining structure comes from the fact that the errors between branches are uncorrelated. The natureof this receiver is easily seen from a simple case: assume the case of P<M point interferers. If vectorsbi are taken as the noise eigenvectors of sw,R  each one acts as a spatial interference canceller.B. Extended Matched Desired Impulse Response (EMDIR) receiverA different way to build a spatial front-end is to obtain a spatial combiner b that maximizes the SINRat its output. Let us first define the signal model of equation as:WDHY += (1)                                                          1 This work has been partially supported by CICyT of Spain  (TIC98-0412, TIC98-0703, TIC99-0849) and CIRIT of Catalunya (1998SGR-00081) and by EC -IST-199-10322, SATURN project.where matrix D is a Toeplitz matrix built at chip time from QPSK complex spreaded and scrambledsymbols:LLNCLNdNdNddLdLddLdLd´+-/Îúúúúûùêêêêëé-------= )1()1()2()1()1()1()()0()2()1(LMOMMLLD (2)where N stands for the number of chips in the pilot, L is the length of the estimated physical channel,and all terms d(n) belong to the set {-1-j, -1+j, 1+j, 1-j}. It is usually the case that the symbols inmatrix D are uncorrelated, so IDD NH @ . H contains (column-wise) the L-length response of thephysical propagation channel seen at each sensor:[ ] [ ])1()1()0()1(21 -=/Î= ´+ LhhhC iiiTiMLM LL hhhhH        (3)Figure 1. Optimum combining receiver with reduced rank approximation (M>R). The gains at each branchare given by the eigenvalues of the noise-plus-interference spatial correlation matrix for the NIMI receiver.The MDIR receiver developed in [Lagunas] is then given by:Ntosubjectmin HHHswH =DHbDHbbRbb,   (4)It may be shown [Lagunas] that the choice of the beamformer is obtained as the generalisedeigenvector b of the equation:DHbDHbR HHsw l=,     (5)associated to the minimum eigenvalue l, and the impulse response seen at the output of thebeamformer bj is jj Hbh =~. Being fixed to 1 the signal power at the output of the beamformer bjthrough the restriction in equation 4, lj takes the value of the inverse of the signal-plus-noise-plus-interference power at the output of the beamformer bj. At this point, a straightforward question arises:could the different beamformer outputs be efficiently combined as in figure 1? Or, in other words, isthere any diversity inherent to the multiple beamformers obtained from the MDIR solution? Theanswer to this question is given by the following property:Property 1. The noises at the output of the M beamformers obtained from equation 5 are uncorrelated,unless the eigenvalues associated are equal.Proof. Let us extend equation 5 with all the eigenvectors as:...y1(nT)y2(nT)yM(nT)+...)(ˆ ndbRb1...  RAKE 11/s1  RAKE RRe{.}...... 1/sRUmBSRDHBSDHBR sdHHsw ,, == (6)By left-multiplying with the conjugate transpose of B we obtain on the left hand side of the equation,the correlation matrix of the noises at the output of the different beamformers:BRSBBSRBBRB sdHsdHswH,,, == (7)We have used in the last equality the fact that the left-hand side of the equation is an hermitian matrixand the eigenvalues are real. With no loss of generality, let us assume that S has one multipleeigenvalue s, so since the product above is commutative it can be written as:úûùêëé¢úûùêëé=úúûùêêëéúûùêëé¢=S00IEDDCEDDCS00IBRSBssHHsdH,         (8)By operating it is easy to see that D = 0 and that E has to be diagonal. Therefore we can conclude that:diagonal is        where, SS00CBRB ¢¢úûùêëé¢¢s=swH  (9) Therefore, we can use the multiple beamformers provided by the MDIR receiver and coherentlycombine their outputs according to figure 1. Note however that the number of eigenvectors given byequation (5) depend on the rank of the signal matrix DHDH HH  (assuming full rank of the noise-plus-interference matrix), each yielding a different beamformer output with different noise level, givenby the eigenvalue. A rank higher than one, precludes the existence of both spatial and temporaldispersion in the desired user. Another property of interest for the analysis of the performance of theMDIR receiver is the following:Property 2. The channels associated to the beamformers having different eigenvalues ii Hbh =~areorthonormal, that is, jijHi -= dhh~~ .Proof. The diagonality of matrix DHBDHB HHH  stated in property 1 (equation 8), along with therestriction in equation 4 completes the proof.III. BER equationsBER equations are derived here for the two receivers, assuming Gaussian temporally white interference.This assumption is quite restrictive and conclusions should be drawn carefully.A. NIMI ReceiverFor the M sensor NIMI receiver, the multiple beamformer operation in figure 1 can also be expressed asa spatial whitening of the received signal [Vidal]. The selected R branch outputs are maximum-ratiocombined with orthogonal interference plus noise terms nr. The resulting decision variable Um (seefigure 1) is given by:( ) åååå=-== =+=+=RrrPcHwmRrrRrPcLlwrlmm nESFtracebnESFhbU1111 02. HHR (10)The variance is given by (since the noise is spatially whitened after the spatial processor):)(21122 HwPcRrrn traceSFEHHR-=== åss         (11)and the BER yields (R is the number of branches in figure 1):÷÷÷øöçççèæ=÷÷÷øöçççèæ=÷øöçèæ= åå==-RiibRiHiiibHwbNIMI EQtraceEQtraceEQBER111 2)(2)(2 ll vvHHR (12)where li are the P non-zero eigenvalues of the Hermitian matrix Hw HHR1- .B. EMDIR ReceiverFor the M sensor EMDIR, one has to analyze the number P of significant branches (the number ofdifferent non-zero eigenvalues). The P outputs are combined with orthogonal interference plus noiseterms: nr are incorrelated as it has been previously demonstrated. If the resultant decision variable isconsidered gaussian distributed:ååå===+=þýüîíì===+=RiiPcmiHiiiRiiPcRiiHimm nESFRbnESFbU111  1~~~~~hhHbhhh (13)Since, as previously proved, the noises at each branch are uncorrelated (and assumed all temporallywhite), the variance is now computed as:åå====RiiPcRiinESF11222lss (14)where lj is the noise power associated to the j-th branch:HHHRHhHHRhHbHRbDHbDHbR~~~~1111111HwjHwjjjHwjjjHHjjw N----=Þ==Þ=Llll        (15)Using property 2 ( IHH =H~~ ) then it turns out that:( )#1112222HwPcRiiPcRiin traceESFESFHHR-===== åå lss         (16)where (.)# is the pseudoinverse operator. Note that the l are the same as in equation 12. The BER yields:( )÷÷÷÷÷÷øöççççççèæ=÷÷÷÷÷÷øöççççççèæ÷÷øöççèæ=÷÷÷øöçççèæ=åå==- Ri ibRiHiiibHwbEMDIRREQtraceREQtraceREQBER1212#1212122llvvHHR      (17)It can be concluded that:· The E-MDIR and W-VRAKE are not equivalent, but in two cases both receivers achieve the sameBER (in Gaussian scenario): when Rw is diagonal and, when R=1 is chosen. Otherwise, according tothe equations 12 and 17, NIMI outperforms E-MDIR, which is not an unexpected result since wehave derived the equations considering Gaussian noise-plus-interference.· For the non-Gaussian case, simulations in section IV indicate that E-MDIR is better. Its performancedepends on the noise-plus-interference spatial distribution as well as the desired signal spatial-temporal distribution: highly dispersive channels yield a matrix HHH with low dispersion ofeigenvalues, so the use of multiple branches becomes interesting. Equations 12 and 17 can be used tohave an estimate of the gain obtained in using diversity.· The NIMI receiver requires the computation of the noise-plus-interference matrix, which is usuallydifficult to compute and may lead to numerical errors. On the contrary, the EMDIR receiver may beeasily reformulated using Ry instead of Rw [Lagunas].· The architecture in figure 1 is dynamically re-configurable by nature. Assume that the number ofusers at a certain moment is low. Certainly, some of the RAKE combiners at the base station will beunused and therefore (hardware permitting) might be incorporated to additional branches.IV. Experimental performance evaluationA. Propagation channel modelIn order to evaluate the receiver in a realistic mobile scenario, we have carried out simulations basedon a Gaussian stationary uncorrelated hypothesis for the channel, assuming independence betweenangular and Doppler spread, as it has been experienced from measurements taken in downtownStockholm in the 1,8 GHz band [Pedersen]. There, it is empirically shown that azimuth spectrumfollows a Laplacian law, along with Gaussian distribution for the directions of arrival (f) around themean angular position of the user. The angular spread (that is the standard deviation of theGaussian, fs ) is taken 8º. The number of rays impinging the array is fitted as a Poisson randomvariable of mean 25. The power delay spread will be based on the pedestrian and vehicular models fortemporal spreading recommended in the SMG2 documents for UTRA [ETSI-UTRA]. The amplitudeassociated with each propagation path (a) is a complex Gaussian random variable whose powerdecreases as the time delay and the angular direction of arrival with respect to the mobile positionincrease. A classical Clarke’s bath-shaped Doppler spectrum is obtained by assuming multiplereflections close around the mobile. The carrier frequency is 2,0 GHz. All sensors have flat spatialresponse in a sectored area of 120º, and are linearly and uniformly spaced at d/l=0,5.B. SimulationsA set of simulations has been performed using up to 9 users of spreading factor 16 in the FDD modeof UTRA [ETSI-UTRA]. Equal power for the traffic and the pilot bits has been assumed. The channelhas been estimated using all the chips of the pilot, so the autointerference of the traffic is very low. Allusers are assumed to have controlled transmitted power with no errors (1 dB) errors showed nodifference in performance. Eb/No is 15 dB. The speeds of users are 3 km/h, for the pedestrian channeland 50 Km/h for the vehicular channel. The E-MDIR, with different number of eigenvectors, theconventional V-RAKE and NIMI have been tested and its performance plotted in figure 2.C. Evaluation of resultsIn all cases, the performance was superior to the conventional VRAKE receiver, so we can concludethat substantial gain from the use of spatial beamforming is achieved. E-MDIR also performs betterthan the NIMI receiver in all cases. Not surprisingly, a significant reduction in BER is obtained for theE-MDIR when using 2 beamformers, in particular for the vehicular channel, whose delay spread islarger than for the pedestrian. This is verified in figure 3, where the cumulative function of the ratiobetween the increasing eigenvalues and the maximum eigenvalue of the MDIR receiver is depicted,for different number of active users. It is clear that the second eigenvalue (that is, the SNIR associatedto the output of the second beamformer) is always significant, although it decreases slightly as thenumber of active users increase. Note that the third eivenvalue is only significant for a low number ofusers, so it can be discarded.V. References[ETSI-UTRA] “Submission of Proposed Radio Transmission Technologies: the ETSI UMTSTerrestrial Radio Access (UTRA) ITU-R RTT Candidate Submission”, ETSI SMG2.[Jung] P. Jung, J. Blanz, “Joint detection with coherent receiver antenna diversity in CDMA mobileradio systems”, IEEE Trans. On Vehicular Technology, vol. 44, Feb. 1995.[Lagunas] M. A. Lagunas, J. Vidal, A. I. Perez, “Joint beamforming and Viterbi equalizers in wirelesscommunications”, Proc. 31st Asilomar Conf. On Signals, Systems and Computers, Nov. 1997, alsoin "Joint Array Combining and MLSE for Single-User Receivers in Multipath Gaussian MultiuserChannels", to appear in IEEE Journal on Selected Areas in Communications.[Mestre] X. Mestre, J. R. Fonollosa, “Algorithms for Flexible Multi-Standard Array Processing: Part3”, Deliverable D711, AC347/UPC/A72/PI/I007/b1, ACTS 0347 SUNBEAM.[Pedersen] K. Pedersen, P. Mogensen, B. Fleury, “A Stochastic Model of the Temporal andAzimuthal Dispersion seen at the Base Station in Outdoor Propagation Environments”, to appearin IEEE Trans. on Vehicular Technology.[Rupf] M. Rupf, F. Tarköy, J. L. Massey, “User-Separating Demodulation for Code-DivisionMultiple Access Systems”, IEEE Journ. Select. Areas in Comm., June 1994.[Verdú] S. Verdú, Multiuser Detection, Prentice-Hall, 1998.[Vidal] J. Vidal, M. Cabrera, A. Agustin, “Full Exploitation of Diversity in Space-Time MMSEReceivers”, VTC-2000, Boston, September 2000.1 2 3 4 5 6 7 8 910-510-410-310-210-1USERSBEREb/No = 15 dB       8sensorsVRAKE    NIMI     MDIR-1 evMDIR-2 evMDIR-3 evMDIR-4 ev1 2 3 4 5 6 7 8 910-510-410-310-210-1USERSBEREb/No = 15 dB       8sensorsVRAKE    NIMI     MDIR-1 evMDIR-2 evMDIR-3 evMDIR-4 evFigure 2. Probability of error for a different number of active users, all transmitting controlled power, for thedifferent receivers. Pedestrian channel (left) and vehicular channel (right).-25 -20 -15 -10 -5 000.20.40.60.81 1 user  Eb/No = 20 dB-25 -20 -15 -10 -5 000.20.40.60.81 3 users  Eb/No = 20 dB-25 -20 -15 -10 -5 000.20.40.60.81 5 users  Eb/No = 20 dB-25 -20 -15 -10 -5 000.20.40.60.81 7 users  Eb/No = 20 dB( ) ( )dBabsP maximaxi llll /  vsplotted is  / <2l8lFigure 3. Cumulative functions of the ratio of the MDIR eigenvalues to the maximum eigenvalue.Vehicular channel.

https://upcommons.upc.edu/bitstream/2117/104070/1/10.1.1.414.9200.pdf

Diversity mdir receiver for space-time dispersive channels

Abstract

Similar works

Full text

Available Versions

UPCommons

UPCommons. Portal del coneixement obert de la UPC