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XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SPThe other approach, which requires the knowledge of thedownlink channel, is based on the estimation of this channel bythe MU. This information is then fed back to the BS, where thechannel estimation is used to carry out TD. Switched transmitdiversity [8] and transmit adaptive array [9] are examples offeedback-based TD, also called close loop TD. The advantageof using feedback is that the BS can have an estimation of theimpulse response of the downlink channel. This knowledgemakes possible to the BS to compensate for the phases ofeach multipath, eliminating thus the fading. There are twodrawbacks, however: useful rate reduction and feedback delay.The insertion of training symbols is needed so that channelestimation is possible at the MU. This estimation must be thenfed back to the BS using the uplink channel. Although bothpoints imply on useful-rate reduction in both the downlinkand uplink, the impact of this rate reduction on the systemis not remarkable and it is worthy due to the correspondinggain. On the other hand, the feedback delay, which is thedelay between the downlink channel estimation at the MUand its exploitation by the BS, is a more critical issue. Thisdelay makes the feedback approach not very robust in practicalconditions since the downlink channel estimation is very likelyto be out-of-date at the moment of its use by the BS. Indeed,it only takes the displacement of a fraction of wavelength tocause a significant change of the multipath phases, leading toa completely different fading condition. In this case, trying tocompensate for the multipath phases is not possible and mayeven create a deep fading instead of a milder one.In this work, we propose a diversity technique that isdirectly based on the criterion of minimizing the variationof the power received by the MU. This technique uses thesecond order statistics of the downlink channel. The channelcovariance matrix (CCM) is formed from the physical characteristicsof the channel (the physical paths), which does notchange as quickly as the multipath phases. Hence, we canrely on this relatively stationary information to perform TD.Moreover, the CCM is of much interest since the downlinkchannel covariance matrix (DCCM) can be estimated directlyat the BS, avoiding feedback. For TDD (time division duplex)systems, this is a very straightforward task. Since both linksuse the same frequency, the uplink channel covariance matrix(UCCM) is identical to the DCCM, and the estimation of theformer can be easily obtained form the received signal in theuplink. Although in FDD (frequency division duplex) systemsthe multiple antenna response (i.e., the steering vector) differsfrom one link to the other due to their frequency separation, itis possible to estimate the DCCM from the UCCM, as showedby Asté in [10], [11].Having estimated the DCCM, several works (see for example[12]–[14]) proposes to use this information to performbeamforming by using a purely spatial filter. We propose,however, to use a space-time filter to maximize the diversityorder, besides beamforming. We rely on the fact that the MUis already equipped with a temporal equalizer in order tocompensate for frequency-selective fading channels, e.g., inmacrocells. This equalizer let us take advantage of the channelspace diversity by exploiting the spatial decorrelation to emituncorrelated copies of the desired signal delayed by one ors(n)Fig. 1.ÈÈz −1 z −1 z −1 x 1(n)w∗ 1 (0) w∗ 1 (1)w∗ 1(L − 2) w1 ∗ (L − 1)z −1 z −1 z −1w∗ 2 (0) w∗ 2 (1)w∗ 2(L − 2) w2 ∗ (L − 1)w∗ K (0) w∗ K (1) w∗ K(L − 2) wK ∗ (L − 1)Èz −1 z −1 z −1w ∗ (0) w ∗ (1) w ∗ (L−2) w ∗ (L−1)Transmit Space-Time Filterx 2(n)x K(n)more symbol periods. By doing so, we are transforming thespatial diversity at the BS side to time diversity at the MUside. This conversion is specially useful when the channel isflat-fading, i.e., the time-spread is zero.The paper is organized as follows. In the next section, thesystem model used in this work is presented and an expressionfor the received power by the mobile user is derived. Then,in Section III, we present the proposed criterion and also anadaptive algorithm to find the optimum solution. The resultsof computer simulations are presented in Section IV, wherethe performance of the proposed technique is assessed andits behavior is studied. The performance of the proposedalgorithm is also compared to more classical techniques.Finally, in Section V, we draw some conclusions and presentsome open issues.The following notations are used throughout the paper.Vectors are by default in column orientation, whereas T , Hand ∗ stand for transpose, conjugate transpose, and conjugate,respectively. ‖x‖ is the 2-norm of vector x, E{·} denotesmathematical expectation and ∗ stands for convolution.II. SYSTEM MODELWe consider the downlink of a wireless communicationsystem, where the BS is equipped with K antennas and theMU has only one antenna. The TD processing is done bymeans of a space-time filter, as depicted in Fig. 1. The signaltransmitted by the k-th antenna is given byL−1∑x k (n) = wk(n) ∗ ∗ s(n) = wk(l)s(n ∗ − l) (1)where s(n) are the transmitted symbols to the MU and w k (n)are the coefficients of the temporal equalizer related to antennak, which is assumed to have length L.l=0