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XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SPthe proposed technique transforms the spatial diversity atthe BS side into time diversity at the MU side, which canbe exploited by a temporal equalizer. Our proposition thentakes into account the existent systems and only makes minorchanges to increase the diversity gain at the MU side. Theperformance of the proposed technique is however related tothe specific equalizer used at the MU. Here we assume thatthe MU uses an ideal receiver, which is capable of recoveringall the signal energy spread across time.As stated in the previous Section, at each block t a differentaverage power P t is received by the MU’s antenna. Thevariation of these received powers P t is caused by the fading.We propose thus to find a (fixed) space-time transmit filter Wthat is computed in order that the received power P t at theMU is as constant as possible over a finite training window.By doing so, we are minimizing the fading effect, i.e., thereceived power variation. This criterion can be expressed asW opt = arg minWt f∑t=t i(W H R t W − 1 ) 2(14)where t i and t f are the initial and final blocks of the trainingwindow, respectively.In order to keep the same transmit power of the singleantenna (no transmit filter) case, the optimum transmit filteris normalizedW on = W opt‖W opt ‖ . (15)This normalized optimum filter W on is then used to transmitthe subsequent data blocks. In addition, to ensure the desiredtarget SNR at the MU, a power control is done at the BS.We assume that this power control is integrated in the signals(n), i.e., this signal is already scaled in order that the receivedpower at the MU respects the target SNR.This novel criterion for transmit diversity is called ConstantPower Approach (CPA). This criterion can be optimized byusing one of the many optimization techniques existing in theliterature. In the following we propose an adaptive algorithm tooptimize the proposed criterion. It is not our goal in this workto find the best optimization technique but only to provide onetechnique in order to assess the performance of the proposedCPA.A. Obtaining W optOne can easily associate (14) with a constant modulus (CM)criterion. This criterion has been for long time investigatedand some algorithms to optimize it have been proposed inthe literature. All these algorithms are based on the followingcriterionJ CMA = arg minW∑ (W H x(n)x(n) H W − 1 ) 2. (16)nBy comparing (16) and (14), one can easily identify thecovariance matrix R t with the instantaneous signal covariancematrix x(n)x(n) H . Thus, there is a fundamental differencebetween both criteria since the CMA assumes that the matrixx(n)x(n) H has rank 1 while the matrix R t can have (andusually has) rank greater than one.Then, the already existing algorithms, such as theCMA [15], the ACMA [16] and the finite-interval constantmodulus algorithm [17], can not be directly used to optimize(14). It is our belief that these algorithms could bemodified to optimize (14). In this work, however, we proposea novel algorithm to preform this task.Based on (14), let us define the cost function to be minimizedasJ =t f∑t=t i(WHk X k (t) − 1 ) 2, (17)where X k (t) = R t W k and k is the iteration index. Thiscriterion can be easily identified as a MSE (mean squareerror) criterion. The minimization of this criterion can be doneiteratively by using the Newton’s method [18].Thus, applying the Newton’s method to (17), we obtain thatW k+1 = W k − αR −1k p k (18)where the coefficient α is taken less than 1 to avoid thedivergence of the algorithm andR k =p k =t f∑t=t iX k (t)X H k (t) =t f∑t=t iX k (t) =t f∑t f∑t=t iR t W k .t=t iR t W k W H k R H t (19a)(19b)By taking (experimentally) α = 1 4, we obtain the proposedConstant Power Algorithm (CPA):W k+1 = 1 2 W k + 1 2 R−1 k p k . (20)As we have said at the beginning of this Section, wejust present an algorithm to optimize the criterion of (14).The analytical convergence of this algorithm has not beenproved. Simulations results however indicate that the algorithmconverges. Indeed, the algorithm has never diverged in all themany cases simulated.IV. SIMULATION RESULTSWe consider the downlink of a 120 ◦ sector of a cell ofa wireless system. The data is transmitted in blocks and weassume, without loss of generality, that the channel realizationis independent from one block to another, i.e., the phases ofeach path varies from one block to another. The BS is equippedwith K antennas and, unless specified otherwise, the interelementdistance is λc2 , where λ c is the carrier wavelength.The transmit space-time filter is K × L (see Fig. 1), where Lis the number of temporal coefficients in each spatial branch.We assume that the instantaneous DCCMs R t are perfectlyknown at the BS, for all t.In order to assess the performance of the proposed technique,for each training block, a different channel was drawnand the corresponding DCCMs R t were used as input for theproposed algorithm, which computes the optimum transmitfilter W opt , see (14). The normalized optimum filter W on ,see (15), was then used to compute the received power P t atthe MU for the data blocks. With the assumption that the