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VI INTERNATIONAL TELECOMMUNICATIONS SYMPOSIUM (ITS2006), SEPTEMBER 3-6, 2006, FORTALEZA-CE, BRAZIL10 0 P TX[dB]10 −1Downlink Beamforming (DB)Alamouti (TD)Eigen−BeamformingmBER−TD−DB10 −210 −2BERBER10 −310 −310 −410 −50 5 10 15 20 25Fig. 2: Performance for ∆ = 5 ◦ NLOS channels and 4-QAMmodulation as a function of the transmit power P TX .10 −42 4 6 8 10 12 14 16 18 20IterationFig. 3: Convergence of the mBER-TD-DB algorithm forP TX =20 dB.simulations for a flat non-line-of-sight (NLOS) scenario, whichcorresponds to a Rayleigh channel, and for a flat line-of-sight(LOS) scenario, corresponding to a Rician channel.100P TX=5 dBl=1l=2A. NLOS scenarioThe NLOS scenario is the same as the one simulated in [1]and corresponds to a flat-fading Rayleigh channel, i.e., allthe channel coefficients are Rayleigh distributed. This channelwas defined in [12] and has only one path perpendicular tothe multiple-transmit antennas (”broadside” as in [12]) withan angle spread of ∆. The mean DCCM can be obtainedin closed form as in [1, eq. (57)]. We have used this meanDCCM to obtain the instantaneous DCCM for each block b byconsidering the instantaneous channel generated as describedin [12, eq. (7)]. We have considered an angle spread of 5 ◦ .Fig. 2 shows the BER for all simulated techniques as afunction of the transmit power P TX . We can see that theproposed mBER-TD-DB has the same performance as theoptimum Eigen-Beamforming and they outperform the othertwo techniques. The mBER-TD-DB follows the DB up to10 dB since the other diversity branches are too weak andtheir use would only waste power. After 10 dB, the mBER-TD-DB begins to use the second diversity branch to exploitthe channel diversity. This makes the BER curve to changeits slope due to diversity. At high P TX regime (equivalent tohigh SNR regime), the mBER-TD-DB attains the same slopeas the Alamouti scheme, but with a gain in transmit power ofabout 1.75 dB in this scenario.The evolution of the BER during the convergence of themBER-TD-DB algorithm is shown in Fig. 3, for a transmitpower of 20 dB. It can be seen that the algorithm presents afast convergence, typically between 10 and 20 iterations.The radiation patterns for each precoder layer for themBER-TD-DB for a transmit power of 5 dB and 20 dB areshown in Fig. 4. For P TX = 5 dB, we see that the first layer(l = 1) radiates in the direction of the user, i.e., in the 5 ◦cone around 0 ◦ , while the second layer (l = 2) is switchedoff.This is exactly the DB solution, since there is only oneGain [dB]Gain [dB]−10−20−30−100 −80 −60 −40 −20 0 20 40 60 80 100Angle100−10−20P TX=20 dB l=1l=2−30−80 −60 −40 −20 0 20 40 60 80AngleFig. 4: Radiation pattern of the precoder layers formBER-TD-DB for a transmit power of 5 dBand 20 dB in the NLOS scenario.significant diversity branch at such small transmit power. Onthe other hand, for P TX = 20 dB, the first layer continuesto radiate mostly in the direction of 0 ◦ , while the secondlayer radiates avoiding this region, in order to create a seconddiversity branch uncorrelated to the first one. The dashed curveshows the total radiated power from the two branches, whichbecomes less directive. The total radiated power tends to beasymptotically omni-directional for high SNR, since the arraygain becomes negligible when compared to the diversity gain.We have shown that the proposed mBER-TD-DB is able tojointly achieve TD and perform DB, performing as well asthe, also optimum, Eigen-Beamforming in a NLOS Rayleighscenario. In the sequel, we will show that mBER-TD-DBoutperforms Eigen-Beamforming in other scenarios, being anattractive solution for the general application.