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Recent work on wireless beamforming has focused on multiuser diversity effects, where terminals in a cellular system are chosen opportunistically from a pool of terminals based on their responses to test beams. Orthogonality between the test beams is typically chosen to aid subsequent interference-free transmission to the corresponding terminals. However, much of this work assumes that i) the pool of terminals on a given time-frequency resource is large enough that a subset of terminals can be found whose spatial signatures match the orthogonal test beams; ii) the responses to the test beams of the entire pool are known to the base station; iii) beamforming considerations can drive traffic scheduling and resource allocation. These conditions are not always met. Rather, we examine orthogonalizing a given set of data-carrying beams for terminals that are scheduled on distinct time-frequency resources. The scheduled terminals are not chosen for their spatial signatures, but rather for their need to receive data. Our orthogonalization is chosen to maximize the beamforming gain to the scheduled terminals, whose channels are generally not spatially orthogonal. Unscheduled terminals may then ldquoeavesdroprdquo on pilots embedded in the orthogonal beams and thereby learn their own channel state information. This process eliminates the need for separate dedicated orthogonal training signals. We show how this scheme may be deployed in frequency-division duplex and time-division duplex systems. We quantify the price in beamforming gain paid for orthogonalizing a set of beams. One result analytically shows that the average price is at most 1.4 dB in SNR.