Orthogonalizing a random set of beams

Recent work on wireless beamforming has focused on multi-user diversity effects, where terminals are chosen opportunistically 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 frequency-band is large enough that a subset of terminals can be found whose spatial signatures match the test beams; (ii) the responses to the test beams of the entire pool are known to the basestation; (iii) beamforming considerations can drive traffic scheduling and resource allocation. These conditions are not always met. Rather, we examine orthogonalizing a given set of beams for terminals that are chosen randomly or according to other resource considerations. Our orthogonalization is chosen to maximize the beamforming gain to the desired terminals, with the intent that other terminals may then ldquoeavesdroprdquo on the beamformed signals, knowing that the beams are orthogonal. These orthogonal beams can be used for training channel state information even if the actual beams are not known. We distinguish between frequency-division duplex and time-division duplex systems and show that there are training advantages for each.