We consider transmission beamforming techniques for frequency-division-duplex (FDD) wireless communication systems using adaptive arrays to improve the signal quality of the array transmission link. We develop a simple effective transmission beamforming technique based on an approximated frequency tranlsation (AFT) to derive the tranmsiion beamforming weights from the uplink channel vector. This technique exploits the invariance of the short-time averaged fast fading statistics to small frequency translations. A simple approximate relationship that relates the transmission channel vector to the reception channel vector is derived. We have developed its practical alternative in which the frequency translation of the channel vector is performed at the principal angle of arrival (AOA) of the u;link synthestic angular spectrum instead of the mean AOA. To analyze the performance of the proposed methods, we consider the power loss incurred by applying the estimated channel vector instead of the true downlink channel vector. The performance is analyzed as a function of the mean AOA, the angular spread, the number of elements, frequncy difference between the uplink and the downlink, and the angle distribution. Their performance is also compared with that of the direct weight reuse method and the AOA based methods.
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