A point-to-point multiantenna wireless channel is considered. Based on channel information, a receiver selects a transmit beamforming vector, which contains transmit antenna gains, from a vector set or codebook. The codebook index for the selected beamforming vector that maximizes channel capacity is relayed to the transmitter via a rate-limited feedback channel. Previously, we have proposed a Random Vector Quantization (RVQ) codebook, which consists of independent isotropically distributed vectors and showed that it performs close to the optimal codebook. However, RVQ requires exhaustive search to locate the desired beamformer. To lessen the search complexity, we propose a tree-structured (TS) RVQ. Numerical results show that number of computations required for TS-RVQ search can be orders of magnitude fewer than that required for RVQ search for given performance.
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