Hierarchical Quantization and Its Application to multiuser eigenmode Transmissions for MIMO Broadcast Channels with Limited Feedback

We consider the problem of designing the vector quantizer for a multiuser eigenmode transmission applied to a MIMO broadcast channel with limited feedback. We propose a hierarchical vector quantization method based on the idea that the CDI can be refined by permitting multiple feedback steps between receivers and transmitter. 

At each new quantization level a new codebook is built based on the codebook and on the best codeword at the previous level. We firstly give a general definition of a hierarchical quantizer. Then we build a hierarchical quantizer based on the Fourier codebook. 

Finally, we propose an algorithm for implementing the hierarchical quantization principle. The proposed algorithm improves the channel quantization quality if the channel vector remains almost constant during different feedback steps, whereas allows backward steps to lower levels, in order to track channel variations. Simulations comparison with respect to the Fourier codebook and to the random vector quantization technique, confirm the effectiveness of the proposed approach.