Optimal Feedback Rate Sharing Strategy in Zero-Forcing MIMO Broadcast Channels

In this paper, we consider a multiple-input multiple-output broadcast channel with limited feedback where all users share the feedback rates. Firstly, we find the optimal feedback rate sharing strategy using zero-forcing transmission scheme at the transmitter and random vector quantization at each user. We mathematically prove that equal sharing of sum feedback size among all users is the optimal strategy in the low signal-to-noise ratio (SNR) region, while allocating whole feedback size to a single user is the optimal strategy in the high SNR region. For the mid-SNR region, we propose a simple numerical method to find the optimal feedback rate sharing strategy based on our analysis and show that the equal allocation of sum feedback rate to a partial number of users is the optimal strategy. It is also shown that the proposed simple numerical method can be applicable to finding the optimal feedback rate sharing strategy when different path losses of the users are taken into account. Our proposed feedback rate sharing scheme can be extended to the system with stream control and is still useful for the systems with other techniques such as regularized zero-forcing and spherical cap codebook.