Variable feedback rate design for Tomlinson-Harashima precoded MISO broadcast channels with random vector quantization

In this paper, we study the variable feedback strategy design for each user in the multiple-input single-output (MISO) broadcast (BC) systems. We adopt Tomlinson-Harashima precoder (THP) with random vector quantization (RVQ) feedback mechanism to pre-eliminate the users' interference at the receiver side. Under the limitation of total feedback rate, we flexibly allocate the feedback rate of each user to conduct THP by maximizing the overall channel capacity criterion. Owing to the non-convexity of the design problem, it is difficult to yield the optimum solution. We then use the discrete majorization theory to derive the optimum strategies for the high and the low signal-to-noise ratio (SNR) regions. Interestingly, the results show that the equal feedback strategy for each user is optimum in the low SNR region, whereas that allocates the whole feedback amount to a single user in the high SNR region. Simulations verify the theoretical result of our design.