On optimal precoding in wireless multicast systems

Precoding has been extensively studied for point-to-point communications, including the problems of constructing the precoding codebook and selecting the best precoder. This paper investigates precoding for a multicast channel in which a base station is sending the same information to all users and each user sends back the index of its best precoding matrix. It is assumed that users do not collaborate and that no channel state information is known at the base station. Optimization problems are formulated to reduce the packet drop rate. A set of probabilistic algorithms that effectively reduce the average package drop rate are presented. It is shown numerically that these new schemes lead to significant improvements.