Hierarchical Rate Splitting to General MIMO Fading Channels

We consider a general point-to-point fading multiple-input multiple-output (MIMO) Gaussian channel. The channel suffers block fading and is with finite channel states, among which there is no degraded order due to the multi-antenna deployment. To guarantee reliable transmissions under the arbitrary unpredictable fading state, we generalize the layered broadcast approach in the channel by inducing the general rate splitting scheme. It assigns the specific sub-message layers for every possible state set and splits the transmission rate by allocating power to each layer. Under this scheme, a generalized broadcast approach is designed to be suitable for multi-antenna transmission. The maximum average rate subject to a transmit power constraint can be determined by a non-convex optimization problem over power allocation and rate tuple. We propose an iterative algorithm based on certain properties that the optimal solution would meet under some necessary conditions. It can output one local optimum for the optimization and thus assist in obtaining a scheme with a decent performance.