Broadcasting on the Grassmannian: Enhancing the multiplexing gain

It is known that in multiantenna broadcast channels without transmitter-side channel state information (CSIT), time-sharing (orthogonal transmission) achieves the maximum multiplexing gain if perfect receiver-side channel state information (CSIR) is available to all receivers, or if no receiver has CSIR. We show that orthogonal strategies are not optimal in cases where some receivers have more CSIR than others. A superposition signaling is proposed to transmit to two receivers simultaneously on Grassmannians, achieving higher multiplexing gain compared with orthogonal transmissions. The information for the two receivers is conveyed by the row and column spaces of the transmitted matrix, respectively, which is constructed from a product of two matrices that each lie on different Grassmannians. This multiplicative superposition allows the two receivers to be interference-free from the other´s signals even without CSIT.