On the achievable rates and degrees of freedom of causally cognitive MISO broadcast channels

Abstract

This paper explores the problem of how a secondary transmitter could serve several users simultaneously by utilizing the spectrum of a primary system while imposing no impact on it (i.e. satisfying the coexistence constraint), even if the primary system keeps active all the time. The difficulty of this problem lies in that how the secondary system should tackle the interference encountered at multiple secondary receivers. In the cognitive transmission framework, the core of the above problem include two aspects: 1) How to learn quickly the message(s) of the primary system? 2) How to efficiently address the interference at multiple secondary receivers with the knowledge of the primary message? To solve these two problems, our main idea is to fully exploit the advantages of multiple antennas and the potential of transmitter cognition of the interfered message, in order to achieve the goal of fast exploration and full exploitation. In information theoretic terms, the above problem is equivalent to studying the achievable rate of the causally cognitive MISO broadcast channel under the so-called coexistence constraint. For this problem, we propose an efficient achievable scheme which is essentially based on the dirty paper coding and the zero-forcing beamforming and proves to be capable of realizing rather considerable sum rate and degrees of freedom for the secondary system. Our scheme exploits an interesting result regarding the capacity region of the MIMO Gaussian broadcast channel with states known only to the encoders.