Crystallized Rate Regions for MIMO Transmission

Abstract

When considering the multiuser SISO interference channel, the allowable rate region is not convex and the maximization of the aggregated rate of all the users by the means of transmission power control becomes inefficient. Hence, a concept of the crystallized rate regions has been proposed, where the time-sharing approach is considered to maximize the sumrate. In this paper, we extend the concept of crystallized rate regions from the simple SISO interference channel case to the MIMO/OFDM interference channel. As a first step, we extend the time-sharing convex hull from the SISO to the MIMO channel case. We provide a non-cooperative game-theoretical approach to study the achievable rate regions, and consider the Vickrey-Clarke-Groves (VCG)mechanism design with a novel cost function. Within this analysis, we also investigate the case of OFDM channels, which can be treated as the special case of MIMO channels when the channel transfer matrices are diagonal. In the second step, we adopt the concept of correlated equilibrium into the case of two-user MIMO/OFDM, and we introduce a regret-matching learning algorithm for the system to converge to the equilibrium state. Moreover, we formulate the linear programming problem to find the aggregated rate of all users and solve it using the Simplex method. Finally, numerical results are provided to confirm our theoretical claims and show the improvement provided by this approach.