Owing to the structure of the Gaussian multiple-input multiple-output (MIMO)broadcast channel (BC), associated optimization problems such as capacityregion computation and beamforming optimization are typically non-convex, andcannot be solved directly. One feasible approach to these problems is totransform them into their dual multiple access channel (MAC) problems, whichare easier to deal with due to their convexity properties. The conventionalBC-MAC duality is established via BC-MAC signal transformation, and has beensuccessfully applied to solve beamforming optimization,signal-to-interference-plus-noise ratio (SINR) balancing, and capacity regioncomputation. However, this conventional duality approach is applicable only tothe case, in which the base station (BS) of the BC is subject to a single sumpower constraint. An alternative approach is minimax duality, established by Yuin the framework of Lagrange duality, which can be applied to solve theper-antenna power constraint problem. This paper extends the conventionalBC-MAC duality to the general linear constraint case, and thereby establishes ageneral BC-MAC duality. This new duality is applied to solve the capacitycomputation and beamforming optimization for the MIMO and multiple-inputsingle-output (MISO) BC, respectively, with multiple linear constraints.Moreover, the relationship between this new general BC-MAC duality and minimaxduality is also presented. It is shown that the general BC-MAC duality offersmore flexibility in solving BC optimization problems relative to minimaxduality. Numerical results are provided to illustrate the effectiveness of theproposed algorithms.
展开▼
