On the Sum Rate Capacity of MIMO Broadcast Channels in Cognitive Radio Networks with Interference Power Constraints

This paper investigates the sum rate capacity of MIMO broadcast channels (MIMO-BCs) in cognitive radio networks. A suboptimal user-selection algorithm is proposed to achieve a large sum rate capacity with reduced complexity. This algorithm consists of two steps. First, zero-forcing beamforming is utilized as a downlink precoding technique that precancels inter-user interference. Second, singular value decomposition is applied to the channel matrices of all the secondary users and only consider the singular vectors corresponding to the maximum singular values. The proposed user-selection algorithm chooses singular vectors which are nearly orthogonal to each other and nearly orthogonal to the vector of primary users. With this algorithm, the sum rate capacity of MIMO-BCs in CR networks with interference power constraints and transmit power constraints is derived. We formulate the sum rate capacity as a multi-constraint optimization problem and develop an algorithm to solve the problem in its equivalent form. Finally, numerical simulations are conducted to corroborate our theoretical results in flat Rayleigh fading environments. It is shown that the proposed algorithms are capable of achieving a large sum rate capacity with a very low complexity.