Worst-case performance optimization for robust power control in downlink beamforming

In this paper,11Part of the algorithm in this paper has been presented in IEEE ISIT’2008 [1]. we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition.