A Multiobjective Optimization Approach for Coexisting Wireless Systems under Channel State Information Uncertainty

This paper considers an underlay access strategy for coexisting wireless networks where the secondary system utilizes the spectrum owned by the primary system to simultaneously support multiple secondary users. In the considered scenario, the throughput performance of each system is limited by the interference imposed by the other. Hence, improving the performance of one system conflicts with that of the other. We analyze the fundamental trade-off between the tolerance interference level at the users of the primary system and the total achievable throughput of the users of the secondary system. We introduce a beamforming design problem as a multiobjective optimization problem with contradictory objectives, i.e., minimizing the interference imposed on each primary user while maximizing the intended signal received at every secondary user, taking into account the uncertainty in the estimation of channel state information (CSI). Assuming the uncertainty of the CSI is confined in hyper-spherical sets, we then map the proposed optimization problem to a robust counterpart under the worst case of CSI estimation error. We finally transform the robust counterpart into a standard semidefinite programming form which is convex and can be solved by standard optimization packages. Simulation results confirm the effectiveness of the proposed scheme against various levels of CSI estimation error.