  This work considers worst-case utility maximization (WCUM) problem for a
downlink wireless system where a multiantenna base station communicates with
multiple single-antenna users. Specifically, we jointly design transmit
covariance matrices for each user to robustly maximize the worst-case (i.e.,
minimum) system utility function under channel estimation errors bounded within
a spherical region. This problem has been shown to be NP-hard, and so any
algorithms for finding the optimal solution may suffer from prohibitively high
complexity. In view of this, we seek an efficient and more accurate suboptimal
solution for the WCUM problem. A low-complexity iterative WCUM algorithm is
proposed for this nonconvex problem by solving two convex problems
alternatively. We also show the convergence of the proposed algorithm, and
prove its Pareto optimality to the WCUM problem. Some simulation results are
presented to demonstrate its substantial performance gain and higher
computational efficiency over existing algorithms.
