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We address the problem of resource allocation on an OFDMA downlink under fairness constraints with limited channel state information (CSI). Target QoS corresponds to a minimum user data rate, a target bit-error rate and a maximum outage probability. The only available CSI is the channel average gain of each user. This partial CSI can be viewed as a shadowed pathloss that yields a modified user distribution on which resource allocation is based. Under these constraints, we provide the optimal resource allocation that maximizes the user rate. Compared to full-CSI-based allocation schemes, our solution offers a significant complexity and feedback reduction as well as a good robustness to CSI estimation errors.