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The ergodic resource allocation (ERA) problem for uplink transmission in underlay cognitive radio networks (CRNs) is investigated. The objective is to maximize the ergodic sum-rate of secondary users (SUs) considering the unavailability of perfect channel state information (CSI), and subject to transmit power limitations of SUs, and the interference threshold constraint to guarantee the quality of service of primary users. Since with average-based formulation of ERA, the interference threshold constraint and transmit power limitations of SUs do not hold instantaneously, one can replace the average-based constraints in ERA with their outage-based counterparts. For the uncertainty on the CSI values, we utilize the robust optimization theory where the uncertain parameters are modeled as a sum of the estimated value and error which is assumed to be bounded. We then map the considered ERA problems to their …