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We propose an adaptive radio resource allocation algorithm for a multiple-input multiple-output (MIMO) orthogonal frequency division multiple access (OFDMA) based uplink cognitive radio network (CRN). The CRN has multiple secondary users (SUs) coexisting with multiple primary users (PUs). The aim is to admit as many SUs as possible in various subcarriers while ensuring no interference is leaked to PUs. This is achieved by letting the SUs to transmit signals through the null-space of the channels seen between SUs and the primary network basestation (PNBS). Subcarriers are allocated based on the correlation coefficient of the left singular vector of the MIMO channels seen between various SUs and the secondary network basestation (SNBS). Once the SUs are allocated in various subcarriers, the radio resource management in terms of power and bit allocation is performed on a per user basis using an integer linear programming framework. The performance of the algorithm has been evaluated using simulation results.