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The concept of cognitive radio is to exploit efficiently the spectrum resources by allowing the coexistence of the primary and secondary users in the same bandwidth without interfering the performance of primary users. Three coexisting models (overlay, underlay and interleave) were presented in recent literature. In this study, the authors propose a hybrid cognitive network model with overlay and underlay models, whereby a primary link leases its fractions of transmission time to the secondary users for their cooperation (i.e. these nodes form as a virtual multiple input multiple output (VMIMO) group) under the outage constraints of the primary and secondary systems. A new cooperative protocol between primary and secondary users is presented. The authors attempt to achieve the maximum transmission capacity of the secondary users under the primary and secondary outage constraints, which depend on the secondary density in the cognitive network. This study gives the upper bound density of the secondary transmitters that are modelled as a homogeneous marked Poisson point process. The maximum density is achieved by computing an optimal set of system parameters such as power control factor of the secondary user and the dirty paper coding (DPC) parameter. Simulation results illustrate that the maximum secondary density obtained using VMIMO is superior to that obtained by direct primary transmission.