In this article, we deal with a novel access protocol design for cognitive cooperative networks with multiple antennas. According to the principles of cognitive radio, the secondary user (SU) can exploit the primary user (PU) burstiness to access the licensed spectrum in the proposed access protocol. To get more access opportunities to the licensed spectrum, the SU simultaneously relays the PU's packets and transmits its own packets based on the superposition coding. Furthermore, to concurrent transmission of the PU's packets and SU's packets based on the superposition coding such that they are received without the interference at the primary receiver and secondary receiver respectively, two weight vectors at the SU equipped with multiple antennas are designed based on zero-forcing algorithm. Specifically, from a networking perspective, we analyze the performance of the proposed access protocol in terms of the maximum stable throughput and the average end-to-end delay for both the PU and SU based on the principles of queueing theory. In addition, to protect the PU's performance and exhibit the advantage of adopting multiple antenna technology, we jointly optimize the parameter of superposition coding and the number of antennas, and define the maximum stable throughput cooperative gain compared to the non-cooperative access scheme. More importantly, the impact of imperfect channel state information (CSI) at the SU on the maximum stable throughput and the average end-to-end delay performance is evaluated in the simulations from a practical point of view. Analysis and simulation results demonstrate that the proposed access protocol achieves significant performance gains for both the PU and the SU, outperforms the existing cooperative access protocol based on the dirty-paper coding, and keeps robust against to the imperfect CSI.