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In this article, we quantify the achievable spatial throughput of a multi-antenna Poisson cognitive radio network (CRN) collocated with a Poisson multi-antenna primary network. CR users employ Slotted-ALOHA medium access control. The success probability (SP) of a primary link is quantified in the presence of the secondary and primary interferers. It is demonstrated that two fold gains are experienced by employing multiple antennas at primary, i.e., (i) the fixed high desired SP threshold is met; (ii) CRs can also be accommodated without QoS deterioration. Further in this paper, the maximum permissible medium access probability (MAP) for CRN is derived from the link SP and primary users QoS constraint. The impact of the number of antennas and modulation employed at the primary on the permissible MAP of the CRN is also explored. Assuming that CR users employ multi-hop communication, QoS aware relaying with a radian sector forwarding area is studied. The average forward progress (AFP) and isolation probability for a CR user with QoS based connectivity is characterized under the permissible MAP. The spatial throughput for the CRN is quantified by the analysis of the AFP and the permissible MAP. It is shown that there exists an optimal MAP which maximizes the spatial throughput of the CRN. This optimal MAP is coupled with the permissible MAP, density of users, number of antennas and modulation schemes employed in both primary and secondary networks. Lastly, a few important design questions are investigated for multi-hop MIMO underlay CRNs.