In this paper, we investigate the per-tier outage probability of multiuser multiple-input multiple-output (MU-MIMO) transmissions in heterogeneous networks (HetNets) with joint interference constraint. In the tier of cellular cell, user equipment (UE) is required to report measured channel information and the base station (BS) adopts ZF-based precoding MU-MIMO transmission to achieve multiuser diversity gain. With the constraint of cross-tier interference and unpredicted inter-beam interference, we derive the closed-form expression of outage probability of downlink MU-MIMO transmissions. Considering the capacity of nodes in the tier of ad hoc networks, a max-SINR scheduler and codebook-based MU-MIMO transmission are employed. The scheduler selects the best receiving nodes for each beam in predefined codebook according to measured signal to interference plus noise ratio (SINR), and the transmitting node performs data transmissions using orthogonal beams. In the presence of inter-node interference, inter-beam interference, and cross-tier interference, we obtain the closed-form expression of outage probability of MU-MIMO transmissions when downlink or uplink transmissions occur in cellular cell. Additionally, in case that the outage probability in ad hoc networks should satisfy quality of service (QoS) requirement, a restricted area in cellular cell in which the outage probability in ad hoc networks is not greater than a required threshold is explored. Numerical results show that the unpredictable inter-beam interference in cellular cell degrades the outage probability slightly. The restricted area increases with the outage probability threshold.
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