In this paper, the outage performance of nonorthogonal multiple access (NOMA) is investigated in a downlink space division multiple access (SDMA) network with a multi-antenna base station and randomly deployed users. The NOMA technology is concurrently exploited with SDMA to further improve spectral efficiency. With limited channel state information (CSI) feedback taken into account, an analytical framework is proposed to evaluate outage performance for a given user. An expression for the outage probability is derived in closed form. Moreover, the diversity order and the effect of the number of feedback bits on the outage performance of NOMA are analyzed. Numerical results are demonstrated to verify our analytical findings and show that different from the perfect CSI case there always exists performance floor in the considered network due to limited feedback.