The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that singlestream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks. In multiuser MIMO (multiple-input, multiple-output) channels, the spatial multiplexing capability offered by multiple antennas can be advantageously exploited to significantly increase the achievable throughput. In single-cell point-to-multipoint channels, the achievable sum rate scales linearly with the number of transmit antennas, even when the mobile users have only a single antenna. By duality, linear increase with the number of receiver antennas can also be achieved in multipoint-to-point channels, even with a single-antenna transmitter. Extensive research on MIMO broadcast channels over the last few years has revealed that the capacity can be boosted by transmitting to multiple users simultaneously, by means of Space Division Multiple Access (SDMA), rather than trying to maximize the capacity of a singleuser link [1], [2] . Nevertheless, all these promising gains critically depend on accurate channel state information (CSI), and in contrast to point-to-point channels, the quality of CSI affects the multiplexing gain of multiuser MIMO systems. As a result, a considerable amount of effort has been dedicated to multiuser MIMO systems operating with partial CSI at the transmitter (CSIT) in the absence of out-ofcell interference [3] . In this paper we are interested in the capacity gains that SDMA may provide in decentralized (ad hoc) networks with both intra-cell due to imperfect CSIT and other user interference due to uncoordinated concurrent transmissions. We aim at answering whether and how aggressive use of multiple antennas through SDMA may increase the network throughput under a broad set of scenarios. Specifically, we build upon the practically relevant limited feedback model, in which each user is allowed to feed back B-bit quantized information on its channel direction based on a predetermined codebook known at both the transmitter and the receivers. Due to the high implementation complexity and sensitivity to channel errors of the optimal scheme (dirty paper coding [4]), linear precoding based on zero-forcing beamforming (ZFBF) [5] is employed here. ZFBF has been shown to achieve full multiplexing gain while exhibiting reduced complexity [6] , [7] . ZFBF is also used both for its asymptotic optimality in MIMO point-tomultipoint channels and its analytical tractability. In short, it is a logical starting point for understanding the effect of imperfect CSIT in interference-limited networks.
This conclusion is also confirmed in REF for a clustered ad hoc network with quantized beamforming.
Downlink SDMA with Limited Feedback in Interference-Limited Wireless Networks
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