On the Outage Probability of Distributed MAC with ZF Detection

Distributed scheduling is an attractive approach for the Multiple-Access Channel (MAC). However, when a subset of the users access the channel simultaneously, distributed rate coordination is necessary, and is a major challenge, since the channel capacity of each user highly depends on the channels of other active users. That is, given a detection technique, e.g., Zero-Forcing (ZF), the rate at which a user can transmit depends on the channels other transmitting users have, a knowledge which is usually unavailable in distributed schemes. Fixing a rate and accepting some outage probability when this rate is too high is common practice in these cases.

In our research, we investigate the outage probability for multi-user scheduling under Single-Input- Multiple-Output (MU-SIMO) MAC with ZF detection in the presence of large number of users, when no coordination between users is allowed. In particular, we consider a practical threshold-based scheduling algorithm in which the users schedule themselves distributively if their channel gain has exceeded a predefined threshold value. Interestingly, such a distributed algorithm achieves the optimal ergodic capacity scaling law when the threshold value is properly set, and hence, it is asymptotically optimal.

We define the outage event of this threshold-based scheme for ZF detection, and characterize the correlation between the above-threshold users’ channels. This enables us to attain the individual outage probability when the number of above-threshold users is random. Then, we derive tight upper and lower bounds on the outage probability. Our bounds provide an interesting relation between the fraction of degrees-of-freedom that remain unutilized, the transmission rate and the threshold value, and the resulting outage probability for all SNR values. In fact, we show that for transmission rates in the order , where  is the number of users, the upper and lower bounds are tight, and result in a fixed outage probability, which asymptotically follows the Beta distribution.