In our first year of the research, we investigated the outage probability for a practical distributed threshold-based multi-user scheduling under Single-Input- Multiple-Output (MU-SIMO) MAC with ZF detection in the presence of a large number of users, when there is no coordination between the users. In the second year, we have extended the results attained in the first year under this thrust in several aspects. First, we have leveraged the outage probability bounds, attained on the first year to derive bounds on the effective user’s rate and users’ sum-rate (a.k.a. outage rate and outage sum-rate, respectively). Second, we have extended the results attained for homogeneous users (users with similar channel distribution) to a more realistic case in which users experience different channel gain statistics due to diverse ranges, terrain, landscape, etc., for which the outage probability of each user follows a different distribution.
The outage probability is defined as the probability that the receiver will not be able to decode a transmission of a scheduled-user (above-threshold). This means that that outage event is from the perspective of the transmitting (scheduled) user. Accordingly, when computing the outage probability, we distinguish between two events: (i) when more users than the number of receive antennas have attempted transmission (have exceeded the threshold), for which we assume that the ZF detection fails irrespective of the transmission rate (ii) when there is at least one transmitting user and the number of simultaneous transmitting users does not exceed the number of receive antennas, yet, some of the transmitting users transmit at a rate that is higher than its predefined transmission rate. When computing a user attainable rate and the overall sum-rate, we have to consider a third event in which no user has exceeded the threshold, i.e., no user has attempted a transmission, and the transmission opportunity has been lost. Note that when determining the threshold for the distributed user selection mechanism and when determining the transmission rate, all three events should be considered. We have provided above-threshold outage rate bounds for users under ZF detection, for sufficiently large number of users. We further provide an approximation to the optimal rate-threshold pair which needs to be selected in order to maximize both the individual rate and the sum-rate, when the number of users is asymptotically large.
We have shown that the analytical results developed for homogeneous users can be easily adapted to the heterogeneous users’ case, where diverse users experience differing channel statistics. In order to cope with the heterogeneous case, one can set a single unified threshold for all users irrespective of their channel gain distribution, for which the results of the homogeneous users can be generalized, with the proper adaptation of the threshold and the above-threshold tail distribution for the Gamma distribution. However, setting a collective threshold value impacts fairness as users with favorable statistics (e.g., users who are closer to the receiver) are more likely to exceed the threshold. In this case, not only those advantaged users can transmit in higher data rates, but they also get more transmission opportunities than the rest. To prevent such unfairness, users may utilize a customized threshold, each according to its channel statistics. We show that also for this case the homogeneous users’ results can be generalized with the proper adjustments of the relevant parameters.
We have conducted numerous simulations (numerical results) which support our analysis, and show that our results apply also to relatively small number of users.