Design and analysis of multi-carrier multiple access systems without feedback

In this paper we study a multiple access system without feedback supporting multiple carriers for delay critical applications with a small loss tolerance. In such a system, users transmits R times within the next N timeslots, in order to improve their success probability. In an earlier work, we considered the same problem in a single carrier system and demonstrated that the distribution of properly designed user codes significantly improved the success probability over a random selection strategy. These user codes, that determine the R slots used for transmission, corresponded to so-called 2-(N, R, 1) designs. Mainly motivated by DVB-RCS satellite systems, this paper considers a system with multiple carriers with the limitation that at any time, at most one slot, and thus carrier, can be used by a single user. We introduce two static and four dynamic slot assignment schemes and under some mild assumptions provide closed form formulas for the success probability in each of these systems. For the last dynamic scheme we will show how group divisible designs are the multi-carrier equivalent of the 2-(N, R, 1) designs of the single carrier system and provide a simple procedure to construct these user codes. Finally, we compare all of the proposed assignment schemes and show that the group divisible designs are superior, especially for large population sizes. Some engineering rules with respect to their usage are also provided. For two of the dynamic schemes we also compare two different strategies in case there are not enough user codes available for all users.