On the Convex Hull of the Achievable Capacity Region of the Two User FDM OMA Downlink

Abstract

In multiple access channel systems, such as a mobile communication network, it is important to determine how to share the available resources (for example bandwidth and power) among the users. In recent years, one of the promising scheme is Non-Orthogonal Multiple Access (NOMA), where, unlike the traditional Orthogonal Multiple Access, OMA solution, signals for the different users overlap in some domain (power-domain NOMA, code-domain NOMA, etc). In order to evaluate the performance of any NOMA scheme, we need to compare the achievable bit rates of the users (the capacity region) to an OMA case with comparable parameters (for example, same total bandwidth, same total power and same channel conditions, etc). To make this comparison, we first need to know the capacity region for the OMA cases. Many papers make such comparison without detailing the derivation of the capacity region of the OMA case they compare to [1], [2], [3], [4]. In some cases, we have only one free parameter to choose (for example in uplink frequency division multiplexing systems for two users, it is the bandwidth ratio between the users), and the achievable capacity can be directly calculated for both users depending on the single parameter (hence the boundary of the capacity region is trivial). In other cases, such as downlink frequency division multiplexing systems, even for only two users, we have to allocate optimally two resources between the users: the bandwidth and the base station’s available power. Hence, it is far from being trivial to determine which combination is better and where the boundary of the capacity region is. In this paper, we provide a derivation for that case.