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To find out an optimal power allocation among users, and an optimal power pricing strategy at the Relay-assisted 5G wireless system, we propose a Variational Inequality (VI) based approach. We modeled the issues and provided an algorithm to resolve the issues, from the aspects of theoretical analysis and simulation analysis. The results indicated the VI-based solution was effective for the scenarios with both public and private budget limits. Introduction As the development of communication technology in wireless networks, relay technologies with a great deal of potential applications are considered as one of the hot research topics and have been studied widely in the mobile communication systems, such as the future 3GPP LTE-Advanced [1] and IEEE 802.16j [2, 3] based mobile systems. Moreover, relay transmission has obtained much attention as one of the promising transmission strategies for exploiting spatial diversity gains via single antenna nodes in wireless networks. A variety of relay strategies have been developed over the past ten years. The simplest strategy is the analog repeater [4]. Many more advanced strategies are also used to process the received signals, such as amplify-and-forward (AF) [5], decode-and-forward (DF) and compress-and-forward (CF). Practically, a relay station (RS) as a transmitter shares its transmission resources to repeat or forward the data from other peers, usually to the areas which are not covered by the signal of the transmitters. Hence, relays enable to expand the broadcast range of a base station (BS) beyond primary signal coverage area, or to improve involved services and performances in a part of the main coverage area where terminal devices receive poor signals due to geographic referenced constraints. In other words, with the help of the relays in wireless communication networks, the throughput performance of the whole system will be efficiently enhanced, as well as the benefits of end users (e.g., mobile terminals). Research into cooperative communication using game theory or auction theory has become increasingly popular in recent years. Many studies have appeared in the literature, e.g. [6]. However, none of them considers the situation that the user’s budget is limited for paying the relay’s services, a very common situation in practice. In this paper, to find an optimal power allocation among users, and an optimal power pricing strategy at the RS with the help of the game theory, subject to the budget limits (i.e., an upper bound of user’s possible payment for the relay’s service) in the multi-user relay-assisted wireless networks, we propose a Variational Inequality (VI) based approach. We modeled the issues and provided an algorithm to resolve the issues, from the aspects of theoretical analysis and simulation analysis. The results indicated the VI-based solution was effective for the scenarios with both public and private budget limits. A Variational Inequality Approach This section focuses on investigating an approach to resolve the issues mentioned above. Additionally, the existence and the uniqueness of the VI solution is proven, and the unique VI solution is obtained through an iterative algorithm. Numerical simulations validate the proposed scheme.

A Variational Inequality Based Approach for Power Trading in Multi-User Relay-Assisted Systems