A Game Theoretical Approach for Reliable Packet Transmission in Noncooperative BIC-OFDM Systems

In this work, we investigate the power allocation (PA) problem aimed at minimizing the users' packet error rate (PER) over a noncooperative link, i.e., a link where the set of users, employing packet-oriented BIC-OFDM systems, compete for the same bandwidth. For these kind of systems, the PER is not available in closed-form, but a very efficient solution is offered by the effective SNR mapping (ESM) technique. This method allows each user to evaluate a single scalar value, the effective SNR (ESNR), accounting for all the SNIRs experienced over the active subcarriers, and to univocally map it into a PER value. Thus, in order to derive a decentralized strategy allowing each user to minimize its own PER, the problem is described as a strategic game, called min-PER game, with the set of player, utilities and strategies represented by the competitive users, the ESNRs and the set of feasible power allocations, respectively. We will show both the existence of at least one Nash Equilibrium (NE) for the min-PER game and its equivalence with a Nonlinear Variational Inequality (NVI) problem. Finally, relying on the theory of contraction mappings, we will derive a distributed algorithm to reach the NE of the game.