Multichannel NOMA-ALOHA game with fading

Non-orthogonal multiple access (NOMA) can improve the spectral efficiency by exploiting the power domain and successive interference cancellation, and in order to improve the throughput, it can be applied to random access that plays a crucial role in the Internet of Things to support connectivity for a number of devices with sparse activity. In this paper, we formulate a game when NOMA is applied to ALOHA to decide users' access or transmission probabilities. We consider a payoff function based on an energy-efficiency metric and drive the mixed strategy Nash equilibrium (NE). Once the NOMA-ALOHA game is successfully formulated, we generalize it to take into account users' different fading and multiple orthogonal channels, which might be necessary for NOMA-ALOHA to support a number of users in a realistic environment. A distributed algorithm based on gradient play is derived to find the mixed strategy NE (or transmission probabilities) of multichannel NOMA-ALOHA with fading.