Dynamic power control in a fading downlink channel subject to an energy constraint

A central controller chooses a state-dependent transmission rate for each user in a fading, downlink channel by varying transmission power over time. For each user, the state of the channel evolves over time according to an exogenous continuous-time Markov chain (CTMC), which affects the quality of transmission. The traffic for each user, arriving at the central controller, is modeled as a finite-buffer Markovian queue with adjustable service rates. That is, for each user data packets arrive to the central controller according to a Poisson process and packet size is exponentially distributed; an arriving packet is dropped if the associated buffer is full, which results in degradation of quality of service. The controller forwards (downlink) the arriving packets to the corresponding user according to an optimally chosen transmission rate from a fixed set Ai of available values for each user i, depending on the backlog in the system and the channel state of all users. The objective is to maximize quality of service subject to an upper bound on the long-run average power consumption. We show that the optimal transmission rate for each user is solely a function of his own packet queue length and channel state; the dependence among users is captured through a penalty rate. Further, we explicitly characterize the optimal transmission rate for each user.