Power Is Knowledge: Distributed and Throughput Optimal Power Control in Wireless Networks

Consider N devices that transmit packets for T time slots, where device n uses transmission power $P_{n}\left ({{t}}\right)$ at time slot t. Independently at each time slot, a packet arrives at device n with probability $\lambda _{n}$ . The probability of successfully transmitting a packet $\mu _{n}\left ({{\boldsymbol {P}}}\right)$ is a function of the transmission powers of all devices $\boldsymbol {P}$ and the channel gains $\left \{{{ g_{m,n}}}\right \} $ between them. This function is unknown to the devices that only observe binary reward $r_{n}\left ({{\boldsymbol {P}}}\right)$ of whether the transmission was successful (ACK/NACK). All packets of device n that were not successfully transmitted yet at time slot t wait in a queue $Q_{n}\left ({{t}}\right)$ . The centralized max-weight scheduling (MWS) can stabilize the queues for any feasible $\boldsymbol {\lambda }$ (i.e., throughput optimality). However, MWS for power control is intractable even as a centralized algorithm, let alone in a distributed network. We design a distributed yet asymptotically throughput optimal power control for the wireless interference channel, which has long been recognized as a major challenge. Our main observation is that the interference $I_{n}\left ({{t}}\right)=\sum g_{m,n}^{2}P_{m}\left ({{t}}\right)$ can be leveraged to evaluate the weighted throughput if we add a short pilot signal with power $P_{m}\propto Q_{m}\left ({{t}}\right)r_{m}\left ({{\boldsymbol {P}}}\right)$ after transmitting the data. Our algorithm requires no explicit communication between the devices and learns to approximate MWS, overcoming its intractable optimization and the unknown throughput functions. We prove that, for large T, our algorithm can achieve any feasible $\boldsymbol {\lambda }$ . Numerical experiments show that our algorithm outperforms the state-of-the-art distributed power control, exhibiting better performance than our theoretical bounds.