Optimal EE-delay relation in wireless systems

It is widely accepted that a tradeoff exists between transmit power and average delay. In this paper, we consider wireless systems transmitting randomly arrived traffic over fading channels with statistical quality-of-service requirement, characterized by a delay bound and a delay bound violation probability. We study the relation between the maximal energy efficiency (EE) and the delay bound with given delay violation probability. We prove that the EE-delay tradeoff vanishes if the average total power consumption, including transmit and circuit powers of the base station, linearly increases with the average service/transmission rate. By taking massive multi-input-multi-output (MIMO) system as an example, we show that if the required total power consumption is a linear function of the service rate, the maximal EE is independent of the delay bound. If the required total power is strictly convex in the service rate, then the EE can be improved by extending the delay.