Effective Energy Efficiency of Ultra-reliable Low Latency Communication

Effective Capacity defines the maximum communication rate subject to a specific delay constraint, while effective energy efficiency (EEE) indicates the ratio between effective capacity and power consumption. We analyze the EEE of ultra-reliable networks operating in the finite blocklength regime. We obtain a closed form approximation for the EEE in quasi-static Nakagami-$m$ (and Rayleigh as sub-case) fading channels as a function of power, error probability, and latency. Furthermore, we characterize the QoS constrained EEE maximization problem for different power consumption models, which shows a significant difference between finite and infinite blocklength coding with respect to EEE and optimal power allocation strategy. As asserted in the literature, achieving ultra-reliability using one transmission consumes huge amount of power, which is not applicable for energy limited IoT devices. In this context, accounting for empty buffer probability in machine type communication (MTC) and extending the maximum delay tolerance jointly enhances the EEE and allows for adaptive retransmission of faulty packets. Our analysis reveals that obtaining the optimum error probability for each transmission by minimizing the non-empty buffer probability approaches EEE optimality, while being analytically tractable via Dinkelbach's algorithm. Furthermore, the results illustrate the power saving and the significant EEE gain attained by applying adaptive retransmission protocols, while sacrificing a limited increase in latency.