Optimum Energy Allocation for Massive Spread-Spectrum Multiple Access in Networks of Uncoordinated Energy-Limited Terminals

Abstract

This paper derives the energy allocation policy that maximizes the aggregate spectral efficiency of an uncoordinated spread-spectrum multiple access network operating in the large-user regime and subject to a long-term per-user average energy constraint. Focusing on a network of autonomous energy-limited devices, we consider that the receiver operates under noise-dominant conditions and that every transmitter is able to estimate accurately its own slowly time-varying channel with no feedback from the receiver. The aggregate spectral efficiency is derived in terms of the statistical distribution of the channel power gains and of the Packet Error Rate (PER) curve of the common modulation and error correcting code employed by all users. Using Variational Calculus, we obtain a closed-form expression for the optimum energy profile at low average Es/No and prove that the aggregate spectral efficiency converges to a non-vanishing value if the user population is large and terminals implement an uncoordinated admission control based on the known PER curve.