Dynamic Power Control under Energy and Delay Constraints

1 Information-theoretic limits of fading channels have been discussed extensively in the literature under average power constraints. In this paper, we introduce total energy constraints on transmission and study dynamic power control on a time varying channel. Three types of delay constraints are discussed: no delay constraint, soft delay constraint and strict delay constraint. We consider a block fading channel modeled as a finite state Markov chain and study binary power control schemes for both variable rate and constant rate systems. For variable rate systems, we search for the optimal transmission policy that maximizes the minimum value of the expected sum-of-rates over the total communication window. Under no delay constraints, the optimal policy is extremely selective in that it stipulates transmission only on the best channel state, and the corresponding energy efficiency (the ratio of average mutual information to energy) serves as an upper bound for all delay constrained cases. Under delay constraints, the optimal policies are less selective and result in threshold rules on both the received signal strength (channel state) and the residual battery energy. Further, the energy efficiency is observed to increase with the Doppler frequency. For constant rate systems, optimal schemes are obtained to minimize the maximum value of the outage probability. It is observed that the outage probability decreases with the Doppler frequency in the strict delay constraint case. In addition, repetition diversity is also considered under a strict delay constraint. This work is supported in part by the NSF under a CAREER award CCR 9874976 and the New Jersey Commission on Science and Technology under the New Jersey Center for Wireless Communication Technologies.