An energy harvesting AWGN channel with a finite battery

In energy harvesting communication systems, the transmitter is adapted to harvest energy per time slot. The harvested energy is either used right away or is stored in a battery to facilitate future transmissions. We consider the problem of determining the Shannon capacity of an energy harvesting transmitter communicating over an additive white Gaussian noise (AWGN) channel, where the amount of energy harvested per time slot is a constant ρ and the battery has capacity σ. This imposes a new kind of power constraint on the transmitted codewords, and we call the resulting constrained channel a (σ, ρ) power constrained AWGN channel. When σ is 0 or ∞, the capacity of this channel is known. For the finite battery case, we obtain an expression for the channel capacity. We obtain bounds on capacity by considering the volume of S_n(σ, ρ) ⊆ ℝⁿ, which is the set of all length n sequences satisfying the (σ, ρ) constraints.