On Achievable Rates of AWGN Energy-Harvesting Channels With Block Energy Arrival and Non-Vanishing Error Probabilities

Abstract

This paper investigates the achievable rates of an additive white Gaussian noise (AWGN) energy-harvesting (EH) channel with an infinite battery. The EH process is characterized by a sequence of blocks of harvested energy, which is known causally at the source. The harvested energy remains constant within a block while the harvested energy across different blocks is characterized by a sequence of independent and identically distributed (i.i.d.) random variables. The blocks have length L, which can be interpreted as the coherence time of the energy arrival process. If L is a constant or grows sublinearly in the blocklength n, we fully characterize the first-order term in the asymptotic expansion of the maximum transmission rate subject to a fixed tolerable error probability ε. The first-order term is known as the ε-capacity. In addition, we obtain lower and upper bounds on the second-order term in the asymptotic expansion, which reveal that the second order term scales as L n for any ε less than 1/2. The lower bound is obtained through analyzing the save-and-transmit strategy. If L grows linearly in n, we obtain lower and upper bounds on the εcapacity, which coincide whenever the cumulative distribution function (cdf) of the EH random variable is continuous and strictly increasing. In order to achieve the lower bound, we have proposed a novel adaptive save-and-transmit strategy, which chooses different save-and-transmit codes across different blocks according to the energy variation across the blocks.1 If the constraint E[E 3 1 ] < +∞ is replaced with the less stringent one E[E 2 1 ] < +∞, all the achievability results in this paper continue to hold. In fact, the only place that requires E[E 3 1 ] < +∞ is the use of the Berry-Esséen theorem in Section VI-B in the course of proving the converse of Theorem 1.

Finite Blocklength Analysis of Energy Harvesting Channels

“…The bound in (40) was used to develop a finite blocklength converse for EH-AWGN channels extended to the block i.i.d. energy arrivals regime [14]. We shall derive the same result for EH-AWGN channels under maximal probability of error criterion but using (41).…”

“…In quasi-static fading channels, [18] also modified the meta converse suitably to obtain the desired bounds. Moreover we give an alternate, shorter proof of the converse bound for EH-AWGN channels, which was first shown in [14]. Additionally, we analyze DMCs with energy harvesting and provide the finite blocklength converse bounds for them.…”

“…The achievability result with second-order O( √ n) was shown in [1] for EH-AWGN channels. Both achievability and converse results for EH-AWGN channels were further refined recently in [14], which considered block i.i.d. energy arrivals.…”

“…Later, in Section 10, we will compare and discuss our results and methods in detail with those available in [14,18].…”

Optimizing Energy Harvesting Decode-and-Forward Relays With Decoding Energy Costs and Energy Storage

“…For example, the accumulation time interval begins from prior to nearly half of the block time, with an extra energy storage needed. In practice, most EH processes, such as the power harvested from PV and RF sources, admit such models [51], [54], [55]. Or without extra storage cost, with fast varying e among blocks, principally, e needs to be predicted only once at the start of the block, with the tiny time taken with a certain precision.…”