On the Capacity of M-ary ASK Two-Hop Channel With Finite Battery Energy Harvesting Relay

In this paper, we study the problem of joint information and energy transfer in an
${M}$
-ary amplitude shift keying (ASK) two-hop channel with an energy harvesting relay. We consider two realistic assumptions; a finite battery size at the relay and energy loss in transmitting energy. We model the energy loss at the relay, where for sending an energy-containing symbol, the relay must receive multiple energy-containing symbols. Thus, we face a channel with memory. We model the energy saved in the battery as the channel state with the challenge that the receiver does not know the channel state. We propose two different achievable schemes, the first one is based on state-dependent superposition coding and the second one (for the binary case) is based on the equivalent timing channel approach. Both of our schemes are based on block Markov coding and backward decoding techniques. We derive achievable rates with single-letter expressions. In addition, we propose a single-letter upper bound for the system. In summary, the fundamental achievement of this work is proposing single-letter bounds for an energy harvesting relay with memory.